500 



NA TURE 



[March 24, 1892 



of the condition of the aether at the earth's surface, this agree- 

 ment must involve some particular supposition as to the propa- 

 i;ation of light in moving refracting media. 



The theory of these phenomena must evidently turn upon the 

 question whether the aether at the earth's surface is at rest, 

 absolutely, or relatively to the earth ; ^ and this fundamental 

 question has not yet received a certain answer. The independ- 

 ence of terrestrial optical phenomena of the eirth's motion in 

 its orbit is, of course, more easily explained upon the latter 

 alternative; or rather no explanation is required. But in that 

 case the difficulty is thrown upon stellar aberration, which 

 follows a more simple law than we should expect to apply in 

 the case of an aether disturbed by the passage of a body in its 

 neighbourhood. Prof. Stokes has, indeed, attempted a theory 

 on these lines,- by supposing the aetherial motion to be what is 

 called in hydrodynamics irrotational. In strictness there is, 

 however, no such motion possible, subject to the condition of 

 vanishing absolutely at a great distance, and relatively at the 

 earth's surface ; and it does not appear that the objection thus 

 arising can be satisfactorily met. 



If we start from the experimental facts which have the most 

 direct bearing upon the question under discussion, we are led 

 to regard Fresnel's views (doubtless in some generalized form) 

 as the more plausible. From the results of Fizeau and Michel- 

 son relative to air, we may conclude with tolerable confidence 

 that a small mass of ponderable matter, of very low refracting 

 power, moving in space, would not appreciably carry the aether 

 with it. The extension of the argument to a body as large as 

 the earth is not unnatural, though it involves certainly an ele- 

 ment of hypothesis. In like maimer, if the globe were of water, 

 we should expect the aether to be carried forward, but not to the 

 fiill amount. The simple t supposition open to us is that, in any 

 kind of ponderable matter, forming part of a complex mass, the 

 a;iher is carried forward with a velocity dependent upon the 

 local refracting power, but independent of the refracting power 

 and velocity of other parts of the mass. In the earth's atmo- 

 sphere, where the refracting power is negligible, the aether 

 would be sensibly undisturoed. 



If we agree to adopt this point of view provisionally, we have 

 next to consider the relation between the velocity of luminous 

 propagation in moving ponderable matter and the refractive 

 index. The character of this relation wa< discovrred by Fresnel, 

 whose argument may be thrown into the following form. 



Consider the behaviour of the aether when a plate of ponder- 

 able matter (index — ju.) is carried forward through vacuum with 

 velocity » in a direction perpendicular to its plane. If D be 

 the density of the aether in vacuum, and Dj the density in the 

 refracting medium, then, according to Fresnel's views as to the 

 cause of refraction, Dj = ^-D. The aether is thus condensed as 

 the ]>late reaches it ; and if we assume that the whole quantity 

 of aether is invariable, this consideration leads to the law giving 

 the velocity (xv) with which the denser aether within the plate 

 n ust be supposed to be carried forward. For conceive two 

 ideal planes, one in the plate and one in the anterior vacuous 

 region, to move forward with velocity v. The whole amount of 

 aether between the planes must remain unchanged. Now, the 

 quantity entering (per unit area and time) is Dv, and the quantity 

 leaving is T)i(v - xv). Hence, 



X = I - ix-\ 

 so that the velocity with which the aether in the plate is carried 

 forward is v{i - fJ."-), tending to vanish as y. approaches unity. 

 If V be the velocity of light in vacuum, and V/fj. the velocity in 

 the medium at rest, then the absolute velocity of light in the 

 moving medium is 



V/;U±Z.(l-;U-2) (I) 



Whatever may be thought of the means by which it is ob- 

 tained, it is not a little remarkable that this formula, and no 

 other, is consistent with the facts of terrestrial refraction, if we 

 once admit that the aether in the atmosphere is at absolute rest. It 

 is not probable that the aether, in mdving refracting bodies, can 

 properly be regarded as itself in motion ; but if we knew more 

 al)out the matter we might come to see that the objection is 

 verbal rather than real. Perhaps the following illustration may 

 as-ist the imagination. Compare the aether in vacuum to a 

 stretched string, the transverse vibrations of which represent 



I An accusation of crudeness might fairly be brought against this phraseo- 

 ' Jgy ; but an attempt to express the argument in more general language 

 would probably fail, and would in any case be tedious. 

 ^ Phil. IMag., xxviii., 1846, p. 76 ; xxix., 1846, p. (5. 



light. If the string is loaded, the velocity of propagation of 

 waves is diminished. This represents the passage of light through 

 stationary refracting matter. If now the loads be imagined to 

 run along the string with a velocity not insensible in comparison 

 with that of waves, the velocity of the latter is modified. The 

 substitution of a membrane for a string will allow of a still 

 closer parallel. It appears that the suggested model would lead 

 to a somewhat different law of velocity from that of Fresnel ; but 

 in bringing it forward the object is merely to show that we need 

 not interpret Fresnel's language too literally. 



We will now consider a few examples of the application of 

 the law of velocity in a moving medium; and first to the ex- 

 periment of Boscovitch, in which stellar aberration is observed 

 with a telescope filled with water. We have only to suppose 

 the space between the two screens of our former explanation to 

 be occupied by water, which is at rest relatively to the screens. 

 In consequence of the movement of the water, the wave, after 

 traversing the first aperture, is carried laterally with the velocity 

 z/(i - ju"-), and this is to be subtracted from the actual velocity 



V of the aperture in the posterior screen. The difference is 

 fiT'^v. The ratio of this to the velocity of light in water (V/^u) 

 gives the angular displacement of the second aperture nece-sary 

 to compensate for the motion. We thus obtain /^"'z'/V. This 

 angle, being measured in water, corresponds to vjN in air ; so 

 that the result of the motion is to make the star appear as if it 

 were in advance of its real place by the angle z'/V, precisely as 

 would have happened had the telescope contained air or vacuum 

 instead of water. 



We will now calculate the effect of the motion of a plate per- 

 pendicular to its own plane upon the retardation of luminous 

 waves moving in the same (or in the opposite) direction. The 

 velocity of the plate is v, its index is ^, and its thickness is a. 

 Denoting, as before, the velocity of the aether within the plate 

 by XV, and supposing, in the first place, that the signs of v and 



V are the same, we have, for the absolute velocity of the wave in 

 the plate, 



V//i 4- XV. 



We have now lo express the time (/) occupied by the wave in 

 traversing the plate. This is not to be found by simply divid- 

 ing d by the above written velocity ; for during the time t the 

 anterior face of the plate (which the wave reaches last) is carried 

 forward through the distance vt. Thus, to determine / we have 



whence 



(V/,u -^r xv)t- d ^ vt, 



Nt 



d I -t- (^- - \)ii.vlN 



(2) 



The time, ^0, which would have been occupied in traversing the 

 same distance {,d +vi), had the plate been away, is given by 



so that 



Thus 



V^. 



Vtf) = d + v( ; 

 f.v/V 



d I i- (x - l)iiviV 



v{t - 1,) _ M(x - ^m 



(3) 



(4) 



Substituting in this Fresnel's value of x, viz. (i - fT-), and 

 neglecting as insensible the square of vjY, we find 



d 1 + {x — l)iiv/V 



si's value of x, vi 

 square of v/V, we 



V(.'-^„)=(A. - l)dii -v/Y) (S) 



If we suppose that part of the original wave traverses the plate, 

 and that part passes alongside, (5) gives the relative retardation 

 — that is, the distance between the wave fronts which were 

 originally in one plane. It would appear at first sight that this 

 result would give us the means of rendering v evident. For the 

 retardation, depending upon the sign of o/V, will be altered 

 I when the direction of the light is reversed, and this we have it 

 I in our power to bring about by simply turning our apparatus 

 through 180°. A more careful examination will, however, lead 

 us to a different conclusion. 



The most obvious way of examining the retardation would be 

 to use homogeneous light, and, by producing regular interfer- 

 ence of the two portions, to observe the position of the fringes, 

 and any displacement that might result from a shift of the 

 apparatus relatively to the direction of the earth's motion. But 

 if we employ for this purpose a terrestrial flame, e.^. that of a 

 Bunsen's burner containing sodium, we have to take into 



NO. I 169, VOL. 45j 



