( 079 ) 



.ip for llie inagnclic force and pntting the magnetic permeability = 1, 

 we have for the metal 



1 1 . 



c c 



ll is found by tlicsc equalions (hat in electromagnetic waves travel- 

 ling in Ihe direction of the positive c, <I" and .<p can have the direc- 

 tions of OX and O }\ and vabies eqnal to the real pai-ts of the 

 conijtlcx quantities 



a being the amplitude of the electric force, and tho conslanls «and 

 y. t)eing given In' 



Similarly, waves travelling in the opposite direction may l)e repre- 

 sented b}' 



^•,.:=ae ' , 'Vy = — >« ^"^ • • i'^^) 



For the aether the corresponding formulae are somewhat simpler; 

 in the first case 



n . . n 



inl — I — ~ int — 2 — ~ 



(i,- = ae ' , /p, = a. '' .... (29) 



and in the second 



• . • " • t • " 



Jilt -\- I — z int-\-i — - 



(r-,. = ag ' , J^y=:-ag ' .... (30) 



Now, if rays fall perpendicularly on the front surface of the plate, 

 we may unite all the systems of waves arising from the repeated 

 reflexions into the following parts : l^"^ . a reflected system in the 

 aether, 2"^'. transmitted \vaves in the aether behind the plate, 3"^ . waves 

 in the plate, travelling towards the back surface and 4^'^ rays in the 

 metal, going in the opposite direction. Representing the incident rays 

 and the motions mentioned under these four iieads by the equations 

 (29), (30), (29), (27), (28), with the values a„ a„ a,, (^ „ a, of the 

 amplitude, we have, in virtue of the conditions at the two surfaces 

 (continuity of ^x and ^y) 



«1 + «2 = «4 + «5' 



«J — «^ = X («4 — «5), 



n 

 — .s -\-s — < — A 



71 a, e — xa,e ^=.a,e '^ . 



