High-Frequency Induct ion-Coil. 323 



An interesting approximation is obtained when R 2 K 2 is 

 small in comparison with RiK l5 and is disregarded. Our 

 three formulae just obtained then become 



^ 2 -R 2 (L l K l -L 2 K 2 y+R 1 M.^K 1 ^ ' " v ; 



Js ~R 2 (L 1 K 1 -L 2 K 2 ) 9 ^-R 1 M2K 1 2, ' * v °' 



^[(LiKj - L 2 K 2 ) 2 + 4M 2 K 1 K 2 _ 



T -^_ -(L 1 K 1 -L,K 9 )v / (L 1 K 1 -L 2 K 2 ) 2 + 4M 2 K 1 K 2 ] ,. 



l ^"~ 2K 2 [R 2 (L 1 K 1 -L 2 K 2 )« + K 1 M*K 1 *J ' ^' ; 



It will be noticed that R x and R 2 are involved in the same 

 way in all the denominators, and that the numerators differ 

 only by a constant factor which does not involve the resist- 

 ances, except the first, which has a term in -^-. Solving 



these equations for R 2 (L 1 K 1 — L 2 K 2 ) 2 + RjMXR^ 2 , and dividing 

 by M 2 K 1 2 , 



B |B (L l K 1 -L f K,)' . nV ° i ( L ' + L '|) 



^1 + ^2 M2Ki2 - y-g 



7lK 9 Vn 2 



V 2 2 



nCtf ( LjKj - L 2 K 2 ) 2 + 4M 2 K 1 K 2 



_ -(L 1 K 1 ^L 2 K 2 )v/(L 1 K 1 --L 2 K 2 ) 2 + 4M 2 K 1 K 2 ] (28) 



2M 2 K 1 2 K 2 I, 2 



In the case where the secondary circuit is closed, the 

 expression for the current is of the form 



I = ^ = *-«'[(-«A+/3B)cos/3* 



+ (-/3A-aB)sm/3t]—yCe-y t . (29) 

 /-» 00 

 The integral 1 T*dt then consists of two principal parts. 



The last is, by direct integration, 



7 2 2 _ 7 C 2 

 2y 2 ' 



The first part, by the preceding discussion, is 



(-«A + /3B) + (-/3A-"B) 2 = (^ + ^ 2 )(A 2 + B 2 ) 



4« 4« 



