520 Mr. 0. J. Lodge on a Modification of Mance's 



galvanometer-needle proportional to the amount of variation. 

 The quantity of electricity flowing into or out of the condenser 

 through the galvanometer-coil will be equal to the variation 

 of potential, Y, taking place between its terminals multiplied 

 by S, its statical capacity ; and the throw of the galvanometer- 

 needle a will be proportional to this quantity multiplied by the 

 galvanometer-constant r, which depends directly on the num- 

 ber of turns of wire on it. The resistance of the galvanometer 

 is quite immaterial. If H is the strength of the magnetic 

 field in which the needle hangs and T the time of a complete 

 oscillation of the needle in that field, we have 



. a TrrSY 

 Sm 2 = -HT- < 3 > 



By using, therefore, a galvanometer with a very large number 

 of turns, and a condenser of great capacity, one can increase 

 the sensitiveness of the method to any extent. 



The investigation of the distribution of currents throughout 

 the circuit becomes very simple now that there is no con- 

 tinuous current through the branch g. The connexions are 

 shown in fig. 3, where AC is the branch r, whose resistance 

 can be changed at pleasure from infinity to something near 

 ^ero. Let A, B, C, D, be the potentials of the four corners ; 

 let d be the resistance of the battery we wish to measure, e its 

 electromotive force, and u the strength of the current passing 

 through it. We want the difference of potential B — D to 

 be wholly independent of the potentials of A and C, which 

 will be altered by changing r. Now as there is no current 

 through g, we have the same current passing through b as 

 through a — that is, 



similarly 

 hence 



A-B B-C jy Ab + Ca 

 = — _ - or B = — 



a o a + b 



( A-€)c + Cd 

 V - ' c + d 



R _T) _ (A-C)(bd-ac) + €c(a + b) m 



which shows that the difference of potentials between the ter- 

 minals of the condenser is independent of the potentials A and 

 C as soon as the condition bd—ac = is satisfied. 



We may conveniently write the above expression in terms 

 of the strength of the current u passing through the battery 



