174 



ELECTROMETRY. 



on the two similar masses m^ and - m' 2 of the other sphere, which 

 gives 



f= 



;;/,;;/, mtH, + injn 



We shall thus obtain the values of ;;/, m v and / as a function of 

 the potentials of the two spheres. 



When the masses m and ;// 1 are equal, and therefore the poten- 

 tials are equal, the expressions become simpler, and give 



(5) 



V 2 





2C 



fr* 



from which we can deduce the ratio -. 



m* 



In order to control these formulae, we will make ^=4. We get 

 then 



m = rV x 0*80262, 



/ = V 2 x 0-03761, 

 7 = ^x0-05838. 



If these results are compared respectively with the corresponding 

 values 0-80258, - 0-03766, 0-05846 of Sir W. Thomson's table (177), 

 we see that the approximation given by the formulas (5) is then about 

 o-oo i ; while the simple formulas leave still a relative error greater 

 than o o6. 



When the distance d is considerably greater, we may expand the 



expressions (5) as a function of increasing powers of - ; we thus 

 obtain 



m * _r 1 



C+ I I 



