502 



NATURE 



[March 24, 1892 



observation. The value calculated from (i - /i~2) would be 

 •0036." 



We have seen that, so far as the first power of f/V is con- 

 cerned, Fresnel's theory agrees with all the facts of the case. 

 The question whether it is possible to contrive an experiment in 

 which z^'/V- shall be sensible, has been considered by Michel- 

 son,^ who, having arrived at an affirmative conclusion, proceeded 

 to attack this very difficult experimental problem. Tn Michel- 

 son's apparatus interference is brought about between two rays, 

 coming of course originally from the same source, one of which 

 has traversed to and fro a distance, D, parallel to the earth's 

 motion, and the other a like distance in the perpendicular direc- 

 tion. The phase of the latter ray is considered by Michelsnn to 

 be unaffected by the earth's motion. As to the former, it is 

 retarded by the amount 



D 



V 



2D 



V 



2D 



or, reckoned in distance at velocity V, 

 2Dz'VV2. 



(6) 



" Considering only the velocity of the earth in its orbit, 

 the ratio t^/V = lo"-* approximately, and z/'/V- = lo"^ If 

 D = 1200 mm., or, in wave-lengths of yellow light, 2,000,000, 

 then in terms of the same unit, 2D v'^fV' = '04. 



"If, therefore, an apparatus is so constructed as to permit two 

 pencils of light, which have travelled over paths at right angles 

 to each other to interfere, the pencil which has travelled in the 

 direction of the earih's motion, will in reality travel '04 of a 

 wave-length further than it would have done were the earth at 

 rest. The other pencil, bein^ at right angles to the motion, 

 would not be affected. 



"If now the apparatus be revolved through 90°, so that the 

 second pencil is brought into the direction of the earth's motion, 

 its path will be lengthened '04 wave- length. The total change 

 in the position of the interference bands would be 'oS of the 

 distance between the bands, a quantity easily measurable." 



In the actual experiment, the earth's velocity was not avail- 

 able to the full extent, and the displacement to be expected on 

 this account was reduced to "048 ; but Michelson considers 

 that some addition to it should be made on account of the 

 motion of the solar system as a whole. The displacement 

 actually found was "022 ; and when the apparatus was em- 

 ployed in such azimuths that the rotation should have had no 

 effect in any case, "034. These results are very small, and 

 Michelson gives reasons for regarding them as partially system- 

 atic errors of experiment. He concludes that there is no real 

 displacement of the bands, and that the hypothesis of a .stationary 

 aether is thus shown to be inconsistent with fact. 



It has, however, been recently pointed out by Lorentz - that 

 Michelson has over-estimated the effect to be expected according 

 to Fresnel's views. The ray which travels perpendicularly to 

 the earth's motion is not unaffected thereby, but is retarded to 

 the amount represented by D z/'/V^. The outstanding rela- 

 tive retardation is thus only Dz/'/V-, instead of the double 

 of that quantity, .\ccepting this correction, we have to expect, 

 according to Fresnel's views, a shift of only '024 of a band in 

 Michelson 's experiment. 



Under these circumstances Michelson's results can hardly be 

 regarded as weighing heavily in the scale. It is much to be 

 wished that the experiment should be repeated with such im- 

 provements as experience suggests. In observations spread 

 over a year, the effects, if any, due to the earth's motion in its 

 orbit, and to that of the solar system through space, would be 

 separated. 



On the whole, Fresnel's hypothesis of a stationary aether 

 appears to be at the present time the more probable ; but the 

 question must be considered to be an open one. Further 

 evidence would be most important ; but it is difficult to see from 

 what quarter anything essentially now can be expected. It 

 might be worth while for astronomers to inquire whether it is 

 really true, as is generally assumed, that stellar aberration is 

 independent of the position upon the earth's surface from which 

 the observation is made. Another question that might, perhaps, 

 be submitted with advantage to an experimental examination is 

 whether the propagation of light in air is affected by the rapid 



^ American Journal, xxii. p. 120(1881). 



- " Over den invloed dien de beweging der aarde of de licht ver.schijnselen 

 uitoefent." (Amsterdam, 1886.) 



motion of heavy masses parallel to, and in the immediate neigh- 

 bourhood of, the ray. 



If we once admit the principle that, whatever the explanation 

 may be, no ordinary ^ terrestrial observation is affected by the 

 earth's motion, it is easy to give an account of what must 

 happen when the light comes from an external source which 

 may have a motion in the line of sight. Imagine, for example, 

 a spectroscopic examination of a soda flame situated on a star 

 and vibrating in identical periods with tliose of terrestrial soda 

 flame-s. In accordance with Doppler's principle, the wave- 

 lengths are altered by a relative motion in the line of sight, and 

 the fact may be rendered evident by a comparison between the 

 spectra of the star and of the terrestrial flame, held so as to be 

 seen in the same direction. The simplest case is when the flame 

 is entirely external to the apparatus, so that both lights are 

 treated in precisely the same way. It is evident that, under 

 these circumstances, the difference between the two cannot fail 

 to become apparent ; and this way of regarding the matter 

 shows also that the apparent displacement of the bright lines in 

 the stellar spectrum is dependent upon the relative, and not 

 further upon the absolute, motions of the star and of the earth. 

 The mean of observations, equally distributed over the year, 

 would thus give data for determining the relative motion in the 

 line of sight of the star and of the solar system. 



If the external source be the sun itself, it might be thought 

 that the spectra must agree almost perfectly, the eccentricity of 

 the earth's orbit being so very small. But th-; sun is a revolving 

 body, and consequently a distinction must be made according 

 to the part of the sun from which the light proceeds. It is 

 found, in fact, that a very sensible shift takes place in the posi- 

 tion of the dark lines according as the light under observation 

 comes from the advancing or from the retreating limb. This 

 circumstance has been successfully emplayed by Thollon and 

 Cornu to distinguish between lines having a solar and a ter- 

 restrial origin. In the latter case it is a matter of indifference 

 from which part of the sun the light proceeds. 



In general optical theory the finiteness of the velocity of light 

 is usually disregarded. Velocities at least ten times greater 

 than that of the earth in its orbit are, however, known to astro- 

 nomers ; and such must begin to exercise a sensible influence 

 upon radiation. Moreover, in so wide a generalization as the 

 theory of exchanges, the neglect of even a small quantity is 

 unsatisfactory. Prof. Balfour Stewart has discussed the in- 

 fluence of the motion of a plate exercising selective absorption 

 upon the equilibrium of radiation within an inclosure. He 

 argues that a disturbance will ensue, involving a violation of 

 the second law of thermodynamics, unless compensated by 

 some other effect not hitherto recognized. It appears, how- 

 ever, more probable that the whole radiation coming/re;;/ and 

 through a plate would not be altered by its motion. Whatever 

 effect (in accordance with Doppler's law) the motion has upon 

 the radiation from the plate, a similar effect would probably be 

 produced upon the absorbing power. On this view the only 

 result of the motion would be to change the wave-length of the 

 rays most powerfully emitted and absorbed, but without dis- 

 turbing the balance required by the theory of exchanges. The 

 moving plate would in fact be equivalent to a stationary one of 

 slightly different quality. * Rayleigh. 



1887. 



SOCIETIES AND ACADEMIES. 

 London. 

 Mathematical Society, March 10. — Prof Greenhill, 

 F.R.S., President, in the chair. — The President and Mr. S. 

 Roberts, F. U.S., spoke upon the loss the Society had sustained 

 by the recent decease of Dr. Hirst, F. R.S., touching more 

 especially upon the great services he had rendered to it in the 

 early days of its existence. — The following paper was read : — 

 The simplest equivalent of a given optical path, and the obser- 

 vations required to determine it, by Dr. J. Larmor. To specify 

 an optical path through a heterogeneous medium like the atmo- 

 sphere, or through an arrangement of refracting substances like 

 an optical instrument, we require the geometrical curve followed 

 by the filament of light, and also the character of the modifica- 

 tion produced on a filament following this path across the medium. 



I This qualification is inserted in order to exclude such an experiment as 

 that of Michelson, just described, in which an attempt is made to render 

 sensible an effect depending on w-'/V-. 



= B.A. Report, 1871. 



NO, 



I 169, VOL. 45] 



