PEOGEESS OF ELECTEICAL THEOEY. 207 



mathematician to compare the results of the theory hi detail with 

 those of experimental measures. Coulomb undertook both .portions 

 of the task. He examined the electricity of portions of bodies by 

 means of a little disk (his tangent plane) which he applied to them 

 and then removed, and which thus acted as a sort of electric taster. 

 His numerical results (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 elec- 

 tricity 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 deter- 

 mine the distribution, and the distribution reciprocally determines the 

 attraction and repulsion. The problem was of the same nature 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 artifices he was able to show that the 

 results of his experiments and of his calculations gave an agreement 

 sufficiently near to entitle him to consider the theory as established on 

 a solid basis. 



Thus, at this period, mathematics was behind experiment ; and a 

 problem was proposed, in which theoretical numerical results were 

 wanted for comparison with observation, but could not be accurately 

 obtained; as was the case in astronomy also, till the time of the 

 approximate solution of the Problem of Three Bodies, and the conse- 

 quent formation of the Tables of the Moon and Planets on the theory 

 of universal gravitation. After some time, electrical theory was 

 relieved from this reproach, mainly in consequence of the progress 

 which astronomy had occasioned in pure mathematics. About 1801, 



