Electromagnetic to the Electrostatic Unit. 299 



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 : 



1 — 



cd\ 1+ -. — \ r . \\ 1 + i — — v- 



i c(a + b + d) ) ( d{a + c+g) 



where n is the number of complete oscillations of the armature 

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

 magnetic measure ; and the other letters are the resistances of 

 the various arms of the bridge, as shown in the figure. 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 <z, 

 I) and g the above equation may be replaced by the approxi- 



CI 



mate one C= -, which is true to within a hundredth of one 



nca 



per cent. The electrostatic capacity. C, is determined by cal- 

 culation from the geometrical constants of the condenser. The 



C 

 ratio of these values of the capacity — is v 2 , the square root of 



v.; 



which, v, is the quantity sought. 



Advantages of the method. 



Thus 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 the 

 capacities, and any error in the latter enters into v by only half 

 its amount. 



There are several important advantages of this method of 

 measuring the electromagnetic capacity. In the first place, a 

 knowledge of the exact electromotive force and resistance of 

 the battery is not required-, and their constancy is not essen- 

 tial. In the second place, since it is a null method, such 

 uncertain quantities as logarithmic decrement, torsion of the 

 suspending fibre and period of the needle are not required ; the 

 galvanometer can readily be made more sensitive than a bal- 

 listic galvanometer ; its "constant" need not be known; and 

 the field of force may be variable both in intensity and direc- 

 tion without prejudice to the experiment. On the other hand, 



