Mr maxwell, ON FARADAY'S LINES OF FORCE. 67 



ee' / dr 



te I dr !> , dV\ 



— 1 + a — +or -—] 

 r" V dt dt' 



(2) That when electricity is moving in a conductor, the velocity of the positive fluid 

 relatively to the matter of the conductor is equal and opposite to that of the negative fluid. 



(3) The total action of one conducting element on another is the resultant of the 

 mutual actions of the masses of electricity of both kinds which are in each. 



(4) The electro-motive force at any point is the difference of the forces acting on the 

 positive and negative fluids. 



From these axioms are deducible Ampere's laws of the attraction of conductors, and those 

 of Neumann and others, for the induction of currents. Here then is a really physical theory, 

 satisfying the required conditions better perhaps than any yet invented, and put forth by a 

 philosopher whose experimental researches form an ample foundation for his mathematical 

 investigations. What is the use then of imagining an electro-tonic state of which we have no 

 distinctly physical conception, instead of a formula of attraction which we can readily under- 

 stand .'' I would answer, that it is a good thing to have two ways of looking at a subject, and 

 to admit that there are two ways of looking at it. Besides, I do not think that we have any 

 right at present to understand the action of electricity, and I hold that the chief merit of a 

 temporary theory is, that it shall guide experiment, without impeding the progress of the true 

 theory when it appears. There are also objections to making any ultimate forces in nature 

 depend on the velocity of the bodies between which they act. If the forces in nature are to 

 be reduced to forces acting between particles, the principle of the Conservation of Force re- 

 quires that these forces should be in the line joining the particles and functions of the distance 

 only. The experiments of M. Weber on the reverse polarity of diamagnetics, which have been 

 recently repeated by Professor Tyndall, establish a fact which is equally a consequence of 

 M. Weber's theory of electricity and of the theory of lines of force. 



With respect to the history of the present theory, I may state that the recognition of 

 certain mathematical functions as expressing the "electro-tonic state" of Faraday, and the use 

 of them in determining electro-dynamic potentials and electro-motive forces, is, as far as I am 

 aware, original ; but the distinct conception of the possibility of the mathematical expressions 

 arose in my mind from the perusal of Prof. W. Thomson's papers "On a Mechanical Represen- 

 tation of Electric, Magnetic and Galvanic Forces," Cambridge and Dublin Mathematical 

 Journal, January, 1847, and his " Mathematical Theory of Magnetism," Philosophical Transac- 

 tions, Part I. 1851, Art. 78, &c. As an instance of the help which may be derived from other 

 physical investigations, I may state that after I had investigated the Theorems of this paper 

 Professor Stokes pointed out to me the use which he had made of similar expressions in his 

 "Dynamical Theory of Diffraction," Section 1, Cambridge Transactions, Vol. I.X. Part i. 

 Whether the theory of these functions, considered with reference to electricity, may lead to new 

 mathematical ideas to be employed in physical research, remains to be seen. I propose in the 

 rest of this paper to discuss a few electrical and magnetic problems with reference to spheres. 

 These are intended merely as concrete examples of the methods of which the theory has been 

 given ; I reserve the detailed investigation of cases chosen with special reference to experiment 

 till I have the means of testing their results. 



9 — z 



