ELECTEOMETEES. 221 



charge. He now removed the carrier ball, and touched it 

 with an insulated ball exactly equal to it in dimensions ; 

 he was thus able to halve the charge of the carrier. Putting 

 it back, he tested the force. Again the charge of the 

 carrier was halved, and again he determined the force, and 

 so on. The charge on the torsion ball was then altered, 

 and a new series of experiments proceeded with. By a 

 series of experiments of this kind he found that the force 

 between the two balls is proportional to the product of 

 the quantities of electricity on them, the distance remaining 

 the same ; and combining the latter with the former law, 

 he showed that the force is proportional to 



m x m! 



d 2 



where m and m' are the charges of the balls, and d the 

 distance between their centres. But in stating this law you 

 must be careful to mention the limitations as to the 

 dimensions of the balls and as to effects of induction to 

 which I have just referred. 



The experiments that I have been speaking of were not 

 so much electrometric experiments as experiments on the 

 fundamental laws of electricity ; but the next experiments 

 of Coulomb were of a purely electrometric character. They 

 were for the purpose of determining the distribution of 

 electricity over variously shaped conductors. Except in cer- 

 tain simple cases, the mathematical problem of determining 

 the distribution of electricity over a conductor is extremely 

 difficult. Poisson had, however, worked out the case for 

 two equal spheres in contact, assuming the truth of 

 Coulomb's law of the inverse square of the distance. Now 

 it is plain that nothing could give a better test of the truth 

 of the law than the comparison of the distribution given 

 by the calculation of Poisson with the distribution deter- 

 mined by experiment. 



Coulomb used for these experiments another instrument, 

 slightly different from the carrier ball, namely, the proof- 

 plane, which consists simply of a very small piece of thin 

 metal insulated on a thin arm of shellac, which is applied 

 to the surface of the conductor to be tested, and then 

 carried away from the conductor. It is then brought to 



