158 ELEMENTS OF STATIC ELECTRICITY. 



Both being the same size, the charge is equally divided 

 between them ; and, being at the same potential, the 

 movable ball g is repelled to a distance indicated by 

 the number on the lower scale : at which point the 

 force of repulsion is balanced by the torsion of the wire. 



The cap b is then turned in opposition to the repul- 

 sion, so as to bring the ball g nearer to g'\ the distance 

 being indicated on the upper scale. The torsion of the 

 wire is thus increased, and repulsion again balanced by 

 torsion in the new position. 



It is known that the force of torsion is proportional 

 to the angle of torsion : and since this force has to be 

 increased to oppose the increase of repulsion, as the 

 balls are brought closer, the point to be determined is 

 the ratio of increase of force, as compared with the 

 reduction of distance between the balls; which is done 

 by comparing the distances from zero, indicated on the 

 upper and lower scales. 



The following is one of Coulomb's experiments for 

 this purpose : The first distance to which the movable 

 ball g was repelled being 36, it was found necessary, 

 in order to reduce this distance to 18, to turn the cap 

 b through 126; and to reduce the distance to 8 re- 

 quired an additional rotation of the cap through 441. 



The distances 36, 18, and 8i are to each other, 

 practically, in the ratio of 1, i, and I ; and the forces 

 of repulsion at these points were balanced by torsions 

 of 36, of 126+ 18= 144, and of 441 4 126 -f 8= 

 5751, respectively. 



Now since 144 = 4x36, and 575| (practically 576) 

 =16x36, it will be seen that as the distance between 

 the balls is divided by 2 or by 4, the force of repulsion 

 is multiplied by 4 or by 16 ; and thus Coulomb proved 



