REFLECTED AT THE SURFACE OF A CRYSTAL. 49 



But 18 



r 



since the first part vanishes. 



Denote i&-8x8y e-^^smfdy hy F ; 



M-rfldRA F dR, 



then J* 



The next term 2 (0 ^ +2^- <V 2 ) 5$ is derived from (a') in precisely the same 

 way that we obtained () from (a). 

 The result is 2 (0 / + <V 2 ) * ft. 



= - ( T - - cos 0, cos 6 (cos 2 0, - 2 sin 2 0,) 

 \ 2 e, 



In the same manner the value of 2 dtf dy 1 Sa, may be derived from (b'). 



The value of F, is 2 d * Stf e~ "' sin 



Lastly, 2(0/ + ^5y 2 )(/3 / -/3)=Q ! ,,(A-|S)(e'); and the other quantities in 

 equation (10) are zero. 



The sum of (') and (If) = - ^ (I + R) cos (cos 2 0-2 sin 2 + 3 sin 2 0) 



21 



M fdl dR\ 0-2^ FrfR < 



+ I + I cos (cos 2 02 sin 2 + 3 sin 2 0) + ' 



<? ,. M./dl dR\ , FdR, 



= - (I + R)cos0+ (^- + -5-) COS0 + - '. 

 2 e \dx dx) f dy 



The sum of (0 and (d'} = - T - COS0, cos 6 (cos 2 0,-2 sin* 0, + 3 sin a 0,) 



\ 6 f dx/ 



(r 2 M' // T'\ F d T 



^T-~ ?LL\ C os 0' sin 6' (cos 2 0' - 2 sin 2 0' + 3 sin 2 0') + S ^i 



VOL. XV. PART I. 



