of Light and the Theory of a Quasi-labile yEther. 



/and G in (25) as constant, as well as B and F. 

 equations may be written 



249 

 These 



l^ 



ttF 



•y_i 



Differentiating, we get 



f 



pi 



or 



47r2BcZ|-=-K/)' 

 7rF^^ = -7ry<i(p-); 



47r2B^ d log^' = -Ip^ d log/, 



/2 



Z2 



^2 ,/|2 ^2r 

 TtF ^ ^ log "2- = ^ ^ log p-^ 



Hence, if we write V for the wave-velocity (Ifp), n for the 

 index of refraction, and \ for the wave-length in vacuo, we 

 have for the ratio of the two parts into which we have divided 

 the potential energy on the elastic theory, 



hh^ , TT^B/i^ _ d log V _ d log n ,^^. 



T^~l^~ dlogp ~~dh^' ' ' ^ ^ 



and for the ratio of the two parts into which we have divided 

 the kinetic energy on the electrical theory, 



g/A^ . 7rF/^A^ _ f^logy _ ^logn 

 p^ ' p^ dlogp 6? log A,* 



It is interesting to see that these ratios have the same value. 

 This value may be expressed in another form, which is sug- 

 gestive of some important relations. If we write U for what 

 Lord Eayleigh has called the velocity of a group of waves ^, 



(27) 



5=1- 

 V 



dlosY 



(ZlogV 

 dlogl 



v-u 



diogl V 

 dlogY _Y-V 



dlogp 



U 



(28) 



* See his "Note on Progressive Waves," Proc. Lond, Math. Soc. 

 vol. ix. No. 125, reprinted in his ' Theory of Sound,' vol. ii. p. 297. 



