Capacity for Induction-coils andTesla Coils. 225 



frequency, and damping coefficient. The expression for the 

 secondary potential was worked out in certain cases from 

 the "constants'''' of the circuits, and found to agree closely 

 with experiment both in wave-form and in maximum 

 potential as deduced from the observed spark-length. 



According to this theory the secondary potential at time 

 t after the interruption of the primary current is repre- 

 sented, if the resistances of the circuits are neglected, by the 

 expression 



2ttL 



2\ l 'Q n \ n 2 



V 2 = s — o " (n 2 sin 2irn x t — n x sin 2irn 2 t). . (1) 



?i 2 —n^ 



in which L 21 is the coefficient of induction of: the primary 

 coil on the secondary, i is the primary current interrupted,, 

 and n 1? n 2 are the two frequencies of oscillation of the system 

 (n 2 > ny). For given values of L 21 , i , n x and n 2 , the value 

 of V 2 is stationary at times given by dV 2 /dt=0, i. e. 



COS 27T/Z^ — cos27r/? 2 £ = 0, .... (2) 



or sin 7r(/^ -\rn 2 )t . sin 7r(» 2 — n l )t = 0. . . . (3) 



The stationary values of V 2 therefore occur at the times 



1 2 



* = 0, 



W 



n 1 -\-n 2 i »i -}-/t 2 ' n i + n 2 i 



and _J_ 2 3 



n 2~ w l' n 2 — n l' > u 2~~ n \' > 



At any stationary value we have, by (2), 



sin 27rn 2 t= ± sin 27ra 1 £ 3 .... (5) 



the upper sign giving the numerical minima of V 2 , the lower 

 sign the maxima. 



Substituting in (1) we find that the numerical maxima lie 

 on the {t, y) curve 



y = 2irL 2l i ^ _' sin 2th^, . . . . (G) 

 the minima on the curve 



y-ftriwb^-™*"H« ( 7 ) 



In dealing with the greatest sparking potential of an 

 induction-coil we are only concerned with the greatest 

 maximum of V a in the first half-period of the slower oscil- 

 lation. Even though there should be a closer coincidence 

 of maxima of the two waves in some subsequent halt-period, 

 the amplitudes are by this time so much reduced by the 



Phil Mag. S. 6. Vol. 30. No. 176. Aug. 1915. Q 



