540 Prof. Arthur Schuster on 



distinction between the effects of the force E cos ret and 

 E cos nt is given by 



(n— ic)t = \ nearly. 



This means that the difference in phase between the forces at 

 the time t may amount to nearly 30°. If we introduce the 

 periodic times of vibration of the two forces T x = 27r/ft and 

 T 2 = 27r//e, we may say that, in order that they should intro- 

 duce a difference in the energy amounting to two per cent, of 

 a vibrating system whose natural period is 27r/ft, it is neces- 

 sary that they should continue to act for m vibrations where 



— ^-jL — = ^— / v/ , 24 = *08 approximately. 



If the vibrating system is subject to friction, and the differ- 

 ence in the energy absorbed is two per cent., it follows that 

 the friction must be sufficiently small to allow a single impulse 

 to produce vibrations which do not appreciably diminish in 

 m vibrations, where m is the number determined by the above 

 equation. 



All these considerations tend to show that if a medium 

 absorbs strongly some particular wave-length and transmits 

 another wave-length near it, the particles must be capable of 

 being set into vibration by an impulse, and that the periodic 

 disturbance of the particle produced by the impulse must last 

 the longer, the more sudden the variation in the coefficient of 

 absorption. The fact that a substance draws a distinction 

 between two periods in the incident light which are near 

 together implies a regularity of vibration in the substance 

 capable of being produced by irregular impulses of the medium. 



If we produce an interference-pattern on a photographic 

 screen, and by this means are able to observe interference 

 with large difference of path, the case is exactly analogous to 

 that in which a grating or prism is used. The regularity 

 which enables us to observe the interference lies in the instru- 

 ment of investigation, and does not prove anything with 

 respect to the regularity of white light. Our eye is an 

 instrument which distinguishes light of different wave- 

 lengths ; this implies a certain regularity in the motion pro- 

 duced by an impulsive disturbance of the medium. If an 

 impulse reaching the retina did not call forth periodic 

 motion in nerve-fibres persisting for some appreciable time, 

 the interference-spectra observed, say, with Lloyd's mirror 

 would be identical with that indicated by a thermopile, as 

 shown in fig. 7. But we see a succession of a few spectra, 

 and may gain a rough idea of the number of periods 



