92 APPLICATION OF THE PRECEDING RESULTS 



potential function at -4's centre, arising from the whole exterior 

 space, will be 



* pdxdydz 



and the value of the same function at j&'s centre will be 



[pdxdydz 

 J P ' 



the integrals extending over all the space exterior to the con- 

 ducting system under consideration. 



If now, Q be the total quantity of electricity on A's surface, 

 and Q' that on J5's, their radii being a and a' ; it is clear, the 

 value of the potential function at -4's centre, arising from the 

 system itself, will be 



seeing that) we may neglect the part due to the wire, on account 

 of its fineness^ and that due to the other sphere, on account of 

 its distance. In a similar way, the value of the same function 

 at j5's centre will be found to be 



a 



But (art* 1) the value of the total potential function must be 

 constant throughout the whole interior of the conducting system, 

 and therefore its value at the two centres must be equal ; hence 



Q f 



-- j_ / 



a J 



pdxdydz 



Although />, in the present case, is exceedingly small, the 

 integrals contained in this equation may not only be considerable, 

 but very great, since they are of the second dimension relative 

 to space. The spheres, when at a great distance from each 

 other, may therefore become highly electrical, according to the 

 observations of experimental philosophers, and the charge they 

 will receive in any proposed case may readily be calculated ; 

 the value of p being supposed given. When one of the spheres, 





