66 



Mr maxwell, ON FARADAY'S LINES OF FORCE. 



Law III. The entire magnetic intensity round the boundary of any surface measures 

 the quantity of electric current which passes through that surface. 



Law IV. The quantity and intensity of electric currents are connected by a system of 

 equations of conduction. 



By these four laws the magnetic and electric quantity and intensity may be deduced from 

 the values of the electro-tonic functions. I have not discussed the values of the units, as that 

 will be better done with reference to actual experiments. We come next to the attraction of 

 conductors of currents, and to the induction of currents within conductors. 



Law V. The total electro-magnetic potential of a closed current is measured by the product 

 of the quantity of the current multiplied by the entire electro-tonic intensity estimated in the 

 same direction round the circuit. 



Any displacement of the conductors which would cause an increase in the potential will be 

 assisted by a force measured by the rate of increase of the potential, so that the mechanical 

 work done during the displacement will be measured by the increase of potential. 



Although in certain cases a displacement in direction or alteration of intensity of tJie 

 current might increase the potential, such an alteration would not itself produce work, and 

 there will be no tendency towards this displacement, for alterations in the current are due to 

 electro-motive force, not to electro-magnetic attractions, which can only act on the conductor. 



Law VI. The electro-motive force on any element of a conductor is measured by the 

 instantaneous rate of change of the electro-tonic intensity on that element, whether in magnitude 



or direction. i 



The electro-motive force in a closed conductor is measured by the rate of change of the 

 entire electro-tonic intensity round the circuit referred to unit of time. It is independent of the 

 nature of the conductor, though the current produced varies inversely as the resistance; and 

 it is the same in whatever way the change of electro-tonic intensity has been produced, whether 

 bv motion of the conductor or by alterations in the external circumstances. 



In these six laws I have endeavoured to express the idea which I believe to be the mathe- 

 matical foundation of the modes of thought indicated in the Expenmental Researches. I do 

 not think that it contains even the shadow of a true physical theory; in fact, its chief merit as a 

 temporary instrument of research is that it does not, even in appearance, account for anything. 



There exists however a professedly physical theory of electro-dynamics, which is so elegant, 

 so mathematical, and so entirely different from anything in this paper, that I must state its 

 axioms, at the risk of repeating what ought to be well_known. It is contained in M. W. 

 Weber's Electro-dynamic Measurements, and may be found in the Transactions of the 

 Leibnitz Society, and of the Royal Society of Sciences of Saxony *. The assumptions are, 



(1) That two particles of electricity when in motion do not repel each other with the 

 same force as when at rest, but that the force is altered by a quantity depending on the 

 relative motion of the two particles, so that the expression for the repulsion at distance r is 



• When this was written, I was not aware that part of M. 

 Weber's Memoir is translated in Taylor's Scientific Memoirs, 

 Vol. V. Art. XIV. The value of his researches, both experimen. 



tal and theoretical, renders the study of his theory necessary to 

 every electrician. 



