ON FARADAY'S LINES OF FORCE. 157 



mathematics more consistent with nature than the formula of attractions, and no 

 theory better established in the minds of men than that of the action of bodies 

 on one another at a distance. The laws of the conduction of heat in uniform 

 media appear at first sight among the most different in their physical relations 

 from those relating to attractions. The quantities which enter into them are 

 temperature, Jloio of heat, conductivity. The word force is foreign to the subject. 

 Yet we find that the mathematical laws of the uniform motion of heat in 

 homogeneous media are identical in form with those of attractions varying in- 

 versely as the square of the distance. We have only to substitute source of 

 heat for centre of attraction, flow of heat for accelerating effect of attraction at 

 any point, and temperature for potential, and the solution of a problem in 

 attractions is transformed into that of a problem in heat. 



This analogy between the formulae of heat and attraction was, I believe, 

 first pointed out by Professor William Thomson in the Camb. Math. Journal, 

 Vol. III. 



Now the conduction of heat is supposed to proceed by an action between 

 contiguous parts of a medium, while the force of attraction is a relation be- 

 tween distant bodies, and yet, if we knew nothing more than is expressed in 

 the mathematical formulae, there would be nothing to distinguish between the 

 one set of phenomena and the other. 



It is true, that if we introduce other considerations and observe additional 

 facts, the two subjects will assume very different aspects, but the mathematical 

 resemblance of some of their laws will remain, and may still be made useful 

 in exciting appropriate mathematical ideas. 



It is by the use of analogies of this kind that I have attempted to bring 

 before the mind, in a convenient and manageable form, those mathematical ideas 

 which are necessary to the study of the phenomena of electricity. The methods 

 are generally those suggested by the processes of reasoning which are found in 

 the researches of Faraday*, and which, though they have been interpreted 

 mathematically by Prof. Thomson and others, are very generally supposed to be 

 of an indefinite and unmathematical character, when compared with those em- 

 ployed by the professed mathematicians. By the method which I adopt, I hope 

 to render it evident that I am not attempting to establish any physical theory 

 of a science in which I have hardly made a single experiment, and that the 

 limit of my design is to shew how, by a strict application of the ideas and 



* See especially Series xxxvm. of the Experimental Researches, and Phil. Mag. 1852. 



