PROGRESS OF ELECTRICAL THEORY. 31 



(the intensity being still measured by the torsion- 

 balance,) are the fundamental facts of the theory of 

 the electrical fluid. Without entering into detail, 

 we may observe that he found the electricity to be 

 entirely collected at the surface of conductors, 

 (which Beccaria had before shown to be the case,) 

 and that he examined and recorded the electric 

 intensity at the surface of globes, cylinders, and 

 other conducting bodies, placed within each other's 

 influence in various ways. 



The mathematical calculation of the distribution 

 of two fluids, all the particles of which attract and 

 repel each other according to the above law, was a 

 problem of no ordinary difficulty ; as may easily be 

 imagined, when it is recollected that the attraction 

 and repulsion determine the distribution, and the 

 distribution reciprocally determines the attraction 

 and repulsion. The problem was of the same na- 

 ture as that of the figure of the earth; and its 

 rigorous solution was beyond the powers of the 

 analysis of Coulomb's time. He obtained, however, 

 approximate solutions with much ingenuity; for 

 instance, in a case in which it was obvious that the 

 electric fluid would be most accumulated at and 

 near the equator of a certain sphere, he calculated 

 the action of the sphere on two suppositions : first, 

 that the fluid was all collected precisely at the 

 equator; and next, that it was uniformly diffused 

 over the surface ; and he then assumed the actual 

 case to be intermediate between these two. By such 



