32 HISTORY OF ELECTRICITY. 



artifices he was able to show that the results of his 

 experiments and of his calculations gave an agree- 

 ment 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 com- 

 parison with observation, but could not be accu- 

 rately obtained ; as was the case in astronomy also, 

 till the time of the approximate solution of the 

 Problem of Three Bodies, and the consequent form- 

 ation 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 astro- 

 nomy had occasioned in pure mathematics. About 

 1801, there appeared in the Bulletin des Sciences 1 '', 

 an exact solution of the problem of the distribution 

 of electric fluid on a spheroid, obtained by M. Biot, 

 by the application of the peculiar methods which 

 Laplace had invented for the problem of the figure 

 of the planets. And in 1811, M. Poisson applied 

 Laplace's artifices to the case of two spheres acting 

 upon one another in contact, a case to which many 

 of Coulomb's experiments were referrible ; and the 

 agreement of the results of theory and observation, 

 thus extricated from Coulomb's numbers, obtained 

 above forty years previously, was very striking and 

 convincing 13 . It followed also from Poisson's calcu- 

 12 No. li. w Mem. A. P. 1811. 



