44 Prof. Thomson on the Mathematical Theory of 



undertaken by Mr. Snow Harris and Mr. Faraday, and in their 

 memoirs, published in the Philosophical Transactions, we find 

 detailed accounts of their researches. All the experiments, 

 however, which they have made, having direct reference to the 

 distribution of electricity in equilibrium, are, I think, in full 

 accordance with the laws of Coulomb, and must therefore, 

 instead of objections to his theory, be considered as confirming 

 it. As however many have believed Coulomb's theory to be 

 overturned by these investigations, and as others have at least 

 been led to entertain doubts as to its certainty or accuracy, the 

 following attempt to explain the apparent difficulties is made 

 the subject of the first of a series of papers in which various 

 parts of the mathematical theory of electricity, and corresponding 

 problems in the theories of magnetism and heat, will be coft^ 

 sidered. ^'^ 



2. We may commence by examining some experimental re- 

 sults published in Mr. Harris's first memoir " On the Element- 

 ary Laws of Electricity*.'' After describing the instruments 

 employed in his researches, Mr. Harris gives the details of some 

 experiments with reference to the attraction exercised by an 

 insulated electrified body on an uninsulated conductor placed in 

 its neighbourhood. The first result which he announces is that, 

 when other circumstances remain the same, the attraction varies 

 as the square of the quantity of electricity with which the insu- 

 lated body is charged. It is readily seen, as was first remarked 

 by Dr. Whewell in his " Report on the Theories of Electricity, 

 &c.t/' that this is a rigorous deduction from the mathematical 

 theory, following from the fact that the quantity of electricity 

 induced upon the uninsulated body is proportional to the charge 

 on the electrified body by which it is attracted. 



The remaining results have reference to the force of attraction 

 at different distances, and with bodies of different forms opposed. 

 As these are generally very irregular (such as " plane circular 

 areas backed by small cones"), we should not, according to 

 Coulomb's theory, expect any very simple laws, such as Mr. 

 Harris discovers, to be rigorously true. Accordingly, though 

 they are announced by him without restriction, we must examine 

 whether the experiments from which they have been deduced 

 are of a sufficiently comprehensive character to lead to any 

 general conclusions with respect to electrical action. Now in 

 the first place, we find that in all of them the attraction is 

 "independent of the form of the unopposed parts" of the 

 bodies, which will be the case only when the intensity of the 

 induced electricity on the unopposed parts of the uninsulated 



* Philosophical Transactions, 1834. 

 t British Association Report for 1837. 



