524 Mr. A. 0. Allen on 



Further, a : , — a 2 , a 3 , and —/are proportional to 



1 



|3 



/3 2 



y 



L/(P+K) 



-1 

 (P+R)/L 



L/(P+R) 

 -1 

 (P+R)//L 



1 1 



a /3 



a 2 (3 2 



L/(P+R) 

 -1 



(P+R)/L 



1 



/3 2 



P + R 



) 



P + R 



P + R. 



L 



times the 



A'. 



and it is obvious that (taking a to denote the root 



the 2nd and 3rd vanish, while the 1st is 

 4th. Hence, finally, 



All the factors are present to fix two rates of decay differing 

 in general from that corresponding to a, but they fail to be 

 operative because the amplitudes are zero. To sum up : 

 the short-circuit isolates the upper half from the lower as if 

 the galvanometer-resistance were infinite; the two halves 

 discharge independently but at equal rates, owing to the 

 equality of the time-constants of the condenser circuit and 

 inductance circuit; when Q = R, there is no flow by the 

 short-circuit. 



If the battery circuit is not short-circuited but broken, 

 the only difference is that the root a. is 



P + Q 



x=fe at , y= — h, it= — 



P + Q 



Q 



Xm 



The galvanometer-arm isolates the right-hand side from the 

 if its resistance were zero : the time-constants of 



as 



left, 



the two discharges are ^ — _- and 



H + b 



L 



which of course are 



equal. xt ^ ° P + Q' 



§ 3. In Rimington's method (Phil. Mag. vol. xxiv., July 

 1887) the double adjustment is avoided, and the continuous 

 balance sacrificed, by putting K in parallel with only a 

 portion s of the resistance S. The equation for z is then 



gZ = R^ — Sy — (Gr + R + S) z— sic 



upon short-circuiting, and putting 



Rs R(Q + S) 



/, 



/ 



S(Q + S-*)/, S(Q + S-0" 

 for the initial values of x } y, 7/, .it is evident that z is not 



