440 



NA TURE 



[A/arc k II, 1886 



leigh's value F'-76'for the arrangement considered by him, but 

 to point out that, if only one revolving mirror is used, the ex- 

 periment cann t be performrd in this way. The lens spoken of 

 in Lord Rayleigh's s cond note is, then, a necessary condition 

 of the experiment. When the lens is used it seems to me, how- 

 ever, that the result ought not to be a neutralisation of effects, 

 but rather an equal rotation in the opposite direction. I have 

 Lord Rayleigh's authority for stating that he agrees with this 

 conclusion. 



The method of Foucault's revolving mirror thus measures 

 neither I' nor U, nor V^IU, but V^I{2V - U). As Fand U 

 differ by a small amount only, the last expression becomes nearly 

 equal to U, so that Michelson's experiment is in complete agree- 

 ment with theory. 



In Foucault's experiment, it is well known, the displacement 

 of an image is measured which is due to the rotation of a 

 reflecting mirror in the time of passage of the light from the 

 mirror to a fixed mirror and back again. But in order that this 

 quantity should be capable of measurement, it is necessary that 

 a displacement of the mii-ror should not by itself alone cause a 

 displacement of tlie image. 



The following consideration will show what conditions this 

 imposes on the arrangement of the experiment. 



In the accompanying figure let A B be the position of a wave- 

 front as it leaves the mirror {supposed fixed). Let c n be the 

 position as it returns to the mirror. I have drawn the wave- 

 surfaces plane, for the sake of simplicity, but the argument 

 remains the same if they are curved. The point A may cirre- 

 spond to the point c on the returning front or to the point D. If 

 now the mirror is displaced through a small angle, the wave- 

 front takes a different position, a' b. If this displacement shall 

 not change the position of the image after reflection from the 

 miri-or, the returning wave must turn through the same angle and 

 take up the position c' D. But it is easily seen that, in order 

 that this may be possible, the point A must correspond to D and 

 11 to c, for the optical length along any ray between two wave- 



to the wave-front on its journey, whether it is refracted, reflected, 

 or inverted, that side of it which left the receding part of the 

 rotating mirror will always gain on the other. When the wave- 

 front returns to the revolving mirror, it will have rotated 

 through the angle given in Lord Rayleigh's second note ; but 

 we have to consider the direction of rotation. 



If that part of the wave-front which left the receding half of 

 the mirror will return again to the receding half, the final rota- 

 tion of wave-front will be in the same direction as the rotation 

 of the mirror ; and the displacement of the image which depends 

 on the relative rotation of mirror and wave-front will be dimin- 

 ished. In this case, however, as I have shown, we want a 

 second revolving mirror, otherwise the image of the slit will 

 be drawn out into a band. 



In the experiments hitherto performed, the wave-front is 

 inverted an odd number of times between the two mirrors, and 

 hence that part which left the receding side of the revolving 

 mirror will now be on the preceding side. The relative rotation 



i being increased, the observed displac menl of the image will be 

 increased. 



I The total observed rotation w i!l thus, with Lord Rayleigh's 

 notation, be 



V\ 



fronts remains the same ; also, owing to the maximum-minimum 

 property, we can still measure optical lengths in the displaced 

 position along the original paths ; and the length of the ray 

 leaving A having been shortened by a distance A a', the ray 

 leaving B must be shortened by an equal amount, c c' — that is 

 to say, the ray arriving at c must be the one leaving B, and the 

 ray arriving at D must be the one which left A. We may then 

 express the condition of a stationary image thus : The wave- 

 surface nnist be inverted by the optical arrangement interposed, 

 and the magnifying power of this optical arrangement must be 

 equal to one. The last part of the condition is rendered neces- 

 sary by the fact that the width of beam must remain the same ; 

 otherwise A a' could not be equal to c c'. If both conditions 

 are fulfilled, the image will remain distinct in the rotating 

 miri-or, otherwise it would be drawn out into a band. 



But an arrangement is possible, at any rate theoretically, in 

 which the wave-surface is not inverted. We might have a 

 second mirror rotating in such a way as to neutralise the effect 

 ofdisplacement. For this purpose the second mirror ought tu 

 rotate twice as fast as the first, the light being sent on to this 

 second mirror on its way back only, after reflection from the 

 first revolving mirror. As the angular velocity of the two 

 mirrors must have their velocity accurately adjusted, the e.xperi- 

 ment would be difficult to perform, but it is important to point 

 out that it is theoretically possible. 



Returning now to Foucault's arrangement, consider two suc- 

 cessive wave-fronts as they leave the revolving mirror. The 

 distances between them will be larger on the receding than on 

 the preceding side of the mirror. That part of the wave-front 

 which is on the receding side will thus be propagated more 

 quickly in a medium having dispersion, and whatever happens 



the velocity of light calculated will be Vjy ' 



■="(■ 



d\oaV\ 



-j-j — - j, the apparent velocity becomes equal to 



V-I(2V- V). If' 2_ is small comp.ired to unity, we may write 



(/ log\ 

 the expression for the apparent velocity approximately 



'i - '!JJ3Z\ 



^ i/cosxj 



U. 



In the case of bisulphide of carbon, J. W. G., m the passage 

 quoted above, gives for the green rays Kj P'— I '637, Kj U= 1 767, 

 A' being the velocity in viaio. From this we get for the 

 theoretical value of the quantity observed in Michelson's experi- 

 ment l'758> being identical wi;h the value 176 .actually 

 observed. 



If a second rotating min-or is used, as described, Lord 

 Rayleigh's value F^/ 6'^ remains true. 



We have then as a final result, that, while the aberration of 

 light measures V, and the eclipses of Jupiter's satellites and 

 Fizeau's experiments me.asure U : Foucault's revolving mirror 

 measure-^ either K-/(2f'- U), or V^jU. 



Arthur Schuster 



Variable Stars 



In the last number of Nature (p. 397) Prof. Seeliger, of 

 Munich, is represented as thinking "it not improbable that 

 the blazing forth of the A^crz'a may have been due to a collision 

 which caused an enormous development of heat and light." It 

 appears to me that the collision hypothesis is not necessary, and 

 that the variability of a star is a physico-chemical consequence 

 of mere cooling. This conclusion is based on considerations 

 relating to the formation of the chemical elements. 



If we suppose a mass of primitive matter, say gaseous, to be 

 cooling down, it will from a chemical point of view undergo a 

 series of changes such as are indicated in the known traniforma- 

 tions I to Ij, NO2 to N2O4, &c. ; in short, it will produce a 

 succession of polymers. When, however, each stage of poly- 

 merisation is exactly reached, the formation of each new polymer 

 being attended with an increase of density, will, from a physical 

 point of view, lead to an evolution of heat. This evolution of 

 heat will occur periodically as polymerisation goes on ; and if the 

 heat be sufficiently intense, there will be a corresponding 

 periodic development of light. The number of such periods 

 will doubtless depend on the nature of the primitive matter, and 

 the difference between its temperature and that of its environ- 

 ment. I cannot recall an instance where, in the laboratory, 

 more than three polymeinc jieriods have been attained ; but 

 celestial events have a wider range and greater possibilities. 



The evolution of heat which necessarily occurs at the point of 

 polymerisation involves of course a partial reversal of the poly- 

 merisation. Elements therefore will be formed which may be 

 regarded as derived from successive polymers by virtue of such 

 reversal. 



