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



The expressions for the electro-motive forces in y and « are similar. The distribution of 

 currents due to these forces depends on the form and arrangement of the conducting media 

 and on the resultant electric tension at any point. 



The discussion of these functions would involve us in mathematical formulae, of which this 

 paper is already too full. It is only on account of their physical importance as the mathema- 

 tical expression of one of Faraday's conjectures that I have been induced to exhibit them at 

 all in their present form. By a more patient consideration of their relations, and with the 

 help of those who are engaged in physical inquiries both in this subject and in others not 

 obviously connected with it, I hope to exhibit the theory of the electro-tonic state in a form 

 in which all its relations may be distinctly conceived without reference to analytical calcula- 

 tions. 



Summary of the Theory of the Electro-tonic State. 



We may conceive of the electro-tonic state at any point of space as a quantity determinate 

 in magnitude and direction, and we may represent the electro-tonic condition of a portion of 

 space by any mechanical system which has at every point some quantity, which may be a 

 velocity, a displacement, or a force, whose direction and magnitude correspond to those of the 

 supposed electro-tonic state. This representation involves no physical theory, it is only a kind 

 of artificial notation. In analytical investigations we make use of the three components of the 

 electro-tonic state, and call them electro-tonic functions. We take the resolved part of the 

 electro-tonic intensity at every point of a closed curve, and find by integration what we may 

 call the entire electro-tonic intensity round the curve, 



Peop. I. If on any surface a closed curve be dratvn, and if the surface within it be 

 divided into small areas, then the entire intensity round the closed curve is equal to the sum 

 of the intensities round each of the small areas, all estimated in the same direction. 



For, in going round the small areas, every boundary line between two of them is passed 

 along twice in opposite directions, and the intensity gained in the one case is lost in the other. 

 Every effect of passing along the interior divisions is therefore neutralized, and the whole 

 effect is that due to the exterior closed curve. 



Law I. The entire electro-tonic intensity round the boundary of an element of surface 

 measures the quantity of magnetic induction which passes through that surface, or, in other 

 words, the number of lines of magnetic force which pass through that surface. 



By Prop. I. it appears that what is true of elementary surfaces is true also of surfaces of 

 finite magnitude, and therefore any two surfaces which are bounded by the same closed curve 

 will have the same quantity of magnetic induction through them. 



Law II. The magnetic intensity at any point is connected with the quantity of magnetic 

 induction by a set of linear equations, called the equations of conduction*. 



• See Art. (28). 



Vol. X. Part I. 



