of Luminoxis TViwes in Tramparent Bodies. 211 



and similarly we may show that 



^= 2^ ^_ "^^'r 

 de " dii" dt"" ~''' d^' 



Also, since the vibrations are transversal, we have 



pct + q^^sy = (6.) 



We shall now simplify the equations (1.), (2.), (3.), by the 

 conditions just obtained. 



Since «,^, y are functions of ?/ alone, we have by (4.), 



aa:^ - du^^ ^Udy " dlF^ ^' ^''•' 

 hence, and by (5.), the equation (1.) becomes 



^dtfi 



^,-.=(A;>^^B(,^+o)^: 



-^^-^)H^^-S)-c 



or, smce q- + s^ — \ — j^\ 



d- a 



B)^:=(A-B)y. 



/ d^'oL d-^ iPy. 



(7.) 



= - C«by(6.), 

 and similar equations for /3 and y. 



We have therefore -r-o + t-, ?s « = : 



du^ M^ — Y> 



and by (5.) this gives 



Now the most general value of a. which satisfies these equa- 

 tions, is 



a. =■ a cos k (u t — u + b) + a' cask (vi + 7i -^ s'), 

 where a s a' e' are arbitrary constants, 



and /.2 = - — ^ . 



This value of « represents two waves, one transmitted for- 

 wards and the other backwards, with the same velocity v ; 

 confining our attention to the wave transmitted forward, 

 we may put 



a = a cos k {u i—u), omitting s also; and similarly 

 P2 



