DUBLIN UNIVERSITY PRESS SERIES.
A HISTORY
OF THE
THEORIES OF AETHER AND ELECTRICITY
FKOM THE AGE OF DESCAKTES TO THE CLOSE OF THE NINETEENTH CENTURY.
BY
E. T. WH1TTAKER,
Hon. Sc.D. (DubL}; I.E.S.; Roy at Astronomer of Ireland.
LONGMANS, GREEN, AND CO.,
39 PATERNOSTER ROW, LONDON, NEW YORK, BOMBAY, AND CALCUTTA.
HODGES, FIGGIS, & CO., LTD., DUBLIN. 1910.
MM*
DUBLIN :
PRINTED AT UHE UNIVERSITY PRESS, BY PONSONBY AND OIBRS.
THE author desires to record his gratitude to Mr. W. W. EOUSE BALL, Fellow of Trinity College, Cambridge, and to Professor W. McF. ORR, F.R.S., of the Royal College of Science for Ireland ; these friends have read the proof-sheets, and have made many helpful suggestions and criticisms.
Thanks are also 'due to the BOARD OF TRINITY COLLEGE, DUBLIN, for the financial assistance which made possible the publication of the work.
236360
CONTENTS.
CHAPTEK I.
y THE THEORY OF THE AETHER IN THE SEVENTEENTH CENTURY.
Page
Matter and aether, . . . . . . .1
The physical writings of Descartes, ..... 2
Early history of magnetism : Petrus Peregrinus, Gilbert, Descartes, 7 Fermat attacks Descartes' theory of light : the principle of least
time, ........ 10
Hooke's undulat>ry theory : the advance of wave -fronts, . . 11
Newton overthrows Hooke's theory of colours, . . .15
Conception of the aether in the writings of Newton, . . 17
Newton's theories of the periodicity of homogeneous light, and of
fits of easy transmission, • • . . ,20
The velocity of light : Galileo, Roemer, . . . .21
Huygens' Traite de la lumiere : his theories of the propagation of
waves, and of crystalline optics, • . . .22
Newton shows that rays obtained by double refraction have sides :
his objections to the undulatory theory, . . .28
X
CHAPTER II.
ELECTRIC AND MAGNETIC SCIENCE, PRIOR TO THE INTRODUCTION OF THE POTENTIALS.
The electrical researches of Gilbert : the theory of emanations, . 29 State of physical science in the first half of the eighteenth century, 32 Gray discovers electric conduction : Desaguliers, . . • 37
The electric fluid, ....... 38
Du Fay distinguishes vitreous and resinous electricity, . .39
Xollet's effluent and affluent streams, . . . .40
The Leyden phial, ..... . . 41
The one-fluid theory : ideas of Watson and Franklin, . . 42
Final overthrow by Aepinus of the doctrine of effluvia, . . 48
Priestley discovers the law of electrostatic force, . . .50
viii Contents.
Page
Cavendish, . ... 51
Michell discovers the law of magnetic force, . . . .54
The two-fluid theory : Coulomb, . . . . .56
Limited mobility of the magnetic fluids, . . .58
Poisson's mathematical theory of electrostatics, . . .59
The equivalent surface- and volume-distributions of magnetism :
Poisson's theory of magnetic induction, . . .64
Green's Nottingham memoir, . . . . .65
CHAPTER III. GALVANISM, FROM GALVANI TO OHM.
Sulzer's discovery, ... . .67
Galvanic phenomena, ....... 68
Rival hypotheses regarding the galvanic fluid, , . .70
The voltaic pile, ....... 72
Nicholson and Carlisle decompose water voltaically, . . 75
Davy's chemical theory of the pile, ..... 76
Grothuss' chain, . . . . . . .78
De La Rive's hypothesis, . . . . . .79
Berzelius' scheme of electro-chemistry, . . . .80
Early attempts to discover a connexion between electricity and
magnetism, . ... 83
Oersted's experiment : his explanation of it, . . .85
The law of Biot and Savart, . . . . . .86
The researches of Ampere on electrodynamics, . . 87
Seebeck's phenomenon, . . . . . .90
Davy's researches on conducting power, . . . .94
Ohm's theory : electroscopic force, . . . . .95
CHAPTER IV. THE LUMINIFEBOUS MEDIUM, FROM BRADLEY TO FRESNEL.
Bradley discovers aberration, . . . . .99
John Bernoulli's model of the aether, .... 100
Maupertuis and the principle of least action, . . . 102
Views of Euler, Courtivron, Melvill, .... 104
Young defends the undulatory theory, and explains the colours of
thin plates, ... ... 105
Laplace supplies a corpuscular theory of double refraction, . . 109
Contents. ix
Page
Young proposes a dynamical theory of light in crystals, . . 110
Researches of Malus on polarization, .... Ill
Recognition of biaxal crystals, ... . 113
Fresnel successfully explains diffraction, . . . 114
His theory of the relative motion of aether and matter, . . 115
Young suggests the transversality of the vibrations of light, . 121
Fresnel discusses the dynamics of transverse vibrations, . . 123
Fresnel's theory of the propagation of light in crystals, . • . 125
Hamilton predicts conical refraction, . . . ] 31
Fresnel's theory of reflexion, ..... 133
CHAPTER V. I,THE AETHER AS AN ELASTIC SOLID.
Astronomical objection to the elastic-solid theory : Stokes'
hypothesis. . . . . . . .137
Navier and Cauchy discover the equation of vibration of an elastic
solid, 139
Poisson distinguishes condensational and distortional waves, . 141
Cauchy's first and second theories of light iq, crystals, . . 143
Cauchy's first theory of reflexion, ..... 145
His second theory of reflexion, ..... 147
The theory of reflexion of MacCullagh and Neumann, . . 148
Green discovers the correct conditions at the boundaries, . . 151
Green's theory of reflexion : objections to it, . . . 152
MacCullagh introduces a new type of elastic solid, . . . 154
W. Thomson's model of a rotationally-elastic body, . . 157
Cauchy's third theory of reflexion : the contractile aether, . . 158
Later work of W. Thomson and others on the contractile aether, . 159
Green's first and second theories of light in crystals, . . 161
Influence of Green, ....... 167
Researches of Stokes on the relation of the direction of vibration of
light to its plane of polarization, .... 168
The hypothesis of aeolotropic inertia, .... 171
Rotation of the plane of polarization of light by active bodies, . 173
MacCullagh's theory of natural rotatory power, . . 175
MacCullagh's and Cauchy's theory of metallic reflexion, . . 177
Extension of the elastic -solid theory to metals, . . 179
Lord Rayleigh's objection, .... . 181
Cauchy's theory of dispersion, • . . 182
Boussinesq's elastic-solid theory, ..... 185
x Contents.
CHAPTEE VI.
FARADAY.
Page
Discovery of induced currents : lines of magnetic force, . . 189
Self-induction, . . . . . . .193
Identity of frictional and voltaic electricity : Faraday's views on the
nature of electricity, . . . . . 194
Electro-chemistry, . . ".. • . • *. . . . 197
Controversy between the adherents of the chemical and contact
hypotheses, . » . . . . . 201
The properties of dielectrics, . . . . . 206
Theory of dielectric polarization : Faraday, W. Thomson, and
Mossotti, . . : . . . . .211
The connexion between magnetism and light, . . . 213
Airy's theory of magnetic rotatory polarization, . « . 214
Faraday's Thoughts on Ray -Vibrations, . ..''-. . . 217
Researches of Faraday and Pliicker on diamagnetism, . . 218
CHAPTER VII.
THE MATHEMATICAL ELECTRICIANS OF THE MIDDLE OF THE NINETEENTH
CENTURY.
F. Neumann's theory of induced currents : the electrodynamic
potential, . . . . . ; . . 222
W. Weber's theory of electrons, . . . . .225
Riemann's law, . . . ... . 231
v-Proposals to modify the law of gravitation, . .. . . 232
Weber's theory of paramagnetism and diamagnetism : later theories, 234
Joule's law : energetics of the voltaic cell, .... 239
Researches of Helmholtz on electrostatic and electrodynamic energy, 242 W. Thomson distinguishes the circuital and irrotational magnetic
vectors, ........ 244
His theory of magnecrystallic action, .... 245
His formula for the energy of a magnetic field, . . . 247
Extension of this formula to the case of fields produced by currents, 249 Kirchhoff identifies Ohm's electroscopic force with electrostatic
potential, . . . . . . / 251
The discharge of a Leyden jar : W. Thomson's theory, . . 253
The velocity of electricity and the propagation of telegraphic signals, 254
Clausius' law of force between electric charges : crucial experiments, 261
Nature of the current, ...... 263
The thermo-electric researches of Peltier and W. Thomson, • 264
Contents. xi
CHAPTER VIII. MAXWELL.
Page
Gauss and Riemann on the propagation of electric actions, . . 268
Analogies suggested by W. Thomson, .... 269
Maxwell's hydrodynamical analogy, ..... 271
The vector potential, ...... 273
Linear and rotatory interpretations of magnetism, . . . 274
Maxwell's mechanical model of the electromagnetic field, . . 276
Electric displacement, ...... 279
Similarity of electric vibrations to those of light, . . . 281
Connexion of refractive index and specific inductive capacity, . 283 Maxwell's memoir of 1864, . . ... .284
The propagation of electric disturbances in crystals and in metals, . 288
Anomalous dispersion, ...... 291
The Max well -Sellmeier theory of dispersion, . . . 292
Imperfections of the electromagnetic theory of light, . . 295
The theory of L. Lorenz, ...... 297
Maxwell's theory of stress in the electric field, . . . 300
The pressure of radiation, ...... 303
Maxwell's theory of the magnetic rotation of light, . . . 307
CHAPTER IX.
MODELS OF THE AETHER.
Analogies in which a rotatory character is attributed to magnetism, 310
Models in which magnetic force is represented as a linear velocity, 311 Researches of W. Thomson, Bjerknes, and Leahy, on pulsating and
oscillating bodies, ...... 316
MacCullagh's quasi-elastic solid as a model of the electric medium, 318 The Hall effect, . . . . . .320
Models of Riemann and Fitz Gerald, . . . . 324
Vortex-atoms, . . . . . . .326
The vortex-sponge theory of the aether : researches of W. Thomson,
Fitz Gerald, and Hicks, , . . . . .327
CHAPTER X.
THE FOLLOWERS OF MAXWELL.
Helmholtz and H. A. Lorentz supply an electromagnetic theory of
reflexion, ....... 337
Crucial experiments of Helmholtz and Schiller, . . . 338
xii Contents.
Page
Convection -currents : Rowland's experiments, . . . 339 The moving charged sphere : researches of J. J. Thomson, Fitz Gerald,
and Heaviside, . . . . . . . 340
Conduction of rapidly -alternating currents, .... 344
Fitz Gerald devises the magnetic radiator, .... 345
Poynting's theorem, ....... 347
Poynting and J. J. Thomson develop the theory of moving lines of
force, . . . . . . . 349
Mechanical momentum in the electromagnetic field, . . 352
New derivation of Maxwell's equations by Hertz, . . . 353
Hertz's assumptions and Weber's theory, .... 356
Experiments of Hertz on electric waves, .... 357
The memoirs of Hertz and Heaviside on fields in which material
bodies are in motion, ...... 365
The current of dielectric convection, ..... 367
Kerr's magneto-optic phenomenon, . ... 368
Rowland's theory of magneto-optics, .... 369
The rotation of the plane of polarization in naturally active bodies, 370
CHAPTER XI.
CONDUCTION IN SOLUTIONS AND GASES, FROM FARADAY TO J. J. THOMSON.
The hypothesis of Williamson and Clausius, . . . 372
Migration of the ions, ...... 373
The researches of Hittorf and Kohlrausch, .... 374
Polarization of electrodes, ...... 375
Electrocapillarity, .... . 376
Single differences of potential, . . . . . 379
Helmholtz' theory of concentration-cells, .... 381
Arrhenius' hypothesis, ... ... 383
The researches of Nernst, ... . 386
Earlier investigations of the discharge in rarefied gases, . . 390
Faraday observes the dark space, ..... 391
Researches of Pliicker, Hittorf, Goldstein, and Varley, on the
cathode rays, .... . 393
Crookes and the fourth state of matter, .... 394 Objections and alternatives to the charged-particle theory of
cathode rays, ....... 395
Giese's and Schuster's ionic theory of conduction in gases, . . 397
J. J. Thomson measures the velocity of cathode rays, . . 400
Contents. xiii
Page
Discovery of X-rays : hypotheses regarding them, . . 401
Further researches of J. J. Thomson on cathode rays : the ratio m/e, 404
Vitreous and resinous electricity, . . . 406
Determination of the ionic charge by J. J. Thomson, . . 407
Becquerel's radiation : discovery of radio-active substances, . 408
CHAPTER XII.
THE THEORY OF AETHER AND ELECTRONS IN THE CLOSING YEARS OF THE NINETEENTH CENTURY.
Stokes' theory of aethereal motion near moving bodies, . . 411
Astronomical phenomena in which the velocity of light is involved, 413
Crucial experiments relating to the optics of moving bodies, . 416
Lorentz' theory of electrons, ...... 419
The current of dielectric convection : Rontgen's experiment, . 426
The electronic theory of dispersion, ..... 428
Deduction of Fresnel's formula from the theory of electrons, . 430
Experimental verification of Lorentz' hypothesis, . . . 431
Fitz Gerald's explanation of Michelson's experiment, . . 432 Lorentz' treatise of 1895, . . . . . . . 433
Expression of the potentials in terms of the electronic charges, . 436
Further experiments on the relative motion of earth and aether, . 437 Extension of Lorentz' transformation : Larmor discovers its
connexion with Fitz Gerald's hypothesis of contraction, . 440 Examination of the supposed primacy of the original variables :
fixity relative to the aether : the principle of relativity, . 444
The phenomenon of Zeeman, ..... 449
Connexion of Zeeman's effect with the magnetic rotation of light, . 452
The optical properties of metals, ..... 454
The electronic theory of metals, ..... 456
Thermionics, ........ 464
INDEX, . 470
MEMOKANDUM ON NOTATION.
VECTORS are denoted by letters in clarendon type, as E.
The three components of a vector E are denoted by Ex, Ey, Ez ; and the magnitude of the vector is denoted by E, so that
The vector product of two vectors E and H, which is denoted by [E . H], is the vector whose components are (EyHz - E^H^ EZHX - E*HZ, EtHy - EyHx}. Its direction is at right angles to the direction of E and H, and its magnitude is represented by twice the area of the triangle formed by them.
The scalar product of E and H is EXHX + EyEy + E^. It is denoted by (E . H).
OJ^j (1 jjj O Jjj
The quantity — -f — y -I- — is denoted by div E.
The vector whose components are
J — f *t — * ^ . — y _ *\
is denoted by curl E.
If V denote a scalar quantity, the vector whose components are 8F 8F 9F\ - 5T» * ^7' - -5T 1S denoted b7 grad ^
The symbol V is used to denote the vector operator whose
898
components are — , — , — . dx dy 82
Differentiation with respect to the time is frequently indicated by a dot placed over the symbol of the variable which is differentiated.
THEORIES OF AETHER AND ELECTRICITY.
CHAPTEK I.
THE THEORY OF THE AETHER IN THE SEVENTEENTH CENTURY.
THE observation of the heavens, which has been pursued con- tinually from the earliest ages, revealed to the ancients the regularity of the planetary motions, and gave rise to the conception of a universal order. Modern research, building on this foundation, has shown how intimate is the connexion between the different celestial bodies. They are formed of the same kind of matter ; they are similar in origin and history ; and across the vast spaces which divide them they hold perpetual intercourse.
Until the seventeenth century the only influence which was known to be capable of passing from star to star was that of light. Newton added to this the force of gravity ; and it is now recognized that the power of communicating across vacuous regions is possessed also by the electric and magnetic attractions.
It is thus erroneous to regard the heavenly bodies as isolated in vacant space; around and between them is an incessant conveyance and transformation of energy. To the vehicle of this activity the name aetlier has been given.
The aether is the solitary tenant of the universe, save for that infinitesimal fraction of space which is occupied by ordinary matter. Hence arises a problem which has long engaged attention, and is not yet completely solved : What relation subsists between the medium which fills the interstellar void and the condensations of matter that are scattered throughout it?
B
$5 l ' r The ^Theory of the • -Aether
The history of this problem may be traced back continuously to the earlier half of the seventeenth century. It first emerged clearly in that reconstruction of ideas regarding the physical universe which was effected by Eene Descartes.
Descartes was born in 1596, the son of Joachim Descartes, Counsellor to the Parliament of Brittany. As a young man he followed the profession of arms, and served in the campaigns of Maurice of Nassau, and the Emperor ; but his twenty-fourth year brought a profound mental crisis, apparently not unlike those which have been recorded of many religious leaders ; and he resolved to devote himself thenceforward to the study of philosophy.
The age which preceded the birth of Descartes, and that in which he lived, were marked by events which greatly altered the prevalent conceptions of the world. The discovery of America, the circumnavigation of the globe by Drake, the over- throw of the Ptolemaic system of astronomy, and the invention of the telescope, all helped to loosen the old foundations and to make plain the need for a new structure. It was this that Descartes set himself to erect. His aim was the most ambitious that can be conceived ; it was nothing less than to create from the beginning a complete system of human knowledge.
Of such a system the basis must necessarily be metaphysical ; and this part of Descartes' work is that by which he is most widely known. But his efforts were also largely devoted to the mechanical explanation of nature, which indeed he regarded as one of the chief ends of Philosophy.*
The general character of his writings may be illustrated by a comparison with those of his most celebrated contemporary, f Bacon clearly defined the end to be sought for, and laid down the method by which it was to be attained; then, recognizing that to discover all the laws of nature is a task beyond the
* Of the works M'hich bear on our present subject, the Dioptrique and the Me'teores were published at Leyden in 1638, and the Principia Philosophiae at Amsterdam in 1644, six years before the death of its author.
t The principal philosophical works of Bacon were written about eighteen years before those of Descartes.
in the SeventeentJi Century. 3
powers of one man or one generation, he left to posterity the work of filling in the framework which he had designed. Descartes, on the other hand, desired to leave as little as possible for his successors to do ; his was a theory of the universe, worked out as far as possible in every detail. It is, however, impossible to derive such a theory inductively unless there are at hand sufficient observational data on which to base the induction ; and as such data were not available in the age of Descartes, he was compelled to deduce phenomena from preconceived principles and causes, after the fashion of the older philosophers. To the inherent weakness of this method may be traced the errors that at last brought his scheme to ruin.
The contrast between the systems of Bacon and Descartes is not unlike that between the Eoman republic and the empire of Alexander. In the one case we have a career of aggrandizement pursued with patience for centuries ; in the other a growth of fungus-like rapidity, a speedy dissolution, and an immense influence long exerted by the disunited fragments. The grandeur of Descartes' plan, and the boldness of its execution, stimulated scientific thought to a degree before unparalleled ; and it was largely from its ruins that later philosophers constructed those more valid theories which have endured to our own time.
Descartes regarded the world as an immense machine, operating by the motion and pressure of matter. " Give me matter and motion," he cried, " and I will construct the universe." A peculiarity which distinguished his system from that which afterwards sprang from its decay was the rejection of all forms of action at a distance ; he assumed that force cannot be com- municated except by actual pressure or impact. By this assumption he was compelled to provide an explicit mechanism in order to account for each of the known forces of nature — a task evidently much more difficult than that which lies before those who are willing to admit action at a distance as an ultimate property of matter.
Since the sun interacts with the planets, in sending them
B 2
4 The Theory of the Aether
light and heat and influencing their motions, it followed from Descartes' principle that interplanetary space must be a plenum,, occupied by matter imperceptible to the touch but capable of serving as the vehicle of force and light. This conclusion in turn determined the view which he adopted on the all- important question of the nature of matter.
Matter, in the Cartesian philosophy, is characterized not by impenetrability, or by any quality recognizable by the senses,, but simply by extension ; extension constitutes matter, and matter constitutes space. The basis of all things is a primitive,, elementary, unique type of matter, boundless in extent and infinitely divisible. In the process of evolution of the universe three distinct forms of this matter have originated, correspond- ing respectively to the luminous matter of the sun, the transparent matter of interplanetary space, and the dense, opaque matter of the earth. " The first is constituted by what has been scraped off the other particles of matter when they were rounded ; it moves with so much velocity that when it meets other bodies the force of its agitation causes it to be broken and divided by them into a heap of small particles that are of such a figure as to fill exactly all the holes and small interstices which they find around these bodies. The next type includes most of the rest of matter ; its particles are spherical, and are very small compared with the bodies we see on the earth ; but nevertheless they have a finite magnitude, so that they can be divided into others yet smaller. There exists in addition a third type exemplified by some kinds of matter — namely, those which, on account of their size and figure, cannot be so easily moved as the preceding. I will endeavour to show that all the bodies of the visible world are composed of these three forms of matter, as of three distinct elements ; in fact, that the sun and the fixed stars are formed of the first of these elements, the interplanetary spaces of the second, and the earth, with the planets and comets, of the third. For, seeing that the sun and the fixed stars emit light, the heavens transmit it, and the earth, the planets, and the comets reflect it, it appears to me that there
in the Seventeenth Century. 5
is ground for using these three qualities of luminosity, trans- parence, and opacity, in order to distinguish the three elements of the visible world.*
According to Descartes' theory, the sun is the centre of an immense vortex formed of the first or subtlest kind of inatter.f The vehicle of light in interplanetary space is matter of the second kind or element, composed of a closely packed assemblage of globules whose size is intermediate between that of the vortex-matter and that of ponderable matter. The globules of the second element, and all the matter of the first element, are constantly straining away from the centres around which they turn, owing to the centrifugal force of the vortices ;J so that the globules are pressed in contact with each other, and tend to move outwards, although they do not actually so move.§ It is the transmission of this pressure which constitutes light ; the action of light therefore extends on all sides round the sun and fixed stars, and travels instantaneously to any distance. |j In the Dwptrique$ vision is compared to the perception of the presence of objects which a blind man obtains by the use of his stick ; the transmission of pressure along the stick from the object to the hand being analogous to the transmission of pressure from a luminous object to the eye by the second kind of matter.
Descartes supposed the " diversities of colour and light " to he due to the different ways in which the matter moves.** In the Meteores,^ the various colours are connected with different rotatory velocities of the globules, the particles winch rotate most rapidly giving the sensation of red, the slower ones of yellow, and the slowest of green and blue — the order of colours being taken from the rainbow. The assertion of the dependence of colour
* Principia, Part iii, § 52.
t It is curious to speculate on the impression which would have been produced had the spirality of nehulse heen discovered hefore the overthrow of the Cartesian theory of vortices.
J Ibid., §§ 55-59. § Ibid., § 63. || Ibid., § 64. IT Discours premier.
** Principia, Part iv, § 195. ft Discours Huitieme.
6 The Theory of the Aether
on periodic time is a curious foreshadowing of one of the great discoveries of Newton.
The general explanation of light on these principles was amplified by a more particular discussion of reflexion and refraction. The law of reflexion— that the angles of incidence and refraction are equal — had been known to the Greeks ; but the law of refraction — that the sines of the angles of incidence and refraction are to each other in a ratio depending on the media — was now published for the first time.* Descartes gave it as his own ; but he seems to have been under considerable obligations to Willebrord Snell (b. 1591, d. 1626), Professor of Mathematics at Leyden, who had discovered it experimentally (though not in the form in which Descartes gave it) about 1621. Snell did not publish his result, but communicated it in manuscript to several persons, and Huygens affirms that this manuscript had been seen by Descartes.
Descartes presents the law as a deduction from theory. This, however, he is able to do only by the aid of analogy ;. when rays meet ponderable bodies, " they are liable to be deflected or stopped in the same way as the motion of a ball or a stone impinging 011 a body " ; for " it is easy to believe that the action or inclination to move, which I have said must be taken for light, ought to follow in this the same laws as motion."f Thus he replaces light, whose velocity of propagation he believes to be always infinite, by a projectile whose velocity varies from one medium to another. The law of refraction is then proved as follows J : —
Let a ball thrown from A meet at B a cloth CBE, so weak that the ball is able to break through it and pass beyond, but with its resultant velocity reduced in some definite proportion,, say 1 : k.
Then if BI be a length measured on the refracted ray equal to AB, the projectile will take k times as long to describe BI as it took to describe AB. But the component
* Dioptrique, Discount second. t Jbid., Discows premier.
% Ibid., Discotirs second.
in the Seventeenth Century. 7
of velocity parallel to the cloth must be unaffected by the impact; and therefore the projection BE of the refracted ray must be k times as long as the projection BC of the incident
I
ray. So if i and r denote the angles of incidence and refraction, we have
• BE BC
or the sines of the angles of incidence and refraction are in a constant ratio ; this is the law of refraction.
Desiring to include all known phenomena in .his system, Descartes devoted some attention to a class of effects which were at that time little thought of, but which were destined to play a great part in the subsequent development of Physics.
The ancients were acquainted with the curious properties possessed by two minerals, amber (riXtKrpov) and magnetic iron ore (77 \iOos Mayv?}r/e). The former, when rubbed, attracts light bodies : the latter has the power of attracting iron.
The use of the magnet for the purpose of indicating direc- tion at sea does not seem to have been derived from classical antiquity ; but it was certainly known in the time of the Crusades. Indeed, magnetism was one of the few sciences which progressed during the Middle Ages ; for in the thirteenth century Petrus Peregrinus,* a native of Maricourt in Picardy, made a discovery of fundamental importance.
Taking a natural magnet or lodestone, which had been rounded into a globular form, he laid it on a needle, and marked
* His Epistola was written in 1269.
8 The Theory of the Aether
the line along which the needle set itself. Then laying the needle on other parts of the stone, he obtained more lines in the same way. When the entire surface of the stone had been covered with such lines, their general disposition became evident; they formed circles, which girdled the stone in exactly the same way as meridians of longitude girdle the earth ; and there were two points at opposite ends of the stone through which all the circles passed, just as all the meridians pass through the Arctic and Antarctic poles of the earth.* Struck by the analogy, Peregrinus proposed to call these two points the poles of the magnet : and he observed that the way in which magnets set themselves and attract each other depends solely on the position of their poles, as if these were the seat of the magnetic power. Such was the origin of those theories of poles and polarization which in later ages have played so great a part in Natural Philosophy.
The observations of Peregrinus were greatly extended not long before the tune of Descartes by William Gilberd or Gilbertf (6. 1540, d. 1603). Gilbert was born at Colchester: after studying at Cambridge, he took up medical practice in London, and had the honour of being appointed physician to Queen Elizabeth. In 1600 he published a work* on Magnetism and Electricity, with which the modern history of both subjects begins.
Of Gilbert's electrical researches we shall speak later : in magnetism he made the capital discovery of the reason why magnets set in definite orientations with respect to the earth ; which is, that the earth is itself a great magnet, having one of its poles in high northern and the other in high southern latitudes. Thus the property of the compass was seen to be included in the general principle, that the north-seeking pole of
* " Procul dubio oranes lineae hujusmodi in duo puncta concurrent sicut omnes orbes meridian! in duo concurrunt polos mundi oppositos."
t The form in the Colchester records is Gilberd.
J Gulielmi Gilberti de Magnete, Magneticisque corporibus, et de magno magnete tellure : London, 1600. An English translation by P. F. Mottelay was published in 1893.
in the Seventeenth Century. 9
every magnet attracts the south-seeking pole of every other magnet, and repels its north-seeking pole.
Descartes attempted* to account for magnetic phenomena by his theory of vortices. A vortex of fluid matter was postulated round each magnet, the matter of the vortex entering by one pole and leaving by the other : this matter was supposed to act on iron and steel by virtue of a special resistance to its motion afforded by the molecules of those substances.
Crude though the Cartesian system was in this and many other features, there is no doubt that by presenting definite conceptions of molecular activity, and applying them to so wide a range of phenomena, it stimulated the spirit of inquiry, and prepared the way for the more accurate theories that came after. In its own day it met with great acceptance: the confusion which had resulted from the destruction of the old order was now, as it seemed, ended by a reconstruction of knowledge in a system at once credible and complete. Nor did its influence quickly wane ; for even at Cambridge it was studied long after Newton had published his theory of gravitation ;f and in the middle of the eighteenth century Euler and two of the Bernoullis based the explanation of magnetism on the hypothesis of vertices.*
Descartes' theory of light rapidly displaced the conceptions which had held sway in the Middle Ages. The validity of his explanation of refraction was, however, called in question by his fellow-countryman Pierre de Ferinat (b. 1601, d. 1665),§ and a controversy ensued, which was kept up by the Cartesians long after the death of their master. Fermat
* Principia, Part iv, § 133 sqq.
•f Winston has recorded that, having returned to Cambridge after his ordination in 1693, he resumed his studies there, " particularly the Mathematicks, and the Cartesian Philosophy : which was alone in Vogue with us at that Time. But it was not long before I, with immense Pains, but no Assistance, set myself with the utmost Zeal to the study of Sir Isaac Newton's M-onderful Discoveries." — \Vhiston's Memoirs (1749), i, p. 36.
J Their memoirs shared a prize of the French Academy in 1743, and were printed in 1752 in the Heciieil des pieces qui ontremporte les prix de VAcad., tome v. § Renati Descartes Epistolae, Pars tertia ; Amstelodami, 1683. The Fennat correspondence is comprised in letters xxix to XLVI.
10 The Theory of the Aether
eventually introduced a new fundamental law, from which he proposed to deduce the paths of rays of light. This was the celebrated Principle of Least Time, enunciated* in the form, " Nature always acts by the shortest course." From it the law of reflexion can readily be derived, since the path described by light between a point 011 the incident ray and a point on the reflected ray is the shortest possible consistent with the con- dition of meeting the reflecting surfaces. t In order to obtain the law of refraction, Fermat assumed that " the resistance of the media is different," and applied his "method of maxima and minima " to find the path which would be described in the least time from a point of one medium to a point of the other. In 1661 he arrived at the solution.* "The result of my work," he writes, " has been the most extraordinary, the most unforeseen, and the happiest, that ever was ; for, after having performed all the equations, multiplications, antitheses, and other operations of my method, and having finally finished the problem, I have found that my principle gives exactly and precisely the same proportion for the refractions which Monsieur Descartes has established." His surprise was all the greater, as he had supposed light to move more slowly in dense than in rare media, whereas Descartes had (as will be evident from the demonstration given above) been obliged to make the contrary supposition. Although Fermat's result was correct, and, indeed, of high permanent interest, the principles from which it was derived were metaphysical rather than physical in character, and con- sequently were of little use for the purpose of framing a mechanical explanation of light. Descartes' theory therefore held the field until the publication in 1667§ of the Micrographics
* Epist. XLII, written at Toulouse in August, 1657, to Monsieur de la Chambre ; reprinted in (Euvres de Fermat (ed. 1891), ii, p. 354.
t That reflected light follows the shortest path was no new result, for it had been affirmed (and attributed to Hero of Alexandria) in the Ke<t>aA.cua rwv OTTTIKUHT of Heliodorns of Larissa, a work of which several editions were published in the seventeenth, century.
J Epist. XLIII, written at Toulouse on Jan. 1, 1662 ; reprinted in (Euvres de Fermat, ii, p. 457 ; i, pp. 170, 173.
§ The imprimatur of Viscount Brouncker, P.R.S., is dated Nov. 23, 1664.
in the Seventeenth Centnry. 11
of Eobert Hooke (b. 1635, d. 1703), one of the founders of the Eoyal Society, and at one time its Secretary.
Hooke, who was both an observer and a theorist, made two experimental discoveries which concern our present subject ; but in both of these, as it appeared, he had been anticipated. The first* was the observation of the iridescent colours which are seen when light falls on a thin layer of air between two glass plates or lenses, or on a thin film of any transparent substance. These are generally known as the " colours of thin plates," or " Newton's rings " ; they had been previously observed by Boyle.f Hooke's second experimental discovery,^ made after the date of the Micrographia, was that light in air is not propagated exactly in straight lines, but that there is some illumination within the geometrical shadow of an opaque body. This observation had been published in 1665 in. a posthumous work§ of Francesco Maria Grimaldi (b. 1618, d. 1663), who had given to the phe- nomenon the name diffraction.
Hooke's theoretical investigations on light were of great importance, representing as they do the transition from the Cartesian system to the fully developed theory of undulations. He begins by attacking Descartes' proposition, that light is a tendency to motion rather than an actual motion. " There is," he observes, 1 1 " no luminous Body but has the parts of it in motion more or less " ; and this motion is " exceeding quick." Moreover, since some bodies (e.g. the diamond when rubbed or heated in the dark) shine for a considerable time without being wasted away, it follows that whatever is in motion is not per- manently lost to the body, and therefore that the motion must be of a to-and-fro or vibratory character. The amplitude of the vibrations must be exceedingly small, since some luminous bodies (e.g. the diamond again) are very hard, and so cannot yield or bend to any sensible extent.
* Micrographia, p. 47. t Boyle's Works (ed. 1772), i, p. 742.
% Hooke's Posthumous Works, p. 186.
§ Pkysico- Mathesis de lumine, coloribits, et iride. Bologna, 1665 ; book i, prop. i. || Micrographia, p. 55.
12 The Theory of the Aether
Concluding, then, that the condition associated with the emission of light by a luminous body is a rapid vibratory motion of very small amplitude, Hooke next inquires how light travels through space. " The next thing we are to consider," he says, " is the way or manner of the trajection of this motion through the interpos'd pellucid body to the eye : And here it will be easily granted —
" First, that it must be a body susceptible and impartible of this motion that will deserve the name of a Transparent ; and next, that the parts of such a body must be homogeneous, or of the same kind.
" Thirdly, that the constitution and motion of the parts must be such that the appulse of the luminous body may be commu- nicated or propagated through it to the greatest imaginable distance in the least imaginable time, though I see no reason to affirm that it must be in an instant.
" Fourthly, that the motion is propagated every way through an Homogeneous medium by direct or straight lines extended every way like Eays from the centre of a Sphere.
" Fifthly, in an Homogeneous medium this motion is propa- gated every way with equal velocity, whence necessarily every pulse or vibration of the luminous body will generate a Sphere, which will continually increase, and grow bigger, just after the same manner (though indefinitely swifter) as the waves or rings on the surface of the water do swell into bigger and bigger circles about a point of it, where by the sinking of a Stone the motion was begun, whence it necessarily follows, that all the parts of these Spheres undulated through an Homogeneous medium cut the Kays at right angles."
Here we have a fairly definite mechanical conception. It resembles that of Descartes in postulating a medium as the vehicle of light ; but according to the Cartesian hypothesis the disturbance is a statical pressure in this medium, while in Hooke's theory it is a rapid vibratory motion of small amplitude. In the above extract Hooke introduces, moreover, the idea of the wave-swrface, or locus at any instant of a disturbance gene-
in the Seventeenth Century. 13
rated originally at a point, and affirms that it is a sphere, whose, centre is the point in question, and whose radii are the rays of light issuing from the point.
Hooke's next effort was to produce a mechanical theory of refraction, to replace that given by Descartes. " Because," he says, "all transparent mediums are not Homogeneous to one another, therefore we will next examine how this pulse or motion will be propagated through differingly transparent mediums. And here, according to the most acute and excellent Philosopher Des Cartes, I suppose the sine of the angle of inclination in the first medium to be to the sine of refraction in the second, as the density of the first to the density of the second. By density, I mean not the density in respect of gravity (with which the refractions or transparency of mediums hold no proportion), but in respect only to the trajeetion of the Kays of light, in which respect they only differ in this, that the one propagates the pulse more easily and weakly, the other more slowly, but more strongly. But as for the pulses themselves, they will by the refraction acquire another property, which we shall now endeavour to explicate.
"We will suppose, therefore, in the first Figure, ACFD to be
a physical Kay, or ABC and DEFto be two mathematical Kaysr trajected from a very remote point of a luminous body through
14 The Theory of the Aether
an Homogeneous transparent medium LL, and DA, EB, FC, to be small portions of the orbicular impulses which must therefore cut the Rays at right angles : these Rays meeting with the plain surface NO of a medium that yields an easier transitus to the propagation of light, and falling obliquely on it, they will in the medium MM be refracted towards the perpendicular of the surface. And because this medium is more easily trajected than the former by a third, therefore the point 0 of the orbicular pulse FG will be moved to If four spaces in the same time that F, the other end of it, is moved to three spaces, therefore the whole refracted pulse to H shall be oblique to the refracted Rays GHK and £/."
Although this is not in all respects successful, it represents a decided advance on the treatment of the same problem by Descartes, which rested on a mere analogy. Hooke tries to determine what happens to the wave-front when it meets the interface between two media ; and for this end he intro- duces the correct principle that the side of the wave-front which first meets the interface will go forward in the second medium with the velocity proper to that medium, while the other side of the wave-front which is still in the first medium is still moving with the old velocity : so that the wave-front will be deflected in the transition from one medium to the other.
This deflection of the wave-front was supposed by Hooke to be the origin of the prismatic colours. He regarded natural or white light as the simplest type of disturbance, being consti- tuted by a simple and uniform pulse at right angles to the direction of propagation, and inferred that colour is generated by the distortion to which this disturbance is subjected in the process of refraction. "The Ray,"* he says, " is dispersed, split, and opened by its Refraction at the Superficies of a second medium, and from a line is opened into a diverging Superficies, and so obliquated, whereby the appearances of Colours are produced."
* Hooke, Posthnmo/is Works, p. 82.
in the Seventeenth Century. \ 5
" Colour/' he says in another place,* " is nothing but the disturbance of light by the communication of the pulse to other transparent mediums, that is by the refraction thereof." His precise hypothesis regarding the different colours wasf "that Blue is an impression on the Retina of an oblique and confus'd pulse of light, whose weakest part precedes, and whose strongest follows. And, that red is an impression on the Retina of an oblique and confus'd pulse of light, whose strongest part precedes, and whose weakest follows."
Hooke's theory of colour was completely overthrown, within a few years of its publication, by one of the earliest discoveries of Isaac Xewton (b. 1642, d. 1727). Newton, who was elected a Fellow of Trinity College, Cambridge, in 1667, had in the beginning of 1666 obtained a triangular prism, " to try- therewith the celebrated Phaenomena of Colours." For this purpose, " having darkened my chamber, and made a small hole in my window-shuts, to let in a convenient quantity of the Sun's light, I placed my Prisme at his entrance, that it might be thereby refracted to the opposite wall. It was at first a very pleasing divertisement, to view the vivid and intense colours produced thereby ; but after a while applying myself to consider them more circumspectly, I became surprised to see them in an oblong form, which, according to the received laws of Refraction, I expected should have been circular" The length of the coloured spectrum was in fact about five times as great as its breadth.
This puzzling fact he set himself to study ; and after more experiments the true explanation was discovered — namely, that ordinary white light is really a mixture of rays of every variety of colour, and that the elongation of the spectrum is due to the differences in the refractive power of the glass for these different rays.
" Amidst these thoughts," he tells us,+ " I was forced from
*To the Royal Society, February 15, 1671-2.
t Micrographia, p. 64.
J Phil. Trans., Xo. 80, February 19, 1671-2.
16 The Theory of the Aether
Cambridge by the intervening Plague " ; this was in 1666, and his memoir on the subject was not presented to the Koyal Society until five years later. In it he propounds a theory of colour directly opposed to that of Hooke. " Colours," he says, "are not Qualifications of light derived from Refractions, or Reflections of natural Bodies (as 'tis generally believed), but Original and connate properties, which in divers Rays are divers. Some Rays are disposed to exhibit a red colour and no other : some a yellow and no other, some a green and no other, and so of the rest. Nor are there only Rays proper and particular to the more eminent colours, but even to all their intermediate gradations.
" To the same degree of Refrangibility ever belongs the same colour, and to the same colour ever belongs the same degree of Refrangibility."
" The species of colour, and degree of Refrangibility proper to any particular sort of Rays, is not mutable by Refraction, nor by Reflection from natural bodies, nor by, any other cause, that I could yet observe. When any one sort of Rays hath been well parted from those of other kinds, it hath afterwards obstinately retained its colour, notwithstanding my utmost endeavours to change it."
The publication of the new theory gave rise to an acute controversy. As might have been expected, Hooke was foremost among the opponents, and led the attack with some degree of asperity. When it is remembered that at this time Newton was at the outset of his career, while Hooke was an older man, with an established reputation, such harshness appears par- ticularly ungenerous; and it is likely that the unpleasant consequences which followed the announcement of his first great discovery had much to do with the reluctance which Newton ever afterwards showed to publish his results to the world.
In the course of the discussion Newton found occasion to explain more fully the views which he entertained regarding the nature of light. Hooke charged him with holding the
in the Seventeenth Century. 17
doctrine that light is a material substance. Now Newton had, as a matter of fact, a great dislike of the more imaginative kind of hypotheses ; he altogether renounced the attempt to construct the universe from its foundations after the fashion of Descartes, and aspired to nothing more than a formulation of the laws which directly govern the actual phenomena. His theory of gravitation, for example, is strictly an expression of the results of observation, and involves no hypothesis as to the cause of the attraction which subsists between ponderable bodies ; and his own desire in regard to optics was to present a theory free from speculation as to the hidden mechanism of light. Accordingly, in reply to Hooke's criticism, he protested* that his views on colour were in no way bound up with any particular conception of the ultimate nature of optical processes.
Xewton was, however, unable to carry out his plan of connecting together the phenomena of light into a coherent and reasoned whole without having recourse to hypotheses. The hypothesis of Hooke, that light consists in vibrations of an aether, he rejected for reasons which at that time were perfectly cogent, and which indeed were not successfully refuted for over a century. One of these was the incompetence of the wave- theory to account for the rectilinear propagation of light, and another was its inability to embrace the facts — discovered, as we shall presently see, by Huygens, and first interpreted correctly by Newton himself — of polarization. On the whole, he seems to have favoured a scheme of which the following may be taken as a summaryf : —
All space is permeated by an elastic medium or aether, which is capable of propagating vibrations in the same way as the
*Phil. Trans, vii, 1672, p. 5086.
t Cf. Newton's memoir in Phil. Trans, vii, 1672 ; his memoir presented to the Royal Society in December, 1675, which is printed in Birch, iii, p. 247; his Opticks, especially Queries 18, 19, 20, 21, 23, 29; the Scholium at the end of the Principia ; and a letter to Boyle, written in February, 1678-9, which is printed in Horsley's Newtoni Opera, p. 385.
In the Principia, Book I., section xiv, the analogy between rays of light and streams of corpuscles is indicated ; but Newton does not commit himself to any theory of light based on this.
C
18 The Theory of the Aether
air propagates the vibrations of sound, but with far greater velocity.
This aether pervades the pores of all material bodies, and is the cause of their cohesion ; its density varies from one body to another, being greatest in the free interplanetary spaces. It is not necessarily a single uniform substance : but just as air contains aqueous vapour, so the aether may contain various " aethereal spirits," adapted to produce the phenomena of electricity, magnetism, and gravitation.
The vibrations of the aether cannot, for the reasons already mentioned, be supposed in themselves to constitute light. Light is therefore taken to be " something of a different kind, propagated from lucid bodies. They, that will, may suppose it an aggregate of various peripatetic qualities. Others may suppose it multitudes of unimaginable small and swift corpuscles of various sizes, springing from shining bodies at great distances one after another; but yet without any sensible interval of time, and continually urged forward by a principle of motion, which in the beginning accelerates them, till the resistance of the aethereal medium equals the force of that principle, much after the manner that bodies let fall in water are accelerated till the resistance of the water equals the force of gravity. But they, that like not this, may suppose light any other corporeal emanation, or any impulse or motion of any other medium or aethereal spirit diffused through the main body of aether, or what else they can imagine proper for this purpose. To avoid dispute, and make this hypothesis general, let every man here take his fancy ; only whatever light be, I suppose it consists of rays differing from one another in contingent circumstances, as bigness, form, or vigour."*
In any case, light and aether are capable of mutual inter- action; aether is in fact the intermediary between light and ponderable matter. When a ray of light meets a stratum of aether denser or rarer than that through which it has lately been passing, it is, in general, deflected from its rectilinear * Royal Society, Dec. 9, 1675.
in the Seventeenth Century. 19
course ; and differences of density of the aether between one material medium and another account on these principles for the reflexion and refraction of light. The condensation or rarefaction of the aether due to a material body extends to some little distance from the surface of the body, so that the inflexion due to it is really continuous, and not abrupt; and this further explains diffraction, which Newton took to be " only a new kind of refraction, caused, perhaps, by the external aethers beginning to grow rarer a little before it came at the opake body, than it was in free spaces."
Although the regular vibrations of Newton's aether were not supposed to constitute light, its irregular turbulence seems to have represented fairly closely his conception of heat. He supposed that when light is absorbed by a material body, vibrations are set up in the aether, and are recognizable as the heat which is always generated in such cases. The conduction of heat from hot bodies to contiguous cold ones he conceived to be effected by vibrations of the aether propagated between them ; and he supposed that it is the violent agitation of aethereal motions which excites incandescent substances to emit light.
Assuming with Newton that light is not actually con- stituted by the vibrations of an aether, even though such vibrations may exist in close connexion with it, the most definite and easily conceived supposition is that rays of light are streams of corpuscles emitted by luminous bodies. Although this was not the hypothesis of Descartes himself, it was so thoroughly akin to his general scheme that the scientific men of Newton's generation, who were for the most part deeply imbued with the Cartesian philosophy, instinctively selected it from the wide choice of hypotheses which Newton had offered them ; and by later writers it was generally associated with Newton's name. A curious argument in its favour was drawn from a phenomenon which had then been known for nearly half a century : Vincenzo Cascariolo, a shoemaker of Bologna, had discovered, about 1630, that a substance, which afterwards
C 2
20 The Theory of the Aether
received the name of Bologna stone or Bologna phosphorus, has- the property of shining in the dark after it has been exposed for some time to sunlight ; and the storage of light which seemed to be here involved was more easily explicable on the corpuscular theory than on any other. The evidence in this quarter, however, pointed the other way when it was found that phosphorescent substances do not necessarily emit the same kind of light as that which was used to stimulate them.
In accordance with his earliest discovery, Newton considered colour to be an inherent characteristic of light, and inferred that it must be associated with some definite quality of the corpuscles or aether-vibrations. The corpuscles corresponding to different colours would, he remarked, like sonorous bodies of different pitch, excite vibrations of different types in the aether ; and " if by any means those [aether- vibrations] of unequal bignesses be separated from one another, the largest beget a Sensation of a Red colour, the least or shortest of a deep Violet, and the intermediate ones, of intermediate colours ; much after the manner that bodies, according to their several sizes, shapes, and motions, excite vibrations in the Air of various bignesses, which, according to those bignesses, make several Tones in Sound."*
This sentence is the first enunciation of the great principle that homogeneous light is essentially periodic in its nature, and that differences of period correspond to differences of colour. The analogy with Sound is obvious ; and it may be remarked in passing that Newton's theory of periodic vibrations in an elastic medium, which he developed! in connexion with the explanation of Sound, would alone entitle him to a place among those who have exercised the greatest influence on the theory of light, even if he had made no direct contribution to the latter subject.
* Phil. Trans, vii (1672), p. 5088.
t Newton's Prmcipia, Book ii., Props, xliii.-l.
in the Seventeenth Century. 21
Newton devoted considerable attention to the colours of thin, plates, and determined the empirical laws of the phenomena with great accuracy. In order to explain them, he supposed that " every ray of light, in its passage through any refracting surface, is put into a certain transient constitution or state, which, in the progress of the ray, returns at equal intervals, and disposes the ray, at every return, to be easily transmitted through the next refracting surface, and, between the returns, to be easily reflected by it."* The interval between two consecutive dispositions to easy transmission, or •" length of fit," he supposed to depend on the colour, being greatest for red light and least for violet. If then a ray of homogeneous light falls on a thin plate, its fortunes as regards transmission and reflexion at the two surfaces will depend on the relation which the length of fit bears to the thickness of the plate ; and on this basis he built up a theory of the colours of thin plates. It is evident that Newton's "length of fit" corresponds in some measure to the quantity which in the undulatory theory is called the wave-length of the light ; but the suppositions of easy transmission and reflexion were soon found inadequate to explain all Newton's experimental results — .at least without making other and more complicated additional assumptions.
At the time of the publication of Hooke's Micrographia, and Newton's theory of colours, it was not known whether light is propagated instantaneously or not. An attempt to settle the question experimentally had been made many years previously by Galileo,f who had stationed two men with lanterns at a considerable distance from each other ; one of them was directed to observe when the other uncovered his light, and exhibit his own the moment he perceived it. But the interval of time required by the light for its journey was too small to be perceived in this way ; and the discovery was
* Optic ks, Book ii., Prop. 12.
t Discorri e dimostrazioiti matemaliche, p. 43 of the Elzevir edition of 1638.
22 The Theory of the Aether
ultimately made by an astronomer. It was observed in 1675 by Olof Roemer* (b. 1644, d. 1710) that the eclipses of the first satellites of Jupiter were apparently affected by an unknown disturbing cause ; the time of the occurrence of the phenomenon was retarded when the earth and Jupiter, in the course of their orbital motions, happened to be most remote from each other, and accelerated in the contrary case. Eoemer explained this by supposing that light requires a finite time for its pro- pagation from the satellite to the earth ; and by observations of eclipses, he calculated the interval required for its passage from the sun to the earth (the light-equation, as it is called) to be 11 minutes, f
Shortly after Roemer's discovery, the wave-theory of light was greatly improved and extended by Christiaan Huygens (b. 1629, d. 1695). Huygens, who at the time was living in Paris, communicated his results in 1678 to Cassini, Eoemer, De la Hire, and the other physicists of the French Academy, and prepared a manuscript of considerable length on the subject. This he proposed to translate into Latin, and to publish in that language together with a treatise on the Optics of Telescopes ; but the work of translation making little progress, after a delay of twelve years, he decided to print the work on wave-theory in its original form. In 1690 it appeared at Ley den, J under the title Traite de la lumiere ou sont expliquees les causes de ce qui luy arrive dans la reflexion et dans la refraction. Et parti-
*Mem. de 1'Acad. x. (1666-1699), p. 575.
t It was soon recognized that Roemer's value was too large ; and the astronomers of the succeeding half-century reduced it to 7 minutes. Delambre, by an investigation whose details appear to have been completely destroyed, published in 1817 the value 493 -2s, from a discussion of eclipses of Jupiter's satellites during the previous 150 years. Glasenapp, in an inaugural dissertation published in 1875, discussed the eclipses of the first satellite between 1848 and 1870, and derived, by different assumptions, values between 496s and 501s, the most probable value being 500-88. Sampson, in 1909, derived 498'64S from his own readings of the Harvard Observations, and 498'79S from the Harvard readings, with probable errors of about + 0'02". The inequalities of Jupiter's surface give rise to some difficulty in exact determinations.
% Huygens had by this time returned to Holland.
in the Seventeenth Century. 23
culierement dans Vetrange refraction du cristal d'Islande. Par C.ff.D.Z*
The truth of Hooke's hypothesis, that light is essentially a form of motion, seemed to Huygens to be proved ]}y the effects observed with burning-glasses ; for in the combustion induced at the focus of the glass, the molecules of bodies are dissociated ; which, as he remarked, must be taken as a certain sign of motion, if, in conformity to the Cartesian philosophy, we seek the cause of all natural phenomena in purely mechanical actions.
The question then arises as to whether the motion is that of a medium, as is supposed in Hooke's theory, or whether it may be compared rather to that of a flight of arrows, as in the corpuscular theory. Huygens decided that the former alter- native is the only tenable one, since beams of light proceeding in directions inclined to each other do not interfere with each other in any way.
Moreover, it had previously been shown by Torricelli that light is transmitted as readily through a vacuum as through air ; and from this Huygens inferred that the medium or aether in which the propagation takes place must penetrate all matter, and be present even in all so-called vacua.
The process of wave-propagation he discussed by aid of a principle which was nowf introduced for the first time, and has since been generally known by his name. It may be stated thus : Consider a wave-front,* or locus of disturbance, as it exists at a definite instant t0 : then each surface-element of the wave-front may be regarded as the source of a secondary wave, which in a homogeneous isotropic medium will be propagated outwards from the surface-element in the form of a sphere whose radius at any subsequent instant t is proportional to (t-t0) ; and the wave-front which represents the whole distur-
* i.e. Cbristiaan Huygens de Zuylichem. The custom of indicating names by initials was not unusual in that age.
t Traite de la lum., p. 17.
I It maybe remarked that Huygens' " waves " are really what modern writers, following Hooke, call " pulses "; Huygens never considered true wave-trains having the property of periodicity.
24 The Theory of the Aether
bance at the instant t is simply the envelope of the secondary waves which arise from the various surface elements of the original wave-front.* The introduction of this principle enabled Huygens to succeed where Hooke and other contemporary wave-theoristsf had failed, in achieving the explanation of refraction and reflexion. His method was to combine his own principle with Hooke's device of following separately the fortunes of the right-hand and left-hand sides of a wave-front when it reaches the interface between two media. The actual explana- tion for the case of reflexion is as follows : —
Let AB represent the interface at which reflexion takes place, AHC the incident wave-front at an instant £0, GMB the position which the wave-front would occupy at a later instant t if the propagation were not interrupted by reflexion. Then by
"G
Huygens' principle the secondary wave from A is at the instant t a sphere ENS of radius equal to AG : the disturbance from Ht after meeting the interface at K, will generate a secondary wave TV oi radius equal to KM, and similarly the secondary wave corresponding to any other element of the original wave-
* The justification for this was given long afterwards by Fresnel, Annales de chimie, xxi.
t e.g. Ignace Gaston Pardies and Pierre Ango, the latter of whom published a work on Optics at Paris'in 1682.
in the Seventeenth Century. 25
front can be found. It is obvious that the envelope of these secondary waves, which constitutes the final wave-front, will be a plane BN, which will be inclined to AB at the same angle as AC. This gives the law of reflexion.
The law of refraction is established by similar reasoning, on the supposition that the velocity of light depends on the medium in which it is propagated. Since a ray which passes from air to glass is bent inwards towards the normal, it may be inferred that light travels more slowly in glass than in air.
Huygens offered a physical explanation of the variation in velocity of light from one medium to another, by supposing that transparent bodies consist of hard particles which interact with the aethereal matter, modifying its elasticity. The opacity of metals he explained by an extension of the same idea, supposing that some of the particles of metals are hard (these account for reflexion) and the rest soft : the latter destroy the luminous motion by damping it.
The second half of the Theorie de la lumiere is concerned with a phenomenon which had been discovered a few years pre- viously by a Danish philosopher, Erasmus Bartholin (b. 1625, d. 1698). A sailor had brought from Iceland to Copenhagen a number of beautiful crystals which he had collected in the Bay of Eoerford. Bartholin, into whose hands they passed, noticed* that any small object viewed through one of these crystals appeared double, and found the immediate cause of this in the fact that a ray of light entering the crystal gave rise in general to two refracted rays. One of these rays was subject to the ordinary law of refraction, while the other, which was called the extraordinary ray, obeyed a different law, which Bartholin did not succeed in determining.
The matter had arrived at this stage when it was taken up by Huygens. Since in his conception each ray of light corresponds to the propagation of a wave-front, the two rays in Iceland spar must correspond to two different wave-fronts propagated
* Ejcperimenta cristatti Islandici disdiaclastici : 1669.
26 The Theory of the Aether
simultaneously. In this idea he found no difficulty ; as he says : " It is certain that a space occupied by more than one kind of matter may permit the propagation of several kinds of waves, different in velocity; for this actually happens in air mixed with aethereal matter, where sound-waves and light- waves are propagated together."
Accordingly he supposed that a light-disturbance generated at any spot within a crystal of Iceland spar spreads out in the form of a wave-surface, composed of a sphere and a spheroid having the origin of disturbance as centre. The spherical wave- front corresponds to the ordinary ray, and the spheroid to the extraordinary ray ; and the direction in which the extraordinary ray is refracted may be determined by a geometrical construc- tion, in which the spheroid takes the place which in the ordinary construction is taken by the sphere.
Thus, let the plane of the figure be at right angles to the intersection of the wave-front with the surface of the crystal ; let AB represent the trace of the incident wave-front ; and suppose that in unit time the disturbance from B reaches the interface at T. In this unit-interval of time the disturbance from A will have spread out within the crystal into a sphere and spheroid : so the wave-front corresponding to the
ordinary ray will be the tangent-plane to the sphere through the line whose trace is T, while the wave-front corresponding to the extraordinary ray will be the tangent-plane to the spheroid through the same line. The points of contact N
in the Seventeenth Century. 27
and M will determine the directions AN and A M of the two- refracted rays* within the crystal.
Huygens did not in the Thtoi-ie de la lumiere attempt a detailed physical explanation of the spheroidal wave, but communicated one later in a letter to Papin,f written in December, 1690. " As to the kinds of matter contained in Iceland crystal," he says, " I suppose one composed of small spheroids, and another which occupies the interspaces around these spheroids, and which serves to bind them together. Besides these, there is the matter of aether permeating all the crystal, both between and within the parcels of the two kinds of matter just mentioned ; for I suppose both the little spheroids, and the matter which occupies the intervals around them, to be composed of small fixed particles, amongst which are diffused in perpetual motion the still finer particles of the aether. There is now no reason why the ordinary ray in the crystal should not be due to waves propa- gated in this aethereal matter. To account for the extraordinary refraction, I conceive another kind of waves, which have for vehicle both the aethereal matter and the two other kinds of matter constituting the crystal. Of these latter, I suppose that the matter of the small spheroids transmits the waves a little more quickly than the aethereal matter, while that around the spheroids transmits these waves a little more slowly than the same aethereal matter. . . . These same waves, when they travel in the direction of the breadth of the spheroids, meet with more of the matter of the spheroids, or at least pass with less obstruction, and so are propagated a little more quickly in this sense than in the other ; thus the light-disturbance is propagated as a spheroidal sheet."
Huygens made another disco veryj of capital importance when
* The word ray in the wave-theory is always applied to the line which goes from the centre of a wave (i.e. the origin of the disturbnnce) to a point on its surface, whatever may be the inclination of this line to the surface-element on which it abuts; for this line has the optical properties of the "rays" of the emission theory.
t Huygens' (Envres, ed. 1905, x., p. 177.
+ T/ieorie de la lumiere, p. 89.
28 Theory of the Aether in the Seventeenth Century.
experimenting with the Iceland crystal. He observed that the two rays which are obtained by the double refraction of a single ray afterwards behave in a way different from ordinary light which has not experienced double refraction ; and in particular, if one of these rays is incident on a second crystal of Iceland spar, it gives rise in some circumstances to two, and in others to only one, refracted ray. The behaviour of the ray at this second refraction can be altered by simply rotating the second crystal about the direction of the ray as axis ; the ray under- going the ordinary or extraordinary refraction according as the principal section of the crystal is in a certain direction or in the direction at right angles to this.
The first stage in the explanation of Huygens' observation was reached by Newton, who in 1717 showed* that a ray obtained by double refraction differs from a ray of ordinary light in the same way that a long rod whose cross-section is a rectangle differs from a long rod whose cross-section is a circle : in other words, the properties of a ray of ordinary light are the same with respect to all directions at right angles to its direction of propagation, whereas a ray obtained by double refraction must be supposed to have sides, or properties related to special directions at right angles to its own direction. The refraction of such a ray at the surface of a crystal depends on the relation of its sides to the principal plane of the crystal.
That a ray of light should possess such properties seemed to Newton f an insuperable objection to the hypothesis which regarded waves of light as analogous to waves of sound. On this point he was in the right : his objections are perfectly valid against the wave-theory as it was understood by his contemporaries J, although not against the theory § which was put forward a century later by Young and Fresnel.
* The second edition of Newton's Opticks, Query 26. t Opticks, Query 28.
J In which the oscillations are performed in the direction in which the wave advances.
§ In which the oscillations are performed in a direction at right angles to that in which the wave advances.
29 )
CHAPTEE II.
ELECTRIC AND MAGNETIC SCIENCE PRIOR TO THE INTRODUCTION OF THE POTENTIALS.
THE magnetic discoveries of Peregrinus and Gilbert, and the vortex-hypothesis by which Descartes had attempted to explain them,* had raised magnetism to the rank of a separate science by the middle of the seventeenth century. The kindred science of electricity was at that time in a less developed state ; but it had been considerably advanced by Gilbert, whose researches in this direction will now be noticed.
For two thousand years the attractive power of amber had been regarded as a virtue peculiar to that substance, or possessed by at most one or two others. Gilbert provedf this view to be mistaken, showing that the same effects are induced by friction in quite a large class of bodies ; among which he mentioned glass, sulphur, sealing-wax, and various precious stones.
A force which was manifested by so many different kinds of matter seemed to need a name of its own; and accordingly Gilbert gave to it the name electric, which it has ever since retained.
Between the magnetic and electric forces Gilbert remarked many distinctions. The lodestone requires no stimulus of friction such as is needed to stir glass and sulphur into activity. The lodestone attracts only magnetizable substances, whereas electrified bodies attract everything. The magnetic attraction between two bodies is not affected by interposing a sheet of paper, or a linen cloth, or by immersing the bodies in water j whereas the electric attraction is readily destroyed by screens. Lastly, the magnetic force tends to arrange bodies in definite
*Cf. pp. 7-9. t De Magnete, lib. ii., cap. 2.
30 Electric and Magnetic Science
orientations ; while the electric force merely tends to heap them together in shapeless clusters.
These facts appeared to Gilbert to indicate that electric phenomena are due to something of a material nature, which under the influence of friction is liberated from the glass or amber in which under ordinary circumstances it is imprisoned. In support of this view he adduced evidence from other quarters. Being a physician, he was well acquainted with the doctrine that the human body contains various humours or kinds of moisture — phlegm, blood, choler, and melancholy, — which, as they predominated, were supposed to determine the temper of mind; and when he observed that electrifiable bodies were almost all hard and transparent, and therefore (according to the ideas of that time) formed by the consolidation of watery liquids, he concluded that the common menstruum of these liquids must be a particular kind of humour, to the possession of which the electrical properties of bodies were to be referred. Friction might be supposed to warm or otherwise excite or liberate the humour, which would then issue from the body as an effluvium and form an atmosphere around it. The effluvium must, he remarked, be very attenuated, for its emission cannot be detected by the senses.
The existence of an atmosphere of effluvia round every electrified body might indeed have been inferred, according to Gilbert's ideas, from the single fact of electric attraction. For he believed that matter cannot act where it is not ; and hence if a body acts on all surrounding objects without appearing to touch them, something must have proceeded out of it unseen.
The whole phenomenon appeared to him to be analogous to the attraction which is exercised by the earth on falling bodies. For in the latter case he conceived of the atmospheric air as the effluvium by which the earth draws all things downwards to itself.
Gilbert's theory of electrical emanations commended itself generally to such of the natural philosophers of the seventeenth century as were interested in the subject ; among whom were
prior to the Introduction of the Potentials. 31
numbered Niccolo Cabeo (b. 1585, d. 1650), an Italian Jesuit who was. perhaps the first to observe that electrified bodies repel as well as attract ; the English royalist exile, Sir Kenelm Digby (b. 1603, d. 1665); and the celebrated Robert Boyle (b. 1627, d. 1691). There were, however, some differences of opinion as to the manner in which the effluvia acted on the small bodies and set them in motion towards the excited electric; Gilbert himself had supposed the emanations to have an inherent tendency to reunion with the parent body ; Digby likened their return to the condensation of a vapour by cooling ; and other writers pictured the effluvia as forming vortices round the attracted bodies in the Cartesian fashion.
There is a well-known allusion to Gilbert's hypothesis in Newton's Opticks.*
" Let him also tell me, how an electrick body can by friction emit an exhalation so rare and subtle,t and yet so potent, as by its emission to cause no sensible diminution of the weight of the electrick body, and to be expanded through a sphere, whose diameter is above two feet, and yet to be able to agitate and carry up leaf copper, or leaf gold, at a distance of above a foot from the electrick body ? "
It is, perhaps, somewhat surprising that the Newtonian doctrine of gravitation should not have proved a severe blow to the emanation theory of electricity ; but Gilbert's doctrine was now so firmly established as to be unshaken by the overthrow of the analogy by which it had been originally justified. It was, however, modified in one particular about the beginning of the eighteenth century. In order to account for the fact that electrics are not perceptibly wasted away by excitement, the earlier writers had supposed all the emanations to return ultimately to the body which had emitted them ; but the corpuscular theory of light accustomed philosophers to the idea of emissions so subtle as to cause no perceptible loss ; and
* Query 22.
t " Subtlety," says Johnson, " which in its original import means exility of particles, is taken in its metaphorical meaning for nicety of distinction."
32 Electric and Magnetic Science
after the time of Newton the doctrine of the return of the- electric effluvia gradually lost credit.
Newton died in 1727. Of the expositions of his philosophy which were published in his lifetime by his followers, one at least deserves to be noticed for the sake of the insight which it affords into the state of opinion regarding light, heat, and electricity in the first half of the eighteenth century. This was the Physices elementa matlwmatica experimentis confirmata of Wilhelm Jacob s'Gravesande (b. 1688, d. 1742), published at Ley den in 1720. The Latin edition was afterwards reprinted several times, and was, moreover, translated into French and English : it seems to have exercised a considerable and, on the whole, well-deserved influence on contemporary thought.
s'Gravesande supposed light to consist in the projection of corpuscles from luminous bodies to [the eye ; the motion being very swift, as is shown by astronomical observations. Since many bodies, e.g. the metals, become luminous when they- -are heated, he inferred that every substance possesses a natural store of corpuscles, which are expelled when it is heated to incandescence ; conversely, corpuscles may become united to a material body ; as happens, for instance, when the body is exposed to the rays of a fire. Moreover, since the heat thus acquired is readily conducted throughout the substance of the body, he concluded that corpuscles can penetrate all substances, however hard and dense they be.
Let us here recall the ideas then current regarding the nature of material bodies. From the time of Boyle (1626-1691) it had been recognized generally that substances perceptible to the senses may be either elements or compounds or mixtures ; the compounds being chemical individuals, distinct from mere mixtures of elements. But the substances at that time accepted as elements were very different from those which are now known by the name. Air and the calces* of the metals figured in the list, while almost all the chemical elements now recognized were
prior to the Introduction oj the Potentials. 33
omitted from it ; some of them, such as oxygen and hydrogen, because they were as yet undiscovered, and others, such as the metals, because they were believed to be compounds.
Among the chemical elements, it became customary after the time of Newton to include light-corpuscles.* That some- thing which is confessedly imponderable should ever have been admitted into this class may at first sight seem surprising. But it must be remembered that questions of ponderability counted for very little with the philosophers of the period. Three- quarters of the eighteenth century had passed before Lavoisier enunciated the fundamental doctrine that the total weight of the substances concerned in a chemical reaction is the same after the reaction as before it. As soon as this principle came to be universally applied, light parted company from the true elements in the scheme of chemistry.
We must now consider the views which were held at this time regarding the nature of heat. These are of interest for our present purpose, on account of the analogies which were set up between heat and electricity.
The various conceptions which have been entertained concerning heat fall into one or other of two classes, according as heat is represented as a mere condition producible in bodies, or as a distinct species of matter. The former view, which is that universally held at the present day, was advocated by the great philosophers of the seventeenth century. Bacon maintained it in the Novum Organum : " Calor," he wrote, " est niotus expansivus, cohibitus, et nitens per partes minores."f Boyle+ affirmed that the " Nature of Heat " consists in " a various, vehement, and intestine commotion of the Parts among themselves." Hooke§ declared that " Heat is a property of a body arising from the motion or agitation of its parts." And Newton|| asked : " Do not
* Newton himself (Oplicks, p. 349) suspected that light-corpuscles and ponderable matter might be transmuted into each other : much later, Boscovich (Theoria, pp. 215, 217) regarded the matter of light as a principle or element in the constitution of natural bodies.
t Nov. Org., Lib. n., Aphor. xx. J Mechanical Production of Heat and Cold.
§ Micrographia, p. 37. || Opticks.
D
34 Electric and Magnetic Science
all fixed Bodies, when heated beyond a certain Degree, emit light and shine ; and is not this Emission performed by the vibrating Motion of their Parts ? " and, moreover, suggested the converse of this, namely, that when light is absorbed by a material body, vibrations are set up which are perceived by the senses as heat.
The doctrine that heat is a material substance was main- tained in Newton's lifetime by a certain school of chemists. The most conspicuous member of the school was Wilhelm Homberg (b. 1652, d. 1715) of Paris, who* identified heat and light with the sulphureous principle, which he supposed to be one of the primary ingredients of all bodies, and to be present even in the inter- planetary spaces. Between this view and that of Newton it might at first seem as if nothing but sharp opposition was to be expected, j- But a few years later the professed exponents of the Principia and the Opticks began to develop their system under the evident influence of Homberg's writings. This evolution may easily be traced in s'Gravesande, whose starting-point is the admittedly Newtonian idea that heat bears to light a relation similar to that which a state of turmoil bears to regular rectilinear motion ; whence, conceiving light as a projection of corpuscles, he infers that in a hot body the material particles and the light-corpusclesj are in a state of agitation, which becomes more violent as the body is more intensely heated.
s'Gravesande thus holds a position between the two opposite camps. On the one hand he interprets heat as a mode of motion ; but on the other he associates it with the presence of a particular kind of matter, which he further identifies with the matter of light. After this the materialistic hypothesis made
* Mem. del'Acad., 1705, p. 88.
t Though it reminds us of a curious conjecture ofNewtoa'i: "Is not the strength and vigour of the action between light and sulphureous bodies one reason M-liy sulphureous bodies take fire more readily and burn more vehemently than other bodies do? "
J I have thought it best to translate s'Gravesande's ignis by " light-corpuscles." This is, I think, fully justified by such of his statements as Quando ignis per lineas rectas oculos nostros intrat, ex motu gttein fibris in fundo oculi cont/tninicai ideam luminis excitat.
prior to the Introduction of the Potentials. 35
rapid progress. It was frankly advocated by another member of the Dutch school, Hermann Boerhaave* (6. 1668, d. 1738), Professor in the University of Leyden, whose treatise on chemistry was translated into English in 1727.
Somewhat later it was found that the heating effects of the rays from incandescent bodies may be separated from their luminous effects by passing the rays through a plate of glass, which transmits the light, but absorbs the heat. After this discovery it was no longer possible to identify the matter of heat with the corpuscles of light ; and the former was consequently accepted as a distinct element, under the name of caloric.^ In the latter part of the eighteenth and early part of the nineteenth centuries} caloric was generally conceived as occupying the interstices between the particles of ponderable matter — an idea which fitted in well with the observation that bodies commonly expand when they are absorbing heat, but which was less com- petent to explain the fact§ that water expands when freezing. The latter difficulty was overcome by supposing the union between a body and the caloric absorbed in the process of melting to be of a chemical nature; so that the consequent changes in volume would be beyond the possibility of prediction.
As we have already remarked, the imponderability of heat did not appear to the philosophers of the eighteenth century to be a sufficient reason for excluding it from the list of chemical elements ; and in any case there was considerable doubt as to whether caloric was ponderable or not. Some experimenters believed that bodies were heavier when cold than when hot; others that they were heavier when hot than when cold. The century was far advanced before Lavoisier and Eumford finally
* Boerhaave followed Homberg in supposing the matter of heat to be present ia all so-called vacuous spaces.
t Scheele in 1777 supposed caloric to be a compound of oxygen and phlogiston, and light to be oxygen combined with a greater proportion of phlogiston.
J In suite of the experiments of Benjamin Thompson, Count Eumford (b. 1753, .d. 1814), in the closing years of the eighteenth century. These should have -sufficed to re-establish the older conception of heat.
§ This had been known since the time of Boyle.
D 2
36 Electric and Magnetic Science
proved that the temperature of a body is without sensible influence on its weight.
Perhaps nothing in the history of natural philosophy is more amazing than the vicissitudes of the theory of heat. The true hypothesis, after having met with general acceptance throughout a century, and having been approved by a succession of illus- trious men, was deliberately abandoned by their successors in favour of a conception utterly false, and, in some of its developments, grotesque and absurd.
We must now return to s'Gravesande's book. The pheno- mena of combustion he explained by assuming that when a body is sufficiently heated the light-corpuscles interact with the material particles, some constituents being in consequence sepa- rated and carried away with the corpuscles as flame and smoke. This view harmonizes with the theory of calcination which had been developed by Becher and his pupil Stahl at the end of the- seventeenth century, according to which the metals were sup- posed to be composed of their calces and an element phlogiston. The process of combustion, by which a metal is changed into its- calx, was interpreted as a decomposition, in which the phlogiston separated from the metal and escaped into the atmosphere ; while the conversion of the calx into the metal was regarded as a union with phlogiston.*
s'Gravesande attributed electric effects to vibrations induced in effluvia, which he supposed to be permanently attached to such bodies as amber. " Glass," he asserted, " contains in it, and has about its surface, a certain atmosphere, which is excited by Friction and put into a vibratory motion ; for it attracts and
* The correct idea of combustion had been advanced by Hooke. "The disso- lution of inflammable bodies," he asserts in the Micrographia, " is performed by a substance inherent in and mixed with the air, that is like, if not the very same with, that which is fixed in saltpetre." But this statement met with little favour at the time, and the doctrine of the compound nature of metals survived in full vigour until the discovery of oxygen by Priestley and Scheele in 1771-5. In 1775 Lavoisier reaffirmed Hooke's principle that a metallic calx is not the metal minus phlogiston, but the metal plus oxygen; and this idea, which carried with it the recognition of the elementary nature of metals, was generally accepted by the end' of the eighteenth century.
prior to the Introduction of the Potentials. 37
repels light Bodies. The smallest parts of the glass are agitated by the Attrition, and by reason of their elasticity, their motion is vibratory, which is communicated to the Atmosphere above- mentioned : and therefore that Atmosphere exerts its action the further, the greater agitation the Parts of the Glass receive when a greater attrition is given to the glass."
The English translator of s'Gravesande's work was himself destined to play a considerable part in the history of electrical science. Jean Theophile Desaguliers (b. 1683, d. 1744) was an Englishman only by adoption. His father had been a Huguenot pastor, who, escaping from France after the revocation of the Edict of Nantes, brought away the boy from La Kochelle, concealed, it is said, in a tub. The young Desaguliers was afterwards ordained, and became chaplain to that Duke of Chandos who was so ungratefully ridiculed by Pope. In this situation he formed friendships with some of the natural philosophers of the capital, and amongst others with Stephen Gray, an experimenter of whom little is known* beyond the fact that he was a pensioner of the Charterhouse.
In 1729 Gray communicated, as he says,f " to Dr. Desaguliers and some other Gentlemen " a discovery he had lately made, " showing that the Electrick Vertue of a Glass Tube may be •conveyed to any other Bodies so as to give them the same Property of attracting and repelling light Bodies as the Tube does, when excited by rubbing : and that this attractive Vertue might be carried to Bodies that were many Feet distant from the Tube."
This was a result of the greatest importance, for previous workers had known of no other way of producing the attractive emanations than by rubbing the body concerned.* It was found
* Those M*ho are interested in the literary history of the eighteenth century will recall the controversy as to whether the verses on the death of Stephen Gray were written hy Anna "Williams, whose name they bore, or by her patron Johnson.
| Phil. Trans, xxxvii (1731), pp. 18, 227, 285, 397.
j Otto von Guericke (b. 1602, d. 1686) bad, as a matter of fact, observed the conduction of electricity along a linen thread ; but this experiment does not seem to have been followed up. Cf. Experimenta novamagdeburgica, 1672.
38 Electric and Magnetic Science
o
that only a limited class of substances, among which the metals were conspicuous, had the capacity of acting as channels for the transport of the electric power ; to these Desaguliers, who. con- tinued the experiments after Gray's death in 1736, gavfc^ the name non-electrics or conductors.
After Gray's discovery it was no longer possible to believe that the electric effluvia are inseparably connected with the bodies from which they are evoked by rubbing ; and it became necessary to admit that these emanations have an independent existence, and can be transferred from one body to another. Accordingly we find them recognized, under the name of the electric fluidft as one of the substances of which the world is constituted. The imponderability of this fluid did not, for the reasons already mentioned, prevent its admission by the side of light and caloric into the list of chemical elements.
The question was actively debated as to whether the electric fluid was an element sui generis, or, as some suspected, was another manifestation of that principle whose operation is seen in the phenomena of heat. Those who held the latter view urged that the electric fluid and heat can both be induced by friction, can both induce combustion, and can both be transferred from one body to another by mere contact ; and, moreover, that the best conductors of heat are also in general the best con- ductors of electricity. On the other hand it was contended that the electrification of a body does not cause any appreciable rise in its temperature; and an experiment of Stephen Gray's brought to light a yet more striking difference. Gray,J in 1729,. made two oaken cubes, one solid and the other hollow, and showed that when electrified in the same way they produced exactly similar effects ; whence he concluded that it was only the surfaces which had taken part in the phenomena. Thus while heat is disseminated throughout the substance of a body, the electric fluid resides at or near its surface. In the middle of
* Phil. Trans, xli. (1739), pp. 186, 193, 200, 209: Dissertation concerning Electricity, 1742.
t The Cartesians defined a fluid to be a body whose minute parts are in a continual agitation. J Phil. Trans, xxxvii., p. 35.
prior to the Introduction of the Potentials. 39
the eighteenth century it was generally compared to an envelop- ing atmosphere. " The electricity which a non-electric of great length (for example, a hempen string 800 or 900 feet long) receives, runs from one end to the other in a sphere of electrical Effluvia" says Desaguliers in 1740 ^and a report of the French Academy in 1733 says :f " Around an electrified body there is formed a vortex of exceedingly fine matter in a state of agitation,, which urges towards the body such light substances as lie within its sphere of activity. The existence of this vortex is more than a mere conjecture ; for when an electrified body i& brought close to the face it causes a sensation like that of encountering a cobweb. "J
The report from which this is quoted was prepared in connexion with the discoveries of Charles-Francois du Fay (b. 1698, d. 1739), superintendent of gardens to the King of France. Du Fay§ accounted for the behaviour of gold leaf when brought near to an electrified glass tube by supposing that at first the vortex of the tube envelopes the gold-leaf, and so attracts it towards the tube. But when contact occurs, the gold-leaf acquires the electric virtue, and so becomes surrounded by a vortex of its own. The two vortices, striving to extend in contrary senses, repel each other, and the vortex of the tube, being the stronger, drives away that of the gold-leaf. " It is then certain/' says du Fay,H " that bodies which have become electric by contact are repelled by those which have rendered them electric ; but are they repelled likewise by other electrified bodies of all kinds ? And do electrified bodies differ from each other in no respect save their intensity of electrification ? An examination of this matter has led me to a discovery which I should never have foreseen, and of which I believe no one hitherto has had the least idea."
* Phil. Trans, xli., p. 636. t Hist, de 1'Acad., 1733, p. 6.
t This observation had been made first by Hawksbee at the beginning of the century.
§ Mem. de 1'Acad. des Sciences, 1733, pp. 23, 73, 233, 457 ; 1734, pp. 341, 503; 1737, p. 86 ; Phil. Trans, xxxviii. (1734), p. 258.
|| Mem. de 1'Acad., 1733, p. 464.
40 Electric and Magnetic Science
He found, in fact, that when gold-leaf which had been electrified by contact with excited glass was brought near to an excited piece of copal,* an attraction was manifested between them. " I had expected," he writes, " quite the opposite effect, since, according to my reasoning, the copal and gold-leaf, which were both electrified, should have repelled each other." Proceeding with his experiments he found that the gold-leaf, when electrified and repelled by glass, was attracted by all electrified resinous substances, and that when repelled by the latter it was attracted by the glass. " We see, then," he continues, " that there are two electricities of a totally different nature — namely, that of transparent solids, such as glass, crystal, &c., and that of bituminous or resinous bodies, such as amber, copal, sealing-wax, &c. Each of them repels bodies which have contracted an electricity of the same nature as its own, and attracts those whose electricity is of the contrary nature. We see even that bodies which are not themselves electrics can acquire either of these electricities, and that then their effects are similar to those of the bodies which have communicated it to them."
To the two kinds of electricity whose existence was thus demonstrated, du Fay gave the names vitreous and resinous, by which they have ever since been known.
An interest in electrical experiments seems to have spread from du Fay to other members of the Court circle of Louis XV ; and from 1745 onwards the Memoirs of the Academy contain a series of papers on the subject by the Abbe Jean-Antoine Nollet {&. 1700, d. 1770), afterwards preceptor in natural philosophy to the Koyal Family. Nollet attributed electric phenomena to the movement in opposite directions of two currents of a fluid, " very subtle and inflammable," which he supposed to be present in all bodies under all circumstances.f When an electric is excited by friction, part of this fluid escapes from its pores, forming an effluent stream; and this loss is repaired by an
* A hard transparent resin, used in the preparation of varnish. t Cf. Nollet' s lieeherchet, 1749, p. 245.
prior to the Introduction of the Potentials. 41
dtfiucnt stream of the same fluid entering the body from outside. Light bodies in the vicinity, being caught in one or other of these streams, are attracted or repelled from the excited electric.
Nollet's theory was in great vogue for some time ; but six or seven years after its first publication, its author came across a work purporting to be a French translation of a book printed originally in England, describing experiments said to have been made at Philadelphia, in America, by one Benjamin Franklin. "He could not at first believe," as Franklin tells us in his AutobiograpJvy, " that such a work came from America, and said it must have been fabricated by his enemies at Paris to decry his system. Afterwards, having been assured that there really existed such a person as Franklin at Philadelphia, which he had doubted, he wrote and published a volume of letters, chiefly addressed to me, defending his theory, and denying the verity of my experiments, and of the positions deduced from them."
We must now trace the events which led up to the discovery which so perturbed Nollet.
In 1745 Pieter van Musschenbroek (6. 1692, d. 1761), Professor at Leyden, attempted to find a method of preserving electric charges from the decay which was observed when the charged bodies were surrounded by air. With this purpose he tried the effect of surrounding a charged mass of water by an envelope of some non-conductor, e.g., glass. In one of his experiments, a phial of water was suspended from a gun- barrel by a wire let down a few inches into the water through the cork; and the gun-barrel, suspended on silk lines, was applied so near an excited glass globe that some metallic fringes inserted into the gun-barrel touched the globe in motion. Under these circumstances a friend named Cimaeus, who happened to grasp the phial with one hand, and touch the gun- barrel with the other, received a violent shock ; and it became evident that a method of accumulating or intensifying the electric power had been discovered.*
* The discovery was made independently in the same year by Ewald Georg von Kleist, Dean of Kumrain.
42 Electric and Magnetic Science
o
Shortly after the discovery of the Leyden phial, as it was named by Nollet, had become known in England, a London apothecary named William Watson (6. 1715, d. 1787)* noticed that when the experiment is performed in this fashion the observer feels the shock " in no other parts of his body but his arms and breast " ; whence he inferred that in the act of discharge there is a transference of something which takes the shortest or best- conducting path between the gun-barrel and the phial. This idea of transference seemed to him to bear some similarity to Nollet's doctrine of afflux and efflux; and there can indeed be little doubt that the Abbe's hypothesis, though totally false in itself, furnished some of the ideas from which Watson, with the guidance of experiment, constructed a correct theory. In a memoiirt)read to the Eoyal Society in October, 1746, he propounded the doctrine that electrical actions are due to the presence of an " electrical aether/' which in the charging or discharging of a Leyden jar is transferred, but is not created or destroyed. The excitation of an electric, according to this view, consists not in the evoking of anything from within the electric itself without compensation, but in the accumulation of a surplus of electrical aether by the electric at the expense of some other body, whose stock is accordingly depleted. All bodies were supposed to possess a certain natural store, which could be drawn upon for this purpose.
" I have shewn," wrote Watson, " that electricity is the effect of a very subtil and elastic fluid, occupying all bodies in contact with the terraqueous globe ; and that every-where, in its natural state, it is of the same degree of density ; and that glass and other bodies, which we denominate electrics per sey. have the power, by certain known operations, of taking this fluid from one body, and conveying it to another, in a quantity sufficient to be obvious to all our senses; and that, under
* Watson afterwards rose to eminence in the medical profession, and was knighted.
t Phil. Trans, xliv., p. 718. It may here he noted that it was Watson who improved the phial by coating it nearly to the top, both inside and outside, with tinfoil.
prior to the Introduction of the Potentials. 43
certain circumstances, it was possible to render the electricity in some bodies more rare than it naturally is, and, by communi- cating this to other bodies, to give them an additional quantity, and make their electricity more dense."
In the same year in which Watson's theory was proposed, a certain Dr. Spence, who had lately arrived in America from Scotland, was showing in Boston some electrical experiments. Among his audience was a man who already at forty years of age was recognized as one of the leading citizens of the English colonies in America, Benjamin Franklin of Philadelphia (b. 1706, d. 1790). Spence's experiments " were," writes Franklin,* " imperfectly performed, as he was not very expert ; but, being on a subject quite new to me, they equally surprised and pleased me." Soon after this, the "Library Company" of Philadelphia (an institution founded by Franklin himself) received from Mr. Peter Collinson of London a present of a glass tube, with some account of its use. In a letter written to Collinson on July llth, 1747,f Franklin described experiments made with this tube, and certain deductions which he had drawn from them.
If one person A, standing on wax so that electricity cannot pass from him to the ground, rubs the tube, and if another person B, likewise standing on wax, passes his knuckle along near the glass so as to receive its electricity, then both A and B will be capable of giving a spark to a third person C standing on the floor; that is, they will be electrified. If, however, A and B touch each other, either during or after the rubbing, they will not be electrified.
This observation suggested to Franklin the same hypothesis that (unknown to him) had been propounded a few months previously by Watson : namely, that electricity is an element present in a certain proportion in all matter in its normal condition ; so that, before the rubbing, each of the persons A, B, and C has an equal share. The effect of the rubbing is to
* Franklin's Autobiography.
t Franklin's New Experiments and Observations on Electricity, letter ii.
44 Electric and Magnetic Science
transfer some of A's electricity to the glass, whence it is transferred to B. Thus A has a deficiency and B a superfluity of electricity ; and if either of them approaches C, who has the normal amount, the distribution will be equalized by a spark. If, however, A and B are in contact, electricity flows between them so as to re-establish the original equality, and neither is then electrified with reference to C.
Thus electricity is not created by rubbing the glass, but only transferred to the glass from the rubber, so that the rubber loses exactly as much as the glass gains ; the, total quantity of electricity in any insulated system is invariable. This assertion is usually known as the principle of conservation of electric charge.
The condition of A and B in the experiment can evidently be expressed by plus and minus signs : A having a deficiency - e and B a superfluity + e of electricity. Franklin, at the commencement of his own experiments, was not acquainted with du Fay's discoveries ; but it is evident that the electric fluid of Franklin is identical with the vitreous electricity of du Fay, and that du Fay's resinous electricity is, in Franklin's theory, merely the deficiency of a stock of vitreous electricity supposed to be possessed naturally by all ponderable bodies. In Franklin's theory we are spared the necessity for admitting that two quasi-material bodies can by their union annihilate each other, as vitreous and resinous electricity were supposed to do.
Some curiosity will naturally be felt as to the considerations which induced Franklin to attribute the positive character to vitreous rather than to resinous electricity. They seem to have been founded on a comparison of the brush discharges from conductors charged with the two electricities; when the electricity was resinous, the discharge was observed to spread over the surface of the opposite conductor " as if it flowed from it." Again, if a Ley den jar whose inner coating is electrified vitreously is discharged silently by a conductor, of whose pointed ends one is near the knob and the other near the outer coating, the point which is near the knob is seen in the dark to be illumi-
prior to the Introduction of the Potentials. 45
nated with a star or globule, while the point which is near the outer coating is illuminated with a pencil of rays; which suggested to Franklin that the electric fluid, going from the inside to the outside of the jar, enters at the former point and issues from the latter. And yet again, in some cases the flame of a wax taper is blown away from a brass ball which is discharging vitreous electricity, and towards one which is discharging resinous electricity. But Franklin remarks that the interpretation of these observations is somewhat conjectural, and that whether vitreous or resinous electricity is the actual electric fluid is not certainly known.
Regarding the physical nature of electricity, Franklin held much the same ideas as his contemporaries ; he pictured it as an elastic* fluid, consisting of " particles extremely subtile, since it can permeate common matter, even the densest metals, with such ease and freedom as not to receive any perceptible resistance." He departed, however, to some extent from the conceptions of his predecessors, who were accustomed to ascribe all electrical repulsions to the diffusion of effluvia from the excited electric to the body acted on ; so that the tickling sensation which is experienced when a charged body is brought near to the human face was attributed to a direct action of the effluvia on the skin. This doctrine, which, as we shall see, practically ended with Franklin, bears a suggestive resemblance to that which nearly a century later was introduced by Faraday ; both explained electrical phenomena without intro- ducing action at a distance, by supposing that something which forms an essential part of the electrified system is present at the spot where any electric action takes place ; but in the older theory this something was identified with the electric fluid itself, while in the modern view it is identified with a state of stress in the aether. In the interval between the fall of one school and the rise of the other, the theory of action at a distance was dominant.
The germs of the last-mentioned theory may be found in
*i.c., repulsive of its own particles.
46 Electric and Magnetic Science
Franklin's own writings. It originated in connexion with the explanation of the Ley den jar, a matter which is discussed in his third letter to Collinson, of date September 1st, 1747. In charging the jar, he says, a quantity of electricity is taken away from one side of the glass, by means of the coating in contact with it, and an equal quantity is communi- cated to the other side, by means of the other coating. The glass itself he supposes to be impermeable to the electric fluid, so that the deficiency on the one side can permanently coexist with the redundancy on the other, so long as the two sides are not connected with each other ; but when a con- nexion is set up, the distribution of fluid is equalized through the body of the experimenter, who receives a shock.
Compelled by this theory of the jar to regard glass as impenetrable to electric effluvia, Franklin was nevertheless well aware* that the interposition of a glass plate between an electrified body and the objects of its attraction does not shield the latter from the attractive influence. He was thus driven to supposef that the surface of the glass which is nearest the excited body is directly affected, and is able to exert an influence through the glass on the opposite surface ; the latter surface, which thus receives a kind of secondary or derived excitement, is responsible for the electric effects beyond it.
This idea harmonized admirably with the phenomena of the jar ; for it was now possible to hold that the excess of electricity on the inner face exercises a repellent action through the substance of the glass, and so causes a deficiency on the outer faces by driving away the electricity from it.J
Franklin had thus arrived at what was really a theory of action at a distance between the particles of the electric fluid ; and this he was able to support by other experiments. " Thus," he writes,§ " the stream of a fountain, naturally dense and con- tinual, when electrified, will separate and spread in the form of a brush, every drop endeavouring to recede from every other
* New Experiments, 1750, § 28. t Hid., 1750, § 34.
J Ibid., 1750, § 32. § Letter v.
prior to the Introduction of the Potentials. 47
drop.' In order to account for the attraction between oppositely charged bodies, in one of which there is an excess of electricity as compared with ordinary matter, and in the other an excess of ordinary matter as compared with electricity, he assumed that " though the particles of electrical matter do repel each other, they are strongly attracted by all other matter " ; so that " common matter is as a kind of spunge to the electrical fluid."
These repellent and attractive powers he assigned only to the actual (vitreous) electric fluid; and when later on the mutual repidsion of resinously electrified bodies became known to him,* it caused him considerable perplexity.f As we shall see, the difficulty was eventually removed by.Aepinus.
In spite of his belief in the power of electricity to act at a distance, Franklin did not abandon the doctrine of effluvia. "The form of the electrical atmosphere," he says,} "is that of the body it surrounds. This shape may be rendered visible in a still air, by raising a smoke from dry rosin dropt into a hot tea- spoon under the electrified body, which will be attracted, and spread itself equally on all sides, covering and concealing the body, And this form it takes, because it is attracted by all parts of the surface of the body, though it cannot enter the substance already replete. Without this attraction, it would not remain round the body, but dissipate in the air." He observed, however, that electrical effluvia do not seem to affect, or be affected by, the air ; since it is possible to breathe freely in the neighbourhood of electrified bodies ; and moreover a current of dry air does not destroy electric attractions and repulsions. §
Kegarding the suspected identity of electricity with the matter of heat, as to which Nollet had taken the affirmative position, Franklin expressed no opinion. " Common fire," he
* He refers to it in his Paper read to the Royal Society, December 18, 1755. t Cf. letters xxxvii and xxxviii, dated 1761 and 1762. 1 New Experiment* , 1750, § 15. § Letter vii, 1751.
48 Electric and Magnetic Science
writes,* " is in all bodies, more or less, as well as electrical fire. Perhaps they may be different modifications of the same element ; or they may be different elements. The latter is by some suspected. If they are different things, yet they may and do subsist together in the same body."
Franklin's work did not at first receive from European philosophers the attention which it deserved ; although Watson generously endeavoured to make the colonial writer's merits known,f and inserted some of Franklin's letters in one of his own papers communicated to the Eoyal Society. But an account of Franklin's discoveries, which had been printed in England, happened to fall into the hands of the naturalist Buffon, who was so much impressed that he secured the issue of a French transla- tion of the work ; and it was this publication which, as we have seen, gave such offence to Nollet. The success of a plan proposed by Franklin for drawing lightning from the clouds soon engaged public attention everywhere; and in a short time the triumph of the one-fluid theory of electricity, as the hypothesis of Watson and Franklin is generally called, was complete. Collet, who was obdurate, "lived to see himself the last of his sect, except Monsieur B — of Paris, his eleve and immediate disciple." J
The theory of effluvia was finally overthrown, and replaced by that of action at a distance, by the labours of one of Franklin's continental followers, Francis Ulrich Theodore Aepinus§ (&. 1724, d. 1802). The doctrine that glass is impermeable to electricity, which had formed the basis of Franklin's theory of the Ley den phial, was generalized by Aepinus|| and his co-worker Johann Karl Wilcke (5. 1732, d. 1796) into the law that all non-conductors are impermeable to the
* Letter v.
Cx_- tPhil. Trans, xlvii, p. 202. Watson agreed with Nollet in rejecting Franklin's J theory of the impermeability of glass. J Franklin's Autobiography.
§ This philosopher's surname had been hellenized from its original form Hoeck to alveivos by one of his ancestors, a distinguished theologian.
|| F. V. T. Aepinus Tentamen Thcoriae Elcctricitatis et Magnetismi : St. Petersburg, 1759.
prior to the Introduction of the Potentials. 49
electric fluid. That this applies even to air they proved by constructing a machine analogous to the Leyden jar, in which, however, air took the place of glass as the medium between two oppositely charged surfaces. The success of this experi- ment led Aepinus to deny altogether the existence of electric effluvia surrounding charged bodies :* a position which he regarded as strengthened by Franklin's observation, that the electric field in the neighbourhood of an excited body is not destroyed when the adjacent air is blown away. The electric fluid must therefore be supposed not to extend beyond the excited bodies themselves. The experiment of Gray, to which we have already referred, showed that it does not penetrate far into their substance; and thus it became necessary to suppose that the electric fluid, in its state of rest, is con- fined to thin layers on the surfaces of the excited bodies. This being granted, the attractions and repulsions observed between the bodies compel us to believe that electricity acts at a distance across the intervening air.
Since two vitreously charged bodies repel each other, the force between two particles of the electric fluid must (on Franklin's one-fluid theory, which Aepinus adopted) be repulsive : and since there is 'an attraction between oppositely charged bodies, the force between electricity and ordinary matter must be attractive. These assumptions had been made, as we have seen, by Franklin; but in order to account for the repulsion between two resinously charged bodies, Aepinus introduced a new supposition — namely, that the particles of ordinary matter repel each other. This, at first, startled his contemporaries; but, as he pointed out, the "unelectrified" matter with which we are acquainted is really matter saturated with its natural quantity of the electric fluid, and the forces due to the matter and fluid balance each other ; or perhaps, as he suggested, a slight want of equality between these forces might give, as a residual, the force of gravitation.
Assuming that the attractive and repellent forces increase as "
* This was also maint.iined about the same time by Giacomo Battista Beet-aria of Turin (b. 1716, d. 1781;.
E
50 Electric and Magnetic Science
<v
the distance between the acting charges decreases, Aepinus applied his theory to explain a phenomenon which had been more or less indefinitely observed by many previous writers, and specially studied a short time previously by John Canton* (&. 1718, d. 1772) and by Wilckef — namely, that if a conductor is brought into the neighbourhood of an excited body without actually touching it, the remoter portion of the conductor acquires an electric charge of the same kind as that of the excited body, while the nearer portion acquires a charge of the opposite kind. This effect, which is known as the induction of electric charges, had been explained by Canton himself and by Franklin} in terms of the theory of electric effluvia. Aepinus showed that it followed naturally from the theory of action at a distance, by taking into account the mobility of the electric fluid in conductors ; and by discussing different cases, so far as was possible with the means at his command, he laid the foundations of the mathematical theory of electrostatics.
Aepinus did not succeed in determining the law according to which the force between two electric charges varies with the distance between them ; and the honour of having first accom- plished this belongs to Joseph Priestley (b. 1733, d. 1804), the discoverer of oxygen. Priestley, who was a friend of Franklin's, had been informed by the latter that he had found cork balls to be wholly unaffected by the electricity of a metal cup within which they were held ; and Franklin desired Priestley to repeat and ascertain the fact. Accordingly, on December 21st, 1766, Priestley instituted experiments, which showed that, when a hollow metallic vessel is electrified, there is no charge on the inner surface (except near the opening), and no electric force in the air inside. From this he at once drew the correct conclusion, which was published in 1767. § " May we not infer," he says, "from
*Phil. Trans, xlviii (1753), p. 350.
t Disputatio physica experimentalis de electricitatibus contrariis : Rostock, 1757.
J In liis paper read to the Royal Society on Dec. 18th, 1755.
§ J. Priestley, The History and Present State of Electricity, with Original Experiments ; London, 1767: page 732. That electrical attraction follows the law of the inverse square had been suspected -by Daniel Bernoulli in 1760: Cf. Sochi's Experiments, Ada Helvetica, iv, p. 214.
prior to the Introduction of the Potentials. 51
this experiment that the attraction of electricity is subject to the same laws with that of gravitation, and is therefore according to the squares of the distances ; since it is easily demonstrated that were the earth in the form of a shell, a body in the inside of it would not be attracted to one side more than another ? "
This brilliant inference seems to have been insufficiently studied by the scientific men of the day ; and, indeed, its author appears to have hesitated to claim for it the authority of a com- plete and rigorous proof. Accordingly we find that the question of the law of force was not regarded as finally settled for eighteen years afterwards.*
By Franklin's law of the conservation of electric charge, and Priestley's law of attraction between charged bodies, electricity was raised to the position of an exact science. It is impossible to mention the names of these two friends in such a connexion without reflecting on the curious parallelism of their lives. In both men there was the same combination of intellectual bold- ness and power with moral earnestness and public spirit. Both .of them carried on a long and tenacious struggle with the reac- tionary influences which dominated the English Government in .the reign of George III ; and both at last, when overpowered in the conflict, reluctantly exchanged their native flag for that of the United States of America. The names of both have been held in honour by later generations, not more for their scientific discoveries than for their services to the cause of religious, intellectual, and political freedom.
The most celebrated electrician of Priestley's contemporaries in London was the Hon. Henry Cavendish (b. 1731, d. 1810), whose interest in the subject was indeed hereditary, for his father, Lord Charles Cavendish, had assisted in Watson's experi- ments of 1747.f In 1771 Cavendish} presented to the Koyal Society an " Attempt to explain some of the principal phenomena of Electricity, by means of an elastic fluid." The hypothesis j
* In 1769 Dr. John Robison (b. 1739, d. 1805), of Edinburgh, endeavoured to determine the law of force by direct experiment, and found it to be tbat of the inverse 2'06th power of the distance.
t Phil. Trans, xlv, p. 67 (1750). J Phil. Trans. Ixi, p. 584 (1771).
E 2
52 Electric and Magnetic Science
adopted is that of the one-fluid theory, in much the same form as that of Aepinus. It was, as he tells us, discovered indepen- dently, although he became acquainted with Aepinus' work before the publication of his own paper.
In this memoir Cavendish makes no assumption regarding the law of force between electric charges, except that it is " inversely as some less power of the distance than the cube " ; but he evidently inclines to believe in the law of the inverse square. Indeed, he shows it to be " likely, that if the electric attraction or repulsion is inversely as the square of the distance, almost all the redundant fluid in the body will be lodged close to the surface, and there pressed close together, and the rest of the body will be saturated"; which approximates closely to the discovery made four years previously by Priestley. Cavendish did, as a matter of fact, rediscover the inverse square law shortly afterwards; but, indifferent to fame, he neglected to communicate to others this and much other work of importance. The value of his researches was not realized until the middle of the nineteenth century, when William Thomson (Lord Kelvin) found in Caven- dish's manuscripts the correct value for the ratio of the electric charges carried by a circular disk and a sphere of the same radius which had been placed in metallic connexion. Thomson urged that the papers should be published ; which came to pass* in 1879, a hundred years from the date of the great discoveries which they enshrined. It was then seen that Cavendish had anticipated his successors in several of the ideas which will presently be discussed — amongst others, those of electrostatic capacity and specific inductive capacity.
In the published memoir of 1771 Cavendish worked out the consequences of his fundamental hypothesis more completely than Aepinus ; and, in fact, virtually introduced the notion of electric potential, though, in the absence of any definite assump- tion as to the law of force, it was impossible to develop this idea to any great extent.
* The Electrical Researches of the Hon. Henry Cavendish, edited by J. Clerk Maxwell, 1879.
prior to the Introduction of the Potentials. 53
One of the investigations with which Cavendish occupied himself was a comparison between the conducting powers of different materials for electrostatic discharges. The question had been first raised by Beccaria, who had shown* in 1753 that when the circuit through which a discharge is passed contains tubes of water, the shock is more powerful when the cross-section of the tubes is increased. Cavendish went into the matter much more thoroughly, and was able, in a memoir presented to the Eoyal Society in 1775,f to say : " It appears from some experiments, of which I propose shortly to lay an account before this Society, that iron wire conducts about 400 million times better than rain or distilled water — that is, the electricity meets with no more resistance in passing through a piece of iron wire 400,000,000 inches long than through a column of water of the same diameter only one inch long. Sea- water, or a solution of one part of salt in 30 of water, conducts 100 times, or a saturated solution of sea-salt about 720 times, better than rain-water."
The promised account of the experiments was published in the volume edited in 1879. It appears from it that the method of testing by which Cavendish obtained these, results was simply that of physiological sensation; but the figures given in the comparison of iron and sea- water are remarkably exact.
While the theory of electricity was being established on a sure foundation by the great investigators of the eighteenth century, a no less remarkable development was taking place in the kindred science of magnetism, to which our attention must now be directed.
The law of attraction between magnets was investigated at an earlier date than the corresponding law for electrically charged bodies. Newton, in the Principia£ says : " The power of gravity is of a different nature from the power of magnetism. For the magnetic attraction is not as the matter attracted. Some bodies are attracted more by the magnet, others less ; most bodies not at all. The power of magnetism, in one and the same
* G. B. Beccaria, DdV ehttridsmo artificiale e natural*, Turin. 1753, p. 113. + Phil. Trans. Ixvi (1776), p. 196. % Book iii, Prop, vi, cor. 5.
54 Electric and Magnetic Science
body, may be increased and diminished ; and is sometimes far stronger, for the quantity of matter, than the power of gravity ; and in receding from the magnet, decreases not in the duplicate, but almost in the triplicate proportion of the distance, as nearly as I could judge from some rude observations."
The edition of ihePrincipia which was published in 1742 by Thomas Le Seur and Francis Jacquier contains a note on this corollary, in which the correct result is obtained that the directive couple exercised on one magnet by another is proportional to the inverse cube of the distance.
The first discoverer of the law of force between magnetic1 \ poles was John Michell (b. 1724, d. 1793), at that time a young Fellow of Queen's College, Cambridge,* who in 1750 published A Treatise of Artificial Magnets ; in ivhich is shown an easy and expeditious method of making them superior to the lest natural ones. In this he states the principles of magnetic theory as followsf : —
" Wherever any Magnetism, is found, whether in the Magnet itself, or any piece of Iron, etc., excited by the Magnet, there are always found two Poles, which are generally called North and South ; and the North Pole of one Magnet always attracts the South Pole, and repels the North Pole of another: and wee versa" This is of course adopted from Gilbert.
"Each Pole attracts or repels exactly equally, at equal distances, in every direction." This, it may be observed, over- throws the theory of vortices, with which it is irreconcilable. " The Magnetical Attraction and Eepulsion are exactly equal to each other." This, obvious though it may seem to us, was really a most important advance, for, as he remarks, " Most people, who
* Michell had taken his degree only two years previously. Later in life he was on terms of friendship with Priestley, Cavendish, and William Herschel ; it was he who taught Herschel the art of grinding mirrors for telescopes. The plan of determining the density of the earth, which was carried out by Cavendish in 1798, and is generally known as the " Cavendish Experiment," was due to Michell. Michell was the first inventor of the torsion-balance ; he also made many valuable contributions to Astronomy. In 1767 he became Rector of Thornhill, Yorks, and lived there until his death.
t Loc. cit., p. 17.
-^
prior to the Introduction of the Potentials. 55
have mention'd any thing relating to this property of the Magnet, have agreed, not only that the Attraction and Repulsion of Magnets are not equal to each other, but that also, they do not observe the same rule of increase and decrease."
" The Attraction and Eepulsion of Magnets decreases, as the Squares of the distances from the respective poles increase." This great discovery, which is the basis of the mathematical theory of Magnetism, was deduced partly from his own observa- tions, and partly from those of previous investigators (e.g. Dr. Brook Taylor and P. Muschenbroek), who, as he observes, had made accurate experiments, but had failed to take into account all the considerations necessary for a sound theoretical discussion of them.
After Michell the law of the inverse square was maintained by Tobias Mayer* of Gottingen (&. 1723, d. 1762), better known as the author of Lunar Tables which were long in use ; and by the celebrated mathematician, Johann Heinrich Lambertf (b. 1728, d. 1777).
The promulgation of the one-fluid theory of electricity, in the middle of the eighteenth century, naturally led to attempts to construct a similar theory of magnetism ; this was effected in 1759 by AepinusJ, who supposed the "poles "to be places at which a magnetic fluid was present in amount exceeding or falling short of the normal quantity. The permanence of magnets was accounted for by supposing the fluid to be entangled in their pores, so as to be with difficulty displaced. The particles of the fluid were assumed to repel each other, and to attract the particles of iron and steel ; but, as Aepinus saw, in order to satis- factorily explain magnetic phenomena it was necessary to assume also a mutual repulsion among the material particles of the magnet.
Subsequently two imponderable magnetic fluids, to which
* Noticed in Gottinger Gelehrter Anzeiger, 1760 : cf. Aepinus, Nov. Comm. Acad. Petrop., 1768, and Mayer's Opera Inedita, herausg. von G. C. Lichtenberg. •\-Histoirede V Acad. de Berlin, 1766, pp. 22, 49. % In the Tentamen, to which reference has already been made.
56 Electric and Magnetic Science
the names boreal and austral were assigned, were postulated by the Hollander Anton Brugmans (5. 1732, d. 1789) and by Wilcke. These fluids were supposed to have properties of mutual attraction and repulsion similar to those possessed by vitreous and resinous electricity.
The writer who next claims our attention for his services both to magnetism and to electricity is the French physicist, Charles Augustin Coulomb* (ft. 1736, d. 1806). By aid of the torsion-balance, which was independently invented by Michell and himself, he verified in 1785 Priestley's fundamental law that the repulsive force between two small globes charged with the same kind of electricity is in the inverse ratio of the square of the distance of their centres. In the second memoir he extended this law to the attraction of opposite electricities.
Coulomb did not accept the one-fluid theory of Franklin, Aepinus, and Cavendish, but preferred a rival hypothesis which had been proposed in 1759 by Kobert Symmer.f " My notion," said Symmer, " is that the operations of electricity do not depend upon one single positive power, according to the opinion generally received; but upon two distinct, positive, and active powers, which, by contrasting, and, as it were, counteracting each other, produce the various phenomena of electricity ; and that, when a body is said to be positively electrified, it is not simply that it is possessed of a larger share of electric matter than in a natural state ; nor, when it is said to be negatively electrified, of a less ; but that, in the former case, it is possessed of a larger portion of one of those active powers, and in the latter, of a larger portion of the other ; while a body in its natural state remains unelectrified, from an equal ballance of those two powers within it."
Coulomb developed this idea : " Whatever be the cause of electricity," he says,J " we can explain all the phenomena by
* Coulomb's First, Second, and Third Memoirs appear in Memoires de 1'Acad., 1785 ; the Fourth in 1786, the Fifth in 1787, the Sixth in 1788, and the Seventh in 1789.
t Phil. Trim*, li (1759), p. 371. j Sixth Memoir, p. 561.
prior to the Introduction of the Potentials. 57
supposing that there are two electric fluids, the parts of the same fluid repelling each other according to the inverse square of the distance, and attracting the parts of the other fluid according to the same inverse square law." " The supposition ^ of two fluids," he adds, " is moreover in accord with all those 7 discoveries of modern chemists and physicists, which have made known to us various pairs of gases whose elasticity is destroyed by their admixture in certain proportions — an effect which could not take place without something equivalent to a repulsion between the parts of the same gas, which is the cause of its elasticity, and an attraction between the parts of different gases, which accounts for the loss of elasticity on combination." J
According, then, to the two-fluid theory, the " natural fluid " contained in all matter can be decomposed, under the influence of an electric field, into equal quantities of vitreous and resinous electricity, which, if the matter be conducting, can then fly to the surface of the body. The abeyance of the characteristic properties of the opposite electricities when in combination was f sometimes further compared to the neutrality manifested by . the compound of an acid and an alkali.
The publication of Coulomb's views led to some controversy between the partisans of the one-fluid and two-fluid theories ; the latter was soon generally adopted in France, but was stoutly opposed in Holland by Van Marum and in Italy by Volta. The chief difference between the rival hypotheses is that, in the ^ two-fluid theory, both the electric fluids are movable within the substance of a solid conductor ; while in the one-fluid theory the actual electric fluid is mobile, but the particles of the conductor are fixed. The dispute could therefore be settled only by a deter- mination of the actual motion of electricity in discharges ; and this was beyond the reach of experiment.
In his Fourth Memoir Coulomb showed that electricity in equilibrium is confined to the surface of conductors, and does not penetrate to their interior substance ; and in the Sixth Memoir* he virtually establishes the result that the electric
* Page 677.
58 Electric and Magnetic Science
force near a conductor is proportional to the surface-density of electrification.
Since the overthrow of the doctrine of electric effluvia by Aepinus, the aim of electricians had been to establish their science upon the foundation of a law of action at a distance, resembling that which had led to such triumphs in Celestial Mechanics. When the law first stated by Priestley was at length decisively established by Coulomb, its simplicity and beauty gave rise to a general feeling of complete trust in it as the best attainable conception of electrostatic phenomena. The result was that attention was almost exclusively focused on action-at-a-distance theories, until the time, long afterwards,, when Faraday led natural philosophers back to the right' path.
Coulomb rendered great services to magnetic theory. It was he who in 1777, by simple mechanical reasoning, completed the overthrow of the hypothesis of vortices.* He also, in the second of the Memoirs already quoted,f confirmed Michell's law, according to which the particles of the magnetic fluids attract or repel each other with forces proportional to the inverse square of the distance. Coulomb, however, went beyond this, and endeavoured to account for the fact that the two magnetic fluids, unlike the two electric fluids, cannot be obtained separately; for when a magnet is broken into two pieces, one containing its north and the other its south pole, it is found that each piece is an independent magnet possessing two poles of its own, so that it is impossible to obtain a north or south pole in a state of isolation. Coulomb explained this by supposing^ that the mag- netic fluids are permanently imprisoned within the molecules of magnetic bodies, so as to be incapable of crossing from one molecule to the next ; each molecule therefore under all circumstances contains as much of the boreal as of the
* Mem. presences par divers Savans, ix (1780), p. 165.
t Mem de 1'Acad., 1785, p. 593. Gauss finally established the law by a much more refined method.
J In his Seventh Memoir, Mem, de 1'Acad., 1789, p. 488.
prior to the Introduction of the Potentials. 59
austral fluid, and magnetization consists simply in a separation of the two fluids to opposite ends of each molecule. Such a hypothesis evidently accounts for the impossibility of separating the two fluids to opposite ends of a body of finite size. The same idea, here introduced for the first time, has since been applied with success in other departments of electrical philosophy.
In spite of the advances which have been recounted, the mathematical development of electric and magnetic theory was scarcely begun at the close of the eighteenth century ; and many erroneous notions were still widely entertained. In a Eeport* which was presented to the French Academy in 1800, it was assumed that the mutual repulsion of the particles of electricity on the surface of a body is balanced by the resistance of the surrounding air; and for long afterwards the electric force outside a charged conductor was confused with a supposed additional pressure in the atmosphere.
Electrostatical theory was, however, suddenly advanced to quite a mature state of development by Simeon Denis Poisson (b. 1781, d. 1840), in a memoir which was read to the French Academy in 1812.f As the opening sentences show, he accepted the conceptions of the two-fluid theory.
" The theory of electricity which is most generally accepted," he says, " is that which attributes the phenomena to two different fluids, which are contained in all material bodies. It is supposed that molecules of the same fluid repel each other and attract the molecules of the other fluid ; these forces of attraction and repulsion obey the law of the inverse square of the distance ; and at the same distance the attractive power is equal to the repellent power; whence it follows that, when all the parts of a body contain equal quantities of the two fluids, the latter do not exert any influence on the fluids contained in neighbouring bodies, and consequently no electrical effects are discernible. This equal and uniform
* On Yolla's discoveries.
t Mem. de Plnstitut, 1811, Part i., p. 1, Part ii., p. 163.
60 Electric and Magnetic Science
distribution of the two fluids is called the natural state ; when this state is disturbed in any body, the body is said to be electrified, and the various phenomena of electricity begin to take place.
"Material bodies do not all behave in the same way with respect to the electric fluid : some, such as the metals, do not appear to exert any influence on it, but permit it to move about freely in their substance ; for this reason they are called conductors. Others, on the contrary — very dry air, for example — oppose the passage of the electric fluid in their interior, so that they can prevent the fluid accumulated in conductors from being dissipated throughout space."
When an excess of one of the electric fluids is communi- cated to a metallic body, this charge distributes itself over the surface of the body, forming a layer whose thickness at any point depends on the shape of the surface. The resultant force due to the repulsion of all the particles of this surface-layer must vanish at any point in the interior of the conductor, since otherwise the natural state existing there would be disturbed ; and Poisson showed that by aid of this principle it is possible in certain cases to determine the distribution of electricity in the surface-layer. For example, a well-known proposition of the theory of Attractions asserts that a hollow shell whose bounding surfaces are two similar and similarly situated ellipsoids exercises 110 attractive force at any point within the interior hollow; and it may thence be inferred that, if an electrified metallic conductor has the form of an ellipsoid, the charge will be distributed on it proportionally to the normal distance from the surface to an adjacent similar and similarly situated ellipsoid.
Poisson went on to show that this result was by no means all
• that might with advantage be borrowed from the theory of
I Attractions. Lagrange, in a memoir on the motion of gravitating
bodies, had shown* that the components of the attractive force
* Mem. de Berlin, 1777. The theorem was afterwards published, and ascribed to Laplace, in a memoir by Legendre on the Attractions of Spheroids, which will be found in the Mem. par divers Snvanx, published in 178o.
prior to the Introduction of the Potentials. 61
at any point can be simply expressed as the derivates of the function which is obtained by adding together the masses of all the particles of an attracting system, each divided by its distance from the point; and Laplace had shown* that this function V satisfies the equation
in space free from attracting matter. Poisson himself showed later, in 1813,f that when the point (z, y, z) is within the substance of the attracting body, this equation of Laplace must be replaced by
W VV VV
^ + w~~vr: p>
where p denotes the density of the attracting matter at the point. In the present memoir Poisson called attention to the utility of this function F in electrical investigations, remarking that its value over the surface of any conductor must be constant.
The known formulae for the attractions of spheroids show that when a charged conductor is spheroidal, the repellent force acting on a small charged body immediately outside it will be directed at right angles to the surface of the spheroid, and will be proportional to the thickness of the surface-layer of electricity at this place. Poisson suspected that this theorem might be true for conductors not having the spheroidal form — a result which, as we have seen, had been already virtually given by Coulomb ; and Laplace suggested to Poisson the following proof, applicable to the general case. The force at a point immediately outside the conductor can be divided into a part s due to the part of the charged surface immediately adjacent to the point, and a part S due to the rest of the surface. At a point close to this, but just inside the con- ductor, the force j^jpll still act; but the forces will evidently
* Mem. de 1'Acad., 1782 (published in 1785), p. 113. t Bull, de la Soc. Philomathique. iii. (1813,, p. 388.
62 Electric and Magnetic Science
be reversed in direction. Since the resultant force at the latter point vanishes, we must have S=s ; so the resultant force at the exterior point is 2s. But s is proportional to the charge per unit area of the surface, as is seen by considering the case of an infinite plate ; which establishes the theorem.
When several conductors are in presence of each other, the distribution of electricity on their surfaces may be determined by the principle, which Poisson took as the basis of his work, that at any point in the interior of any one of the conductors, the resultant force due to all the surf ace -layers must be zero. He discussed, in particular, one of the classical problems of electrostatics — namely, that of determining the surface-density on two charged conducting spheres placed at any distance from each other. The solution depends on Double Gamma Functions in the general case ; when the two spheres are in contact, it depends on ordinary Gamma Functions. Poisson gave a solution in terms of definite integrals, which is equivalent to that in terms of Gamma Functions ; and after reducing his results to numbers, compared them with Coulomb's experiments. f The rapidity with which in a single memoir Poisson passed from the barest elements of the subject to such recondite problems as those just mentioned may well excite admiration. His success is, no doubt, partly explained by the high state of development to which analysis had been advanced by the great mathematicians of the eighteenth century ; but even after allowance has been made for what is due to his predecessors, Poisson' s investigation must be accounted a splendid memorial uof his genius.
Some years later Poisson turned his attention to magnetism ; and, in a masterly paper* presented to the French Academy in 1824, gave a remarkably complete theory of the subject.
His starting-point is Coulomb's doctrine of two imponderable magnetic fluids, arising from the decomposition of a neutral fluid, and confined in their movements to the individual elements
* Mem. <le 1'Acad., v, p. 247.
prior to the Introduction of the Potentials. 63
of the magnetic body, so as to be incapable of passing from one element to the next
Suppose that an amount m of the positive magnetic fluid is located at a point (x y, z) ; the components of the magnetic intensity, or force exerted on unit magnetic pole, at a point (£, »f, £) will evidently be
-m-f-X -m~(-\ -m-(-)
where r denotes ((? - xf + (n - ?/)2 + (Z - z)2j*. Hence if we consider next a magnetic element in which equal quantities of the two magnetic fluids are displaced from each other parallel to_ the ic-axis, the components of the magnetic intensity at (g, i|, 2) will be the negative derivates, with respect to £ ij, £ respectively, of the function
where the quantity A, which does not involve (f, »j, £), may be called the magnetic moment of the element : it may be measured by the couple required to maintain the element in equilibrium at a definite angular distance from the magnetic meridian.
If the displacement of the two fluids from each other in the element is not parallel to the axis of xt it is easily seen that the expression corresponding to the last is
where the vector (A, B, C) now denotes the magnetic moment of the element.
Thus the magnetic intensity at an -external point (£, 77, £) due to any magnetic body has the components
«; - 017 where
ex oy integrated throughout the substance of the magnetic body, and
64 Electric and Magnetic Science
where the vector (A, B, C) or I represents the magnetic moment per unit- volume, or, as it is generally called, the magnetization. The function Fwas afterwards named by Green the magnetic potential.
Poisson, by integrating by parts the preceding expression for the magnetic potential, obtained it in the form
F = [[(I . dS). \ - fjp div I dx dy dz*
the first integral being taken over the surface $ of the magnetic body, and the second integral being taken throughout its volume. This formula shows that the magnetic intensity produced by the body in external space is the same as would be produced by a fictitious distribution of magnetic fluid, consisting of a layer over its surface, of surface-charge (I .- dS) per element dSy together with a volume-distribution of density - div I through- out its substance. These fictitious magnetizations are generally known as Poisson's equivalent surface- and volume-distributions of magnetism.
Poisson, moreover, perceived that at a point in a very small cavity excavated within the magnetic body, the magnetic potential has a limiting value which is independent of the shape of the cavity as the dimensions of the cavity tend to zero ; but that this is not true of the magnetic intensity, which in such a small cavity depends on the shape of the cavity. Taking the cavity to be spherical, he showed that the magnetic intensity within it is
grad F 4 ^-7rl,f where I denotes the magnetization at the place.
* If the components of a vector a are denoted by (ax, ay, az), the quantity drbjc + ayby -f- atkz is called the scalar product of two vectors a and b, and is denoted by (a . b).
The quantity ^— ' + ^ + ^ is called the divergence of the vector a, and is
fix dy 02
denoted by div a.
t The vector whose components are - — , - •?—, - -„— is denoted by grad V.
C£ dy dz J °
prior to the Introduction of the Potentials. 65
This memoir also contains a discussion of the magnetism temporarily induced in soft iron and other magnetizable metals by the approach of a permanent magnet. Poisson accounted for the properties of temporary magnets by assuming that they contain embedded in their substance a great number of small spheres, which are perfect conductors for the magnetic fluids ; so that the resultant magnetic intensity in the interior of one of these small spheres must be zero. He showed that such a sphere, when placed in a field of magnetic intensity F,* must acquire a
magnetic moment of amount -.- F x the volume of the sphere,
in order to counteract within the sphere the force F. Thus if kp denote the total volume of these spheres contained within a unit volume of the temporary magnet, the magnetization will be I, where 4-TrI = kp F,
and F denotes the magnetic intensity within a spherical cavity excavated in the body. This is Poisson s laiv of induced magnetism.
It is known that some substances acquire a greater degree of temporary magnetization than others when placed in the same circumstances : Poisson accounted for this by supposing that the quantity kp varies from one substance to another. But the experimental data show that for soft iron kp must have a value very near unity, which would obviously be impossible if kp is to mean the ratio of the volume of spheres contained within a region to the total volume of the region.f The physical inter- pretation assigned by Poisson to his formulae must therefore be rejected, although the formulae themselves retain their value.
Poisson's electrical and magiietical investigations were generalized and extended in 1828 by George Green* (b. 1793, d. 1841). Green's treatment is based on the properties of the function already used by Lagrange, Laplace, and Poisson, which
* In the present work, vectors will generally be distinguished by heavy type.
t This objection was advanced by Maxwell in § 430 of his Treatise. An attempt to overcome it was made by Betti : cf. p. 377 of his Lessons on the Potential.
J A.n essay on the application of mathematical analysis to the theories of electricity and magnetism, Nottingham, 1828 : reprinted in The Mathematical Papers of the late George Green, p. 1.
F
66 Electric and Magnetic Science.
represents the sum of all the electric or magnetic charges in the field, divided by their respective distances from some given point : to this function Green gave the name potential, by which it has always since been known.*
Near the beginning of the memoir is established the celebrated formula connecting surface and volume integrals, which is now generally called G-reeris Theorem, and of which Poisson's result on the equivalent surface- and volume-distribu- tions of magnetization is a particular application. By using this theorem to investigate the properties of the potential, Green arrived at many results of remarkable beauty and interest. We need only mention, as an example of the power of his method, the following : — Suppose that there is a hollow conducting shell, bounded by two closed surfaces, and that a number of electrified bodies are placed, some within and some without it ; and let the inner surface and interior bodies be called the interior system, and the outer surface and exterior botlies be called the exterior system. Then all the electrical phenomena of the interior system, relative to attractions, repulsions, and densities, will be the same as if there were no exterior system, and the inner surface were a perfect conductor, put in communication with the earth ; and all those of the exterior system will be the same as if the interior system did not exist, and the outer surface were a perfect conductor, containing a quantity of electricity equal to the whole of that originally contained in the shell itself and in all the interior bodies.
It will be evident that electrostatics had by this time attained a state of development in which further progress could be hoped for only in the mathematical superstructure, unless experiment should unexpectedly bring to light phenomena of an entirely new character. This will therefore be a convenient place to pause and consider the rise of another branch of electrical philosophy.
* Euler in 1744 (De melhodis inveniendi . . .) had spoken of the vis potentialis — what would now be called the potential energy — possessed by an elastic body when bent.
CHAPTEE III.
GALVANISM, FROM GALVANI TO OHM.
UNTIL the last decade of the eighteenth century, electricians were occupied solely with statical electricity. Their attention was then turned in a different direction.
In a work entitled Recherches sur Vorigine des sentiments agreables et cUsagr cables, which was published* in 1752, Johann Georg Sulzer (b. 1720, d. 1779) had mentioned that, if two pieces of metal, the one of lead and the other of silver, be joined together in such a manner that their edges touch, and if they be placed on the tongue, a taste is perceived " similar to that of vitriol of iron," although neither of these metals applied separately gives any trace of such a taste. " It is not probable," he says, " that this contact of the two metals causes a solution of either of them, liberating particles which might affect the tongue : and we must therefore conclude that the contact sets up a vibration in their particles, which, by affecting the nerves of the tongue, produces the taste in question."
This observation was not suspected to have any connexion with electrical phenomena, and it played no part in the incep- tion of the next discovery, which indeed was suggested by a mere accident.
Luigi Galvani, born at Bologna in 1737, occupied from 1775 onwards a chair of Anatomy in his native city. For many years before the event which made him famous he had been studying the susceptibility of -the nerves to irritation ; and, having been <- formerly a pupil of Beccaria, he was also interested in electrical experiments. One day in the latter part of the year 1780 he ' had, as he tells us,f " dissected and prepared a frog, and laid it on a table, on which, at some distance from the frog, was an electric machine. It happened by chance that one of my
* Mem. de 1'Acad. de Berlin, 1752, p. 356.
t Aloysii Galvani, De Viribus E 'lee trie itatis in Motu Mnsculari : Commentarii Bononiensi, vii (1791), p. 363.
F 2
68 Galvanism, from Galvani to Ohm.
assistants touched the inner crural nerve of the frog with the point of a scalpel ; whereupon at once the muscles of the limbs were violently convulsed.
" Another of those who used to help me in electrical experi- ments thought he had noticed that at this instant a spark was drawn from the conductor of the machine. I myself was at the time occupied with a totally different matter; but when he drew my attention to this, I greatly desired to try it for myself,. and discover its hidden principle. So I, too, touched one or other of the crural nerves with the point of the scalpel, at the same time that one of those present drew a spark ; and the same phenomenon was repeated exactly as before."*
After this, Galvani conceived the idea of trying whether the electricity of thunderstorms would induce muscular contractions equally well with the electricity of the machine. Having successfully experimented with lightning, he " wished," as he writes,! " to try the effect of atmospheric electricity in calm weather. My reason for this was an observation I had made,, that frogs which had been suitably prepared for these experi- ments and fastened, by brass hooks in the spinal marrow, to the iron lattice round a certain hanging-garden at my house,, exhibited convulsions not only during thunderstorms, but sometimes even when the sky was quite serene. I suspected these effects to be due to the changes which take place during the day in the electric state of the atmosphere ; and so, with some degree of confidence, I performed experiments to test the point; and at different hours for many days I watched frogs which I had disposed for the purpose ; but could not detect any motion in their muscles. At length, weary of waiting in vain, I pressed the brass hooks, which were driven into the spinal marrow, against the iron lattice, in order to see whether contractions could be excited by varying the incidental circum-
* According to a story which has often been repeated, but which rests on no sufficient evidence, the frog was one of a number which had been procured for th& Signora Galvani, who, being in poor health, had been recommended to take a soup, made of these animals as a restorative. f Loc. cit., p. 377.
Galvanism, from Galvani to Ohm. 69
stances of the experiment. I observed contractions tolerably often, but they did not seem to bear any relation to the changes in the electrical state of the atmosphere.
" However, at this time, when as yet I had not tried the experiment except in the open air, I came very near to adopt- ing a theory that the contractions are due to atmospheric electricity, which, having slowly entered the animal and accu- mulated in it, is suddenly discharged when the hook comes in contact with the iron lattice. For it is easy in experimenting to deceive ourselves, and to imagine we see the things we wish to see.
" But I took the animal into a closed room, and placed it on an iron- plate ; and when I pressed the hook which was fixed in the spinal marrow against the plate, behold ! the same spasmodic contractions as before. I tried other metals at different hours on various days, in several places, and always with the same result, except that the contractions were more violent with some metals than with others. After this I tried various bodies which are not conductors of electricity, such as glass, gums, resins, stones, and dry wood ; but nothing happened. This was somewhat surprising, and led me to suspect that electricity is inherent in the animal itself. This suspicion was strengthened by the observation that a kind of circuit of subtle nervous fluid (resembling the electric circuit which is manifested in the Leyclen jar experiment) is completed from the nerves to the muscles when the contractions are produced.
" For, while I with one hand held the prepared frog by the hook fixed in its spinal marrow, so that it stood with its feet on a silver box, and with the other hand touched the lid of the box, or its sides, with any metallic body, I was surprised to see the frog become strongly convulsed every time that I applied this artifice."*
Galvani thus ascertained that the limbs of the frog are con- vulsed whenever a connexion is made between the nerves and muscles by a metallic arc, generally formed of more than one
*This observation was made in 1786.
70 Galvanism > from Galvani to Ohm.
kind of metal ; and he advanced the hypothesis that the convul- sions are caused by the transport of a peculiar fluid from the
' nerves to the muscles, the arc acting as a conductor. To this fluid the names Galvanism and .Animal Electricity were soon generally applied. Galvani himself considered it to be the same as the ordinary electric fluid, and, indeed, regarded the entire phenomenon as similar to the discharge of a Leyden jar.
*' The publication of Gralvani's views soon engaged the attention of the learned world, and gave rise to an animated controversy between those who supported Galvani's own view, those who believed galvanism to be a fluid distinct from ordinary electricity, and a third school who altogether refused to attribute the effects to a supposed fluid contained in the nervous system. The leader of the last-named party was Alessandro Volta (b. 1745, d. 1827), Professor of Natural Philosophy in the University of Pavia, who in 1792 put forward the view* that the stimulus in Galvani's experiment is derived essentially from the connexion of two different metals by a moist body. "The metals used in the
* experiments, being applied to the moist bodies of animals, can by themselves, and of their proper virtue, excite and dislodge the electric fluid from its state of rest ; so that the organs of the
* animal act only passively." At first he inclined to combine this theory of metallic stimulus with a certain degree of belief in such a fluid as Galvani had supposed; but after the end of 17!. '3 he denied the existence of animal electricity altogether.
From this standpoint Volta continued his experiments and worked out his theory. The following quotation from a lettert which he wrote later to Gren, the editor of the Neucs Journal //. Physik, sets forth his view in a more developed form : —
"The contact of different conductors, particularly the metallic, including pyrites and other minerals, as well as charcoal, which I call dry conductors, or of the first class, with moist conductors, or conductors of the second class, agitates or disturbs the electric
f fluid, or gives it a certain impulse. Do not ask in what manner : it is enough that it is a principle, and a general principle. This
*Phil. Trans., 1793, pp. 10, 27. tPhil. Mag. iv (1799), pp. 59, 163, 306.
Galvanism , from Galvani to Okm. 71
impulse, whether produced by attraction or any other force, is different or unlike, both in regard to the different metals and to the different moist conductors ; so that the direction, or at least the power, with which the electric fluid is impelled or excited, is different when the conductor A is applied to the conductor B, or to another C. In a perfect circle of conductors, where either one of the second class is placed between two different from each other of the first class, or, contrariwise, one of the first class is placed between two of the second class different from each other, an electric stream is occasioned by the predominating force either to the right or to the left — a circulation of this fluid, which ceases only when the circle is broken, and which is renewed when the circle is again rendered complete."
Another philosopher who, like Volta, denied the existence of a fluid peculiar to animals, but who took a somewhat different view of the origin of the phenomenon, was Giovanni Fabroni, of Florence (b. 1752, d. 1822), who,* having placed two plates of different metals in water, observed that one of them was partially oxidized when they were put in contact ; from which he rightly concluded that some chemical action is inseparably connected with galvanic effects.
The feeble intensity of the phenomena of galvanism, which compared poorly with the striking displays obtained in electro- statics, was responsible for some falling off of interest in them towards the end of the eighteenth century ; and the last years of their illustrious discoverer were clouded by misfortune. Being attached to the old order which was overthrown by the armies of the French Ke volution, he refused in 1798 to take the oath of allegiance to the newly constituted Cisalpine Eepublic, and was deposed from his professorial chair. A profound melancholy, which had been induced by domestic bereavement, was aggra- vated by poverty and disgrace ; and, unable to survive the loss of all he held dear, he died broken-hearted before the end of the year.f
* Phil. Journal, 4to, iii. 308 ; iv. 120 ; Journal de Physique, vi. 348. t A decree of reinstatement had been granted, but had not come into operation at the time of Galvani's death.
<
72 Galvanism, Jrom Galvani to O/it/i.
Scarcely more than a year after the death of Galvani, the new science suddenly regained ' the eager attention of philo- sophers. This renewal of interest was due to the discovery by Volta, in the early spring of 1800, of a means of greatly increasing the intensity of the effects. Hitherto all attempts to magnify the action by enlarging or multiplying the apparatus had ended in failure. If a long chain of different metals was used instead of only two, the convulsions of the frog were no more violent. But Volta now showed* that if any number of couples, each consisting of a zinc disk and a copper disk in contact, were taken, and if each couple was separated from the next by a disk of moist- ened pasteboard (so that the order was copper, zinc, pasteboard, copper, zinc, pasteboard, &c.), the effect of the pile thus formed was much greater than that of any galvanic apparatus previously introduced. When the highest and lowest disks were simul- taneously touched by the fingers, a distinct shock was felt ; and this could be repeated again and again, the pile apparently possessing within itself an indefinite power of recuperation. It thus resembled a Leyden jar endowed with a power of automati- cally re-establishing its state of tension after each explosion; with, in fact, " an inexhaustible charge, a perpetual action or impulsion on the electric fluid."
Volta unhesitatingly pronounced the phenomena of the pile to be in their nature electrical. The circumstances of Galvani's original discovery had prepared the minds of philosophers for this belief, which was powerfully supported by the similarity of the physiological effects of the pile to those of the Leyden jar, and by the observation that the galvanic influence was conducted only by those bodies — e.g. the metals — which were already known to be good conductors of static electricity. But Volta now supplied a still more convincing proof. Taking a disk of copper and one of zinc, 'he held each by an insulating handle and applied them to each other for an instant. After the disks had been separated, they were brought into contact with a deli-
* I'hil. Trans., 1800, p. 403.
Galvanism, from Galvani to Ohm. 73
oate electroscope, which indicated by the divergence of its straws that the disks were now electrified — the zinc had, in fact, acquired a positive and the copper a negative electric charge.* Thus the mere contact of two different metals, such as those employed in / the pile, was shown to be sufficient for the production of effects ' undoubtedly electrical in character.
On the basis of this result Volta in the same year (1800) put forward a definite theory of the action of the pile. Suppose first that a disk of zinc is laid on a disk of copper, which in turn rests on an insulating support. The experiment just described shows that the electric fluid will be driven from the copper to the zinc. We may then, according to Volta, represent the state or " tension " of the copper by the number - J, and that of the zinc by the number + J, the difference being arbitrarily taken as unity, and the sum being (on account of the insulation) zero. It will be seen that Volta's idea of " tension " was a mingling of two ideas, which in modern electric theory are clearly distin- guished from each other — namely, electric charge and electric potential.
Now let a disk of moistened pasteboard be laid on the zinc, and a disk of copper on this again. Since the uppermost copper is not in contact with the zinc, the contact-action does not take place between them ; but since the moist pasteboard is a conductor, the copper will receive a charge from the zinc. Thus the states will now be represented by - f for the lower copper, + J for the zinc, and + \ for the upper copper, giving a zero sum as before.
If, now, another zinc disk is placed on the top, the states will be represented by - 1 for the lower copper, 0 for the lower zinc and upper copper, and + 1 for the upper zinc.
In this way it is evident that the difference between the numbers indicating the tensions of the uppermost and lowest
* Abraham Bennet (b. 1750, d. 1799) had previously shown (Xew Experiments in Electricity, 1789, pp. 86-102) that many bodies, when separated after contact, f are oppositely electrified ; he conceived that different bodies have different attrac- tions or capacities for electricity.
74 Galvanism , from Galvani to O/im.
disks in the pile will always be equal to the number of pairs of metallic disks contained in it. If the pile is insulated, the sum of the numbers indicating the states of all the disks must be zero; but if the lowest disk is connected to earth, the tension of this disk will be zero, and the numbers indicating the states of all the other disks will be increased by the same amount, their mutual differences remaining unchanged.
The pile as a whole is thus similar to a Leyden jar ; when the experimenter touches the uppermost and lowest disks, he receives the shock of its discharge, the intensity being proportional to the number of disks.
The moist layers played no part in Volta's theory beyond j. that of conductors.* It was soon found that when the moisture is acidified, the pile is more efficient; but this was attributed solely to the superior conducting power of acids.
Yolta fully understood and explained the impossibility of constructing a pile from disks of metal alone, without making use of moist substances. As he showed in 1801, if disks of various metals are placed in contact in any order, the extreme metals will be in the same state as if they touched each other directly without the intervention of the others ; so that the whole is equivalent merely to a single pair. When the metals are arranged in the order silver, copper, iron, tin, lead, zinc, each of them becomes positive with respect to that which precedes it, and negative with respect to that which follows it ; but the moving force from the silver to the zinc is equal to the sum of the moving forces of the metals comprehended between them in the series.
When a connexion was maintained for some time between the extreme disks of a pile by the human body, sensations were experienced which seemed to indicate a continuous activity in the entire system. Yolta inferred that the electric current persists during the whole time that communication by con-
* Volta had inclined, in his earlier experiments on galvanism, to locate the seat of power at the interfaces of the metals with the rnoist conductors. Cf. his letter to Gren, Phil. Mag. iv (1799), p. 62.
Galvanism, from Gaivani to Ohm. 75
ductors exists all round the circuit, and that the current is suspended only when this communication is interrupted. " This endless circulation or perpetual motion of the electric fluid," he says, "may seem paradoxical, and may prove inexplicable ; but it is none the less real, and we can, so to speak, touch and handle it."
Yolta announced his discovery in a letter to Sir Joseph Banks, dated from Como, March 20th, 1800. Sir Joseph, who was then President of the Eoyal Society, communicated the news to William Nicholson (b. 1753, d. .1815), founder of the Journal which is generally known by his name, and his friend Anthony Carlisle (b. 1768, d. 1840), afterwards a distinguished surgeon. On the 30th of the following month, Nicholson and Carlisle set up the first pile made in England. In repeating Volta's experiments, having made the contact more secure at the upper plate of the pile by placing a drop of water there, they noticed* a disengagement of gas round the con- ducting wire at this point ; whereupon they followed up the matter by introducing a tube of water, into which the wires from the terminals of the pile were plunged. Bubbles of an inflammable gas were liberated at one wire, while the other wire became oxidised ; when platinum wires were used, oxygen and hydrogen were evolved in a free state, one at each wire. This effect, which was nothing less than the electric decom- position of water into its constituent gases, was obtained on May 2nd, 1800.f
Although it had long been known that frictional electricity is capable of inducing chemical action,* the discovery of Nicholson and Carlisle was of the first magnitude. It was at once extended by William Cruickshank, of Woolwich (b. 1745,
i's Journal (4to), iv, 179 (1800) ; Phil. Mag. vii, 337 (1800).
t It was obtained independently four months later l>y J. "W. Hitter.
J Beccaria (Lettere deW elettricismo, Bologna, 1758, p. 282) had reduced mercury and other metals from their oxides by discharges ot fractional electricity ; and Priestley had obtained an inflammable gas from certain organic liquids in the same way. Cavendish in 1781 had established the constitution of water by electrically exploding hydrogen and oxygen.
76 Galvanism > from Galvani to Ohm.
d. 1800), who* showed that solutions of metallic salts are also decomposed by the current; and William Hyde Wollaston (ft. 1766, d. 1828) seized on it as a testf of the identity of the electric currents of Volta with those obtained by the discharge of f rictional electricity. He found that water could be decom-
vy posed by currents of either type, and inferred that all differences between them could be explained by supposing that voltaic electricity as commonly obtained is " less intense, but produced in much, larger quantity." Later in the same year (1801), Martin van Mar um (ft. 1750, d. 1837) and Christian Heinrich Pfaff (ft. 1773, d. 1852) arrived at the same conclusion by carrying out on a large scale} Volta's plan of using the pile to
V charge batteries of Leyden jars.
The discovery of Nicholson and Carlisle made a great impression on the mind of Humphry Davy (ft. 1778, d. 1829), a young Cornishman who about this time was appointed Professor of Chemistry at the E-oyal Institution in London. Davy at once began to experiment vvitli Voltaic piles, and in November, 1800,§ showed that they give no current when the water between the
y pairs of plates is pure, and that their power of action is " in great measure proportional to the power of the conducting fluid substance between the double plates to oxydate the zinc." This result, as he immediately perceived, did not harmonize well with Volta's views on the source of electricity in the pile, but was, on the other hand, in agreement with , Eabroni's idea that galvanic effects are always accompanied by chemical action. After a series of experiments he definitely
1 concluded that " the galvanic pile of Volta acts only when the conducting substance between the plates is capable of oxydating the zinc ; and that, in proportion as a greater quantity of oxygen enters into combination with the zinc in a given time, so in proportion is the power of the pile to decompose water and to give the shock greater. It seems therefore reasonable
* Nicholson's Journal (4to), iv (1800), pp. 187,245: Phil. Mag., vii (1800), p. 337.
t Phil. Mag., 1801, p. 427. J Phil. Mag., xii (1802), p. 161.
§ Nicholson's Journal (4to), iv (1800) ; Davy's Works, ii, p. 155.
Galvanism, from Galvani (o Ohm. 77
to conclude, though with our present quantity of facts we are unable to explain the exact mode of operation, that the </ oxydatioii of the zinc in the pile, and the chemical changes connected with it, are somehow the cause of the electrical effects ^ it produces." This principle of oxidation guided Davy in designing many new types of pile, with elements chosen from the whole range of the known metals.
Davy's chemical theory of the pile was supported by Wollaston* and by Nicholson,f the latter of whom urged that the existence of piles in which only one metal is used (with more than one kind of fluid) is fatal to any theory which places the seat of the activity in the contact of dissimilar metals.
Davy afterwards proposed J a theory of the voltaic pile which combines ideas drawn from both the "contact" and " chemical " explanations. Ho supposed that before the circuit is closed, the copper and zinc disks in each contiguous pair assume opposite electrostatic states, in consequence of inherent "electrical energies" possessed by the metals; and when a > communication is made between the extreme disks by a wire, the opposite electricities annihilate each other, as in the dis- charge of a Leyden jar. If the liquid (which Davy compared to the glass of a Leyden jar) were incapable of decomposition, the current would cease after this discharge. But the liquid in the pile is composed of two elements which have inherent attractions for electrified metallic surfaces : hence arises chemical action, which removes from the disks the outermost layers of molecules, whose energy is exhausted, and exposes new metallic surfaces. The electrical energies of the copper and zinc are consequently again exerted, and the process of electro- motion continues. Thus the contact of metals is the cause which disturbs the equilibrium, while the chemical changes continually restore the conditions under which the contact energy can be exerted.
In this and other memoirs Davy asserted that chemical
*Phil. Trans., 1801, p. 427. t Nicholson'* Journal, i (1802), p. 142.
; Phil. Trans., 1807, p. 1.
78 Galvanism, from Galvani to Ohm.
J affinity is essentially of an electrical nature. " Chemical and electrical attractions," he declared,* "are produced by the same cause, acting in one case on particles, in the other on masses, of matter; and the same property, under different modifications, is the cause of all the phenomena exhibited by different voltaic combinations."
The further elucidation of this matter came chiefly from
- researches on electro-chemical decomposition, which we must now consider.
A phenomenon which had greatly surprised Nicholson and Carlisle in their early experiments was the appearance of the products of galvanic decomposition at places remote from each other. The first attempt to account for this was made in 1806 by Theodor von Grothussf (b. 1785, d. 1822) and by Davy,} who advanced a theory that the terminals at which water is decomposed have attractive and repellent powers ; that the pole whence resinous electricity issues has the property of attracting hydrogen and the metals, and of repelling oxygen and acid substances, while the positive terminal has the power of attract- ing oxygen and repelling hydrogen ; and that these forces are sufficiently energetic to destroy or suspend the usual operation of chemical affinity in the water-molecules nearest the terminals. The force due to each terminal was supposed to diminish with the distance from the terminal. When the molecule nearest one of the terminals has been decomposed by the attractive and repellent forces of the terminal, one of its constituents is liberated there, while the other constituent, by virtue of electrical forces (the oxygen and hydrogen being in opposite electrical states), attacks the next molecule, which is then decomposed. The surplus constituent from this attacks the next molecule, and so on. Thus a chain of decompositions and recompositions was supposed to be set up among the molecules intervening between the terminals.
* Phil. Trans., 1826, p. 383. f Ann. de Cliim., Iviii (1806), p. 54.
t Bukerian lecture for 1806, Phil. Trans., 1807, p. 1. A theory similar to that of Grothuss and Davy was communicated by Peter Mark Eoget (b. 1779, d. 1869) in 1807 to the Philosophical Society of Manchester : cf. Roget's Galvanism, § 106.
Galvanism^ from ^Galvani to Ohm. 79
The hypothesis of Grothuss and Davy was attacked in 1825 by Aiiguste De La Kive* (6. 1801, d. 1873) of Geneva, on the ground of its failure to explain what happens when different liquids are placed in series in the circuit. If, for example, a solution of zinc sulphate is placed in one compartment, and water in another, and if the positive pole is placed in the solution of zinc sulphate, and the negative pole in the water, De La Rive found that oxide of zinc is developed round the latter; although decomposition and recomposition of zinc sulphate could not take place in the water, which contained none of it. Accordingly, he supposed the constituents of the decomposed liquid to be bodily transported across the liquids, in close union with the moving electricity. In the electrolysis of water, one current of electrified hydrogen was supposed to leave the positive pole, and become decomposed into hydrogen and electricity at the negative pole, the hydrogen being there liberated as a gas. Another current in the same way carried electrified oxygen from the negative to the positive pole. In this scheme the chain of successive decompositions imagined by Grothuss does not take place, the only molecules decomposed being those adjacent to the poles.
The appearance of the products of decomposition at the separate poles could be explained either in Grothuss' fashion by assuming dissociations throughout the mass of liquid, or in De La Rive's by supposing particular dissociated atoms to travel considerable distances. Perhaps a preconceived idea of economy in Nature deterred the workers of that time from accepting the two assumptions together, when either of them separately would meet the case. Yet it is to this apparent redundancy that later researches have pointed as the truth. Nature is what she is, and not what we would make her.
De La Rive was one of the most thoroughgoing opponents of Volta's contact theory of the pile ; even in the case when two metals are in contact in air only, without the intervention
* Annales de Cnimie, xxviii, 190.
80 Galvanism, from Galvani to Ohm.
of any liquid, he attributed the electric effect wholly to the chemical affinity of the air for the metals.
During the long interval between the publication of the rival hypotheses of Grothuss and De La Bive, little real progress was made with the special problems of the cell ; but mean- while electric theory was developing in other directions. One of these, to which our attention will first be turned, was the electro-chemical theory of the celebrated Swedish chemist, Jons Jacob Berzelius (b. 1779, d. 1848).
Berzelius founded his theory,* which had been in one or two of its features anticipated by Davy,f on inferences drawn from Volta's contact effects. " Two bodies," he remarked, " which have affinity for each other, and which have been brought into mutual contact, are found upon separation to be in opposite electrical states. That which has the greatest affinity for oxygen usually becomes positively electrified, and the other negatively."
This seemed to him to indicate that chemical affinity arises from the play of electric forces, which in turn spring from electric charges within the atoms of matter. To be precise, he supposed each atom to possess two poles, which are the seat of opposite electrifications, and whose electrostatic field is the cause of chemical affinity.
By aid of this conception Berzelius drew a simple and vivid picture of chemical combination. Two atoms, which are about to unite, dispose themselves so that the positive pole of one touches the negative pole of the other ; the electricities of these two poles then discharge each other, giving rise to the heat and light which are observed to accompany the act of combination.! The disappearance of these leaves the compound molecule with the two remaining poles ; and it cannot be dissociated into its constituent atoms again until some means is found of restoring to the vanished poles their charges. Such a means is afforded
* Memoirs of the Acad. of Stockholm, 1812 ; Nicholson's Journal of Nat. Phil., xxxiv (1813), 142, 153, 240, 319; xxxv, 38, 118, 159.
t Pnil. Trans., 1807. J This idea was Davy's.
Galvanism, from Gaivani to Ohm. 81
by the action of the galvanic pile in electrolysis : the opposite electricities of the current invade the molecules of the electrolyte, and restore the atoms to their original state of polarization.
If, as Berzelius taught, all chemical compounds are formed by the mutual neutralization of pairs of atoms, it is evident / that they must have a binary character. Thus he conceived a salt to be compounded of an acid and an oxide, and each of these to be compounded of two other constituents. Moreover, in any compound the electropositive member would be replace- able only by another electropositive member, and the electro- negative member only by another member also electronegative ; so that the substitution of, e.g., chlorine for hydrogen in a compound would be impossible — an inference which was overthrown by subsequent discoveries in chemistry.
Berzelius succeeded in bringing the most curiously diverse facts within the scope of his theory. Thus " the combination 1 of polarized atoms requires a motion to turn the opposite poles to each other; and to this circumstance is owing the facility with which combination takes place when one of the two bodies is in the liquid state, or when both are in that state ; and the extreme difficulty, or nearly impossibility, of effecting an union between bodies, both of which are solid. And again, since each polarized particle must have an electric atmosphere, and as this atmosphere is the predisposing cause of combination, as we have seen, it follows, that the particles cannot act but at certain distances, proportioned to the intensity of their polarity ; and hence it is that bodies, which have affinity for each other, always combine nearly on the instant when mixed in the liquid state, but less easily in the gaseous state, and the union ceases to be possible under a certain degree of dilatation of the gases ; as we know by the experiments of Grothuss, that a mixture of oxygen and hydrogen in due proportions, when rarefied to a certain degree, cannot be set on fire at any temperature whatever." j And again : " Many bodies require an elevation of temperature to
G
82 Galvanism, from Galvani to Ohm.
enable them to act upon each other. It appears, therefore, that heat possesses the property of augmenting the polarity of these bodies."
Berzelius accounted for Volta's electromotive series by assuming the electrification at one pole of an atom to be some- what more or somewhat less than what would be required to neutralize the charge at the other pole. Thus each atom would possess a certain net or residual charge, which might be of either sign ; and the order of the elements in Volta's series could be interpreted simply as the order in which they would stand when ranged according to the magnitude of this residual charge. As we shall see, this conception was afterwards overthrown by Faraday.
Berzelius permitted himself to publish some speculations on the nature of heat and electricity, which bring vividly before us the outlook of an able thinker in the first quarter of the nineteenth century. The great question, he says, is whether v the electricities and caloric are matter or merely phenomena. If the title of matter is to be granted only to such things as are ponderable, then these problematic entities are certainly not matter ; but thus to narrow the application of the term is, he believes, a mistake; and he inclines to the opinion that caloric is truly matter, possessing chemical affinities without obeying the law of gravitation, and that light and all radiations consist in modes of propagating such matter. This conclusion makes it easier to decide regarding electricity. " From the relation which exists between caloric and the electricities," he remarks, "it is clear that what may be true with regard to the materiality of one of them must also be true with regard to that of the other. There are, however, a quantity of phenomena produced by electricity which do not admit of explanation without admitting at the same time that electricity is matter. Electricity, for instance, very often detaches everything which covers the surface of those bodies which conduct it. It, indeed, passes through conductors without leaving any trace of its passage ; but it penetrates non-con-
Galvanism i from Galvani to Ohm. 83
ductors which oppose its course, and makes a perforation precisely of the same description as would have been made by something which had need of place for its passage. We often observe this when electric jars are broken by an over- charge, or when the electric shock is passed through a number of cards, etc. We may therefore, at least with some proba- bility, imagine caloric and the electricities to be matter, destitute of gravitation, but possessing affinity to gravitating bodies. When they are not confined by these affinities, they tend to place themselves in equilibrium in the universe. The ^ suns destroy at every moment this equilibrium, and they send the re-united electricities in the form of luminous rays towards the planetary bodies, upon the surface of which the rays, being arrested, manifest themselves as caloric ; and this last in its turn, during the time required to replace it in equilibrium in the universe, supports the chemical activity of organic and inorganic nature."
It was scarcely to be expected that anything so speculative as Berzelius' electric conception of chemical combination would be confirmed in all particulars by subsequent discovery ; and, as a matter of fact, it did not as a coherent theory survive the lifetime of its author. But some of its ideas have persisted, and among them the conviction which lies at its foundation, that chemical affinities are, in the last resort, of * electrical origin.
While the attention of chemists was for long directed to the theory of Berzelius, the interest of electricians was diverted from it by a discovery of the first magnitude in a different region.
That a relation of some land subsists between electricity and magnetism had been suspected by the philosophers of the eighteenth century. The suspicion was based in part on some curious effects produced by lightning, of a kind which may be illustrated by a paper published in the Philosophical Transactions in 1735.* A tradesman of Wakefield, we are told, "having put
*Phil. Trans, xxxix (1735), p. 74. G 2
84 Galvanism, from Galvani to Ohm.
up a great number of knives and forks in a large box, and having placed the box in the corner of a large room, there happen'd in July, 1731, a sudden storm of thunder, lightning, etc., by which the corner of the room was damaged, the Box split, and a good many knives and forks melted, the sheaths being untouched. The owner emptying the box upon a Counter where some Nails lay, the Persons who took up the knives, that lay upon the Nails, observed that the knives took up the Nails."
Lightning thus came to be credited with the power of magnetizing steel ; and it was doubtless this which led Franklin* in 1751 to attempt to magnetize a sewing-needle by means of the discharge of Leyden jars. The attempt was indeed success- ful ; but, as Van Marum afterwards showed, it was doubtful whether the magnetism was due directly to the current.
More experiments followed. f In 1805 Jean Nicholas Pierre Hachette (b. 1769, d. 1834) and Charles Bernard Desormes (b. 1777, d. 1862) attempted to determine whether an insulated voltaic pile, freely suspended, is oriented by terrestrial mag- netism ; bat without positive result. In 1807 Hans Christian Oersted (&. 1777, d. 1851), Professor of Natural Philosophy in Copenhagen, announced his intention of examining the action of electricity on the magnetic needle ; but it was not for some years that his hopes were realized. If one of his pupils is to be believed,* he was " a man of genius, but a very unhappy experi- menter ; he could not manipulate instruments. He must always have an assistant, or one of his auditors who had easy hands, .to arrange the experiment."
During a course of lectures which he delivered in the winter of 1819-20 on " Electricity, Galvanism, and Magnetism," the idea occurred to him that the changes observed with the compass-needle during a thunderstorm might give the clue to the effect of which he was in search ; and this led him to think that the experiment should be tried with the galvanic circuit
* Letter vi from Franklin to Collinson. f In 1774 the Electoral Academy
of Bavaria proposed the question, " Is there a real and physical analogy between electric and magnetic forces ? " as the subject of a prize.
1 Cf. a letter from Hansteen inserted inBence Jones' Life of Faraday y ii, p. 395.
Galvanism, from Galvani to Ohm. 85
closed instead of open, and to inquire whether any effect is produced on a magnetic needle when an electric current is passed through a neighbouring wire. At first he placed the wire at right angles to the needle, but observed no result. After the end of a lecture in which this negative experiment had been shown, the idea occurred to him to place the wire parallel to the needle : on trying it, a pronounced deflexion was observed, and the relation between magnetism and the electric current was discovered. After confirmatory experiments with more powerful apparatus, the public announcement was made in July, 1820 *
Oersted did not determine the quantitative laws of the ;action, but contented himself with a statement of the qualita- tive effect and some remarks on its cause, which recall the magnetic speculations of Descartes : indeed, Oersted's concep- tions may be regarded as linking those of the Cartesian school to those which were introduced subsequently by Faraday. " To the effect which takes place in the conductor and in the sur- rounding space," he wrote, " we shall give the name of the -conflict of electricity? " The electric conflict acts only on the magnetic particles of matter. All non-magnetic bodies appear penetrable by the electric conflict, while magnetic bodies, or rather their magnetic particles, resist the passage of this conflict Hence they can be moved by the impetus of the contending powers.
" It is sufficiently evident from the preceding facts that the •electric conflict is not confined to the conductor, but dispersed pretty widely in the circumjacent space.
" From the preceding facts we may likewise collect, that this conflict performs circles ; for without this condition, it seems impossible that the one part of the uniting wire, when placed below the magnetic pole, should drive it toward the east, and when placed above it toward the west; for it is the nature of a
* Schweigger's Journal fur Chemie und Physik, zxix (1820), p. 275 ; Thomson's Annals of Philosophy, xvi (1820), p. 273; Ostwald's Klattiter der ' Wi.ssenseha.ften, Nr. 63.
86 Galvanism, from Galvani to Ohm.
circle that the motions in opposite parts should have an opposite1 direction."
Oersted's discovery was described at the meeting of the French Academy on September llth, 1820, by an academician (Arago) who had just returned from abroad. Several investi- gators in France repeated and extended his experiments ; and the first precise analysis of the effect was published by two of these, Jean-Baptiste Biot (b. 1774, d. 1862) and Felix Savart (b. 1791, d. 1841), who, at a meeting of the Academy of Sciences on October 30th, 1820, announced* that the action experienced by a pole of austral or boreal magnetism, when placed at any distance from a straight wire carrying a voltaic current, may be
4 thus expressed : " Draw from the pole a perpiendicular to the wire ; the force on the pole is at right angles to this line and ta the wire, and its intensity is proportional to the reciprocal of the distance." This result was soon further analysed, the attractive force being divided into constituents, each of which was supposed to be due to some particular element of the current ; in its new form the law may be stated thus : the- magnetic force due to an element ds of a circuit, in which a current i is flowing, at a point whose vector distance from ds is r,, is (in suitable units)
i ids
— |ds,r|t or curl — .+ r3 J r
It was now recognized that a magnetic field may be produced as readily by an electric current as by a magnet ; and, as Arago soon showed,§ this, like any other magnetic field, is capable of
* Annales de Chimie, xv (1820), p. 222 ; Journal de Phys., xli, p. 51.
f If a and b denote two vectors, the vector whose components are (aybz — azby^ azb* — a*bz, axby — aybx) is called the vector product of a and b, and is denoted by [a, b]. Its direction is at right angles to those of a and b, and its magnitude is represented by twice the area of the triangle formed by them.
+ If a denotes any vector, the vector whose components are ^-z - -^, -—• - ^-*r
3% 9a* • -,
z-l - -— is denoted by curl a.
fo ty
§ Annales de Chimie, xv (1820), p. 93.
Galvanism, from Galvani to Ohm. 87
inducing magnetization in iron. The question naturally sug- gested itself as to whether the similarity of properties between currents and magnets extended still further, e.g. whether conductors carrying currents would, like magnets, experience ponderomotive forces when placed in a magnetic field, and whether such conductors would consequently, like magnets, exert ponderomotive forces on each other.
The first step towards answering these inquiries was taken by Oersted* himself. " As," he said, " a body cannot put another in motion without being moved in its turn, when it possesses the requisite mobility, it is easy to foresee that the galvanic arc must be moved by the magnet " ; and this he verified experimentally.
The next step came from Andre Marie Ampere (b. 1775, d. 1836), who at the meeting of the Academy on September 18th, exactly a week after the news of Oersted's first discovery had arrived, showed that two parallel wires carrying currents attract each other if the currents are in the same direction, and repel each other if the currents are in opposite directions. During the next three years Ampere continued to prosecute the researches thus inaugurated, and in 1825 published his collected results in one of the most celebrated memoirsf in the history of natural philosophy.
Ampere introduces his work by proclaiming himself a follower of that school which explained all physical phenomena in terms of equal and oppositely directed forces between pairs of particles ; and he renounces the attempt to seek more speculative, though possibly more fundamental, explanations in terms of the motions of ultimate fluids and aethers. Never- theless, he indicates two conceptions of this latter character, on which such explanations might be founded.
In the firstj he suggests that the ponderomotive forces
* Schweigger's Journal fur Chem. u. Phys., xxix (1820), p. 364 ; Thomson's Annals of Philosophy, xvi (1820), p. 375. t Mem. de 1'Acad., vi, p. 175.
% facueil tF observations electro- dynamiques, p. 215 ; and the memoir just cited, pp. 285, 370.
88 Galvanism, from Galvani to Ohm.
between circuits carrying electric currents may be due to " the reaction of the elastic fluid which extends throughout all space, whose vibrations produce the phenomena of light," and which is " put in motion by electric currents." This fluid or aether can, he says, " be no other than that which results from the combination of the two electricities/'
In the second conception,* Ampere suggests that the interspaces between the metallic molecules of a wire which carries a current may be occupied by a fluid composed of the two electricities, not in the proportions which form the neutral fluid, but with an excess of that one of them which is opposite to the electricity peculiar to the molecules of the metal, and which consequently masks this latter electricity. In this inter- molecular fluid the opposite electricities are continually being dissociated and recombined ; a dissociation of the fluid within one inter-molecular interval having taken place, the positive electricity thus produced unites with the negative electricity of the interval next to it in the direction of the current, while the negative electricity of the first interval unites with the positive electricity of the next interval in the other direction. Such interchanges, according to this hypothesis, constitute the electric current.
Ampere's memoir is, however, but little occupied with the more speculative side of the subject. His first aim was to investigate thoroughly by experiment the ponderomotive forces on electric currents.
" When," he remarks, " M. Oersted discovered the action which a current exercises on a magnet, one might certainly have suspected the existence of a mutual action between two circuits carrying currents ; but this was not a necessary consequence ; for a bar of soft iron also acts on a magnetized needle, although there is no mutual action between two bars of soft iron."
Ampere, therefore, submitted the matter to the test of the laboratory, and discovered that circuits carrying electric currents exert ponderomotive forces on each other, and that
* Recucil d' observations electro-dunamiques, pp. 297, 300, 371.
Galvanism, from Gaivani to Ohm. 89
ponderomotive forces are exerted on such currents by magnets. To the science which deals with the mutual action of currents he gave the name electro-dynamics ;* and he showed that the action obeys the following laws : —
(1) The effect of a current is reversed when the direction of the current is reversed.
(2) The effect of a current flowing in a circuit twisted into small sinuosities is the same as if the circuit were smoothed out.
(3) The force exerted by a closed, circuit on an element of another circuit is at right angles to the latter.
(4) The force between two elements of circuits is unaffected when all linear dimensions are increased proportionately, the current-strengths remaining unaltered.
From these data, together with his assumption that the force between two elements of circuits acts along the line joining them, Ampere obtained an expression of this force : the deduction may be made in the following way : —
Let ds, ds' be the elements, r the line joining them, and i, i' the current-strengths. From (2) we see that the effect of ds on ds' is the vector sum of the effects of dx, dy, dz on ds', where these are the three components of ds: so the required force must be of the form —
r x a scalar quantity which is linear and homogeneous in ds ; and it must similarly be linear and homogeneous in ds' ; so using (1), we see that the force must be of the form
F = ill | (ds . ds') 4> (r) + (ds . r) (ds'. r) i/, (r)} , where <£ and i// denote undetermined functions of r.
From (4) it follows that when ds, ds', r are all multiplied by the same number, F is unaffected : this shows that
4>(r) = - and f (r) = - ,
where A and B denote constants. Thus we have
, M(ds.ds') £(ds.r)(ds'. r))
F = n r \ + - — —- — ; •
( r3 r6 )
*. Loc. cit., p. 298.
90 Galvanism , from Galvani to Ohm.
Now, by (3), the resolved part of F along ds' must vanish when integrated round the circuit s, i.e. it must be a complete differential when dr is taken to be equal to - ds. That is to- say,
^(ds.ds')(r.ds') £(ds . r) (ds'. r)2
/o-»3 .f\>£
must be a complete differential ; or
must be a complete differential ; and therefore
7 A BiA
d'^ = --5(dS'r)>
3^ B J
or ~2^" dr = r*dT'
or B = - I A.
Thus finally we have
F = Constant x ii'i || (ds . ds') - -5 (ds . r)(ds'. r)
This is Ampere's formula : the multiplicative constant depends of course on the units chosen, and may be taken to be - 1.
The weakness of Ampere's work evidently lies in the assumption that the force is directed along the line joining the- two elements : for in the analogous case of the action between two magnetic molecules, we know that the force is not directed along the line joining the molecules. It is therefore of interest to find the form of F when this restriction is removed.
For this purpose we observe that we can add to the expression already found for F any term of the form
0(r) . (ds . r) . ds', where 0(r) denotes any arbitrary function of r ; for since
this term vanishes when integrated round the circuit s ; and it
Galvanism, from Galvani to Ohm. 91
contains ds and ds' linearly and homogeneously, as it should. We can also add any terms of the form
rf{r..(ds'.r).x(r)|,
where \(r] denotes any arbitrary function of r, and d denotes differentiation along the arc s, keeping ds' fixed (so that dr = - ds) ; this differential may be written
- ds . (ds'. r) . x(r) - rx(r) (ds'. ds) - * x'(r) r (ds . r) (ds'. r).
In order that the law of Action and Eeaction may not be violated, we must combine this with the former additional term so as to obtain an expression symmetrical in ds and ds' : and hence we see finally that the general value of F is given by the equation
F = -n'rjj|(ds.ds')-J(ds.r)(ds.r)j
+ x(»-; (ds' . r) ds + x(r) (ds . r) . ds' + x(r) (ds . ds')r
+ ix'(r)(ds.r)(ds'.r)r. The simplest form of this expression is obtained by taking
when we obtain
• •/ F = - {(ds . r) . ds' + (ds'. r)ds - (ds . ds')r} .
The comparatively simple expression in brackets is the vector part of the quaternion product of the three vectors ds, r, ds'.*
From any of these values of F we can find the ponderomotive force exerted by the whole circuit s on the element ds' : it is, in fact, from the last expression,
u'f1
[?-3((ds'.r).ds-(ds.ds>},
* The simpler form of F given in the text is, if the term in da' be omitted, the form given by Grassmann, Ann. d. Phys. Ixiv (1845), p. 1. For further work on this subject cf. Tait, Proc. R. S. Edin. viii (1873), p. 220, and Korteweg, Journal fiir Math, xc (1881), p. 45.
92 Galvanism, from Galvani to Ohm.
or i [ds'. B],
where B =
Now this value of B is precisely the value found by Biot and Savart* for the" magnetic intensity at ds' due to the- current i in the circuit s. Thus we see that the ponderomotive force on a current-element ds' in a magnetic field B is i' [ds'. B].
Ampere developed to a considerable extent the theory of the equivalence of magnets with circuits carrying currents; and showed that an electric current is equivalent, in its magnetic effects, to a distribution of magnetism on any surface terminated by the circuit, the axes of the magnetic molecules being everywhere normal to this surface :f such a magnetized surface is called a mayiwtic shell. He preferred, I however, to regard the current rather than the magnetic fluid as the fundamental entity, and considered magnetism to be really an electrical phenomenon : each magnetic molecule owes its properties, according to this view, to the presence within it / of a small closed circuit in which an electric current is perpetually flowing.
The impression produced by Ampere's memoir was great and lasting. Writing half a century afterwards, Maxwell speaks of it as " one of the most brilliant achievements in science." " The whole," he says, " theory and experiment, seems as if it had leaped, full-grown and full-armed, from the brain of the ' Newton of electricity/ It is perfect in form and unassailable in accuracy ; and it is summed up in a formula from which all the phenomena may be deduced, and which must always remain the cardinal formula of electrodynamics."
Not long after the discovery by Oersted of the connexion between galvanism and magnetism, a connexion was discovered between galvanism and heat.| In 1822 Thomas Johann Seebeck
* See ante, p. 86. t Loc. cit., p. 367.
Galvanism, from ^Galvani to Ohm. 93
(b. 1770, d. 1831), of Berlin discovered* that an electric current can be set up in a circuit of metals, without the interposition of any liquid, merely by disturbing the equilibrium of temperature. Let a ring be formed of copper and bismuth soldered together at the two extremities; to establish a current it is only necessary to heat the ring at one of these junctions. To this new class of circuits the name thermo- electric was given.
It was found that the metals can be arranged as a thermo-electric series, in the order of their power of generating currents when thus paired, and that this order is quite different from Volta's order of electromotive potency. Indeed antimony and bismuth, which are near each other in the latter series, are at opposite extremities of the former.
The currents generated by thermo-electric means are generally feeble : and the mention of this fact brings us to the question, which was about this time engaging attention, of the efficacy of different voltaic arrangements.
Comparisons of a rough kind had been instituted soon after the discovery of the pile. The French chemists Antoine FranQois de Fourcroy (b. 1755, d. 1809), Louis Mcolas Yauquelin (b. 1763, d. 1829), and Louis Jacques Thenard (b. 1777, d. 1857) foundf in 1801, on varying the size of the metallic disks constituting the pile, that the sensations produced on the human frame were unaffected so long as the number of disks remained the same; but that the power 'of burning finely drawn wire was altered; and that the latter power was proportional to the total surface of the disks employed, whether this were distributed among a small number of large disks, or a large number of small ones. This was
* Abhandl. d. Berlin Akad. 1822-3 ; Ann. d. Phys. Ixxiii (1823), pp. 115, 430 ; vi (1826), pp. 1, 133, 253.
Volta had previously noticed that a silver plate whose ends were at different temperatures appeared to act like a voltaic cell.
Further experiments were performed by James Gumming (£. 1777, d. 1861), Professor of Chemistry at Cambridge, Trans. Camb. Phil. Soc. ii (1823), p. 47, and by Antoine Cesar Becquerel (b. 1788, d. 1878), Annales de Chimie, xxxi (1826), p. 371. t Ann. de Chimie, xxxix (1801), p. 103.
94 Galvanism, from Galvani to Ohm.
explained by supposing that small plates give a small quantity of the electric fluid with a high velocity, while large plates give a larger quantity with no greater velocity. Shocks, which were supposed to depend on the velocity of the fluid alone, would therefore not be intensified by increasing the size of the plates.
The effect of varying the conductors which connect the terminals of the pile was also studied. Nicolas Grautherot (b. 1753, d. 1803) observed* that water contained in tubes which have a narrow opening does not conduct voltaic currents so well as when the opening is more considerable. This experi- ment is evidently very similar to that which Beccaria had performed half a century previously! with electrostatic discharges.
As we have already seen, Cavendish investigated very -completely the power of metals to conduct electrostatic discharges; their power of conducting voltaic currents was now examined by Davy.J His method was to connect the terminals of a voltaic battery by a path containing water (which it decomposed), and also by an alternative path consisting of the metallic wire under examination. When the length of the wire was less than a certain quantity, the water ceased to be decomposed ; Davy measured the lengths and weights of wires of different materials and cross-sections under these limiting circumstances ; and, by comparing them, showed that the conducting power of a wire formed of any one metal is inversely proportional to its length and directly proportional to its sectional area, but independent of the shape of the cross- section.! The latter fact, as he remarked, showed that voltaic currents pass through the substance of the conductor and not along its surface.
Davy, in the same memoir, compared the conductivities of various metals, and studied the effect of temperature : he found
* Annales de China., xxxix (1801), p. 203. t See p. 53.
% Phil. Trans., 1821, p. 433. His results were confirmed afterwards by Becquerel, Annales de Chiiuie, xxxii (1825), p. 423. 6 These results had been known to Cavendish.
Galvanism , from Galvani to Ohm. 95
that the conductivity varied with the temperature, being " lower in some inverse ratio as the temperature was higher."
He also observed that the same magnetic power is exhibited by every part of the same circuit, even though it be formed of wires of different conducting powers pieced into a chain, so that " the magnetism seems directly as the quantity of electricity which they transmit."
The current which flows in a given voltaic circuit evidently depends not only on the conductors which form the circuit, but also on the driving-power of the battery. In order to form a complete theory of voltaic circuits, it was therefore necessary to extend Davy's laws by taking the driving-power into account. This advance was effected in 1826 by Georg Simom Ohm* (b. 1787, d. 1854).
Ohm had already carried out a considerable amount of experimental work on the subject, and had, e.g., discovered that if a number of voltaic cells are placed in series in a circuit, the current is proportional to their number if the external resistance is very large, but is independent of their number if the external resistance is small. He now essayed the task of combining all the known results into a consistent theory.
For this purpose he adopted the idea of comparing the flow of electricity in a current to the flow of heat along a wire, the theory of which had been familiar to all physicists since the publication of Fourier's Theorie analytique de la chcdeur in 1822. " I have proceeded," he says, " from the supposition that the communication of the electricity from one particle takes place directly only to the one next to it, so that no immediate transition from that particle to any other situate at a greater distance occurs. The magnitude of the flow between two adjacent particles, under otherwise exactly similar circum- stances, I have assumed to be proportional to the difference of
*Ann. d. Phys. vi (1826), p. 459 ; vii, pp. 45,117; Die Galvanische Eette mathematisch bearbeitet : Berlin, 1827 ; translated in Taylor's Scientific Memoirs, ii (1841), p. 401. Cf. also subsequent papers by Ohm in Kastner's Archiv fur d. ges. Naturkhre, and Schweigger's Jahrbuch.
96 • Galvanism, from Galvani to Ohm.
the electric forces existing in the two particles ; just as, in the theory of heat, the flow of caloric between two particles is regarded as proportional to the difference of their temperatures."' '*' The comparison between the flow of electricity and the flow of heat suggested the propriety of introducing a quantity whose behaviour in electrical problems should resemble that of temperature in the theory of heat. The differences in the values of such a quantity at two points of a circuit would provide what was so much needed, namely, a measure of the "driving-power" acting on the electricity between these points. To carry out this idea, Ohm recurred to Volta's theory of the electrostatic condition of the open pile. It was cus- tomary to measure the " tension " of a pile by connecting one terminal to earth and testing the other terminal by an electroscope. Accordingly Ohm says : " In order to investigate the changes which occur in the electric condition of a body A in a perfectly definite manner, the body is each time brought, under similar circumstances, into relation with a second moveable body of invariable electrical condition, called the electroscope ; and the force with which the electroscope is repelled or attracted by the body is determined. This force is termed the electroscopic force of the body A"
" The same body A may also serve to determine the electro- scopic force in various parts of the same body. For this purpose take the body A of very small dimensions, so that when we bring it into contact with the part to be tested of any third body, it may from its smallness be regarded as a substitute for this part : then its electroscopic force, measured in the way described, will, when it happens to be different at the various places, make known the relative differences with regard to electricity between these places."
Ohm assumed, as was customary at that period, that when two metals are placed in contact, " they constantly maintain at the point of contact the same difference between their electro- scopic forces." He accordingly supposed that each voltaic cell possesses a definite tension, or discontinuity of electroscopic
Galvanism, from Galvani to Ohm. 97
force, which is to be regarded as its contribution to the driving- force of any circuit in which it may be placed. This assumption confers a definite meaning on his use of the term " electroscopic force " ; the force in question is identical with the electrostatic potential. But Ohm and his contemporaries did not correctly understand the relation of galvanic conceptions to the j electrostatic functions of Poisson. The electroscopic force in the open pile was generally identified with the thickness of the electrical stratum at the place tested ; while Ohm, recognizing that electric currents are not confined to the surface of the conductors, but penetrate their substance, seems to have thought of the electroscopic force at a place in a circuit as being proportional to the volume-density of electricity there — an idea in which he was confirmed by the relation which, in an analogous case, exists between the temperature of a body and the volume-density of heat supposed to be contained in it.
Denoting, then, by S the current which flows in a wire of conductivity y, when the difference of the electroscopic forces at the terminals is E, Ohm writes
S = yE.
From this formula it is easy to deduce the laws already given by Davy. Thus, if the area of the cross-section of a wire is Ay we can by placing n such wires side by side construct a wire of cross-section nA. If the quantity E is the same for each, equal currents will flow in the wires ; and therefore the current in the compound wire will be ?i times that in the single wire ; so when the quantity E is unchanged, the current is proportional to the cross-section; that is, the conductivity of a wire is directly proportional to its cross-section, which is one of Davy's laws.
In spite of the confusion which was attached to the idea of electroscopic force, and which was not dispelled for some years, the publication of Ohm's memoir marked a great advance in electrical philosophy. It was now clearly understood that the current flowing in any conductor depends only on the
H
98 Galvanism^ from Galvani to Ohm.
conductivity inherent in the conductor and on another variable which bears to electricity the same relation that temperature bears to heat ; and, moreover, it was realized that this latter variable is the link connecting the theory of currents with the older theory of electrostatics. These principles were a sufficient foundation for future progress; and much of the work which was published in the second quarter of the century was no more than the natural development of- the principles laid down by Ohm.*
It is painful to relate that the discoverer had long to wait before the merits of his great achievement were officially recognized. Twenty- two years after the publication of the memoir on the galvanic circuit, he was promoted to a university professorship ; this he held for the five years which remained until his death in 1854.
* Ohm's theory was confirmed experimentally by several investigators, among whom may be mentioned Gustav Theodor Feehner(i. 1801, d. 1887) (Maassbestim- mungen iiber die Galvanische Kette, Leipzig, 1831), and Charles Wheatstone (b. 1802, d. 1875) (Phil. Trans,, 1843, p. 303).
CHAPTER IV.
THE LUMINIFEROUS MEDIUM, FROM BRADLEY TO FRESNEL.
ALTHOUGH Newton, as we have seen, refrained from committing himself to any doctrine regarding the ultimate nature of light, the writers of the next generation interpreted his criticism of the wave-theory as equivalent to an acceptance of the corpuscular hypothesis. As it happened, the chief optical discovery of this period tended to support the latter theory, by which it was first and most readily explained. In 1728 James Bradley (b. 1692, d. 1762), at that time Savilian Professor of Astronomy at Oxford, sent to the Astronomer Royal (Halley) an " Account of a new discovered motion of the Fix'd Stars."* In observing the star y in the head of the Dragon, he had found that during the winter of 1725-6 the transit across the meridian was continually more southerly, while during the following summer its original position was restored by a motion northwards. Such an effect could not be explained as a result of parallax ; and eventually Bradley guessed it to be due to the gradual propagation of light.f
Thus, let CA denote a ray of light, falling on the line BA ; and suppose that the eye of the observer is travelling ^ along BA, with a velocity which is to the velocity of light as BA is to CA. Then the corpuscle of light, by which the object is discernible to the eye at A, would have been at C when the eye was at B. The tube of a telescope must therefore be pointed in the direction BC, in order to receive the rays from an object whose light is really propagated in the direction CA. The angle BCA measures the difference between the real and apparent positions »
of the object ; and it is evident from the figure that the sine of
•Phil. Trans, xxxv (1728), p. 637.
t Roemer, in a letter to Huygens of date 30th Dec., 1677, mentions a suspected displacement of the apparent position of a star, due to the motion of the earth at right angles to the line of sight. Cf . Correspondance de Huygens, viii, p. 53.
H 2
100 The Lumini/erous Medium,
this angle is to the sine of the visible inclination of the object to the line in which the eye is moving, as the velocity of the eye is to the velocity of light. Observations such as Bradley's will therefore enable us to deduce the ratio of the mean orbital velocity of the earth to the velocity of light, or, as it is called,. the constant of 'aberration ; from its value Bradley calculated that light is propagated from the sun to the earth in 8 minutes 12 seconds, which, as he remarked, "is as it were a Mean betwixt what had at different times been determined from the eclipses of Jupiter's satellites."*
With the exception of Bradley's discovery, which was primarily astronomical rather than optical, the eighteenth century was decidedly barren, as regards both the experimental and the theoretical investigation of light ; in curious contrast to the brilliance of its record in respect of electrical researches. But some attention must be given to a suggestive study f of the aether, for which the younger John Bernoulli (b. 1710, d. 1790) was in 1736 awarded the prize of the French Academy. His ideas seem to have been originally suggested by an attempt};
*Struve in 1845 found for the constant of aberration the value 20"'445, which lie afterwards corrected to 20"'463. This was superseded in 1883 by the value 20"-492, determined by M. Nyren. The observations of both Struve and Nyren were made with the transit in the prime vertical. The method now generally used depends on the measurement of differences of meridian zenith distances (Talcott's method, as applied by F. Kiistner, Beobachtungs-Ergebnisse der kon. Stern warte zu Berlin, Heft 3, 1888) ; the value at present favoured for the constant of aberration is 20"-523. Cf. Chandler, Ast. Journal, xxiii, pp. 1, 12 (1903).
The collective translatory motion of the solar system gives rise to aberrational: terms in the apparent places of the fixed stars ; but the principal term of this character does not vary with the time, and consequently is equivalent to a permanent constant displacement. The second-order terms (i.e. those which involve the ordinary constant of aberration multiplied by the sun's velocity) might be measurable quantities in the case of stars near the Pole ; and the same is true of the variations in the first-order terms (i.e. those which involve the sun's velocity not multiplied by the constant of aberration) due to the circumstance that the star's apparent R. A. and Declination, which occur in these terms, are not constant, but are affected by Precession, Nutation, and Aberration. Cf. Seeliger, Ast. Nach., cix., p. 273 (1884).
t Printed in 1752, in the Recueil des pieces qui ont remportes les prix de V Acad.y. tome iii. J Acta eniditorum, MDCCI, p. 19.
from Bradky to Fresnel. 101
which his father, the elder John Bernoulli (b. 1667, d. 1748), had made in 1701 to connect the law of refraction with the mechanical principle of the composition of forces. If two opposed forces whose ratio is ju maintain in equilibrium a particle which is free to move only in a given plane, it follows from the triangle of forces that the directions of the forces must obey the relation
sin i = fj. sin r,
where i and r denote the angles made by these directions with the normals to the plane. This is the same equation as that which expresses the law of refraction, and the elder Bernoulli conjectured that a theory of light might be based on it ; but he gave no satisfactory physical reason for the existence of forces along the incident and refracted rays. This defect his son now proceeded to remove.
All space, according to the younger Bernoulli, is permeated by a fluid aether, containing an immense number of excessively small whirlpools. The elasticity which the aether appears to possess, and in virtue of which it is able to transmit vibrations, is really due to the presence of these whirlpools ; for, owing to -centrifugal force, each whirlpool is continually striving to dilate, and so presses against the neighbouring whirlpools. It will be seen that Bernoulli is a thorough Cartesian in spirit ; not only does he reject action at a distance, but he insists that •even the elasticity of his aether shall be explicable in terms of matter and motion.
This aggregate of small vortices, or " fine-grained turbulent motion," as it came to be called a century and a half later,* is interspersed with solid corpuscles, whose dimensions are small -compared with their distances apart. These are pushed about by the whirlpools whenever the aether is disturbed, but never travel far from their original positions.
A source of light communicates to its surroundings a disturbance which condenses the nearest whirlpools ; these by
* Cf . Lord Kelvin's vortex-sponge aether, described later in this work.
102 The Luminiferous Medium i
their condensation displace the contiguous corpuscles from their equilibrium position ; and these in turn produce condensations in the whirlpools next beyond them, so that vibrations are propagated in every direction from the luminous point. It is curious that Bernoulli speaks of these vibrations as longitudinal, and actually contrasts them with those of a stretched cord, which, " when it is slightly displaced from its rectilinear form, and then let go, performs transverse vibrations in a direction at right angles to the direction of the cord." When it is remembered that the objection to longitudinal vibrations, on the score of polarization, had already been clearly stated by Newton, and that Bernoulli's aether closely resembles that which Maxwell invented in 1861-2 for the express purpose of securing transversality of vibration, one feels that perhaps no man ever so narrowly missed a great discovery.
Bernoulli explained refraction by combining these ideas with those of his father. Within the pores of ponderable bodies the whirlpools are compressed, so the centrifugal force must vary in intensity from one medium to another. Thus a corpuscle situated in the interface between two media is acted on by a greater elastic force from one medium than from the other; and by applying the triangle of forces to find the- conditions of its equilibrium, the law of Snell and Descartes
r may be obtained.
Not long after this, the echoes of the old controversy
' between Descartes and Fermat about the law of refraction were awakened* by Pierre Louis Moreau deMaupertuis (b. 1698,, d. 1759).
It will be remembered that according to Descartes the velocity of light is greatest in dense media, while according to- Fermat the propagation is swiftest in free aether. The argu- ments of the corpuscular theory convinced Maupertuis that on this particular point Descartes was in the right ; but never- theless he wished to retain for science the beautiful method by which Fermat had derived his result. This he now proposed
*Mem. de 1'Acad., 1744, p. 417.
from Bradley to Fresnel. 103
to do by modifying Fermat's principle so as to make it agree with the corpuscular theory; instead of assuming that light follows the quickest path, he supposed that " the path described is that by which the quantity of action is the least " ; and this action he defined to be proportional to the sum of the spaces described, each multiplied by the velocity with which it is traversed. Thus instead of Fermat's expression
dt or
tds
} v
(where t denotes time, v velocity, and ds an element of the path) Maupertuis introduced
/v ds
as the quantity which is to assume its minimum value when the path of integration is the actual path of the light. Since Maupertuis' v, which denotes the velocity according to the corpuscular theory, is proportional to the reciprocal of Fermat's v, which denotes the velocity according to the wave- theory, the two expressions are really equivalent, and lead to the same law of refraction. Maupertuis' memoir is, however, of great interest from the point of view of dynamics ; for his suggestion was subsequently developed by himself and by Euler and Lagrange into a general principle which covers the whole range of Nature, so far as Nature is a dynamical system.
The natural philosophers of the eighteenth century for the most part, like Maupertuis, accepted the corpuscular hypothesis ; 'but the wave-theory was not without defenders. Franklin* declared for it ; and the celebrated mathematician Leonhard Euler (b. 1707, d. 1783) ranged himself on the same side. In a work entitled Nova Theoria Lucis et Colorum, published! while he was living under the patronage of Frederic the Great at Berlin, he insisted strongly on the resemblance between light and sound ; " light is in the aether the same thing as sound in air/' Accepting Newton's doctrine that colour depends on
* Letter xxiii, written in 1752.
tL. Euleri Opuscula varii argumenti, Berlin, 1746, p. 169.
104 The Luminiferous Medium ,
wave-length, he in this memoir supposed the frequency greatest for red light, and least for violet ; but a few years later* he adopted the opposite opinion.
The chief novelty of Euler's writings on light is his explanation of the manner in which material bodies appear coloured when viewed by white light ; and, in particular, of the way in which the colours of thin plates are produced. He denied that such colours are due to a more copious reflexion of light of certain particular periods, and supposed that they represent vibrations generated within the body itself under the stimulus of the incident light. A coloured surface, according to this hypothesis, contains large numbers of elastic molecules, which, when agitated, emit light of period depending only on their own structure. The colours of thin plates Euler explained in the same way ; the elastic response and free period of the plate at any place would, he conceived, depend on its thickness at that place ; and in this way the dependence of the colour on the thickness was accounted for, the phenomena as a whole being analogous to well-known effects observed in experiments on sound.
An attempt to improve the corpuscular theory in another direction was made in 1752 by the Marquis de Courtivron,f and independently in the following year by T. Melville These writers suggested, as an explanation of the different refran- gibility of different colours, that " the differently colour'd rays are projected with different velocities from the luminous body : the red with the greatest, violet with the least, and the inter- mediate colours with intermediate degrees of velocity." On this supposition, as its authors pointed out, the amount of aberration would be different for every different colour ; and the satellites of Jupiter would change colour, from white through green to violet, through an interval of more than half a minute before their immersion into the planet's shadow ; while at emersion the contrary succession of colours should be observed,
* Mem. del' Acad.de Berlin, 1752, p. 262. t Courtivron's Traite cfoptique, 1752. JPhil. Trans, xlviii (1753), p. 262.
from Bradley to FremeL 105
beginning with red and ending in white. The testimony of practical astronomers was soon given that such appearances are not observed ; and the hypothesis was accordingly abandoned.
The fortunes of the wave-theory began to brighten at the end of the century, when a new champion arose. Thomas Young, born at Milverton in Somersetshire in 1773, and trained to the practice of medicine, began to write on optical theory in 1799. In his first paper* he remarked that, according'1 to the corpuscular theory, the velocity of emission of a corpuscle must be the same in all cases, whether the projecting force be that of the feeble spark produced by the friction of two Q pebbles, or the intense heat of the sun itself — a thing almost incredible. This difficulty does not exist in the undulatory theory, since all disturbances are known to be transmitted^ through an elastic fluid with the same velocity. The reluctance which some philosophers felt to filling all space with an elastic fluid he met with an argument which strangely foreshadows the electric theory of light : " That a medium resembling in many properties that which has been denominated ether does really exist, is undeniably proved by the phenomena of electricity. The rapid transmission of the electrical shock shows that the electric medium is possessed of an elasticity as great as is necessary to be supposed for the propagation of light. Whether the electric ether is to be considered the same with the luminous ether, if such a fluid exists, may perhaps at some future time be discovered by experiment : hitherto I have not been able to observe that the refractive power of a fluid undergoes any change by electricity."
Young then proceeds to show the superior power of the^ wave-theory to explain reflexion and refraction. In the corpuscular theory it is difficult to see why part of the light should be reflected and another part of the same beam reflected ; but in the undulatory theory there is no trouble, as is shown by analogy with the partial reflexion of sound from a cloud or _, denser stratum of air : " Nothing more is necessary than to
* Phil. Tni™., 1800, p. 106.
106 The JLuminiferous Medium,
suppose all refracting media to retain, by their attraction, a, greater or less quantity of the luminous ether, so as to make its- density greater than that which it possesses in a vacuum, without increasing its elasticity." This is precisely the hypothesis adopted later by Fresnel and Green.
In 1801 Young made a discovery of the first magnitude* when attempting to explain Newton's rings on the principles of the wave-theory. Eejecting Euler's hypothesis of induced vibrations, he assumed that the colours observed all exist in the incident light, and showed that they could be derived from it by a process which was now for the first time recognized in optical science.
The idea of this process was not altogether new, for it had been used by Newton in his theory of the tides. " It may happen," he wrote, f " that the tide may be propagated from the ocean through different channels towards the same port, and may pass in less time through some channels than through others, in which case the same generating tide, being thus divided into two or more succeeding one another, may produce by composition new types of tide." Newton applied this- principle to explain the anomalous tides at Batsha in Tonkin, which had previously been described by Halley.J
Young's own illustration of the principle is evidently suggested by Newton's. " Suppose," he says,§ " a number of equal waves of water to move upon the surface of a stagnant lake, with a certain constant velocity, and to enter a narrow channel leading out of the lake ; suppose then another similar cause to have excited another equal series of waves, which arrive at the same channel, with the same velocity, and at the same time with the first. Neither series of waves will destroy the other, but their effects will be combined ; if they enter the channel in such a manner that the elevations of one series coincide with those of the other, they must together produce a series of greater joint elevations ; but if the elevations of one
* Phil. Trans., 1802, pp. 12, 387. t Principia, Book in, Prop. 24.
% Phil. Trans, xiv (1684), p. 681. § Young's Works, i, p. 202.
from Bradley to Fremel. 107
series are so situated as to correspond to the depressions of the other, they must exactly fill up those depressions, and the surface of the water must remain smooth. Now I maintain that similar effects take place whenever two portions of light are thus mixed ; and this I call the general law of the interference of light."
Thus, " whenever two portions of the same light arrive to the eye by different routes, either exactly or very nearly in the same direction, the light becomes most intense when the difference of the routes is any multiple of a certain length, and least intense in the intermediate state of the interfering portions ; and this length is different for light of different colours."
Young's explanation of the colours of thin plates as seen by reflexion was, then, that the incident light gives rise to two beams which reach the eye : one of these beams has been reflected at the first surface of the plate, and the other at the second surface ; and these two beams produce the colours by their interference.
One difficulty encountered in reconciling this theory with observation arose from the fact that the central spot in Newton's rings (where the thickness of the thin Him of air is zero) is black and not white, as it would be if the interfering beams were similar to each other in all respects. To account for this Young ' showed, by analogy with the impact of elastic bodies, that when -> light is reflected at the surface of a denser medium, its phase is retarded by half an undulation : so that the interfering beams at the centre of Newton's rings destroy each other. The correctness of this assumption he verified by substituting essence of sassafras (whose refractive index is intermediate between those of crown and flint glass) for air in the space between the lenses ; as he anticipated, the centre of the ring-system was now white.
Newton had long before observed that the rings are smaller ~* when the medium producing them is optically more dense. Interpreted by Young's theory, this definitely proved that the wave-length of light is shorter in dense media, and therefore ^ that its velocity is less.
108 The Lumini/erous Medium,
The publication of Young's papers occasioned a fierce attack on him in the Edinburgh Review, from the pen of Henry Brougham, afterwards Lord Chancellor of England. Young replied in a pamphlet, of which it is said* that only a single copy was sold ; and there can be no doubt that Brougham for the time being achieved his object of discrediting the wave- theory, f
Young now turned his attention to the fringes of shadows. In the corpuscular explanation of these, it was supposed that the attractive forces which operate in refraction extend their influence to some distance from the surfaces of bodies, and inflect such rays as pass close by. If this were the case, the amount of inflexion should obviously depend on the strength of the attractive forces, and consequently on the refractive indices of the bodies — a proposition which had been refuted by the experiments of s'Gravesande. The cause of diffraction effects was thus wholly unknown, until Young, in the Bakerian lecture for 1803,J showed that the principle of interference is concerned in their formation ; for when a hair is placed in the cone of rays diverging from a luminous point, the internal fringes (i.e. those within the geometrical shadow) disappear when the light passing on one side of the hair is intercepted. His conjecture as to the origin of the interfering rays was not so fortunate ; for he attri- buted the fringes outside the geometrical shadow to interference between the direct rays and rays reflected at the diffracting edge ; and supposed the internal fringes of the shadow of a narrow object to be due to the interference of rays inflected by the two edges of the object.
The success of so many developments of the wave-theory led Young to inquire more closely into its capacity for solving the chief outstanding problem of optics — that of the behaviour of light in crystals. The beautiful construction for the extra-
* Peacock's Life of Young.
t" Strange fellow," wrote Macaulay, when half a century afterwards he found himself sitting beside Brougham in the House of Lords, " his powers gone : his spite immortal."
I Phil. Trans., 1804; Young's Works, i, p. 179.
from Bradley ( to FresneL 109
ordinary ray given by Huygens had lain neglected for a century ; and the degree of accuracy with which it represented the observations was unknown. At Young's suggestion Wollaston* investigated the matter experimentally, and showed that the agreement between his own measurements and Huygens' rule was remarkably close. " I think," he wrote, " the result must be admitted to be highly favourable to the Huygeniaii theory ; and, although the existence of two refractions at the same time, in the same substance, be not well accounted for, and still less their interchange with each other, when a ray of light is made to pass through a second piece of spar situated transversely to the first, yet the oblique refraction, when considered alone, seems nearly as well explained as any other optical phenomenon."
Meanwhile the advocates of the corpuscular theory were not idle ; and in the next few years a succession of discoveries on their part, both theoretical and experimental, seemed likely to imperil the good position to which Young had advanced the rival hypothesis.
The first of these was a dynamical explanation of the refraction of the extraordinary ray in crystals, which was published in 1808 by Laplace.f His method is an extension of that by which Maupertuis had accounted for the refraction of the ordinary ray, and which since Maupertuis' day had been so developed that it was now possible to apply it to problems of all degrees of complexity. Laplace assumes that the crystalline medium acts on the light-corpuscles of the extraordinary ray so as to modify their velocity, in a ratio which depends on the inclination of the extraordinary ray to the axis of the crystal : so that, in fact, the difference of the squares of the velocities of the ordinary and extraordinary rays is proportional to the square of the sine of the angle which the latter ray makes with the axis. The principle of least action then leads to a law of refraction identical with that found by Huygens' construction
* Phil. Trans., 1802, p. 381.
tMem. de PInst., 1809, p. 300: Journal de Physique, Jan., 1809; Mem. de la Soc. d'Arcueil, ii.
110 The Luminiferous Medium,
with the spheroid ; just as Maupertuis' investigation led to a law of refraction for the ordinary ray identical with that found by Huygens' construction with the sphere.
The law of refraction for the extraordinary ray may also be deduced from Fermat's principle of least time, provided that the velocity is taken inversely proportional to that assumed in the principle of least action ; and the velocity appropriate to Fermat's principle agrees with that found by Huygens, being, in iact, proportional to the radius of the spheroid. These results are obvious extensions of those already obtained for ordinary refraction.
Laplace's theory was promptly attacked by Young,* who pointed out the improbability of such a system of forces as would be required to impress the requisite change of velocity on the light-corpuscles. If the aim of controversial matter is to convince the contemporary world, Young's paper must be counted unsuccessful ; but it permanently enriched science by proposing a dynamical foundation for double refraction on the principles of the wave-theory. " A solution," he says, " might •be deduced upon the Huygenian principles, from the simplest possible supposition, that of a medium more easily compressible in one direction than in any direction perpendicular to it, as if it consisted of an infinite number of parallel plates connected by a substance somewhat less elastic. Such a structure of the elementary atoms of the crystal may be understood by compar- ing them to a block of wood or of mica. Mr. Chladni found that the mere obliquity of the fibres of a rod of Scotch fir reduced the velocity with which it transmitted sound in the proportion of 4 to 5. It is therefore obvious that a block of such wood -must transmit every impulse in spheroidal — that is, oval — undulations ;• and it may also be demonstrated, as we shall show at the conclusion of this article, that the spheroid will be truly elliptical when the body consists either of plane and parallel strata, or of equidistant fibres, supposing both to be ^extremely thin, and to be connected by a less highly elastic
* Quarterly Eeview, Nov., 1809 ; Young's Works, i, p. 220.
from Bradley to FremeL 111
substance ; the spheroid being in the former case oblate and in the latter oblong." Young then proceeds to a formal proof that "an impulse is propagated through every perpendicular section of a lamellar elastic substance in the form of an elliptic undulation." This must be regarded as the beginning of the dynamical theory of light in crystals. It was confirmed in a striking way not long afterwards by Brewster,* who found that compression in one direction causes an isotropic transparent solid to become doubly-refracting.
Meanwhile, in January, 1808, the French Academy had proposed as the subject for the physical prize in 1810, " To furnish a mathematical theory of double refraction, and to confirm it by experiment." Among those who resolved to compete was Etienne Louis Malus (b. 1775, d. 1812), a colonel of engineers who had seen service with Napoleon's expedition to Egypt. While conducting experiments towards the end of 1808 in a house in the Kue des Enfers in Paris, Malus happened to analyse with a rhomb of Iceland spar the light of the setting sun reflected from the window of the Luxembourg, and was surprised to notice that the two images were of very different intensities. Following up this observation, he found that light which had been reflected from glass acquires thereby a modifi- cation similar to that which Huygens had noticed in rays which have experienced double refraction, and which Newton had explained by supposing rays of light to have " sides." This discovery appeared so important that without waiting for the prize competition he communicated it to the Academy in December, 1808, and published it in the following month.f " I have found," he said, " that this singular disposition, which has hitherto been regarded as one of the peculiar effects of double refraction, can be completely impressed on the luminous molecules by all transparent solids and liquids." " For example, light reflected by the surface of water at an
* Phil. Trans., 1815, p. 60.
tNouveau Bulletin des Sciences, par la Soc. Philomatique. i (1809), p. 266; Memoires de la Soc. d'Arcueil, ii (1809).
112 The Luminiferous Medium,
angle of 52°45' has all the characteristics of one of the beams produced by the double refraction of Iceland spar, whose principal section is parallel to the plane which passes through the incident ray and the reflected ray. If we receive this reflected ray on any doubly- refracting crystal, whose principal section is parallel to the plane of reflexion, it will not be divided into two beams as a ray of ordinary light would be, but will be refracted according to the ordinary law."
After this Malus found that light which has been refracted at the surface of any transparent substance likewise possesses in some degree this property, to which he gave the name polarization. The memoir* which he finally submitted to the Academy, and which contains a rich store of experimental and analytical work on double refraction, obtained the prize in 1810 ; its immediate effect as regards the rival theories of the ultimate nature of light was to encourage the adherents of the corpuscular doctrine ; for it brought into greater prominence the phenomena of polarization, of which the wave-theorists, still misled by the analogy of light with sound, were unable to give any account.
The successful discoverer was elected to the Academy of Sciences, and became a member of the celebrated club of Arcueil.f But his health, which had been undermined by the Egyptian campaign, now broke down completely : and he died, at the age of thirty-six, in the following year.
The polarization of a reflected ray is in general incomplete — i.e. the ray displays only imperfectly the properties of light which has been polarized by double refraction ; but for one particular angle of incidence, which depends on the reflecting body, the polarization of the reflected ray is complete. Malus measured with considerable accuracy the polarizing angles for glass and water, and attempted to connect them with the other optical constants of these substances, the refractive indices and dispersive powers, but without success. The matter was
* Mem. presentes a 1'Inst. par divers Savans, ii (1811), p. 303.
t So called from the village near Paris where Laplace and Berthollet had their country-houses, and where the meetings took place. The club consisted of a dozen of the most celebrated scientific men in France.
from Bradley to Fresnel. 113
afterwards taken up by David Brewster (b. 1781, d. 1868), who in 1815* showed that there is complete polarization by reflexion when the reflected and refracted rays satisfy the condition of being at right angles to each other.
Almost at the same time Brewster made another discovery which profoundly affected the theory of double refraction. It had till then been believed that double refraction is always of the type occurring in Iceland spar, to which Huygens' construction is applicable. Brewster now found this belief to be erroneous, and showed that in a large class of crystals there are two axes, instead of one, along which there is no double refraction. Such crystals are called Uaxal, the simpler type to which Iceland spar belongs being called uniaxal.
The wave-theory at this time was still encumbered with difficulties. Diffraction was not satisfactorily explained ; for polarization no explanation of any kind was forthcoming ; the Huygenian construction appeared to require two different luminiferous media within doubly refracting bodies ; and the universality of that construction had been impugned by Brewster's discovery of biaxal crystals.
The upholders of the emission theory, emboldened by the success of Laplace's theory of double refraction, thought the time ripe for their final triumph ; and as a step to this, in March, 1817, they proposed Diffraction as the subject of the Academy's prize for 1818. Their expectation was disappointed ; and the successful memoir afforded the first of a series of reverses by which, in the short space of seven years, the corpuscular theory was completely overthrown.
The author was Augustin Fresnel (b. 1788, d. 1827), the son of an architect, and himself a civil engineer in the Government service in Normandy. During the brief dominance of Napoleon after his escape from Elba in 1815, Fresnel fell into trouble for having enlisted in the small army which attempted to bar the exile's return ; and it was during a period of enforced idleness following on his arrest that he commenced to study
•Phil. Trans., 1815, p. 125. I
114 The Lumini/erous Medium,
diffraction. In his earliest memoir* he propounded a theory similar to that of Young, which was spoiled like Young's theory by the assumption that the fringes depend on light reflected by the diffracting edge. Observing, however, that the blunt and sharp edges of a knife produce exactly the same fringes, he became dissatisfied with this attempt, and on July 15th, 1816, presented to the Academy a supplement to his paper,f in which, for the first time, diffraction-effects are referred to their true cause — namely, the mutual interference of the secondary waves emitted by those portions of the original wave-front which have not been obstructed by the diffracting screen. Fresnel's method of calculation utilized the principles of both Huygens and Young ; he summed the effects due to different portions of the same primary wave-front, with due regard to the differences of phase engendered in propagation.
The sketch presented to the Academy in 1816 was during the next two years developed into an exhaustive memoir, J which was submitted for the Academy's prize.
It so happened that the earliest memoir, which had been presented to the Academy in the autumn of 1815, had been referred to a Commission of which the reporter was Francois Arago (&. 1786, d. 1853) ; Arago was so much impressed that he sought the friendship of the author, of whom he was later a strenuous champion.
A champion was indeed needed when the larger memoir was submitted ; for Laplace, Poisson, and Biot, who constituted a majority of the Commission to which it was referred, were all zealous supporters of the corpuscular theory. During the examination, however, Fresnel was vindicated in a somewhat curious way. He had calculated in the memoir the diffraction- patterns of a straight edge, of a narrow opaque body bounded by parallel sides, and of a narrow opening bounded by parallel edges, and had shown that the results agreed excellently with
* Annales de Chimie (2), i (1816), p 239 ; (Euvres, i, p. 89.
t (Euvres, i, p. 129.
I Mem. de 1'Acad., v (1826), p. 339 ; (Euvres, i, p. 247.
from Bradley to FresneL 115
his experimental measures. Poisson, when reading the manu- script, happened to notice that the analysis could be extended to other cases, and in particular that it would indicate the existence of a bright spot at the centre of the shadow of a circular screen. He suggested to Fresnel that this and some further consequences should be tested experimentally ; this was done, and the results were found to confirm the new theory. The concordance of observation and calculation was so admirable in all cases where a comparison was possible that the prize was awarded to Fresnel without further hesitation.
In the same year in which the memoir on diffraction was submitted, Fresnel published an investigation* of the influence of the earth's motion on light. We have already seen that aberration was explained by its discoverer in terms of the corpuscular theory ; and it was Young who first showedf how it may be explained on the wave-hypothesis. " Upon con- sidering the phenomena of the aberration of the stars," he wrote, " I am disposed to believe that the luminiferous aether pervades the substance of all material bodies with little or no resistance, as freely perhaps as the wind passes through a grove of trees." In fact, if we suppose the aether surrounding the earth to be at rest and unaffected by the earth's motion, the light- waves will not partake of the motion of the telescope , which we may suppose directed to the true place of the star, and the image of the star will therefore be displaced from the central spider-line at the focus by a distance equal to that which the earth describes while the light is travelling through the telescope. This agrees with what is actually observed.
But a host of further questions now suggest themselves. Suppose, for instance, that a slab of glass with a plane face is carried along by the motion of the earth, and it is desired to adjust it so that a ray of light coming from a certain star shall not be bent when it enters the glass : must the .surface be placed at right angles to the true direction of the
* Annales de Chimie, ix, p. 57 (1818) ; CEnvres, ii, p. 627. t Phil. Trans., 1804, p. 12; Young's Works, i, p. 188. I 2
116 The L uminiferous Medium,
star as freed from aberration, or to its apparent direction as affected by aberration ? The question whether rays coming from the stars are refracted differently from rays origi- nating in terrestrial sources had been raised originally by Michell* ; and Kobison and Wilsonf had asserted that the focal length of an achromatic telescope should be increased when it is directed to a star towards which the earth is moving, owing to the change in the relative velocity of light. AragoJ sub- mitted the matter to the test of experiment, and concluded that the light coming from any star behaves in all cases of reflexion and refraction precisely as it would if the star were situated in the place which it appears to occupy in consequence of aber- ration, and the earth were at rest ; so that the apparent refraction in a moving prism is equal to the absolute refraction in a fixed prism.
Fresnel now set out to provide a theory capable of explaining Arago's result. To this end he adopted Young's suggestion, that the refractive powers of transparent bodies depend on the concentration of aether within them ; and made it more precise by assuming that the aethereal density in any body is pro- portional to the square of the refractive index. Thus, if c denote the velocity of light in vacuo, and if c, denote its velocity in a given material body at rest, so that /u = c/o{ is the refractive index, then the densities p and pl of the aether in interplanetary space and in the body respectively will be connected by the relation
pi = n*P-
Fresnel further assumed that, when a body is in motion, part of the aether within it is carried along — namely, that part which constitutes tne excess of its density over the density of aether in vacuo ; while the rest of the aether within the space occupied by the body is stationary. Thus the density of aether carried
* Phil. Trans., 1784, p. 35.
t Trans. E. S. Edin., i, Hist., p. 30.
J Biot, Astron. Phys., 3rd ed., v, p. 364. The accuracy of Arago's experiment can scarcely have been such as to demonstrate absolutely his result.
ft,
from Bradley to FresneL 117
along is (pi - p) or (^ - l)/o, while a quantity of aether of density p remains at rest. The velocity with which the centre of gravity of the aether within the body moves forward in the direction of propagation is therefore
where w denotes the component of the velocity of the body in this direction. This is to be added to the velocity of propaga- tion of the light- waves within the body ; so that in the moving body the absolute velocity of light is
Many years afterwards Stokes* put the same supposition in a slightly different form. Suppose the whole of the aether within the body to move together, the aether entering the body in front, and being immediately condensed, and issuing from it behind, where it is immediately rarefied. On this assumption a mass pw of aether must pass in unit time across a plane of area unity, drawn anywhere within the body in a direction at right angles to the body's motion; and therefore the aether within the body has a drift- velocity - wp/pl relative to the body : so the velocity of light relative to the body will be Ci - wplp\, and the absolute velocity of light in the moving body will be
v*
v* k
or ci + £^i w, as before.
P
This formula was experimentally confirmed in 1851 by H. Fizeau,f who measured the displacement of interference- fringes formed by light which had passed through a column of moving water.
* Phil. Mag. xxviii (1846) p. 76.
t Annales de Chimie, Ivii (1859), p. 385. Also by A. A. Michelson and E. W. Morley, Am. Journ. Science, xxxi (1886), p. 377.
118 The Luminiferous Medium,
The same result may easily be deduced from an experiment performed by Hoek.* In this a beam of light was divided into two portions, one of which was made to pass through a tube of water AB and was then reflected at a mirror C, the light being afterwards allowed to return to A without passing through the water : while the other portion of the bifurcated beam was made to describe the same path in the reverse order, i.e. passing through the water on its return
,. journey from C instead of on the outward journey,
On causing the two portions of the beam to inter- fere, Hoek found that no difference of phase was produced between them when the apparatus was oriented in the direction of the terrestrial motion.
Let w denote the velocity of the earth, supposed to be directed from the tube towards the mirror. Let c/n denote the velocity of light in the water at rest, and C/A* + <l> the velocity of light in the water when moving. Let I denote the length of the tube. The magnitude of the distance BC does not affect the experiment, so we may suppose it zero.
The time taken by the first portion of the beam to perform its journey is evidently
If i
C/fi + ^ — W C + W '
while the time for the second portion of the beam is I I
+ —.
C - W C/fJL - 0 + W
The equality of these expressions gives at once, when terms of higher orders than the first in w/c are neglected,
0 = Ou2 - 1) w\^\ which is FresneFs expression.!
* Archives Neerl. iii, 180 (1868).
t Fresnel's law may also be deduced from the principle that the amount of light transmitted by a slab of transparent matter must be the same whether the slab is at rest or in motion : otherwise the equilibrium of exchanges of radiation would be tiated. Cf. Larmor, Phil. Trans, clxxxv (1893), p, 775.
from Bradley to Fresnel.
119
On the basis of this formula, Fresnel proceeded to solve the problem of refraction in moving bodies. Suppose that a prism AQ (70 B0 is carried along by the earth's motion in vacuo, its face A(, C0 being at right angles to the direction of motion ; and
that light from a star is incident normally on this face. The rays experience no refraction at incidence ; and we have only to consider the effect produced by the second surface A<>I>0. Sup- pose that during an interval T of time the prism travels from the position AQ C0 Bo to the position A± Ci B^ while the luminous disturbance at C0 travels to £h and the luminous disturbance at A0 travels to D, so that Bv D is the emergent wave-front. Then we have
-1
10
A0D
TC,
If we write CiA\B\ = i, and denote the total deviation of the wave-front by 81, we have
AiD = AJ) - A±AQ cos Si = TC - rw cos 81,
TIC,
120 The Lumniiferous Medium,
and therefore (neglecting second-order terms in w/c]
A
sin A^B^D c - w cos 81 _ c w w ^
-— — • : ~ — ~ — "f- — •*" COo Ol«
sin ^ Ci ct c Ci
Ct-W-
Denoting by 8 the value of 81 when w is zero, we have
sin (i -8) c sin i d
Subtracting this equation from the preceding, we have
8 -Si _ w sin § c
Now the telescope by which the emergent wave-front B\ D is received is itself being carried forward by the earth's motion; and we must therefore apply the usual correction for aberration in order to find the apparent direction of the emergent ray. But this correction is w sin 8/c, and precisely counteracts the effect which has been calculated as due to the motion of the prism. So finally we see that the motion of the earth has no first-order influence on the refraction of light from the stars.
Fresnel inferred from his formula that if observations were made with a telescope filled with water, the aberration would be unaffected by the presence of the water — a result which was verified by Airy* in 1871. He showed, moreover, that the apparent positions of terrestrial objects, carried along with the observer, are not displaced by the earth's motion ; that experi- ments in refraction and interference are not influenced by any motion which is common to the source, apparatus, and observer ; and that light travels between given points of a moving material system by the path of least time. These predictions have also been confirmed by observation: Kespighif in 1861, and Hoek+ in 1868, experimenting with a telescope filled with water and a terrestrial source of light, found that no effect was produced on the phenomena of reflexion and refraction by altering the orienta-
* Proc. Roy. Soc., xx, p. 35. t Mem. Accad. Sci. Bologna, ii, p. 279.
I Ast. Nach., Ixxiii, p. 193.
from Bradtey to Fresnel. 121
tion of the apparatus relative to the direction of the earth's motion. E. Mascart* in 1872 discussed experimentally the question of the effect of motion of the source or recipient of light in all its bearings, and showed that the light of the sun and that derived from artificial sources are alike incapable of revealing by diffraction-phenomena the translatory motion of the earth.
The greatest problem now confronting the investigators of light was to reconcile the facts of polarization with the principles of the wave-theory. Young had long been pondering over this, but had hitherto been baffled by it. In 1816 he received a visit from Arago, who told him of a new experimental result which he and Fresnel had lately obtained! — namely, that two pencils of light, polarized in planes at right angles, do not interfere with each other under circumstances in which ordinary light shows interference-phenomena, but always give by their reunion the same intensity of light, whatever be their difference of path.
Arago had not long left him when Young, reflecting on the new experiment, discovered the long-sought key to the mystery : it consisted in the very alternative which Bernoulli had rejected eighty years before, of supposing that the vibrations of light are executed at right angles to the direction of propagation.
Young's ideas were first embodied in a letter to Arago,J dated Jan. 12, 1817. "I have been reflecting," he wrote, " on the possibility of giving an imperfect explanation of the affection of light which constitutes polarization, without departing from the genuine doctrine of undulations. It is a principle in this theory, that all undulations are simply propagated through homogeneous mediums in concentric spherical surfaces like the
•Ann. de 1'Ecole Noemale, (2) i, p. 157.
t It was not published until 1819, in Annales de Chimie, x ; Fresnel's (Euvres, i, p. 509. By means of this result, Fresnel was able to give a complete explana- tion of a class of phenomena which Arago had discovered in 1811, viz. that when polarized light is transmitted through thin plates of sulphate of lime or mica, and afterwards analysed by a prism of Iceland spar, beautiful complementary colours are displayed. Young had shown that these effects are due essentially to inter- ference, hut had not made clear the part played by polarization.
J Young's JTorks, i., p. 380.
122 The Lumini/erous Medium,
undulations of sound, consisting simply in the direct and retro- grade motions of the particles in the direction of the radius,, with their concomitant condensation and rarefactions. And yet it is possible to explain in this theory a transverse vibration,, propagated also in the direction of the radius, and with equal velocity, the motions of the particles being in a certain constant direction with respect to that radius ; and this is a polarization"
In an article on " Chromatics," which was written in September of the same year* for the supplement to the Encyclopaedia Britannica, he says :f " If we assume as a mathe- matical postulate, on the undulating theory, without attempting to demonstrate its physical foundation, that a transverse motion may be propagated in a direct line, we may derive from this assumption a tolerable illustration of the subdivision of polarized light by reflexion in an oblique plane," by " supposing the polar motion to be resolved " into two constituents, which fare differently at reflexion.
In a further letter to Arago, dated April 29th, 1818, Young recurred to the subject of transverse vibrations, comparing light to the undulations of a cord agitated by one of its extremities.^ This letter was shown by Arago to Fresnel, who at once saw that it presented the true explanation of the non-interference of beams polarized in perpendicular planes, and that the latter effect could even be made the basis of a proof of the correctness of Young's hypothesis : for if the vibration of each beam be supposed resolved into three components, one along the ray and the other two at right angles to it, it is obvious from the Arago- Fresnel experiment that the components in the direction of the ray must vanish : in other words, that the vibrations which constitute light are executed in the wave-front.
It must be remembered that the theory of the propagation of waves in an elastic solid was as yet unknown, and light was
* Peacock's Life of Young, p. 391. t Young's Works, i., p. 279.
JThis analogy had been given by Hooke in a communication to the Royal Society on Feb. 15, 1671-2. But there seems no reason to suppose that Hook e- appreciated the point now advanced by Young.
from Bradley to FresneL 123
still always interpreted by the analogy with the vibrations of sound in air, for which the direction of vibration is the same as that of propagation. It was therefore necessary to give some justification for the new departure. With wonderful insight Fresnel indicated* the precise direction in which the theory of vibrations in ponderable bodies needed to be extended in order to allow of waves similar to those of light : " the geometers," he wrote, " who have discussed the vibrations of elastic fluids hitherto have taken account of no accelerating forces except those arising from the difference of condensation or dilatation between conse- cutive layers." He pointed out that if we also suppose the medium to possess a rigidity, or power of resisting distortion, such as is manifested by all actual solid bodies, it will be capable of transverse vibration. The absence of longitudinal waves in the aether he accounted for by supposing that the forces which oppose condensation are far more powerful than those which oppose distortion, and that the velocity with which condensations are propagated is so great compared with the speed of the oscillations of light, that a practical equilibrium of pressure is maintained perpetually.
The nature of ordinary non-polarized light was next discussed. " If then," Fresnel wrote,f " the polarization of a ray of light consists in this, that all its vibrations are executed in the same direction, it results from any hypothesis on the generation of light-waves, that a ray emanating from a single centre of dis- turbance will always be polarized in a definite plane at any instant. But an instant afterwards, the direction of the motion changes, and with it the plane of polarization ; and these variations follow each other as quickly as the perturbations of the vibrations of the luminous particle : so that even if we could
*Annales de Chiinie, xvii (1821), p. 180; (Eiwres, i, p. 629. Young had already drawn attention to this point. " It is difficult," he says in his Lectures on Natural Philosophy, ed. 1807, vol. i, p. 138, "to compare the lateral adhesion, or the force which resists the detrusion of the parts of a solid, with any form of direct cohesion. This force constitutes the rigidity or hardness of a solid body, and is wholly absent from liquids."
t Loc. cit, p. 185.
124 The Luminiferous Medium,
isolate the light of this particular particle from that of other luminous particles, we should doubtless not recognize in it any appearance of polarization. If we consider now the effect pro- duced by the union of all the waves which emanate from the different points of a luminous body, we see that at each instant, at a definite point of the aether, the general resultant of all the motions which commingle there will have a determinate direction, but this direction will vary from one instant to the next. So direct light can be considered as the union, or more exactly as the rapid succession, of systems of waves polarized in all directions. According to this way of looking at the matter, the act of polarization consists not in creating these transverse motions, but in decomposing them in two invariable directions, and separating the components from each other ; for . then, in each of them, the oscillatory motions take place always in the same plane."
He then proceeded to consider the relation of the direction of vibration to the plane of polarization. " Apply these ideas to double refraction, and regard a uniaxal crystal as an elastic medium in which the accelerating force which results from the displacement of a row of molecules perpendicular to the axis, relative to contiguous rows, is the same all round the axis ; while the displacements parallel to the axis produce accelerating forces of a different intensity, stronger if the crystal is "repulsive," and weaker if it is "attractive." The distinctive character of the rays which are ordinarily refracted being that of propagating themselves with the same velocity in all directions, we must admit that their oscillatory motions are executed at right angles to the plane drawn through these rays and the axis of the crystal; for then the displacements which they occasion, always taking place along directions perpendicular to the axis, will, by hypothesis, always give rise to the same accelerating forces. But, with the conventional meaning which is attached to the expression 'plane, of polarization, the plane of polarization of the ordinary rays is the plane through the axis : thus, in a pencil of polarized light, the
from Bradley, to Fresnel. 125
oscillatory motion is executed at right angles to the plane of polarization"
This result afforded Fresnel a foothold in dealing with the problem which occupied the rest of his life : henceforth his aim was to base the theory of light on the dynamical properties of the luminiferous medium.
The first topic which he attacked from this point of view was the propagation of light in crystalline bodies. Since Brewster's discovery that many crystals do not conform to the type to which Huygens' construction is applicable, the wave theory had to some extent lost credit in this region. Fresnel, now, by what was perhaps the most brilliant of all his efforts,* not only reconquered the lost territory, but added a new domain to science.
He had, as he tells us himself, never believed the doctrine that in crystals there are two different luminiferous media, one to transmit the ordinary, and the other the extraordinary waves. The alternative to which he inclined was that the two velocities of propagation were really the two roots of a quadratic equation, derivable in some way from the theory of a single aether. Could this equation be obtained, he was confident of finding the explanation, not only of double refraction, but also of the polarization by which it is always accompanied.
The first step was to take the case of uniaxal crystals, which had been discussed by Huygens, and to see whether Huygens' sphere and spheroid could be replaced by, or made to depend on, a single surface.f
Now a wave propagated in any direction through a uniaxal
*His first memoir on Double Refraction was presented to the Academy on Nov. 19th, 1821, but has not been published except in his collected works: (Eitvres, ii, p. 261. It was followed by other papers in 1822; and the results were finally collected in a memoir which was printed in 1827, Mem. de VAcad. vii, p. 45, (Euvres, ii, p. 479.
t In attempting to reconstruct Fresnel's course of thought at this period, the present writer has derived much help from the Life prefixed to the (Euvres de Fresnel. Both Fresnel and Young were singularly fortunate in their biographers : Peacock's Life of Young, and this notice of Fresnel, which was the last work of Verdet, are excellent reading.
126 The Luminiferous Medium,
crystal can be resolved into two plane-polarized components ; one of these, the " ordinary ray," is polarized in the principal section, and has a velocity vl9 which may be represented by the radius of Huygens' sphere — say,
Vi = &;
while the other, the " extraordinary ray," is polarized in a plane .at right angles to the principal section, and has a wave- velocity v9, which may be represented by the perpendicular drawn from the centre of Huygens' spheroid on the tangent-plane parallel to the plane of the wave. If the spheroid be represented by the equation
if + z'" x*
— + ^ = 1-
and if (I, m, n) denote the direction-cosines of the normal to the plane of the wave, we have therefore
v,~ = a*(m* + n*) + ?>2/2.
But the quantities 1/Vi and l/t?8, as given by these equations, are easily seen to be the lengths of the semi-axes of the ellipse in which the spheroid
62(?/3 4- z~) + arx- = 1
is intersected by the plane
Ix + my + nz = 0 ;
.and thus the construction in terms of Huygens' sphere and spheroid can be replaced by one which depends only on a single surface, namely the spheroid
Having achieved this reduction, Fresnel guessed that the <?ase of biaxal crystals could be covered by substituting for the latter spheroid an ellipsoid with three unequal axes — say,
xz if z* _+£+_ =
If I/Vi and l/^ denote the lengths of the semi-axes of the .ellipse in which this ellipsoid is intersected by the plane
Ix 4 my + nz - 0,
from Bradley to Fresnel. 127
it is well known that #1 and vz are the roots of the equation in v
; --0;
1 . 1 ,1
tf tf v-
ti £2 «3
and accordingly Fresnel conjectured that the roots of this equation represent the velocities, in a biaxal crystal, of the two plane-polarized waves whose normals are in the direction (I, m, n).
Having thus arrived at his result by reasoning of a purely geometrical character, he now devised a dynamical scheme to suit it.
The vibrating medium within a crystal he supposed to be ultimately constituted of particles subjected to mutual forces ; and on this assumption he showed that the elastic force of restitution when the system is disturbed must depend linearly on the displacement. In this first proposition a difference is apparent between Fresnel's and a true elastic-solid theory ; for in actual elastic solids the forces of restitution depend not on the absolute displacement, but on the strains, i.e., the relative displacements.
In any crystal there will exist three directions at right angles to each other, for which the force of restitution acts in the same line as the displacement : the directions which possess this property are named axes of elasticity. Let these be taken as axes, and suppose that the elastic forces of restitution for unit displacements in these three directions are 1/5], l/c2, l/«s respectively. That the elasticity should vary with the direction of the molecular displacement seemed to Fresnel to suggest that the molecules of the material body either take part in the luminous vibration, or at any rate influence in some way the elasticity of the aether.
A unit displacement in any arbitrary* direction (a, )3, 7) can be resolved into component displacements (cos a, cos /3, cos 7) parallel to the axes, and each of these produces its own effect
128 The Luminiferous Medium ^
independently ; so the components of the force of restitution are
COS a COS )3 COS y €l ft £3
This resultant force has not in general the same direction as the displacement which produced it ; but it may always he decomposed into two other forces, one parallel and the other perpendicular to the direction of the displacement ; and the former of these is evidently
The surface
COS2 a COS2 )3 COS2 7
I {_ I £_
fl €2 £3
X2 V*
£i £2 £3
will therefore have the property that the square of its radius vector in any direction is proportional to the component in that direction of the elastic force due to a unit displacement in that direction : it is called the surface of elasticity.
Consider now a displacement along one of the axes of the section on which the surface of elasticity is intersected by the plane of the wave. It is easily seen that in this case the com- ponent of the elastic force at right angles to the displacement acts along the normal to the wave-front; and Fresnel assumes that it will be without influence on the propagation of the vibrations, on the ground of his fundamental hypothesis that the vibrations of light are performed solely in the wave-front. This step is evidently open to criticism ; for in a dynamical theory everything should be deduced from the laws of motion without special assumptions. But granting his contention, it follows that such a displacement will retain its direction, and will be propagated as a plane-polarized wave with a definite velocity.
Now, in order that a stretched cord may vibrate with unchanged period, when its tension is varied, its length must be increased proportionally to the square root of its tension ; and similarly the wave-length of a luminous vibration of given period is proportional to the square root of the elastic force (per unit
from Bradley to Fresnel. 129
displacement), which urges the molecules of the medium parallel to the wave-front. Hence the velocity of propagation of a wave, measured at right angles to its front, is proportional to the square root of the component, along the direction of dis- placement, of the elastic force per unit displacement ; and the velocity of propagation of such a plane-polarized wave as we have considered is proportional to the radius vector of the surface of elasticity in the direction of displacement.
Moreover, any displacement in the given wave-front can be resolved into two, which are respectively parallel to the two axes of the diametral section of the surface of elasticity by a plane parallel to this wave-front ; and it follows from what has been said that each of these component displacements will be propagated as an independent plane-polarized wave, the velocities of propagation being proportional to the axes of the section,* and therefore inversely proportional to the axes of the section of the inverse surface of this with respect to the origin, which is the ellipsoid
* + £ + *-i.
£i £2 £3
But this is precisely the result to which, as we have seen, Fresnel had been led by purely geometrical considerations ; and thus his geometrical conjecture could now be regarded as substantiated by a study of the dynamics of the medium.
It is easy to determine the wave-surface or locus at any instant —say, t = 1 — of a disturbance originated at some previous instant — say,£ = 0 — at some particular point — say, the origin. For this wave-surface will evidently be the envelope of plane waves emitted from the origin at the instant t = 0 — that is, it will be the envelope of planes
Ix + my + nz - v = 0,
where the constants /, m, n, v are connected by the identical equation I2 + m* + nz = 1,
* It is evident from this that the optic axes, or lines of single wave-velocity, along which there is no double refraction, will be perpendicular to the two circular sections of the surface of elasticity.
K
130 The Lumimferous Medium,
and by the relation previously found — namely, /2 m2 n~
1
By the usual procedure for determining envelopes, it may be shown that the locus in question is the surface of the fourth degree
xz_ _f _fl_ _ n
which is called Fresnel's wave-surface* It is a two-sheeted surface, as must evidently be the case from physical considerations. In uniaxal crystals, for which *2 and c 3 are equal, it degenerates into the sphere
r2 = l/e>, and the spheroid
^ + fl (tf + Z2) = 1.
It is to these two surfaces that tangent-planes are drawn in the construction given by Huygens for the ordinary and extraordinary refracted rays in Iceland spar. As Fresnel observed, exactly the same construction applies to biaxal crystals, when the two sheets of the wave-surface are substi- tuted for Huygens' sphere and spheroid.
" The theory which I have adopted," says Fresnel at the end of this memorable paper, " and the simple constructions which I have deduced from it, have this remarkable character, that all the unknown quantities are determined together by the solution of the problem. We find at the same time the velocities of the ordinary ray and of the extraordinary ray, and their planes of polarization. Physicists who have studied attentively the laws of nature will feel that such simplicity and
* Another construction for the wave-surface is the following, which is due to MacCullagh, Coll. Works, p. 1. Let the ellipsoid
*ix~ + 62^" ~*~ *3~~ = *
be intersected hy a plane through its centre, and on the perpendicular to that plane take lengths equal to the semi-axes of the section. The locus of these extremities is the wave-surface.
from Bradley to FresneL 131
such close relations between the different elements of the phenomenon are conclusive in favour of the hypothesis on which they are based."
The question as to the correctness of Fresnel's construction was discussed for many years afterwards. A striking conse- quence of it was pointed out in 1832 by William Kowan Hamilton (b. 1805, d. 1865), Royal Astronomer of Ireland, who remarked* that the surface defined by Fresnel's equation has four conical points, at each of which there is an infinite number of tangent planes ; consequently, a single ray, proceeding from a point within the crystal in the direction of one of these points, must be divided on emergence into an infinite number of rays, constituting a conical surface. Hamilton also showed that there are four planes, each of which touches the wave- surface in an infinite number of points, constituting a circle of contact : so that a corresponding ray incident externally should be divided within the crystal into an infinite number of refracted rays, again constituting a conical surface.
These singular and unexpected consequences of the theory were shortly afterwards verified experimentally by Humphrey Lloyd,f and helped greatly to confirm belief in Fresnel's theory. It should, however, be observed that conical refraction only shows his form of the wave- surf ace to be correct in its general features, and is no test of its accuracy in all details. But it was shown experimentally by Stokes in 1872J Glazebrook in 1879,§ and Hastings in 1887,1 1 that the construction of Huygens and Fresnel is certainly correct to a very high degree of approximation; and Fresnel's final formulae have since been regarded as unassailable. The dynamical substructure on which he based them is, as we have seen, open to objection ;
* Trans. Roy. Irish Acad., xvii (1833), p. 1.
t Trans. Roy. Irish Acad., xvii (1833), p. 145. Strictly speaking, the bright oone which is usually observed arises from rays adjacent to the singular ray : the latter can, however, be observed, its enfeeblement by dispersion into the conical form causing it to appear dark.
I Proc. R. S., xx, p. 443.
§ Phil. Trans., clxxi, p. 421.
|| Am. Jour. Sci. (3), xxxv, p. 60.
K 2
132 The Luminiferous Medium,
but, as Stokes observed*: "If we reflect on the state of the subject as Fresnel found it, and as he left it, the wonder is, not that he failed to give a rigorous dynamical theory, but that a single mind was capable of effecting so much."
In a second supplement to his first memoir on Double Eefraction, presented to the Academy on November 26th, 1821,-]- Fresnel indicated the lines on which his theory might be extended so as to take account of dispersion. " The molecular groups, or the particles of bodies," he wrote, " may be separated by intervals which, though small, are certainly not altogether insensible relatively to the length of a wave." Such a coarse- grainedness of the medium would, as he foresaw, introduce into the equations terms by which dispersion might be explained ; indeed, the theory of dispersion which was afterwards given by Cauchy was actually based on this principle. It seems likely that, towards the close of his life, Fresnel was contemplating a great memoir on dispersion^ which was never completed.
Fresnel had reason at first to be pleased with the reception of his work on the optics of crystals : for in August, 1822, Laplace spoke highly of it in public ; and when at the end of the year a seat in the Academy became vacant, he was encouraged to hope that the choice would fall on him. In this he was disappointed. §. Meanwhile his researches were steadily continued ; and in January, 1823, the very month of his rejection, he presented to- the Academy a theory in which reflexion and refraction] | are referred to the dynamical properties of the luminiferous media.
*Brit. Assoc. Rep., 1862, p. 254.
t (Euvres, ii, p. 438.
J Cf. the biography in (Euvres de Fresnel, i, p. xcvi.
§ Writing to Young in the spring of 1823, he says : " Tous ces memoires, que dernierement j'ai pre'sentes coup sur coup a 1'Academie des Sciences, ne m'en ont pas cependant otivert la porte. C'est M. Dulong qui a ete nomine pour remplir la place vacante dans la section de physique. . . Vous voyez, Monsieur, que la theorie des ondulations ne m'a point porte honheur : mais cela ne m'en degoute pas : et je me console de ce malheur en m* occupant d'optique avec une nouvelle ardeur."
|| The MSS- was for some time believed to be lost, but was ultimately found among the papers of Fourier, and printed in Mem. de 1'Acad. xi (1832), p. 393 : (Euvres, i, p. 767.
from Bradley to FresneL 133
As in his previous investigations, he assumes that the vibrations which constitute light are executed at right angles to the plane of polarization. He adopts Young's principle, that reflexion and refraction are due to differences in the inertia of the aether in different material bodies, and supposes (as in his memoir on Aberration) that the inertia is proportional to the inverse square of the velocity of propagation of light in the medium. The conditions which he proposes to satisfy at the interface between two media are that the displacements of the adjacent molecules, resolved parallel to this interface, shall be equal in the two media ; and that the energy of the reflected and refracted waves together shall be equal to that of the incident wave.
On these assumptions the intensity of the reflected and refracted light may be obtained in the following way : —
Consider first the case in which the incident light is polarized in the plane of incidence, so that the displacement is at right angles to the plane of incidence ; let the amplitude of the displacement at a given point of the interface be / for the incident ray, g for the reflected ray, and h for the refracted ray.
The quantities of energy propagated per second across unit cross-section of the incident, reflected, and refracted beams are proportional respectively to
where cb c2, denote the velocities of light, and pl} pz the densities of aether, in the two media ; and the cross-sections of the beams which meet the interface in unit area are
cos i, cos i, cos r
respectively. The principle of conservation of energy therefore gives
c,p! cos i ./2 = c,/o! cos i . gz + c2/o2 cos r . h~.
The equation of continuity of displacement at the interface is
/ + 9 = h.
134 The Luminiferous Medium,
Eliminating li between these two equations, and using the formulae
sin2 T Co2 pi
sin2 i C* p2 ' we obtain the equation
Z. _ sm (^ ~ r) g sin (i + r)
Thus when the light is polarized in the plane of reflexion, the amplitude of the reflected wave is
Q-l -T\ (ft ^ -0*\
- — \-. r x the amplitude of the incident vibration.
sin pj + r)
Fresnel shows in a similar way that when the light is polarized at right angles to the plane of reflexion, the ratio of the amplitudes of the reflected and incident waves is
tan (i - r) tan (i + r)
These formulae are generally known as Fresnel' s sine-law and FresneTs tangent-law respectively. They had, however, been discovered experimentally by Brewster some years previously. When the incidence is perpendicular, so that i and r are very small, the ratio of the amplitudes becomes
Limit ,
^ + r
or
where ju2 and //i denote the refractive indices of the media. This formula had been given previously by Young* and Poisson,f on the supposition that the elasticity of the aether is of the same kind as that of air in sound.
When i + r = 90°, tan (i + r) becomes infinite : and thus a theoretical explanation is obtained for Brewster 's law, that if the incidence is such as to make the reflected and refracted rays-
* Article Chromatics, Encycl. Britt. Suppl. t Mem. Inst. ii. (1817).
fro vi Bradley to Fresnel. 135
perpendicular to each other, the reflected light will be wholly polarized in the plane of reflexion.
Fre&nel's investigation can scarcely be called a dynamical theory in the strict sense, as the qualities of the medium are not defined. His method was to work backwards from the known properties of light, in the hope of arriving at a mechanism to which they could be attributed ; he succeeded in accounting for the phenomena in terms of a few simple principles, but was not able to specify an aether which would in turn account for these principles. The " displacement " of Fresnel could not be a displacement in an elastic solid of the usual type, since its normal component is not continuous across the interface between two media.*
The theory of ordinary reflexion was completed by a dis- cussion of the case in which light is reflected totally. This had formed the subject of some of Fresnel's experimental researches several years before; and in two papersf presented to the Academy in November, 1817, and January, 1818, he had shown that light polarized in any plane inclined to the plane of reflexion is partly "depolarized" by total reflexion, and that this is due to differences of phase which are introduced between the components polarized in and perpendicular to the plane of reflexion. " When the reflexion is total," he said, " rays polarized in the plane of reflexion are reflected nearer the surface of the glass than those polarized at right angles to the same plane, so that there is a difference in the paths described." This change of phase he now deduced from the formulae already obtained for ordinary reflexion. Considering light polarized in the plane of reflexion, the ratio of the amplitudes of the reflected and incident light is, as we have seen,
sin (i - r)
sin (i + r) ' when the sine of the angle of incidence is greater than /i2/jui,
* Fresnel's theory of reflexion can, however, he reconciled with the electro- magnetic theory of light, by identifying his "displacement" with the electric force. f (Euvres de Fresnel, i., pp. 441, 487.
136 The Luminiferous Medium.
so that total reflexion takes place, this ratio may be written in the form
where 6 denotes a real quantity defined by the equation
tan
cos ^
Fresnel interpreted this expression to mean that the amplitude of the reflected light is equal to that of the incident, but that the two waves differ in phase by an amount 0. The case of light polarized at right angles to the plane of reflexion may be treated in the same way, and the resulting formulae are completely confirmed by experiment.
A few months after the memoir on reflexion had been presented, Fresnel was elected to a seat in the Academy ; and during the rest of his short life honours came to him both from France and abroad. In 1827 the Royal Society awarded him the Rumford medal ; but Arago, to whom Young had confided the mission of conveying the medal, found him dying ; and eight days afterwards he breathed his last.
By the genius of Young and Fresnel the wave-theory of light was established in a position which has since remained unquestioned ; and it seemed almost a work of supererogation when, in 1850, Foucault* and Fizeau,f carrying out a plan long before imagined by Arago, directly measured the velocity of light in air and in water, and found that on the question so long debated between the rival schools the adherents of the undulatory theory had been in the right.
* Comptes Rendus, xxx (1850), p. 551. t Ibid., p. 562.
( 137 )
CHAPTER V.
THE AETHER AS AN ELASTIC SOLID.
WHEN Young and Fresnel put forward the view that the vibrations of light are performed at right angles to its direction of propagation, they at the same time pointed out that this peculiarity might be explained by making a new hypothesis regarding the nature of the luminiferous medium ; namely, that it possesses the power of resisting attempts to distort its shape. It is by the possession of such a power that solid bodies are distinguished from fluids, which offer no resistance to distortion; the idea of Young and Fresnel may therefore be expressed by the simple statement that the aether behaves as an elastic solid. After the death of Fresnel this conception was developed in a brilliant series of memoirs to which our attention must now be directed.
The elastic-solid theory meets with one obvious difficulty at the outset. If the aether has the qualities of a solid, how is it that the planets in their orbital motions are able to journey through it at immense speeds without encountering any perceptible resistance ? This objection was first satisfactorily answered by Sir George Gabriel Stokes* (b. 1819, d. 1903), who remarked that such substances as pitch and shoemaker's wax, though so rigid as to be capable of elastic vibration, are yet sufficiently plastic to permit other bodies to pass slowly through them. The aether, he suggested, may have this combination of qualities in an extreme degree, behaving like an elastic solid for vibrations so rapid as those of light, but yielding like a fluid to the much slower progressive motions of the planets.
Stokes's explanation harmonizes in a curious way with Fresnel's hypothesis that the velocity of longitudinal waves in
* Trans. Camb. Phil. Soc., viii, p. 287 (1845).
138 The Aether as an Elastic Solid.
the aether is indefinitely great compared with that of the transverse waves ; for it is found by experiment with actual substances that the ratio of the velocity of propagation of longitudinal waves to that of transverse waves increases rapidly as the medium becomes softer and more plastic.
In attempting to set forth a parallel between light and the vibrations of an elastic substance, the investigator is compelled more than once to make a choice between alternatives. He may, for instance, suppose that the vibrations of the aether are executed either parallel to the plane of polarization of the light or at right angles to it ; and he may suppose that the different refractive powers of different media are due either to differences in the inertia of the aether within the media, or to differences in its power of resisting distortion, or to both these causes combined. There are, moreover, several distinct methods for avoiding the difficulties caused by the presence of longitudinal vibrations ; and as, alas ! we shall see, a further source of diversity is to be found in that liability to error from which no man is free. It is therefore not surprising that the list of elastic-solid theories is a long one.
At the time when the transversality of light was dis- covered, no general method had been developed for investi- gating mathematically the properties of elastic bodies; but under the stimulus of Fresnel's discoveries, some of the best intellects of the age were attracted to the subject. The volume of Memoirs of the Academy which contains Fresnel's theory of crystal-optics contains also a memoir by Claud Louis Marie Henri Navier* (&. 1785, d. 1836), at that time Professor of Mechanics in Paris, in which the correct equations of vibratory motion for a particular type of elastic solid were for the first time given. ISTavier supposed the medium to be ultimately constituted of an immense number of particles, which act on each other with forces directed along the lines joining them, and depending on their distances apart ; and showed that if e denote
* Mem. de 1'Acad. vii, p. 375. The memoir was presented in 1821, and published in 1827.
The Aether as an Elastic Solid. 139
the (vector) displacement of the particle whose undisturbed position is (x, y, z], and if p denote the density of the medium, the equation of motion is
p — = - 3n grad div e - n curl curl e,
ot
where n denotes a constant which measures the rigidity, or power of resisting distortion, of the medium. All such elastic properties of the body as the velocity of propagation of waves in it must evidently depend on the ratio n/p.
Among the referees of one of Navier's papers was Augustine Louis Cauchy (b. 1789, d. 1857), one of the greatest analysts of the nineteenth century,* who, becoming interested in the question, published in 1828f a discussion of it from an entirely different point of view. Instead of assuming, as Navier had done, that the medium is an aggregate of point-centres of force, and thus involving himself in doubtful molecular hypotheses, he devised a method of directly studying the elastic properties of matter in bulk, and by its means showed that the vibrations of an isotropic solid are determined by the equation
82e (1 4 \ • p — = - [fc + -n\ grad div e - n curl curl e ;
here n denotes, as before, the constant of rigidity; and the constant &, which is called the modulus of compression^. denotes the ratio of a pressure to the cubical compression produced by it. Cauchy's equation evidently differs from Navier's in that
* Hamilton's opinion, written in 1833, is worth repeating : " The principal theories of algebraical analysis (under which I include Calculi) require to he entirely remodelled ; and Cauchy has done much already for this great object. Poisson also has done much ; but he does not seem to me to have nearly so logical a mind as Cauchy, great as his talents and clearness are ; and both are in my judgment very far inferior to Fourier, whom I place at the head of the French School of Mathematical Philosophy, even above Lagrange and Laplace, though I rank their talents above those of Cauchy and Poisson." (Life of Sir W. It. Hamilton, ii, p. 58.)
t Cauchy, Exercices de Mathematiques iii, p. 160 (1828).
J This notation was introduced at a later period, but is used here in order to avoid subsequent changes.
140 The Aether as an Elastic Solid.
two constants, k and n, appear instead of one. The reason for this is that a body constituted from point-centres of force in Navier's fashion has its moduli of rigidity and compression connected by the relation*
Actual bodies do not necessarily obey this condition; e.g.
for india-rubber, k is much larger than - n ;f and there seems to
o
be no reason why we should impose it on the aether.
In the same year PoissonJ succeeded in solving the diffe- rential equation which had thus been shown to determine the wave-motions possible in an elastic solid. The solution, which is both simple and elegant, may be derived as follows : — Let the displacement vector e be resolved into two components, of which one c is circuital, or satisfies the condition
div c = 0, while the other b is irrotational, or satisfies the condition
curl b = 0. The equation takes the form
+ 5 Vb = °'
o Tlj
* In order to construct a body whose elastic properties are not limited by this equation, William John Macquorn Rankine (b. 1820, d. 1872) considered a con- tinuous fluid in which a number of point-centres of force are situated : the fluid is supposed to be partially condensed round these centres, the elastic atmosphere of each nucleus being retained round it by attraction. An additional volume-elasticity due to the fluid is thus acquired ; and no relation between k and n is now necessary. Cf. Rankine's Miscellaneous Scientific Papers, pp. 81 sqq.
Sir "William Thomson (Lord Kelvin), in 1889, formed a solid not obeying Navier's condition by using pairs of dissimilar atoms. Cf. Thomson's Papers, iii, p. 395. Cf. also Baltimore Lectures, pp. 123 sqq.
t It may, however, be objected that india-rubber and other bodies which fail to fulfil Navier's relation are not true solids. On this historic controversy, cf. Todhunter and Pearson's History of Elasticity, i, p. 496.
J Mem. de 1'Acad., viii (1828), p. 623. Poisson takes the equation in the restricted form given by Navier ; but this does not affect the question of wave- propagation.
The Aether as an Elastic Solid. 141
The terms which involve b and those which involve c must be separately zero, since they represent respectively the irrota- tional and the circuital parts of the equation. Thus, c satisfies. the pair of equations
02-
p T-J- = ?iV2c, div c = 0 ;
vt
while b is to be determined from
dt A particular solution of the equations for c is easily seen to be
cx = A sin A (2 - t /-),
/-), cy = B sinXfz - t /-), cz = 0, \PJ V \PJ
which represents a transverse plane wave propagated with velocity ^/(n/p). It can be shown that the general solution of the differential equations for c is formed of such waves as this, travelling in all directions, superposed on each other A particular solution of the equations for b is
-t E
V
p which represents a longitudinal wave propagated with velocity
the general solution of the differential equation for b is formed by the superposition of such waves as this, travelling in all directions.
Poisson thus discovered that the waves in an elastic solid are of two kinds : those in c are transverse, and are propagated with velocity (n/p)b ; while those in b are longitudinal, and are propagated with velocity {(k+ $n)/p}%. The latter are* waves of dilatation and condensation, like sound-waves ; in the c-waves, on the other hand, the medium is not dilated or condensed, but
* Cf . Stokes, "On the Dynamical Problem of Diffraction," Camb. Phil. Trans., ix (1849).
142 The Aether as an Elastic Solid.
only distorted in a manner consistent with the preservation of a constant density.*
The researches which have been mentioned hitherto have all been concerned with isotropic bodies. Cauchy in 1828f extended the equations to the case of crystalline substances. This, however, he accomplished only by reverting to Navier's plan of conceiving an elastic body as a cluster of particles which attract each other with forces depending on their distances apart ; the aelotropy he accounted for by supposing the particles to be packed more closely in some directions than in others.
The general equations thus obtained for the vibrations of an elastic solid contain twenty-one constants ; six of these depend on the initial stress, so that if the body is initially without stress, only fifteen constants are involved. If, retaining the initial stress, the medium is supposed to be symmetrical with respect to three mutually orthogonal planes, the twenty-one constants reduce to nine, and the equations which determine the vibrations may be written in the form*
dx\ 2x ty 9 dz and two similar equations. The three constants G, H, I re- present the stresses across planes parallel to the coordinate planes in the undisturbed state of the aether. §
* It may easily be shown that any disturbance, in either isotropic or crystalline media, for which the direction of vibration of the molecules lies in the wave-front or surface of constant phase, must satisfy the equation
div 6 = 0,
where e denotes the displacement ; if, on the other hand, the direction of vibration of the molecules is perpendicular to the wave -front, the disturbance must satisfy the equation
curl e = 0. These results were proved by M. O'Brien, Trans. Camb. Phil. Soc., 1842.
t Exercices de Math., iii (1828), p. 188.
J These are substantially equations (68) on page 208 of the third volume of the Exercices.
$ G, H, I are tensions when they are positive, and pressures when they are negative.
The Aether as an Elastic Solid. 1 43
On the basis of these equations, Cauchy worked out a theory of light, of which an instalment relating to crystal-optics was presented to the Academy in 1830.* Its characteristic features will now be sketched.
By substitution in the equations last given, it is found that when the wave-front of the vibration is parallel to the plane of yz, the velocity of propagation must be (h + G)% if the vibration takes place parallel to the axis of y, and (g+ G)$ if it takes place parallel to the axis of z. Similarly when the wave-front is parallel to the plane of zx, the velocity must be (h + H)% if the vibration is parallel to the axis of x, and (/+ H)^ if it is parallel fo the axis of z\ and when the wave-front is parallel to the plane of xy, the velocity must be (g + /)* if the vibration is parallel to the axis of x, and (/ + /)* if it is parallel to the axis of y.
Now it is known from experiment that the velocity of a ray polarized parallel to one of the planes in question is the same, whether its direction of propagation is along one or the other of the axes in that plane: so, if we assume that the vibrations which constitute light are executed parallel to the plane of polarization, we must have
/+#=/+/, ff + I = g+G, k + H=h+G; or, G = H=L
This is the assumption made in the memoir of 1830 : the theory based on it is generally known as Cauchy' s First Theory ;•(• the equilibrium pressures G, H, /, being all equal, are taken to be zero.
Tf, on the other hand, we make the alternative assumption that the vibrations of the aether are executed at right angles to the plane of polarization, we must have
* Mem. de 1'Acad., x, p. 293.
In the previous year (Mem. de 1'Acad., ix, p. 114) Cauchy had stated that the equations of elasticity lead in the case of uniaxal crystals to a wave-surface of which two sheets are a sphere and spheroid as in Huygens' theory.
f The equations and results of Cauchy's First Theory of crystal-optics were independently obtained shortly afterwards hy Franz Ernst Neumann (b. 1798, d. 1895) : cf. Ann. d. Phys. xxv (1832), p. 418, reprinted as No. 76 of Ostwald's Klassiker der exakten Wissenschaften, with notes by A. Wangerin.
144 The Aether as an Elastic Solid.
the theory based on this supposition is known as Caucliy's Second Theory : it was published in 1836.*
In both theories, Cauchy imposes the condition that the section of two of the sheets of the wave-surface made by any one of the coordinate planes is to be formed of a circle and an ellipse, as in Fresnel's theory ; this yields the three conditions
3£c = f(b + c +/) ; 3ca = g(c + a + g) ; Sab = h(a + b + Ji).
Thus in the first theory we have these together with the
equations
£ = 0, H=Q, 1=0,
which express the condition that the undisturbed state of the aether is unstressed ; and the aethereal vibrations are executed parallel to the plane of polarization. In the second theory we have the three first equations, together with f-Q-h-I-g-H;
and the plane of polarization is interpreted to be the plane at right angles to the direction of vibration of the aether.
Either of Cauchy's theories accounts tolerably well for the phenomena of crystal-optics; but the wave-surface (or rather the two sheets of it which correspond to nearly transverse waves) is not exactly Fresnel's. In both theories the existence of a third wave, formed of nearly longitudinal vibrations, is a formidable difficulty. Cauchy himself anticipated that the existence of these vibrations would ultimately be demonstrated by experiment, and in one placef conjectured that they might be of a calorific nature. A further objection to Cauchy's theories is that the relations between the constants do not appear to admit of any simple physical interpretation, being evidently assumed for the sole purpose of forcing the formulae into some degree of conformity with the results of experiment. And further difficulties will appear when we proceed subse- quently to compare the properties which are assigned to the aether in crystal- op tics with those which must be postulated in order to account for reflexion and refraction.
* Comptes Rendus, ii (1836), p. 341 : Mem. de 1'Acad. xviii (1839), p. 153. f Mem. de 1'Acad. xviii, p. 161.
The Aether as an Elastic Solid. 145
To the latter problem Cauchy soon addressed himself, his investigations being in fact published* in the same year (1830) as the first of his theories of crystal-optics.
At the outset of any work on refraction, it is necessary to assign a cause for the existence of refractive indices, i.e. for the variation in the velocity of light from one body to another. Huygens, as we have seen, suggested that transparent bodies consist of hard particles which interact with the aethereal matter, modifying its elasticity- Cauchy in his earlier papersf followed this lead more or less closely, assuming that the density p of the aether is the same in all media, but that its rigidity n varies from one medium to another.
Let the axis of x be taken at right angles to the surface of separation of the media, and the axis of z parallel to the inter- section of this interface with the incident wave-front; and suppose, first, that the incident vibration is executed at right angles to the plane of incidence, so that it may be represented .by
e~ = /( - x cos i -y sin i + rL t \
where i denotes the angle of incidence ; the reflected wave may be represented by
ez = FX cos i - y sin i + t V \/
and the refracted wave by
ez = fi I — x cos r — y sin r + KLt\
where r denotes the angle of refraction, and n' the rigidity of the second medium.
To obtain the conditions satisfied at the reflecting surface, Cauchy assumed (without assigning reasons) that the x- and ^/-components of the stress across the #y-plane are equal in
* Bull, des Sciences Math. xiv. (1830), p. 6.
t As will appear, his views on this subject subsequently changed.
L
146 The Aether as an Elastic Solid.
the media on either side the interface. This implies in the present case that the quantities
tie* dez
n — and n —
dx ty
are to be continuous across the interface : so we have
n cos i'. (/' - 1") = n' cos r . /', ; n sin i.(f' + F) = n' sin r . f\.
Eliminating /'„ we have
F' _ sin (r - i) f sin (r + i)
Now this is Fresnel's sine-law for the ratio of the intensity of the reflected ray to that of the incident ray ; and it is known that the light to which it applies is that which is polarized parallel to the plane of incidence. Thus Cauchy was driven to the conclusion that, in order to satisfy the known facts of reflexion and refraction, the vibrations of the aether must be supposed executed at right angles to the plane of polarization of the light.
The case of a vibration performed in the plane of incidence he discussed in the same way. It was found that Fresnel's tangent-law could be obtained by assuming that ex and the normal pressure across the interface have equal values in the two contiguous media.
The theory thus advanced was encumbered with many diffi- culties. In the first place, the identification of the plane of polarization with the plane at right angles to the direction of vibration was contrary to the only theory of crystal-optics which Cauchy had as yet published. In the second place, no reasons were given for the choice of the conditions at the interface. Cauchy's motive in selecting these particular conditions was evidently to secure the fulfilment of Fresnel's sine-law and tangent-law; but the results are inconsistent with the true boundary-conditions, which were given later by Green.
It is probable that the results of the theory of reflexion had much to do with the decision, which Cauchy now made,* to
*Comptes Rendus, ii. (1836), p. 341.
The Aether as an Elastic Solid. 147
reject the first theory of crystal-optics in favour of the second. After 1836 he consistently adhered to the view that the vibra- tions of the aether are performed at right angles to the plane of polarization. In that year he made another attempt to frame a satisfactory theory of reflexion,* based on the assumption just mentioned, and on the following boundary-conditions: — At the interface between two media curl e is to be continuous, and (taking the axis of x normal to the interface) dex/dx is also to be continuous.
Again we find no very satisfactory reasons assigned for the choice of the boundary- conditions ; and_as the continuity of e itself across the interface is not included amongst the conditions cHosen, they are obviously open to criticism ; but they lead to Fresnel's sine- and tangent-equations, which correctly express the actual behaviour of light. f Cauchy remarks that in order to justify them it is necessary to abandon the assumption of his earlier theory, that the density of the aether is the same in all material bodies.
It may be remarked that neither in this nor in Cauchy's earlier theory of reflexion is any trouble caused by the appear- ance of longitudinal waves when a transverse wave is reflected, for the simple reason that he assumes the boundary-conditions to be only four in number ; and these can all be satisfied without the necessity for introducing any but transverse vibrations.
These features bring out the weakness of Cauchy's method of attacking the problem. His object was to derive the properties of light from a theory of the vibrations of elastic solids. At the outset he had already in his possession the differential equations of motion of the solid, which were to be his starting-point, and the equations of Fresnel, which were to be his goal. It only
* Comptes Rendus, ii. (1836), p. 341 : " Meraoire sur la dispersion delalumiere " (Nouveaux exercices de Math., 1836), p. 203.
t These boundary -conditions of Cauchy's are, as a matter of fact, satisfied by the electric force in the electro-magnetic theory of light. The continuity of <;url e is equivalent to the continuity of the magnetic vector across the interface, and the continuity of (tex/dx leads to the same equation as the continuity of the component of electric force in the direction of the intersection of the interface with the plane of incidence.
L 2
] 48 The Aether as an Elastic Solid.
remained to supply the boundary-conditions at an interface, which are required in the discussion of reflexion, and the relations between the elastic constants of the solid, which are required in the optics of crystals. Cauchy seems to have con- sidered the question from the purely analytical point of view. Given certain differential equations, what supplementary con- ditions must be adjoined to them in order to produce a given analytical result ? The problem when stated in this form admits of more than one solution ; and hence it is not surprising that within the space of ten years the great French mathe- matician produced two distinct theories of crystal-optics and three distinct theories of reflexion,* almost all yielding correct or nearly correct final formulae, and yet mostly irreconcilable with each other, and involving incorrect boundary-conditions and improbable relations between elastic constants.
Cauchy's theories, then, resemble Fresnel's in postulating types of elastic solid which do not exist, and for whose assumed properties no dynamical justification is offered. The same objection applies, though in a less degree, to the original form of a theory of reflexion and refraction which was, discovered about this timef almost simultaneously by James MacCullagh (6. 1809, d. 1847), of Trinity College, Dublin, and Franz Neumann (b. 1798, d. 1895), of Konigsberg. To these authors is due the merit of having extended the laws of reflexion to crystalline media; but the principles of the theory were originally derived in connexion with the simpler ease of isotropic media, to which our attention will for the present be confined.
* One yet remains to be mentioned.
f The outlines of the theory were published by MacCullagh in Brit. Assoc. Rep. 1835 ; and his results were given in Phil. Mag. x (Jan., 1837), and in Proc. Royal Irish Acad. xviii. (Jan., 1837). Neumann's memoir was presented to the Berlin Academy towards the end of 1835, and published in 1837 in Abh. Berl. Ak. aus dem Jahre 1835, Math. Klasse, p. 1. So far as publication is concerned, the priority would seem to belong to MacCullagh; but there are reasons for believing that the priority of discovery really rests with Neumann, who had arrived at his equations a year before they were communicated to the Berlin Academy.
The Aether as an Elastic Solid. 149
MacCullagh and Neumann felt that the great objection to FresnePs theory of reflexion was its failure to provide for the continuity of the normal component of displacement at the interface between two media ; it is obvious that a discontinuity in this component could not exist in any true elastic-solid theory, since it would imply that the two media do not remain in contact. Accordingly, they made it a fundamental con- dition that all three components of the displacement must be continuous at the interface, and found that the sine-law and tangent-law can be reconciled with this condition only by supposing that the aether- vibrations are parallel to the plane of polarization : which supposition they accordingly adopted. In place of the remaining three true boundary-conditions, however, they used only a single equation, derived by assuming that transverse incident waves give rise only to transverse reflected and refracted waves, and that the conservation of energy holds for these — i.e. that the masses of aether put in motion, multiplied by the squares of the amplitudes of vibration, are the same before and after incidence. This is, of course, the same device as had been used previously by Presnel; it must, however, be remarked that the principle is unsound as applied to an ordinary elastic solid; for in such a body the refracted and reflected energy would in part be carried away by longitudinal waves.
In order to obtain the sine and tangent laws, MacCullagh and Neumann found it necessary to assume that the inertia of the luminiferous medium is everywhere the same, and that the differences in behaviour of this medium in different substances are due to differences in its elasticity. The two laws may then be deduced in much the same way as in the previous investigations of Fresnel and Cauchy.
Although to insist on continuity of displacement at the interface was a decided advance, the theory of MacCullagh and Neumann scarcely showed as yet much superiority over the quasi-mechanical theories of their predecessors. Indeed, MacCullagh himself expressly disavowed any claim to regard
150 The Aether as an Elastic Solid.
his theory, in the form to which it had then been brought, as a final explanation of the properties of light. " If we are asked," he wrote, " what reasons can be assigned for the hypotheses on which the preceding theory is founded, we are far from being able to give a satisfactory answer. We are obliged to confess that, with the exception of the law of vis viva, the hypotheses are nothing more than fortunate conjectures. These conjectures are very probably right, since they have led to elegant laws which are fully borne out by experiments ; but this is all we can assert respecting them. We cannot attempt to deduce them from first principles ; because, in the theory of light, such principles are still to be sought for. It is certain, indeed, that light is produced by undulations, propagated, with transversal vibrations, through a highly elastic aether ; but the constitution of this aether, and the laws of its connexion (if it has any connexion) with the particles of bodies, are utterly unknown/'
The needful reformation of the elastic-solid theory of reflexion was effected by Green, in a paper* read to the Cambridge Philosophical Society in December, 1837. Green, though inferior to Cauchy as an analyst, was his superior in physical insight ; instead of designing boundary-equations for the express purpose of yielding Fresnel's sine and tangent formulae, he set to work to determine the conditions which are actually satisfied at the interfaces of real elastic solids.
These he obtained by means of general dynamical principles. In an isotropic medium which is strained, the potential energy per unit volume due to the state of stress is
4 \tex dey
+ (~- + ^} -4r-*~-4~~-4
where e denotes the displacement, and k and n denote the two
* Trans. Camb. Phil. Soc., 1838 ; Green's Math. Papers, p. 245.
The Aether as an, Elastic Solid. 151
elastic constants already introduced; by substituting this value of <f> in the general variational equation
III'0 \w &t + 1* ** + TF*-| ****** = -
* (where p denotes the density), the equation of motion may be deduced.
But this method does more than merely furnish the equation of motion
or,
/ 4 \
pe = - ( k + - n ) grad div e - n curl curl e ; \ • /
pe = -lk + -n\ grad div e + nVze,
which had already been obtained by Cauchy ; for it also yields the boundary-conditions which must be satisfied at the interface between two elastic media in contact ; these are, as might be guessed by physical intuition, that the three components of the displacement* and the three components of stress across the interface are to be equal in the two media. If the axis of x be taken normal to the interface, the latter three quantities are
, 2 \ dex fiez 3ex\ fdev dey
--TI dive+ 27i — , w(-Ji + — ), and n (^ + -£
3 ) dx \to fa J \ty dx
The correct boundary-conditions being thus obtained, it was a simple matter to discuss the reflexion and refraction of an incident wave by the procedure of Fresnel and Cauchy. The result found by Green was that if the vibration of the aethereal molecules is executed at right angles to the plane of incidence, the intensity of the reflected light obeys Fresnel's sine-law, pro- vided the rigidity n is assumed to be the same for all media, but the inertia p to vary from one medium to another. Since the sine-law is known to be true for light polarized in the plane of incidence, Green's conclusion confirmed the hypotheses of
* These first three conditions are of course not dynamical but geometrical.
152 The Aether as an Elastic Solid.
Fresnel, that the vibrations are executed at right angles to the plane of polarization, and that the optical differences between media are due to the different densities of aether within them.
It now remained for Green to discuss the case in which the incident light is polarized at right angles to the plane of inci- dence, so that the motion of the aethereal particles is parallel to the intersection of the plane of incidence with the front of the wave. In this case it is impossible to satisfy all the six boundary-conditions without assuming that longitudinal vibra- tions are generated by the act of reflexion. Taking the plane of incidence to be the plane of yz, and the interface to be the plane of xy, the incident wave may be represented by the equations
6 = A + lz
where, if i denote the angle of incidence, we have
I = . /— cos it m = - /— sin i. \n Mn
There will be a transverse reflected wave,
and a transverse refracted wave,
y); ez = - C — f(t + 1& + my),
where, since the velocity of transverse waves in the second medium is v/W/oz, we can determine ^ from the equation
^•f^.&j
n
there will also be a longitudinal reflected wave,
8 9
ey = D -f(t -\z + my); ez = D -f(t - \z + my),
The Aeiher as an Elastic Solid. 153
where A is determined by the equation
and a longitudinal refracted wave,
7\ 7\
ey = JE - /(* + Aiz + my) ; ez = E - f(t where AI is determined by
Substituting these values for the displacement in the boundary- conditions which have been already formulated, we obtain the equations which determine the intensities of the reflected and refracted waves ; in particular, it appears that the amplitude of the reflected transverse wave is given by the equation
A- E _ ljj>i m? (pi - p2)2 A + B Ip2 I pz (\pz + A!/?I)
Now if the elastic constants of the media are such that the velocities of propagation of the longitudinal waves are of the same order of magnitude as those of the transverse waves, the direction-cosines of the longitudinal reflected and refracted rays will in general have real values, and these rays will carry away some of the energy which is brought to the interface by the incident wavev-G^een avoided this difficulty by adopting Fresnel's suggestion that the resistance of the aether to compression may V\ be very large in comparison with the resistance to distortion, \\ as is actually the case with such substances as jelly and caoutchouc : in this case the longitudinal waves are degraded in much the same way as the transverse refracted ray is degraded when there is total reflexion, and so do not carry away energy. Making this supposition, so that k\ and &2 are very large, the •quantities A and A: have the values m </ - 1, and we have
A- B li pi m (PI - p2f
A + B I 2
154 The Aether as an Elastic Solid.
Thus if BjA denote the modulus of £/A, we have
p\
if>l
This expression represents the ratio of the intensity of the transverse reflected wave to that of the incident wave. It does not agree with Fresnel's tangent- formula : and both on this account and also because (as we shall see) this theory of reflexion does not harmonize well with the elastic-solid theory of crystal- optics, it must be concluded that the vibrations of a Greenian solid do not furnish an exact parallel to the vibrations which constitute light.
The success of Green's investigation from the standpoint of dynamics, set off by its failure in the details last mentioned, stimulated MacCullagh to fresh exertions. At length he succeeded in placing his own theory, which had all along been free from reproach so far as agreement with optical experiments was concerned, on a sound dynamical basis ; thereby effecting that reconciliation of the theories of Light and Dynamics which had been the dream of every physicist since the days of Descartes.
The central feature of MacCullagh's investigation,* which was presented to the Eoyal Irish Academy in 1839, is the intro- duction of a new type of elastic solid. He had, in fact, concluded from Green's results that it was impossible to explain optical phenomena satisfactorily by comparing the aether to an elastic solid of the ordinary type, which resists compression and distortion ; and he saw that the only hope of the situation was to devise a medium which should be as strictly conformable to- dynamical laws as Green's elastic solid, and yet should have its properties specially designed to fulfil the requirements of the theory of light. Such a medium he now described.
If as before we denote by e the vector displacement of a point of the medium from its equilibrium position, it is well
* Trans. Roy. Irish Acad. xxi. : MacCullagh's Coll. Works, p. 145.
The Aether as an Elastic Solid. 155
known that the vector curl e denotes twice the rotation of the part of the solid in the neighbourhood of the point (x, y, z) from its equilibrium orientation. In an ordinary elastic solid, the potential energy of strain depends only on the change of size and shape of the volume- elements ; on their compression and distortion, in fact. For MacCullagh's new medium, on the other hand, the potential energy depends only on the rotation of the volume-elements.
Since the medium is not supposed to be in a state of stress in its undisturbed condition, the potential energy per unit volume must be a quadratic function of the derivates of e ; so that in an isotropic medium this quantity <f> must be formed from the only invariant which depends solely on the rotation and is quadratic in the derivates, that is from (curl e)2 ; thus we may write
to,
*~
The equation of motion is now to be determined, as in the case of Green's aether, from the variational equation
the result is
p—z = - fi curl curl e.
It is evident from this equation that if div e is initially zero it will always be zero: we shall suppose this to be the case, so that no longitudinal waves exist at any time in the medium. One of the greatest difficulties which beset elastic- solid theories is thus completely removed.
The equation of motion may now be written
156 The Aether as an Elastic Solid.
which shows that transverse waves are propagated with velocity
From the variational equation we may also determine the boundary-conditions which must be satisfied at the interface between two media ; these are, that the three components of e are to be continuous across the interface, and that the two components of p curl e parallel to the interface are also to be continuous across it. One of these five conditions, namely, the continuity of the normal component of e, is really dependent on the other four ; for if we take the axis of x normal to the interface, the equation of motion gives
p a"? = ~3^ (» curl e)* + l°* curl e)" / ' . |
and as the quantities p, (n curl e)2, and (/n curl e)y are continuous across the interface, the continuity of c>2ex/dtz follows. Thus the only independent boundary-conditions in MacCullagh's theory are the continuity of the tangential components of e and of fj curl e.* It is easily seen that these are equivalent to the boundary-conditions used in MacCullagh's earlier paper, namely, the equation of vis viva and the continuity of the three components of e : and thus the " rotationally elastic " aether of this memoir furnishes a dynamical foundation for the memoir of 1837.
The extension to crystalline media is made by assuming the potential energy per unit volume to have, when referred to the principal axes, the form
\dz dx J \c>x ty J
where A, B, C denote three constants which determine the optical behaviour of the medium : it is readily seen that the wave-surface is Fresnel's, and that the plane of polarization
* MacCullagh's equations may readily be interpreted in the electro -magnetic theory of light : e corresponds to the magnetic force, p curl e to the electric force, and curl e to the electric displacement.
The Aether as an Elastic Solid. 157
contains the displacement, and is at right angles to the rotation.
MacCullagh's work was regarded with doubt by his own and the succeeding generation of mathematical physicists, and can scarcely be said to have been properly appreciated until FitzGerald drew attention to it forty years afterwards. But there can be no doubt that MacCullagh really solved the problem of devising a medium whose vibrations, calculated in accordance with the correct laws of dynamics, should have the same properties as the vibrations of light.
The hesitation which was felt in accepting the rotationally elastic aether arose mainly from the want of any readily conceived example of a body endowed with such a property. This difficulty was removed in 1889 by Sir William Thomson (Lord Kelvin), who designed mechanical models possessed of rotational elasticity. Suppose, for example,* that a structure is formed of spheres, each sphere being in the centre of the tetrahedron formed by its four nearest neighbours. Let each sphere be joined to these four neighbours by rigid bars, which have spherical caps at their ends so as to slide freely on the spheres. Such a structure would, for small deformations, behave like an incompressible perfect fluid. Now attach to each bar a pair of gyroscopically-mounted flywheels, rotating with equal and opposite angular velocities, and having their axes in the line of the bar : a bar thus equipped will require a couple to hold it at rest in any position inclined to its original position, and the structure as a whole will possess that kind of quasi- elasticity which was first imagined by MacCullagh.
This particular representation is not perfect, since a system of forces would be required to hold the model in equilibrium if it were irrotationally distorted. Lord Kelvin subsequently invented another structure free from this defect. t
* Comptes Eendus, Sept. 16, 1889 : Kelvin's Math, and Phys. Papers, iii, p. 466.
tProc. Roy. Soc. Edinb., Mar. 17, 1890: Kelvin's Math, and Phys. Papers, iii, p. 468.
158 The Aether as an Elastic Solid.
The work of Green proved a stimulus not only to MacCullagh but to Cauchy, who now (1839) published yet a third theory of reflexion.* This appears to have owed its origin to a remark of Green's, f that the longitudinal wave might be avoided in either of two ways — namely, by supposing its velocity to be indefinitely great or indefinitely small. Green curtly dismissed the latter alternative and adopted the former, on the ground that the equilibrium of the medium would be unstable if its compressibility were negative (as it must be if the velocity of longitudinal waves is to vanish). Cauchy, without attempting to meet Green's objection, took up the study of a medium whose elastic constants are connected by the equation
k + ±n = 0,
so that the longitudinal vibrations have zero velocity; and showed that if the aethereal vibrations are supposed to be executed at right angles to the plane of polarization, and if the rigidity •of the aether is assumed to be the same