REFLECTED AT THE SURFACE OF A CRYSTAL. 5ft 



S1P t <COS ? / > and s-l is the difference between the value of this quantity for the 



sm <p cos (p 



ray and for the wave. 



T T . sin 2 ft, cos 6 tan 6 



*-" l - 



and 



sin cos 



T, . sin 3 d>, cos 6 tan e 

 - 



If we suppose, with Mr M'CULLAGH and Mr NEUMANN, that A=l, our for- 

 mula will coincide with that of the former, by supposing that T, the transmitted 

 vibration, is the resolved part (in its proper direction) of the lost vibratory mo- 

 tion T, . This supposition amounts to conceiving that all the motion communi- 

 cated to the interior medium, is due to the motion at first given in a direction per- 

 pendicular to the surface. 



The equation which we have obtained agrees well with experiment. Mr 

 M'CULLAGH has given the application of this equation so fully in his memoir, that 

 I do not think myself justified in discussing it in this place. 



To obtain the result corresponding to the ordinary ray, we have only to 

 write 0' for $ 90 + 6' for 6, and 1 for s, and we get 



tan a= cos (< + $') tan &. 



This equation gives the value of the deviation or shifting of the plane of po- 

 larization. It is precisely the same as that obtained by M. NEUMANN and Mr 

 M'CULLAGH, and agrees closely with experiment. 



Equating the two values of tan a, we have the following equation for deter- 

 mining the value of the polarizing angle : 



a, j. \ ^ a T . A sin 3 rf> . cos 6 tan e 



cos (<b + d>') tan 6 ' + cos (d> + <*,) cot 6 -- ^- . . /' ,. . >> 0. 



1 sin (<p cp ; ) sm a 



SECTION IV. UNIAXAL CRYSTALS, 



We propose, in this section, to determine the polarizing angle by a general 

 process. 



Since we have already shewn that for a non-crystallized medium p=l, and 

 since the value of p for the ordinary ray is the same as for a non-crystallized 

 medium, it follows that p=l, and therefore by equation (IV), //=!. 

 Hence our equations are 



(I-R)sin0 + R / =Tsm<J> / cos0-T'sin0'sin0' + T / , , . (1) 



(I + R)cos(/)=Tcos^ / cos0-T'cos^)'sin0' ..... (2) 



I'- R'= T sin 6 + T' cos & ' _ . ,* s . - . 4 ,/, * (3) 



- / / Q (4) 



sui<p 



