at a Twin Plane of a Crystal. 251 



medium and to — B/+ Cg in the second, gives 

 (Br + C/Zi)©! + (Br + 0^)6' + (Br + C/* 3 )0" 



= -(Br + C^)^-(Br + C/* 2 )^. . . (44) 



The continuity of b, or db/dt, or by (6) dR/dx—d~P/dz, is 

 found, when regard is paid to (37), to be already secured by 

 (42) ; and we have only further to consider the continuity of 

 de/dt, or by (6) of dQ/dx, since P is here independent of y. 

 Thus 



p^Br + C/i^-p^Br + Cfijd' -p 2 {Br + C/* 2 )6>" 



= -p l (Br + Cfi 1 )d i -p 2 (Br^CfM 2 )e 2 . . . (45) 



The coefficients which occur in (44), (45) may be expressed 

 more briefly in terms of the velocities of the various waves. 

 For 



Y 2 = s 2 /(p 2 + r 2 ), (46) 



and thus by (38), 



Br + 0^ = /^, Br + C/^^V/. . . (47) 

 Setting now 



ps/pi = vr } ^2 2 /^]V, 2 = o-, . . . (47') 



the four equations of condition take the form 



® l + 6 / + ad ff =-0 l -ad 2 , 

 <d 1 -0'-.*r(re / '=-d 1 -*Ta9 2 .j 



If we equate the values of 1? 6 2 obtained from the first and 

 second pairs of equations (48), we find 



(<r + l)0' + ( OT +l>0" = O, -, 



( OT - 1)0! + (sr + 1)61' + OT (<r + l)e" = 0, J " ' V ' 



and from these again 



(sr — c) (-ra-<r — 1)' 



f 



(48) 



(50) 



«"- f+^r- 1 ^ • • • • (si) 



(-S7 — O") ("SJ<7 — 1) X ' 



by which the two reflected waves are determined. 



These reflected waves correspond to the incident wave 

 (®u Ply fr), and it is the wave 0' which is reflected according 

 to the ordinary law. If there be a second incident wave 

 (8*j p2, P* 2 ), the corresponding reflected waves are to be found 

 from (50;, (51) by interchanging 6', 0", and by writing for 

 «r, a the reciprocals of these ratios. If both incident waves 



