; - ELECTROSTATICS AND MAGXET18M. 



are quite different In the one we have an attraction acting instantaneously 

 at a distance, in the other heat creeping along from hotter to colder parts. 

 The methods of investigation were also different. In the one the force on a 

 given particle of electricity has to be determined as the resultant of the 

 attraction of all the other particles. In the other we have to solve a certain 

 partial differential equation which expresses a relation between the rates of 

 variation of temperature in passing along lines drawn in three different direc- 

 tion* through a point. Thomson, in this paper, points out that these two 

 problems, so different, both in their elementary ideas and their analytical 

 methods, are mathematically identical, and that, by a proper substitution of 

 electrical for thermal terms in the original statement, any of Fourier's wonderful 

 methods of solution may be applied to electrical problems. The electrician has 

 only to substitute an electrified surface for the surface through which heat is 

 supplied, and to translate temperature into electric potential, and he may at 

 once take possession of all Fourier's solutions of the problem of the uniform 

 flow of heat. 



To render the results obtained in the prosecution of one branch of inquiry 

 available to the students of another is an important service done to science, 

 but it is still more important to introduce into a science a new set of ideas, 

 belonging, as in this case, to what was, till then, considered an entirely uncon- 

 nected science. This paper of Thomson's, published in February 1842, when lie 

 was a very young freshman at Cambridge, first introduced into mathematical 

 science that idea of electrical action carried on by means of a continuous 

 medium which, though it had been announced by Faraday, and used by him 

 as the guiding idea of his researches, had never been appreciated by other 

 of science, and was supposed by mathematicians to be inconsistent with the 

 laws of electrical action, as established by Coulomb, and built on by Poi- 

 It was Thomson who pointed out that the ideas employed by Faraday under 

 the names of Induction, Lines of Force, &c., and implying an action transmitted 

 from one part of a medium to another, were not only consistent with the 

 results obtained by the mathematicians, but might be employed in a mathe- 

 matical form so as to lead to new results. One of these new results, which 

 was, we have reason to believe, obtained by this method, though demonstrated 

 by Thomson by a very elegant adaptation of Newton's method in the theory 

 of attraction, is the "Method of Electrical Images," leading to the "Method 

 "f Electrical Inversion." 



