MEASUREMENT OF CHARGES. 463 



We have again assumed that the capacity of the electrometer 

 is independent of the deflection, which is not strictly correct. Care 

 must finally be taken that the capacities to be compared are without 

 inductive action on one another, and that the capacity of the con- 

 necting wires may itself be neglected. 



The method becomes very exact, especially for capacities which 

 are very near each other, when we work by opposition. The charges 

 of the two capacities being M and M x when they are joined cross- 

 wise, and when one of the common armatures is raised to potential V , 

 we have 



M = CV , M' = C'V . 



Joining the armatures of contrary signs, the final potential is 

 defined by the equation 



it follows that 



C'_V 



C V 



If the capacities are very near, we may write 

 C' V 



1051. MEASUREMENT OF CHARGES. We may also deduce the 

 ratio of two capacities from the ratio of the charges which they 

 acquire for the same potential, or, more generally, in the case of 

 condensers, from the ratio of the charges for the same difference 

 of potential between their armatures. This is the method employed 

 by Gaugain* in an important research on the relations between the 

 distribution of statical electricity in a system of conductors and the 

 permanent currents in a correlated system (213). 



The quantities of electricity were measured by a discharge 

 electrometer (824) with which the electrified bodies were connected 

 by a cotton thread. As the discharge is not complete, we may 

 allow for the residue which corresponds to the final state of the 



* GAUGAIN. Ann. de Chim. et de Phys. [3], Vol. LXIV., p. 174. 1862. 

 See MASCART. Traite d' Electricite Statique, Vol. i., p. 467. 



