270 LECTURES TO SCIENCE TEACHERS. 



electricity is given to the fixed ball ; then if the movable 

 ball is of the same size as the fixed one, the charge of the 

 fixed ball is divided between the two in equal proportions. 

 The balls then repel each other with a force proportional to 

 the square of the charge upon either of them, that is, pro- 

 portional to one fourth of the square of the original charge. 

 If we measure the force exerted between the two balls each 

 of them charged with half the original quantity put into the 

 apparatus, which we can do by observing the extent to 

 which the suspending fibre is twisted and determining its 

 coefficient of torsion, and measure the distance between 

 the balls, which we can do by observing the angle between 

 them and the length of the movable arm, we get the two 

 factors which determine the quantity upon each ball. Then 

 the square of that is equal to one-fourth the square of 

 the original charge. The details of the use of the apparatus 

 would call for a good many remarks if we had time to enter 

 upon it, but that I cannot do now. 



So far as I have spoken of this apparatus it enables us to 

 measure the quantity of electricity which we put into it 

 upon the fixed ball, but that does not yet give us a method 

 of measuring quantities of electricity in general. If I wanted 

 to measure, for instance, the charge of this sphere, I still 

 might do it by means of this apparatus. I should take the 

 fixed ball out of the balance, let it touch the sphere, and then 

 put it in and measure the charge which it has got. The 

 charge taken from the sphere would bear to the charge that 

 the sphere had to begin with, a definite relation which is not, 

 as one might suppose at first sight, the ratio of the surfaces of 

 the spheres. That you will easily see in this way : If we touch 

 this large sphere with a small one, you might suppose that 

 the charge of the large sphere would be divided between the 

 two in the ratio of the surfaces of the large sphere and of the 

 -small one ; but a little consideration shows that that is not 

 the case, for the density of the charge upon the small sphere is 

 greater than the density upon the large sphere. It varies from 

 one part to another, but the average density on the small one 

 is considerably greater than the average density upon the large 

 one. so that the small sphere takes under these circumstances a 

 larger proportion than corresponds merely to its surface, and 

 the ratio in which the electricity divides between the two 

 spheres bears a complicated relation to their sizes. But tables 



