176 ELECTROMETRY. 



or 



(8) V = ^ 



If we make r= i c , R = 2oc, d= lor, which represents almost the 

 conditions of an ordinary balance, the factor of correction for the 

 influence of the cage is o'i. It may be observed that from 



formula (8) the potential of each ball would be simply , if R = zd. 



J( 804. The influence of the case is much greater when the balls 

 are near the sides. The case being still spherical, and of radius R, 

 let us suppose that the centre of rotation of the needle coincides 

 with the centre of the sphere ; let / and /' be the distances from the 

 axis of the fixed and of the movable ball, whose masses are m and m'. 

 Neglecting inequalities of distribution, the electrical image of the 

 mass m' in respect of the case is in the prolongation of the lever /', 

 and does not modify the deflection ; the image of the mass m is at a 

 distance D from the axis (168), 



R 2 



and it is equal to 



D R 

 - = m-j 



The distance x of this image to the ball m is defined by the 

 equation 



R 4 R 2 /' 



- 2 cosa. 



The action of this image on the ball is g , and the arm 



T-\ Jt ' / %" 



of its lever . If / denotes the direct action of the two 



x 



balls, the equation of equilibrium is then 



//' sin a mm'DM sin a 

 (9) f d -T-5 -C(A + a). 



