March 24, 1892] 



NATURE 



5^i 



account the fact that the source is itself io motion. For it is 

 evident that the waves which pass in a given time through any 

 point towards which the source is moving are more numerous 

 than had the source been at rest, and that the wave-lengths are 

 correspondingly shortened. \iv be the velocity of the source, 

 the wave-length is changed from \ to A(i - z^/V). At a point 

 behind, from which the source is retreating, the wave-length 

 is X(i -f viV). We shall have occasion to refer again to this 

 principle, named after Doppler, as applied by Huggins and 

 others to the investigation of the motion of the heavenly bodies 

 in the line of sight. 



Referring now to (5), we see that, although the absolute re- 

 tardation is afifected by v, yet that the retardation as ineastired in 

 wavi-lengths remains unaffected. If, then, there be, in the 

 absence of z', an agreement of phase between the two interfering 

 beams, the introduction of 7/ will cause no disturbance. Conse- 

 quently no shifting of the interference bands is to be expected 

 when the apparatus is turned so that the direction of propaga- 

 gation makes in succession all possible angles with that of the 

 earth's motion. 



The experiment has been modified by Hoek,^ who so 

 arranged matters as to eliminate the part of the retardation 

 independent of v. As before, of two parallel beams A and 

 B, one, A, passes through a plate of refracting medium ; the 

 other, B, through air. The beams are then collected by a lens, 

 at the principal focus of which is placed a mirror. After reflec- 

 tion by this mirror, the beams exchange paths, B returning 

 through the plate, and A through air. Apart, therefore, from a 

 possible effect of the motion, there would be complete com- 

 pensation and no final difference of path. As to the effect of 

 the motion, it would appear at first sight that it ought to be 

 sensible. During the first passage, A is (on account of v) 

 accelerated ; on the return, B is retarded ; and thus we might 

 expect, upon the whole, a relative acceleration of A equal to 

 {/I - \)d . az'/V. But here, again, we have to consider the fact 

 that another part of the apparatus, viz. the mirror, partakes in the 

 motion. In the act of reflection the original retardation of A is 

 increased by twice the distance through which the mirror retreats 

 in the interval between the arrival of the two waves. This dis- 

 tance is (with sufficient approximation) {yL - i)d . vjW ; so that 

 the influence of the movement of the mirror just compensates 

 the acceleration of A which would have resulted in the case of 

 a fixed mirror. On the whole, then, and so long as the square 

 o( Z'/V may be neglected, no displacement of fringes is 10 be 

 expected when the apparatus is turned. The fact that no dis- 

 placement was observed by Hoek, nor in an analogous experi- 

 ment by Mascart,'- proves that if the stationary condition of the 

 aether in terrestrial vacuous spaces be admitted, we are driven 

 to accept Fresnel's law of the rate of propagation in moving 

 refracting media. 



What IS virtually another form of the same experiment was 

 tried by Maxwell,^ with like negative results. In this case, 

 prisms were used instead of plates ; and the efTect if existent, 

 would have shown itself by a displacement of the image of a 

 a spider-line when the instruoient was turned into various 

 azimuths. 



On the basis of Fresnel's vie ws it may, in fact, be proved generally 

 that, so far as the first power ofv/V is concerned, the earth's motion 

 would not reveal itself in any phenomenon of terrestrial refrac- 

 tion, diffraction, or ordinary refraction. The more important 

 special cases were examined by Fresnel himself, and the de- 

 monstration has been completed by Stokes.^ Space will not 

 allow of the reproduction of these investigations here, and this 

 is the less necessary, as the experiment of Hoek, already ex- 

 amined, seems to raise the principal question at issue in the 

 most direct manner. 



Another point remains to be touched upon. We have hitherto 

 neglected dispersion, treating /x as constant. In stationary dis- 

 persing media, ytt may be regarded indifferently as a function of 

 the wave-length or of the periodic time. When, however, the 

 medium is in motion, the distinction acquires significance ; and 

 the question arises, What value of ju are we to understand in 

 the principal term V/ju of (i)? Mascart points out that the 

 entirely negative results of such experiments as those above 

 described indicates that, in spite of the difference of wave-length 



' Archives l^ierlandaises, t. iii. p. 180 (1868); t. iv. p. 443 (1869). 



« Ann. de I' Ecole Normale, t. iii. (1874). 



3 Phil Trans., 186S, p. 532. 



< Phil. Mag., xxviii. p. 76 (1846). See also Mascart, W««. deV Ecole 

 Norm., t. i. (1872), t. iii. (1874); and Verdet, " Q^uvres," t. iv., deuxieme 

 partie. 



due to the motion, we must lake the same value of /* as if the 

 medium and the source had been at rest, or that /u is to be 

 regarded as a function of the period. 



Mascart has experimented also upon the influence of the 

 t-arth's motion upon double refraction, with results which are 

 entirely negative. The theoretical interpretation must remain 

 somewhat ambiguous, so long as we remain in ignorance of the 

 mechanical cause of double refraction. 



Reference has already been made to the important experi- 

 ments by Fizeau and by Michelson upon the velocity of light in 

 moving media. The method, in its main features, is due to the 

 former,^ and is very ingeniously contrived for its purpose. Light 

 issuing from a slit is rendered parallel by a collimating lens, and 

 is then divided into two portions, which traverse tubes contain- 

 ing running water. After passing the tubes, the light falls upon 

 a focussing lens and mirror (as in Hoek's experiment), the effect 

 of which is to interchange the paths. Both rays traverse both 

 tubes ; and, consequently, when ultimately brought together, 

 they are in a condition to produce interference bands. If now 

 the water is allowed to flow through the tubes in opposite direc- 

 tions, one ray propagates itself throughout ivith the motion of 

 the water, and the other against the motion of the water ; and 

 thus, if the motion has any effect up^n the velocity of light, a 

 shift of the bands is to be expected. This shift may be doubled 

 by reversing the fl )w of water in the tubes. 



Fizeau's investigation has recently been repeated in an im- 

 proved form by Michelson." 



" Light from a source at a falls on a half-silvered surface, b, 

 where it divides; one part following the path bcdefbg, 

 and the other the path bfedcbg. This arrangement has 



NO. I 169, VOL. 45] 



I the following advantages : (i) it permits the use of an extended 

 ; source of light, as a gas flame ; (2) it allows any distance be- 

 tween the tubes which may be desired ; (3) it was tried by a 

 i preliminary experiment, by placing an inclined plate of glass at 

 i h. The only effect was either to alter the width of the fringes, 

 or to alter their inclination ; but in no case was the centre of the 

 j central ivhite fringe affected. Even holding a lighted match in 

 ' the path had no effect on this point. 



" The tubes containing the fluid were of brass, 28 mm. in- 

 ternal diameter ; and in the first series of experiments, a little 

 over 3 metres in length, and in the second series a little more 

 j than 6 metres." 



t Even with the longer tubes and the full velocity (about 8 

 I metres per second) the displacement on reversal amounted to 

 less than the width of a fringe. Nevertheless, fairly concordant 

 results were arrived at ; and they showed that the fraction (.• ) 

 of the velocity of the water {v) by which the velocity of light is 

 altered is -434, with a possible error of ± '02. The numerical 

 value of the theoretical expression is 



-v- = I - ;*-2 = -437, 



in very cloSe accordance. 



** The experiment was also tried with air moving with a 

 velocity of 25 metres per second. The displacement was about 

 •01 of a fringe ; a quantity smaller than the probable error of 



' Ann. de Chiwie, III. Ivii. (1859). 



3 .American Journal, vol. xxxi. p. 377 (t886). 



