316 Mr. E. B. Rosa on the Determination o/v, the 



the various arms of the bridge, through the galvanometer 

 from D to C. When p touches R the two surfaces of the 

 condenser are connected, and the latter discharges itself 

 through D R. If now the armature be made to vibrate con- 

 tinuously there will be a series of momentary currents through 

 the galvanometer, and by adjusting the resistance a (c and 

 d being large, fixed resistances), these interrupted currents 

 may be exactly counterbalanced by the steady current from 

 C to D, and the resultant deflexion of the galvanometer is 

 zero. When this is the case there is a relation between the 

 capacity of the condenser, the number of times the latter is 

 charged and discharged per second, and the resistances in the 

 various arms of the bridge. Maxwell gives an approximate 

 value of this relation. Thomson's more complete investigation 

 gives the following equation : — 



a f lm a 2 \ 



a \ (a + c+g)(a + b + d)) 



Cd \ 1+ c(a + b + d)f \ l+ d(a+c+g)) . 



where n is the number of complete oscillations of the armature 

 j) per second ; C is the capacity of the condenser in electro- 

 magnetic measure ; and the other letters the resistances of the 

 various arms of the bridge, as shown in fig. 1. In the present 

 case the values of these resistances were about as follows: — 



a = 40 to 1900 ohms. d = 100,000 ohms. 



b = nearly. g = 6,000 „ 



c = 1,570,000 to 2,450,000 ohms. 



Owing to the very high values of c and d as compared with 

 a, b, and g, the above equation may be replaced by the ap- 

 proximate one, C = —7 which is true to within a hundredth 



of one per cent. The electrostatic capacity, C, is determined 

 by calculation from the geometrical constants of the con- 



denser. The ratio of these values of the capacities, -^ , is v 2 , 



the square root of which, v, is the quantity sought. 



Advantages of the Method, 



Thus there appears at once an important advantage of the 

 method of determining the ratio of the units from the values 

 of a capacity, namely, that v is the square root of the ratio of 



* 



