250 Prof. H. A. Rowland on Magnetic Attractions, 

 The displacement currents a 1 ', b r , and c' will bo 



,_ K dP 

 a ~4tt dt> 

 .,_K dQ 



C "4tt <fc' 

 and they are also expressed by the equations 



47r^=-A 2 G 7 

 47t/jlc' ' — — A 2 H. 

 Hence we have by elimination: — 



K ^{S-^^'-^}- A2F = 0; 



Kfi {S~i c (^'- a ' 6 i) } - A 2 H=0. 



Before the solution of these equations, of course the values of 

 a i> °\i c ii an( i a/ y b' , c must be substituted in terms of F, Gr, 

 and H. 



Let us now take the case of a plane-polarized ray passing 

 in the direction of the axis of z, with a magnetic force c x 

 along the same axis. The magnetic forces a, b, c, the varia- 

 tions of which constitute the waves of light, are very small ; 

 for Maxwell has calculated that in strong sunlight the maxi- 

 mum is about one tenth of the horizontal intensity of the 

 earth's magnetism. Hence we can write 



TZ . Cd 2 ¥ d /7/ ,") d 2 F . 



„ (d 2 a d, , v ) 



am 



dz 2 "> 





and, replacing V and a! by their values, we have 

 |^ 2 F__cc L d 3 G \ d 2 F_ 

 A Id* 2 Airudtdz*) dz 2 > 



Airfjb dtdz 

 K/ "| ^ + 47r^^c^J ^ 2 ~ U * 



