High' Frequency Induction- Coil. 319 



And subject to the initial conditions that when t = 0, 



v 1 =v„ 5=0.. i,=o, 



or 



A, 4- (J 1= V K, 



-«A 2 + /3B 2 - r C 2 = 0, 



which completely determine the constants. Substituting the 

 values of A 2 , B 2 , 2 in the last equation, we get 



A 1 + C^VoKi 



-ak x + B,-7 C^O, f> 



(aa+^Ax + Coft-^Bi + YcO^O, J 

 whose determinant is 



A= -5(« 2 + /3 2 -«7) +07(c-a). 



A 

 VoK 



B 1 = 

 C 1 = 



y(l3c + ab-Pa), 





A 9 = 



V n K 



7 [c(^ + /3a)-/3(a 2 + & 2 )], 



B 8 « ^7W««-^)-«(fl« + &»)] s 



C 2 = 



VoK 



6c(-« 2 -/3 2 ). 



(22) 



(23) 



The quantities which are observable and measurable in the 

 ordinary type of instruments are not the instantaneous po- 

 tentials and currents whose values we have just deduced, but 

 the " effective " values, that is, the square roots of the mean 

 squares. It is desirable then to evaluate an integral of the 

 form \V^dt for the case of a single-damped oscillation, and 

 also for two superposed oscillations. By giving the proper 

 values to certain constants this will include all the cases which 

 we shall need to consider. 



(«) The general exponential form for an oscillation of any 

 amplitude and period is 



