318 Mr. W. P. Boynton on the 



Substituting these values in equation (17), we have 



where 



and 



"■" Ao — \_j\-y — 



_ LiKi — L2K2 



X ~ x/XL 1 K ] ^L 2 K 2 ) a + 4M 2 Sy ; 



MK,K 2 V 



(19) 



ac 

 a — c 



V K 1= 



v/O^K, - L 2 K,) 2 +4M 2 K,K 2 ' 



(20) 



B 2 and D 2 are small of the first order in comparison with A 2 

 and C 2 . 



(2) If the secondary circuit be closed, V 2 drops out, or K 

 may be considered infinite, and our equation (1) becomes 



MX. 2 M\ 



whence 

 where 



1 + LiK 1 X 2 + RiKiX _ 



MK^X 2 - L 2 X 2 + R 2 X~ L 2 X + R 2 



X 1 =— a + i/3, X 2 = — a— iff, X 3 = — 7, 



.r L^ + L^ B 2 i La'^ + M'Rg 

 a " 2 L L X L 2 -M 2 L 2 J ~ 2L 2 (L X L 2 -M 2 ) ; 



L 2 



(21) 



.4: 



M 



tt= -L 2 ' 



RiKCLjLsj-M 2 ) 2«K(L 1 L 2 -M 2 ) 2 



ML S 



C = 



ML 2 2 

 W 



]-, 



R 2 MK (L X L 2 -M 2 ) 

 L7~ ' 



R 2 2 MK 



The general solution may be written 



Qtl =*-«'( A, cos £* + Bj sin £0 + CV"^ 

 Q 2 = e- a ^(A 2 cos fit + B 2 sin £*) + Ci*-*, 



where the constants are related by the equations 

 aAx + ^B^Aa, 

 aB i -\-bA 1 =B 2 , 

 cOi =C 2 . 



