ADVANCE OF ELECTEICAL THEORY. 181 



thus instanced — involve more sciences than two. One 

 illustration of this must suffice. We quote it in full from 

 the History of the Inductive Sciences. In Book XI., chap. 

 11., on "The Progress of the Electrical Theory," Dr 

 Whewell writes : — 



" Thus at that period, mathematics was behind experiment, 

 and a problem was proposed, in which theoretical results were 

 wanted for comparison with observation, but could not be ac- 

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

 of the approximate solution of the problem of three bodies, and 

 the consequent formation of the tables of the moon and planets, 

 on the theory of universal gravitation. After some time, elec- 

 trical theory was relieved from this reproach, mainly in conse- 

 quence of the progress which astronomy had occasioned in pure 

 mathematics. About 1801 there appeared in the Bulletin des 

 Sciences^ an exact solution of the problem of the distribution of 

 electric fluid on a spheroid, obtained by Biot, by the application 

 of the peculiar methods which Laplace had invented for the prob- 

 lem 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 experi- 

 ments were referrible ; and the agreement of the results of 

 theory and observation, thus extricated from Coulomb's num- 

 bers obtained above forty years previously, was very striking and 

 convincing." 



TvTot only do the sciences affect each other after this 

 direct manner, but they affect each other indirectly. 

 Where there is no dependence, there is yet analogy — 

 equality of relations ; and the discovery of the relations 

 subsisting among one set of phenomena, constantly sug- 

 gests a search for the same relations among another set. 

 Thus the established fact that the force of gravitation varies 

 mversely as the square of the distance, being recognized as 

 a necessary characteristic of all influences proceeding from 

 a centre, raised the suspicion that heat and light follow the 

 same law ; which proved to be the case — a suspicion and a 



