312 Mr. G. U. Yule on the Passage of Oscillator 



we will only take the case of both media being non-magnetic, or 



A*s=/*i=l. 

 As a solution of equations (1) and (2) we select 



X 1 =A 1 ^ c *- VA#> +A 1 , '/ (# - v ^ 



X 9 =B 9 ^" 2?) 



where t must be not less than zero, p is either wholly imaginary 

 or complex according as the incident ray is steady or damped: 

 q is as yet undetermined ; A^ is the amplitude of the incident 

 wave-train, A/ of the reflected wave-train, and B 2 of the 

 transmitted wave-train. 



Inserting the value of X 2 given in (4) in equation (2) , and 

 carrying out the differentiation, we get 



^M 1+ £f> < 5 ) 



so q is also partly imaginary. 



A ' B 



To determine -— ^ and ~ we require another pair of equa- 

 Aj A, 



tions. These will be given us by the interface conditions : 



the conditions namely, that there must be no discontinuous 



jump in the values of either the tangential electric force or 



the tangential magnetic force, at any time, in passing from 



the dielectric to the electrolyte. That is, we must have 



X.=X 5 



(iXx dK 2 



Y (Q 



dz dz 

 where 



2=0, / = anything. 



Inserting the values of X x and X 2 in (6) we get, putting 



2 = 0, 



Ai + A^B,, "I 



. ■ .^VA(-A 1 + A/)=- M B 8 ;/- ' " K>) 



A ' B 

 and solving these two equations for -r- , ~, 



Ax Aj 



a/ 



A, 



9 



- 1 



Vft 





9 



+ 1 



•A 





2VA 





Ai . VA+? 



