High- Frequency Induction- Coil. 



317 



A 1 = 



YoK iy g3(c 2 -flc)_V K 1 c > 



C — CL 



^1 = a = — — r > 



}► • d7) 



a — c 



n VqK! [j3 7 a 2 + he? - $a(yc + Sd) ] 



where B : and D x are small of the first order in comparison 

 with A x and Ci. 



a and b of equation (12) are the real part and the coefficient 

 of the imaginary part of k x respectively. From (1) we have 



l + L^V + RiK^ ] + LjK^ - a + iff) 2 -f RiK^ - « + i/3) 



MKit-a + ffl 2 



* 1= =_ 



(-^-^j 2 + L 1 K 1 ( C c 2 + ff 2 ) 2 + R 1 K 1 (-q~^j( Q : 2 + /3 2 ) 

 " ~" MK^+ff 2 ) 2 



from which we get 



a 2 -ff 2 + L 1 K 1 (a 2 + /3 2 ) 2 -R 1 K 1 «( a 2 + ff 2 ) 





&=- 



MK^ + ff 2 ) 2 



2*/3-R 1 K 1 /3( a 2 + /3 2 ) 



MK 1 (a 2 + j 8 2 ) 2 ' 



If a. is so small that we may disregard its square in com- 

 parison with /3 2 , these become 



a ~ MKj/3 2 MK^S 2 ' 



R 1 K li 9 2 -2a . 



MKi/3 3 ' 

 and by substituting 7 and 8 for a and /3, 

 l-L 1 K 1 8 2 _ ff 2 -L 1 K 1 /3 2 8 2 



MK^ 2 - MK^S 2 ; 

 R 1 K 1 8 2 -2 7 



(18) 



c = 



(180 



d = 



MK^ 8 " 

 Substituting the values of ft and 8, we get for a and c 



_ LaKa-LxK!- ^(L^-LaKg)'^ 4M 2 K!K 8 

 a ~ 2MK 2 ; 



_ LgKg-L^H- n/(L 1 K 1 ~L 2 K 2 ) 2 + 4M 2 K 1 K 2 

 2MK X 



