generated in a High-tension Magneto, 149 



■effect on the secondary potential of varying one or other o£ 

 the inductances or capacities. The expressions for the 

 damping factors are given later. 



(2) That E and ^E may be treated as constant during 

 the short interval with which we are concerned. These 

 quantities are in any case small in comparison with the 

 values attained by V/ and V 2 ', and no great error can 

 be introduced by regarding them as constant. 



Thus, omitting the resistance terms in (7) and (8), and 

 introducing two new variables defined by V 1 = Y 1 ' — E and 

 V 2 =V 2 '-(2 + l)E, we have 



,7 2 V /7 2 V 



(L 2 +L s1 )C/^+L 21 C 1 ^f 1 + V 2 -V 1 = 0. . (10) 



Adding (9) and (10) and writing sh 2 for the sum 

 L-j + Lg^L^-j-Lj, where s is a fraction not much greater 

 than unity, we find 



(L 1 +L 21 )O 1 ^+ 5 L 2 C 2 5 2+V 2 ==0 - ' * C 11 ) 



The assumed solutions Y 1 =Ae i ^ t } V 2 =^Be ipt , substituted in 

 (9) and (11) give 



A(l-L 1 C 1 ^ 2 )=B(L 1 + L 12 )C 2 p 2 , . . . (12) 



A(L X + L 21 )CV = B(l-sL 2 C 2 p 2 ), . . . (13) 



leading, after elimination of the ratio B/A_, to the equation 

 for p ( = 27rn), 



^LALA(1 - k 2 ) -pXLA + sL 2 C 2 ) + 1 = 0. . (14) 



Here k 2 is the coupling L 12 L 2 i/L 1 L 2 . 



The system has therefore two frequencies, n lf n 2) given by 

 the equation 



8ttV(1-F) 



= X i \±\/( \ i ';Y 4(1 r P) - (15) 



In the extreme case C^co (primary closed) one of the 

 frequencies is zero and the other is n c = l/27r^/L 2 C 2 (l — k 2 ). 

 In the other extreme case, Ci = 0, one frequency is infinite 

 and the other is given by n = 1/2tt\/ sL 2 C 2 , that is, it is the 

 frequency of the primary and secondary oscillating together 



