generated in a High-tension Magneto. 



153 



amplitudes. It can be shown that the values of the damping 

 factors ki and k 2 are 



;i = w(^P-/3), 



where 



= 4*v(^P+/3), J 



(31) 



and 



1 = lK 1 C l , 2 = JRA, .... (32) 

 /8 = -^^|{(« 1 -^)L 1 1 +(^ + ^>L 2 2 /. (33) 



n " — n 



The phase angles S x and 8 2 would also have been modified 

 by the resistances. We shall, however, for the present 

 retain the condition that the resistances are neglected, and 

 also neglect the small angles Si, $ 2 , gi yen by (30). 



The theory now proceeds as in the case of the induction- 

 coil *. The greatest value of V 2 occurs when 27rn 1 t is not 

 far from tt/2, and the conditions are most favourable if 

 positive maxima of the two oscillations represented in (28) 

 occur simultaneously, i. e. if sin 2^/2x^ = 1 and sin 2irn 2 t = — 1 

 for the same value of t. This requires that the frequency- 

 ratio should have one of the values given by 



= 3, 7, 11, 15, 



(34) 



Assuming this condition to be fulfilled, the expression for 

 the maximum value of V 2 is, by {28), 



V 2 „, = 2,ri (L 1 + L 21 )^^-. 



(35) 



Expressed in terms of u, k 2 , and s by means of (15) this 

 becomes 



(Li + Lsi)^ 



Let 



Y 2m = 

 U = 



a/L 2 C 2 vu + s — 2 V(l — h) u 

 1 



\A + s-2 s/il-k^u 



(36) 



. (37) 



For given values of k 2 and s, U has a maximum value of 

 at 



Vs-l + k* 



u = 1-F. . . . 

 * See Phil. Mag. Aug. 1915, p. 224. 



(38) 



n 



