REFLECTED AT THE SURFACE OF A CRYSTAL. 51 



But (a)=a + 8 a, &c. ; hence if we write this expression by commencing with 

 the portions which relate to the external medium, we have 



<Pa, _ ( . , cb'r 



jX-i"*** 



r r 



This equation differs from equation (5) only in the last line. If, then, in con- 

 formity with our previous notation, we write Q, for 2 (</> r+^8^) we can give 



d 2 CL 

 the value of -r- at once. 



, (-,)- Q x , (,_) .... (14) 

 similarly = + Q f (p-fa-Q,,(J3,-8) .... (15) 



Thus we have obtained the six equations of motion. Let us now obtain from 

 these equations the results to which they give rise. 



In the first place d -^-'^ L =-(Q +Q*<) (-/) ' but from the values of a 



d t d t 



and a,, we have 



-* (-,)= ..... (17) 



hence either Q x + Q x , = c 2 or a-a,=0. 

 NOW 



i a 

 + S m 2 _\ +22 



z I , - _ 



a quantity essentially different from zero. 



We have therefore a-a,=0 ; and, by (17), ^-f-^| i =0 as it ought. 



d t d t 



In the same way it may be shewn that 



/3-/?,=0, and 7-^=0. 

 In the second place, by doubling equation (9), we obtain 2 j-^-, or 



