324 Prof. E. Taylor Jones on the Secondary 



some influence on the make-spark— increasing or diminishing 

 its length — if the interruptions follow one another with very 

 great rapidity, in which case there might be a considerable 

 current flowing, one way or the other, in the primary coil at 

 the moment of make. But in working conditions, chiefly 

 owing to the fact that the secondary discharge at break 

 usually causes rapid damping of the oscillations, this effect is 

 not likely to be of importance, and in the present calculation 

 we shall suppose that the initial value of the primary current 

 at make is zero. 



Denoting ij — E/R x by a, and making use of (3), equations 

 (1) and (2) become 



L 1 J+L 1 A < S L + R„=0, (4) 



I^A -r- 9 ? + L21 tjt -1- RoC 2 ,7 + V 2 = 0. . . (5) 

 dt- " at at 



The solution of equations (4), (5) is of the form x — Ke zt , 

 V 2 = B<?^, where z is a root of the cubic equation 



(L^-LnLMy + CLiRj + LsRO^ + frr 1 + RAV + fr=0, 



... (6) 

 In'all actual cases this equation will have two roots of the 

 form 



, 1= -* 1+ w \ _ (7) 



~2=— h—'lTTHl ... .J 



where i = V — 1 5 the third root being real, say 



* 3 =-S (8) 



The complete solution of (4), (5) is thus 



x=A 1 e z i t -f A 2 <rV + A 3 ^ j (9) 



V^B/iU-lVHB^ 1 f' 



where the A's and B's are to be determined from the initial 

 conditions. These are h = 0, V 2 = 0, i 2 =0, that is 



tf=-E/R l5 V 2 = 0, ^-=(), when^ = 0. . (10) 



Thus, by (9) 



va =-E/Ki. . •] 



SB = (11) 



£B* = J 



