of Luminous Waves in Transparent Bodies. ' 215 

 Hence (1.) becomes 



K-B)i^.(cH-;:i^-c,). = o. 



or, if we denote ^ — ry H — 5 — '-rr- bv k-, 

 «■'— 13 0,- — D 





+ k^o, = 0; 



dii^ 



and in exactly the same manner we have 



^^ « JO 



— -^'- + /t2 « = ; 

 a u- 



and similar equations for determining /3 /3^ y y;. 



From the equation -p^^ + Fa = 0, we conclude, as m 



the former case, first, that the particles must vibrate accord- 

 ing to the cycloidal law ; and secondly, that 



^-' _ /« _ c , c, 



Now in the case where the particles of matter are put in 

 motion solely by the vibrations of the aether, it is, I think, evi- 

 dent that the particles of matter will (except in peculiar cases) 

 vibrate in the same time as the particles do which put them 



in motion *. Now -r-^ is the time of vibration of the particles 

 kv 



2 It 

 of aether, and since k is the same for «, as for «, -j — is that of 



the particles of matter, hence by what has been said we must 

 have in general 0^ = u, and hence it follows that 



\ TT- C Cy 



It now remains to show, that the results we have thus ob- 

 tained are equally true when the particles are arranged as in 

 figure 4, and are therefore true in all cases, whatever be 

 the law of arrangement of the particles; the proof of this is 

 simple, but as it leads to some interesting results which I have 



• We know this to be tlic case when aiirial vibrations put the particles 

 of any l)ody in motion ; provided those particles be capable of vibrating in 

 ant/ limv. 



