﻿of Periodic JEther Disturbance. 811 



and in the irrotational boundary disturbances 



£ = —pg cos {/<;(?/ sin 0— c£)— e}, 



77== y -ggsh 1 e Vi-^coB e c 2 sin {«(y sin ^ — cO — e}, 



<y/ l-^- 2 cosec 2 6> 



and 



-s.sin^! Vl-4kcosec20i r / • a .\ \ 



%i=p x e Yl " cos{#ci(ysui0i— ci*) — € r h 



^i=— y P c \ ^ sin01 Vl "^ cosec2 ^ 1 sin{/ gl (ysin^ 1 -e 1 0-6 i } ; 



Y/l-y- 2 cosec 2 ^ 



where V and Y 1 are the velocities of the irrotational waves. 

 From the boundary conditions, if and only if V=V 1? 



a = /3 = 6 = e 1 = 0, 



_tan(flj-fl) 



r_ tan(6> 1 + 6')' 



,= 52?J ( l +f .) f 



COS &i J 



p ==p 1= =cos0 tan {0\ — 6). 



No restriction is placed upon the magnitude of V, but the 

 solution fails when 6 is in the neighbourhood of sin _1 c/V, 

 and for values less than sin -1 c/V the boundary disturbances 

 become simple periodic functions of x : in both cases, there- 

 fore, no steady state is reached and energy is dissipated in 

 irrotational motion. 



The solution in the case of total internal reflexion may be 

 obtained on replacing the transmitted train by the corre- 

 sponding equivoluminal motion parallel to the boundary. 



3. In a medium in which the molecules are similarly 

 oriented the velocity depends on the direction of trans- 

 mission. Let the direction of a resonator be (I', m', n') 

 and its relative intensity a. Then for a periodic disturbance 

 with the displacement in the direction (/, m, n) the forced 

 oscillation is of intensity 



a(W + mm' +nn'), 



