A History of the Theories of Aether and Electricity (1910) — part 27 of 29

This formula is equivalent to that which Maxwell and Sellmeier* had derived from the elastic-solid theory. Though superficially different, the derivations are alike in their essential feature, which is the assumption that the molecules of the dielectric contain systems which possess free periods of vibration, and which respond to the oscillations of the incident light. The formula may be derived on electro- magnetic principles without any explicit reference to electrons ; all that is necessary is to assume that the dielectric polarization has a free period of vibration.f

When the luminous vibrations are very slow, so that n is small, fjr reduces to the dielectric constant ej ; so that the. theory of Lorentz leads to the expression

e <=

• Cf. p. 293.

t A theory of dispersion, which, so far as its physical assumptions and results are concerned, resembles that described above, was published in the same year (1892) by Helmholtz, Berl. Ber., 1892, p. 1093, Ann d. Phys. xlviii (1893), pp. 389, 723. In this, as in Lorentz' theory, the incident light is supposed to excite sympathetic vibrations in the electric doublets which exist in the molecules of transparent bodies. Helmholtz' equations were, however, derived in a different way from those of Lorentz, being deduced from the Principle of Least Action. The final result is, as in Lorentz' theory, represented (when the effect of damping is neglected) by the Maxwell-Sellmeier formula. Helmholtz' theory was developed further by Reiff, Ann. d. Phys. Iv (1895), p. 82.

In a theory .of dispersion given by Planck, Berl. Ber., 1902, p. 470, the damping of the oscillations is assumed to be due to the loss of energy by radiation : so that no new constant is required in order to express it.

Lorentz, in his lectures on the Iheory of Electrons (Leipzig, 1909), p. 141, suggested that the dissipative term in the equations of motion of dielectric electrons might be ascribed to the destruction of the regular vibrations of tit^electrons within a molecule by the collisions of the molecule with other molecule

Some interesting references to the ideas of Hertz on the elet.:t)magnetic explanation of dispersion will be found in a memoir by Drude, Ann. d. Phys. (6) i (1900), p. 437.

• Cf. p. 283.

430 The Theory of Aether and Electrons in the

for the specific inductive capacity in terms of the number and circumstances of the electrons.*

Eeturning now to the case in which the dielectric is sup- posed to be in motion, the equation for the polarization may be written

from this equation, Fresnel's formula for the velocity of light in a moving dielectric may be deduced. For, let the axis of z be taken parallel to the direction of motion of the dielectric, which is supposed to be also the direction of propagation of the light ; and, considering a plane -polarized wave, take the axis of x parallel to the electric vector, so that the magnetic vector must be parallel to the axis of y. Then equation (III) above becomes

equation (IV) becomes (assuming B equal to H, as is always the case in optics),

The equation which defines the electric induction gives

IV* (1/4**)** + P.;

and equations (1) and (2) give

4arc*Px = (ft - 1) (Ex - wHy). Eliminating Dx, Px, and Hy, we have

-iV- + '

. A»

or, neglecting w~/c2,

dz* = 7 ~W ' ~~? dtfc '*

Substituting Ex = en ^ , so that V denotes the velocity

of light in the moving dielectric with respect to the fixed aether we have

• Cf. p. 211.

t This equation was first given as a result of the theory of electrons by Lorentz in the last chapter of his memoir of 1892, Arch. Neeii. xxv, p. 525. It was also given by Larmor, Phil. Trans., clxxxv (1894), p. 821.

Closing Years of the Nineteenth Century. 431 or (neglecting

C fjC - 1

y - _ + £ - ^, P M"

which is the formula of Fresnel.* The hypothesis of Fresnel, that a ponderable body in motion carries with it the excess of aether which it contains as compared with space free from matter, is thus seen to be transformed in Lorentz' theory into the supposition that the polarized molecules of the dielectric, like so many small condensers, increase the dielectric constant, and that it is (so to speak) this augmentation of the dielectric constant which travels with the moving matter. One evident objection to Fresnel's theory, namely, that it required the relative velocity of aether and matter to be different for light of different colours, is thus removed ; for the theory of Lorentz only requires that the dielectric constant should have different values for light of different colours, and of this a satisfactory explanation is provided by the theory of dispersion.

The correctness of Lorentz' hypothesis, as opposed to that of { Hertz (in which the whole of the contained aether was supposed to be transported with the moving body), was afterwards confirmed by various experiments. In 1901 E. Blondlotf drove a current of air through a magnetic field, at right angles to the lines of magnetic force. The air-current was made to pass between the faces of a condenser, which were connected by a wire, so as to be at the same potential. An electromotive force E' would be produced in the air by its motion in the magnetic field ; and, according to the theory of Hertz, this should produce an electric induction D of amount (e/47rc2) E' (where t denotes the specific inductive capacity of the air, which is practically unity) ; so that, according to Hertz, the faces of the condenser should become charged. According to Lorentz' theory, on the other hand, the electric induction D is determined by the equation

47rc2D = E + (e - 1) E'

• Cf. p. 117. t Comptes Rendus cxxxiii (1901), p. 778.

432 The Theory of Aether and Electrons in the

where E denotes the electric force on a charge at rest, which is zero in the present case. Thus, according to Lorentz' theory, the charges on the faces would have only (e - l)/e of the values which they would have in Hertz' theory ; that is, they would be practically zero. The result of Blondlot's experiment was in favour of the theory of Lorentz.

An experiment of a similar character was performed in 1905 by H. A. Wilson.* In this, the space between the inner and outer coatings of a cylindrical condenser was filled with the dielectric ebonite. When the coatings of such a con- denser are maintained at a definite difference of potential, charges are induced on them ; and if the condenser be rotated on its axis in a magnetic field whose lines of force are parallel to the axis, these charges will be altered, owing to the additional polarization which is produced in the dielectric molecules by their motion in the magnetic field. As before, the value of the additional charge according to the theory of Lorentz is (e - l)/e times its value as calculated by the theory of Hertz. The result of Wilson's experiments was, like that of Blondlot's, in favour of Lorentz.

The reconciliation of the electromagnetic theory with Fresnel's law of the propagation of light in moving bodies was a distinct advance. But the theory of the motionless aether was hampered by one difficulty : it was, in its original form, incompetent to explain the negative result of the experiment of Michelson and Morley.f The adjustment of theory to observation in this particular was achieved by means of a remarkable hypothesis which must now be introduced.

In the issue of " Nature" for June 16th, 1892,J Lodge

mentioned that Fitz Gerald had communicated to him a new

•

suggestion for overcoming the difficulty. This was, to suppose that the dimensions of material bodies are slightly altered when they are in motion relative to the aether. Five months afterwards, this hypothesis of Fitz Gerald's was adopted by

*Phii. Trans, cciv (1905), p. 121.

t Cf. p 417. J Nature, xlvi (1892), p. 165,

Closing Years of the Nineteenth Century. 433

Lorentz, in a communication to the Amsterdam Academy;* after which it won favour in a gradually widening circle, until eventually it came to be generally taken as the basis of all theoretical investigations on the motion of ponderable bodies through the aether.

Let us first see how it explains Michelson's result. On the supposition that the aether is motionless, one of the two portions into which the original beam of light is divided should accomplish its journey in a time less than the other by ur*l/c?, where w denotes the velocity of the earth, c the velocity of light, and I the length of each arm. This would be exactly compensated if the arm which is pointed in the direction of the terrestrial motion were shorter than the other by an amount w2//2c3; as would be the case if the linear dimensions of moving bodies were always contracted in the direction of their motion in the ratio of (1 - w'£/2c~) to unity. This is Fitz Gerald's hypothesis of contraction. Since for the earth the ratio w/c is only

30 km. /sec. 300,000 km./sec.'

the fraction w^jc- is only one hundred-millionth.

Several further contributions to the theory of electrons in a motionless aether were made in a short treatisef which was published by Lorentz in 1895. One of these related to the explanation of an experimental result obtained some years previously by Th. des Coudres,J of Leipzig. Des Coudres had observed the mutual inductance of coils in different circum- stances of inclination of their common axis to the direction of the earth's motion, but had been unable to detect any effect depending on the orientation. Lorentz now showed that this could be explained by considerations similar to those which

• Verslagen d. Kon. Ak. van Wetenschappen, 1892-3, p. 74 (November 26th 1892).

t Versuch einer Theorie Jer electrischen und optischen Erscheinungen in bewegten Eorpern, von H. A. Lorentz ; Leiden, E. J. Brill. It was reprinted by Teubner, of Leipzig, in 1906.

• Ann. d. Phys. xxxviii (1889), p. 73.

2 F

434 The Theory of Aether and Electrons in the

Budde and Fitz Gerald* had advanced in a similar case ; a conductor carrying a constant electric current and moving with the earth would exert a force on electric charges at relative rest in its vicinity, were it not that this force induces on the surface of the conductor itself a compensating electrostatic charge, whose action annuls the expected effect.

The most satisfactory method of discussing the influence of the terrestrial motion on electrical phenomena is to transform the fundamental equations of the aether and electrons to axes moving with the earth. Taking the axis of x parallel to the direction of the earth's motion, and denoting the velocity of the earth by w, we write

x = #1 + wtt y = 2/1, z = Zi,

so that (x-i, yit Zj) denote coordinates referred to axes moving with the earth. Lorentz completed the change of coordinates by introducing in place of the variable t a "local time" tl} defined by the equation

t = tl + m^/c2.

It is also necessary to introduce, in place of d and h, the electric and magnetic forces relative to the moving axes : these aret

d1 = d + [w.h] h1 = h + (l/c2) [d.w];

and in place of the velocity v of an electron referred to^the original fixed axes, we must introduce its velocity Vi relative to the moving axes, which is given by the equation

V, = V - W.

The fundamental equations of the aether and electrons, referred to the original axes, are

div d = 47re2, curl d = - h,

div h = 0, curl h = (1/c2) d +

F = d + [v . h],

where F denotes the ponderomotive force on a particle carrying a unit charge.

• Cf . p. 263. t Cf. pp. 365, 366.

Closing Years of the Nineteenth Century. 435

By direct transformation from the original to the new variables it is found that, when quantities of order iv*/c* and wv/c* are neglected, these equations take the form

divj d! = 4?rc2p, curla di = - Sh^B^,

divt H! = 0, curl, hi = (1/c2) ddj/fy

F = d! + [vlthj, where div, d, stands for

Since these have the same form as the original equations, it follows that when terms depending on the square of the constant of aberration are neglected, all electrical phenomena may be expressed with reference to axes moving with the earth by the same equations as if the axes were at rest relative to the aether.

In the last chapter of the Versuch Lorentz discussed those experimental results which were as yet unexplained by the theory of the motionless aether. That the terrestrial motion exerts no influence on the rotation of the plane of polariza- tion in quartz* might be explained by supposing that two independent effects, which are both due to the earth's motion, cancel each other; but Lorentz left the question undecided. Five years later Larmorf criticized this investigation, and arrived at the conclusion that there should be no first-order effect ; but LorentzJ afterwards maintained his position against Larmor's criticism.

Although the physical conceptions of Lorentz had from the beginning included that of atomic electric charges, the analytical equations had hitherto involved p, the volume-density of electric charge; that is, they had been conformed to the hypothesis of a continuous distribution of electricity in space. It might hastily be supposed that in order to obtain an

• Cf. p. 416. t Larmor, Aether and Matter, 1900.

J Proc. Amsterdam Acad. (English ed.), iv (1902), p. 669. 2 F 2

436 The Theory of Aether and Electrons in the

analytical theory of electrons, nothing more would be required than to modify the formulae by writing e (the charge of an electron) in place of pdxdydz. That this is not the case was shown* a few years after the publication of the Versuch.

Consider, for example, the formula for the scalar potential at any point in the aether,

where the bar indicates that the quantity underneath it is to have its retarded value, f

This integral, in which the integration is extended over all elements of space, must be transformed before the integration can be taken to extend over moving elements of charge. Let de denote the sum of the electric charges which are accounted for under the heading of the volume- element dx'dy'dz in the above integral. This quantity de is not identical with ~p'dx'dy'dz'. For, to take the simplest case, suppose that it is required to compute the value of the potential-function for the origin at the time t, and that the charge is receding from the origin along the axis of x with velocity u. The charge which is to be ascribed to any position x is the charge which occupies that position at the instant t - x/c; so that when the reckoning is made according to intervals of space, it is necessary to reckon within a segment (x2 - a?i) not the electricity which at any one instant occupies that segment, but the electricity which at the instant (t - xjc) occupies a segment (x* - x\ where x\ denotes the point from which the electricity streams to xl in the interval between the instants (t - xz,'c) and (t - x^/c). We have evidently

&'i - %'\ = u (%2 - %i)/c, or xz - x\ = (x2 - #0 (1 + u/c).

For this case we should therefore have

I^ ?' dx'dy'dz' = (l + ^'dx'dy'dz'.

— Xi \ cj

• E. Wiechert, Arch. Neerl. (2) v (1900), p. 549. Cf. also A. Lienard, L' Eclairage elect, xvi (1898), pp. 5, 53, 106. t Cf. p. 298.

Closing Years of the Nineteenth Century. 437

In the general case, it is only necessary to replace u by the component of velocity of the electric charge in the direction of the radius vector from the point at which the potential is to be computed. This component may be written v cos (v . r), where r is measured positively from the point in question to the charge, and v denotes the velocity of the charge. Thus

cde' = {c + v cos (v . r) } ~p dx'dy'dz', and therefore

f de' }cr + (r.v)'

where the integration is extended over all the charges in the field, and the bars over the letters imply that the position of the charge considered is that which it occupied at the instant t - r/c. In the same way the vector- potential may be shown to have the value

r vde' J cr + (r . v

Meanwhile the unsettled problem of the relative motion of earth and aether was provoking a fresh series of experimental investigations. The most interesting of these was due to Fitz Gerald,* who shortly before his death in February, 1901, commenced to examine the phenomena manifested by a charged electrical condenser, as it is carried through space in consequence of the terrestrial motion. On the assumption that a moving charge develops a magnetic field, there will be associated with the condenser a magnetic force at right angles to the lines of electric force and to the direction of the motion: magnetic energy must therefore be stored in the medium, when the plane of the condenser includes the direc- tion of the drift; but when the plane of the condenser is at right angles to the terrestrial motion, the effects of the opposite charges neutralize each other. Fitz Gerald's original idea was that, in order to supply the magnetic energy, there must be a mechanical drag on the condenser at the moment of

• Fitz Gerald's Scientific Writings, p. 557.

438 The Theory of Aether and Electrons in the

charging, similar to that which would be produced if the mass of a body at the surface of the earth were suddenly to become greater. Moreover, it was conjectured that the condenser, when freely suspended, would tend to move so as to assume the longitudinal orientation, which is that of maximum kinetic energy* : the transverse position would therefore be one of unstable equilibrium.

For both effects a search was made by Fitz Gerald's pupil Trouton :f in the experiments designed to observe the turning couple, a condenser was suspended in a vertical plane by a fine wire, and charged. If the plane of the condenser were that of the meridian, about noon there should be no couple tending to alter the orientation, because the drift of aether due to the earth's motion would be at right angles to this plane; at any other hour, a couple should act. The effect to be detected was extremely small ; for the magnetic force due to the motion of the charges would be of order w/c, where w denotes the velocity of the earth ; so the magnetic energy of the system, which depends on the square of the force, would be of order (w/c)' ; and the couple, which depends on the derivate of this with respect to the azimuth, would therefore be likewise of the second order in (w/c).

No couple could be detected. As the energy of the magnetic field must be derived from some source, there seems to be no escape from the conclusion that the electrostatic energy of a charged condenser is diminished by the fraction (w/c)" of its amount when the condenser is moving with velocity w at right angles to its lines of electrostatic force. To explain this diminution, it is necessary to admit Fitz Gerald's hypothesis of contraction. The negative result of the experiment may be taken to indicate^ that the kinetic potential of the system, when the Fitz Gerald contraction is taken into account as a

• Larmor, in Fitz Gerald's Scientific Papers, p 566.

t F. T. Trouton. Trans. Roy. Dub. Soc., April, 1902; F. T. Trouton and H. R. Noble, Phil. Trans, ccii (1903), p. 165.

J Cf. P. Langevin, Comptes Rendus, cxl (1905), p. 1171.

Closing Years of the Nineteenth Century. 439

constraint, is independent of the orientation of the plates with respect to the direction of the terrestrial motion.

It may be remarked that the existence of the couple, had it been observed, would have demonstrated the possibility of drawing on the energy of the earth's motion for purposes of terrestrial utility.

The Fitz Gerald contraction of matter as it moves through the aether might conceivably be supposed to affect in some way the optical properties of the moving matter; for in- stance, transparent substances might become doubly refracting. Experiments designed to test this supposition were per- formed by Lord Eayieigh in 1902,* and by D. B. Brace in 1904t ; but no double refraction comparable with the propor- tion (w/cf of the single refraction could be detected. The Fitz Gerald contraction of a material body cannot therefore be of the same nature as the contraction which would be produced in the body by pressure, but must be accompanied by such concomitant changes in the relations of the molecules to the aether that an isotropic substance does not lose its simply refracting character.

By this time, indeed, the hypothesis of contraction, which originally had no direct connexion with electric theory, had assumed a new aspect. Lorentz, as we have seen,J had obtained the equations of a moving electric system by applying a transformation to the fundamental equations of the aether. In the original form of this transformation, quantities of higher order than the first in w/c were neglected. But in 1900 Larmorg extended the analysis so as to include small quantities of the second order, and thereby discovered a remarkable connexion between the equations of transforma- tion and the equations which represent Fitz Gerald's con-

» Phil. Mag. iv (1902), p. 678. t Phil. Mag. vii (1904), p. 317.

• Cf. p. 434. Cf. also Lorentz, Proc. Amsterdam Acad. (English ed.), i (1899), p. 427.

§ Larmor, Aether and Matter, p. 173.

440 The Theory of Aether and Electrons in the

traction. After this Lorentz* went further still, and obtained the transformation in a form which is exact to all orders of the small quantity w/c. In this form we shall now consider it. The fundamental equations of the aether are

div d = 4irc*p, curl d = - h,

div h = 0, curl h = d/c2 + 47r/ov.

It is desired to find a transformation from the variables x, y, z, t, p, d, h, v, to new variables xlt y^ zly th plt d,, hi, YI, such that the equations in terms of these new variables may take the same form as the original equations, namely :

divi dx = 47rc2jOi, curl, di = - dh^d^, d^ h! = 0, curlj hi = (1/c2) Bdj/9^

Evidently one particular class of such transformations is that which corresponds to rotations of the axes of coordinates about the origin : these may be described as the linear homo- geneous transformations of determinant unity which transform the expression (x2 + if + zz) into itself.

These particular transformations are, however, of little interest, since they do not change the variable t. But in place of them consider the more general class formed of all those linear homogeneous transformations of determinant unity in the variables x, y, z, ct, which transform the expression (x- + y* + z - c't") into itself : we shall show that these trans- formations have the property of transforming the differential equations into themselves.

All transformations of this class may be obtained by the combination and repetition (with interchange of letters) of one of them, in which two of the variables— say, y and z— are unchanged. The equations of this typical transformation may

• Proc. Amsterdam Acad. (English ed.), vi, p. 809. Lorentz' work was completed in respect to the formulae which connect pi, vi, with p, v, by Einstein, Ann. d. Phys., xvii (1905), p. 891. It should be added that the transformation in question had been applied to the equation of vibratory motions many years before by Voigt, Gott. Nach. 1887, p. 41.

Closing Years of the Nineteenth Century. 441

easily be derived by considering that the equation of the

rectangular hyperbola

x2 - (cty = 1

(in the plane of the variables x, ct) is unaltered when any pair of conjugate diameters are taken as new axes, and a new unit of length is taken proportional to the length of either of these diameters. The equations of transformation are thus found to be

x = Xi cosh a + cti sinh a, y = y\y

t = ti cosh a + (x}/c) sinh a, z = z,,

where a denotes a constant. The simpler equations previously given by Lorentz* may evidently be derived from these by writing w/c for tanh a, and neglecting powers of w/c above the first. By an obvious extension of the equations given by Lorentz for the electric and magnetic forces, it is seen that the corresponding equations in the present transformation are

= dXlt hx =

dy = dyi cosh a + chzi sinh a, dz = dzi cosh a - chv. sinh a,

hy = hyi cosh a - (l/c)dzi sinh a, hz = hzi cosh a + (l/c)dyi sinh a.

The connexion between p and pl may be obtained in the following way. It is assumed that if a charge e is attached to a particle which occupies the position (f, 77, J) at the instant ty an equal charge will be attached to the corresponding point (f i, 771} £) at the corresponding instant ti in the transformed system ; so that a charge e attached to an adjacent particle (f + A£ TI + Arj, %+ A£) at the instant t will give rise in the derived system to a charge e at the place

V %1 A «. Ofrl A %l

fi +^Af + ^-AT/4 ^\

at the instant

• Cf. P. 434.

442 The Theory of Aether and Electrons in the

that is to say, at the place

(f ! + Af cosh a, 77, + AT?, £ + A?)

at the instant (^ - sinh a . Af/c). Thus at the instant ^, this charge will occupy the position

(f i + Af cosh a + sinh a . Af . 0^/e, 771 + AT; + sinh a . Af . vyi/c,

£1 + Af + sinh a . A f . vai/c).

The charges corresponding to those in the original system which were at the instant t contained in a volume A| AT? A£ will therefore in the derived system at the instant tl occupy a volume

cosh a + sinh a . vxjc . 0 0

AS,

sinh a .Vyjc 1 0

sinh a . vzjc 0 1 or,

(cosh a + sinh a . vxjc) A? A»j A£.

Thus if jOi denote the volume-density of electric charge in the transformed system, we shall have

pi (cosh a + sinh a . vxjc) = p ;

this equation expresses the connexion between pi and p. We have moreover

dx fix fix dx

~ ($_ dt dt dt

vx, sech a

= c tann a + - ,

cosh a + vXl c^sinha

and similarly

vyi

cosh a + vXl c~l sinh a and

cosh a + vXl c l sinh a

Closi?ig Years of the Nineteenth Century. 443

When the original variables are by direct substitution replaced by the new variables in the differential equations, the latter take the form

div! hi = 0, cur^ ht

that is to say, the fundamental equations of the aether retain their form unaltered, when the variables are subjected to the transformation which has been specified.

We are now in a position to show the connexion of this transformation with Fitz Gerald's hypothesis of contraction. Suppose that two material particles are moving along the axis of x with velocity w - c tanh a. From the relation

vx. sech a vx = c tanh a + — = -

cosh a + vXi c~l sinh a '

it follows that vXl is zero for each of the particles, which implies that they are at rest relative to the new axes. Let %i and x\ denote their coordinates with respect to this latter system ; then the coordinates of one particle at the instant ti, referred to the original axes, will be given by the equations

x = Xi cosh a + ctl sinh o, t — t\ cosh a + Xi c~l sinh a ; and the coordinates of the other particle will be given by xf - x\ cosh o f cti sinh a, tf = tl cosh a + x\ c'1 sinh a ;

so that at time t the latter particle will have the coordinate x", where

x" = of + w (t - t')

= x\ cosh a + ctl sinh a + (x - x) sinh2 a sech a, which gives

x" — x = (a?'i — Xi) (1 — w'/c2)^.

This equation shows that the distance between the par- ticles in the system of measurement furnished by the original axes, with reference to which the particles were moving with velocity w, bears the ratio (1 - w-/c'-)^ : 1 to their distance in the

444 The Theory of Aether and Electrons in the

system of measurement furnished by the transformed axes, with reference to which the particles are at rest. But accord- ing to FitzGerald's hypothesis of contraction, when a material body is in motion relative to the aether, in a direction parallel to the axis of x, its dimensions parallel to this direction contract in precisely this ratio; so that the equation of the body, in terms of the coordinates x}) y^ zly which move with it, is unaltered. Thus the hypothesis of Fitz Gerald may be expressed by the statement .that the equations of the figures of ponderable bodies are covariant with respect to those trans- formations for which the fundamental equations of the aether are covariant.

The covariance holds with respect to all linear homogeneous transformations in the variables (x, y, z, t), of determinant unity, which transform the expression (x"2 + y2- + z~ - c2f) into itself. This group comprises an infinite number of transforma- tions ; so that there are an infinite number of sets of variables resembling (x}) ylt c,, £,), of which any one set (xr, yr, zr, tr) can be derived from any other set (.rs, ys, zs, ts) by a transformation of the group ; among the sets we must of course include the original set of coordinates (x, y, z, t). But hitherto we have proceeded on the assumption that the original set (x, y, z, t) is entitled to a primacy among all the other sets, since the axes (x, y, z) have been supposed to possess the special property of having no motion relative to the aether, and the time repre- sented by the variable t has been understood to be a definite physical quantity. The other sets of variables (.rr, yr, sr, tr) have been regarded merely as symbols convenient for use in problems relating to moving bodies, but not as corresponding to physical entities in the same degree as (x, y, z, t). "We must now inquire whether this view is justified.

The question amounts to asking whether absolute position in space, or at any rate absolute fixity relative to the aether, is something which can be brought within the bounds of human knowledge.

It is well known that the science of dynamics, as founded

Closing Years of the Nineteenth Century. 445

on Newton's laws of motion, does not supply any criterion by which rest may be distinguished from uniform motion ; for if the laws of motion are applicable when the position of bodies is referred to any particular set of axes, they will be equally applicable when position is referred to any other set of axes which have a uniform motion of translation relative to these.

The older theories of electrostatics, magnetism, and electro- dynamics, which are based on the conception of action at a distance, are concerned only with relative configurations and motions, and are therefore useless in the search for a basis of absolute reckoning.

But the existence of an aether, which is postulated in the undulatory theory of light, seems at first sight to involve the conceptions of rest and motion relative to it, and thus to afford a means of specifying absolute position. Suppose, for instance, that a disturbance is generated at any point in free aether; this disturbance will spread outwards in the form of a sphere ; and the centre of this sphere will for all subsequent time occupy an unchanged position relative to the aether. In this way, or in many other ways, we might hope to determine, by electrical or optical experiments, the velocity of the earth relative to the aether.

The failure of such experiments as had been tried led Fitz Gerald* to suggest that the dimensions of material bodies undergo contraction when the bodies are in motion relative to the aether. By the transformation of Lorentz and Larmor, as we have seen, this hypothesis came to be expressed in a new form ; namely that the equation of the figure of the body, referred to a frame of reference moving with it, is always the same, but that frames of reference which are in motion relative to each other are based on different standards of length and time. This way of regarding the matter brings into prominence the fundamental questions involved. Before speaking of lengths and velocities, it is necessary to examine the nature of systems of measurement of space and time.

• Cf . p. 432.

446 The Theory of Aether and Electrons in the

Of the events with which Natural Philosophy is concerned, each is perceived to happen at some definite location at some definite moment. When a material object has been observed to occupy a certain position at a certain instant, the same object may again be observed at a subsequent instant ; but it is impossible to determine whether the object is or is not in the same position, since there is no obvious means of preserving the identity of any location from one moment to another. The physicist, however, finds it convenient to construct a framework of axes in space and time for the purpose of fitting his experiences into an orderly arrangement ; and the ques- tion at issue is whether experience furnishes the means of determining a framework completely and uniquely by absolute properties, or whether the selection inevitably rests on arbitrary choice and accidental circumstance.

In attempting to answer this question, it may first be observed that the choice is always made so as to simplify the description of natural phenomena as much as possible ; thus, the variable which is to measure time is so chosen that its increment in the interval between any two consecutive beats of a pendulum is the same as its increment in the interval between any other two consecutive beats. If the selection of the four variables (x, y, zy t) is well made, it should be possible to express the laws of nature by statements of a simple character, e.g., that a body isolated from the influence of external agents moves through equal intervals of space in equal intervals of time.

Accepting, then, the principle that the framework of axes is to be chosen so as to furnish the simplest possible expression of the natural laws, it becomes of importance to determine which of the natural laws are entitled, by reason of their primary importance, to receive the greatest consideration.