i 



Electric Currents in Netivorks of Conductors. 247 



§ 17. We may apply the same methods to the examination 

 of the case when the current sent through the shunted galva- 

 nometer is not generated by a source of constant electromotive 

 force, but is a discharge from a condenser. 



Let K (fig. 17) be a condenser connected up with a shunted 

 galvanometer, so that when the key k is pressed a discharge 

 passes through the galvanometer and shunt. Call the two 

 cycles x and y. Let Gr be the galvanometer-resistance and S 

 the shunt, and let L x and L 2 be their respective coefficients of 

 self-induction ; the coefficient of mutual induction being zero. 



Let q be the quantity of electricity in the condenser at any 

 instant t . Counting the time from the instant of commencing 

 the discharge, let C be the capacity of the condenser, and let 

 q x and q 2 be the quantities of electricity which have, since the 

 beginning of the epoch, flowed respectively through the gal- 

 vanometer and the shunt. 



If T be the energy function and F the dissipation function, 

 we have, as above, the fundamental equations 



2T=L l3/ 2 + L 2 ^-^) 2 , 

 and 



2F = G/ + S<>--*/) 2 ; 

 or 



2T=L l2 / 2 + L 2 ^ 2 + L 2 y 2 -2L 2 ^, 



2F = G/ + S# 2 + S# 2 -2S^. 

 By the fundamental equation 



ddT dF__ 

 dtdx dx " 



For e we must write -k. 



Writing, then, the cycle equations, we have 



-(L^ + Lgy — L 2 x) + Gy+$y — Sx=0 ; 



from which we deduce easily 

 and 



L.t+%=S. 



