﻿2 Prof. E. Taylor Jones on the most 



The physical meaning of the above results may be further 

 considered in the light of what goes on in the primary 

 circuit after the interruption of the current. An expression 

 for the potential-difference Y 1 of the plates of the primary 

 condenser, at any time t after the interruption of the 

 current i , has been given by Dibbern *. If the resistances 

 of the circuits are neglected, Dibbern's expression becomes 



Vi= E o ni ^ 2 ( — L^! ) sin liDi^t 



27n n 1 2 tt 2 ( 1 T n \ . 



If n 2 //ii has one of the values 3, 7, 11, .... , then at the 

 time t=l/4:n u sin27rn^=l, and sm27rn 2 t= — 1. Conse- 

 quently the value of V x becomes at this instant 



"0 



1 o • t n i n z 



— 27n Ll 



27rC! ' n 2 — n x n 2 — )ii 



This may be expressed in terms of the ratio L 2 C 2 /L 1 ( , ' 1 

 Calling this m, and writing a for „ 2[ n — ^ , we have 

 ^^2 = 2a y^??i(l — & 2 ) , 



Hence Yi 



n 2 — m=\/2a(m + l) — 4a v /??i(l-P)t- 

 z { 1 - S^LAa^y/mCl - P) } 



27TCV 2a(ro + 1) - ±ay/m(l - k 2 ) 



711 = 



Inserting the value of a and condition (2), i. e. ., 

 we find that this expression vanishes. 



It appears, therefore, that if condilions (1) and (2) are 

 satisfied, the amplitudes of the two potential waves in the 

 primary circuit are equal, and that at the instant in question 

 the potentials are at their maxima, but in opposite phase. 

 The primary condenser is therefore uncharged, while at the 

 same moment the secondary potential is at its maximum J, 

 the two waves in the secondary circuit being #ien at their 

 maxima and in the same phase. Further, since dY l /dt = 0, 

 and dV 2 /dt = 0, there is no current in either circuit. The 

 whole of the energy therefore exists at this moment in the 



* E. Dibbern, Ann. ds •■ Physik, xl. 4, p. 938 (1913); Inaug. Diss., 

 Kiel. 



t L. c. p. 581. \ L > c- P- 581. 



