298 PROCEEDINGS OF THE AMERICAN ACADEMY. 



necessarj' to give the observed primarj^ current curve. An examination 

 of the experimental curves of Figure 14 shows that the first part of the 

 primary wave can be approximately represented by the expression 



?l = /i (1 —cos o) t). 



where now /i represents the instantaneous value, and /i the maximum 

 value of the primary current, and « is 2 tt times the secondary frequency. 

 Time is reckoned from the beginning of the primary discharge. 



The corresponding expression for the secondary wave is found by 

 measurements of Figure 14 to be 



?2 = /2 sin {oi>t+ 115""). 



These expressions can now be substituted in the differential equa- 

 tion for the primary circuit, 



r 



Jo I 



in which R^ is the resistance of the gap, ll^ is the resistance of the 

 rest of the primary circuit. 

 Also 



^c = /i — lo- (See Figure 13) 

 whence 



Lxl\ ft) sin mt — Mh CO cos (w^ + 11 5°) + {Rx + R^h (1 — cos ai) 



{Ii — Io)t _ J ^ma>t _ Qo 

 C'l ft>6'i Ci 



Solving for 74 there results 



Qo (Ii-Io)t 



Ii( Zico — -— jsin ft)!? + MIoto cos (at + 115°) 



/l(l —cos at) 



Qo Ii-To 



lA Li<o — • yr^ — h .91 31(0 -^ ) sin cot — .42 il/Zz cos at 

 \ tift) JiJ 



^1 

 if Ri be neglected. 



If appropriate values for the constants of this expression be taken, 



and Rf, plotted to the current ii, the curve shown by the dotted line of 



Figure 16 is obtained. 



