ELECTROMETERS 



159 



that electric repulsion varies inversely as the square of the 

 distance. 



INACCURACY OF THE TORSION BALANCE. In the 

 use of this instrument, as above, the arc is assumed as 

 the distance between the balls, while the actual dis- 

 tance is the chord of the arc ; but since these distances 

 are in the same proportion, the accuracy of the results 

 is not affected. 



It is also assumed that the arm of the lever, by which 

 repulsion produces torsion, is the distance from the 

 center of motion to the cen- 

 ter of the ball g. But this 

 is true only when the balls 

 are in contact. In every 

 other position, this arm is 

 represented by a perpendic- 

 ular from the center, on the 

 chord which cuts the centers 

 of the two balls : and as the 

 ball g moves round, and the 

 chord increases in length, 

 this perpendicular decreases ; 

 and vanishes when the chord 

 equals the diameter. 



This is shown in Fig. 51, where b represents the first 

 position of the balls, when the arm equals a b : but 

 when g moves round to 6*, the line a f represents the 

 arm ; and when it moves to d, the short line a m rep- 

 resents the arm ; and at n the arm vanishes. 



This may be made more plain, by considering that 

 the ball g is moving under the influence of two forces, 

 electric repulsion, and the rigidity of the shellac rod, 

 by which it is held at a fixed distance from the center. 



Fig. 51 Arm and Angle of 

 Repulsion Illustrated. 



