70 Mk maxwell, on FARADAY'S LINES OF FORCE. 



This is the value of the potential outside the sphere. At the surface we have 



so that at the surface 



R=a and — = -;-, 



E 



= — &c. 



a 61 5, 



;+&c. 



and this must also be the value of p for any point within the sphere. 



For the application of the principle of electrical images the reader is referred to Prof. 

 Thomson's papers in the Cambridge and Dublin Mathematical Journal. The only case 



which we shall consider is that in which —^ =/, and 6, is infinitely distant along axis of x, 



"1 

 and £=0. 



The value p outside the sphere becomes then 



;>=/.( -^^). 



and inside p=0. 



IL On the effect of a paramagnetic or diamagnetic sphere in a uniform field of magnetic 



force *. 



The expression for the potential of a small magnet placed at the origin of co-ordinates 

 in the direction of the axis of <r is 



d (m\ , X 

 dx \rj r' 



The effect of the sphere in disturbing the lines of force may be supposed as a first 

 hypothesis to be similar to that of a small magnet at the origin, whose strength is to 

 be determined. (We shall find this to be accurately true.) 



Let the value of the potential undisturbed by the presence of the sphere be 



p = Ix. 



Let the sphere produce an additional potential, which for external points is 



p = A —x, 



and let the potential within the sphere be 



Pi = Bx. 

 Let k' be the coefficient of resistance outside, and k inside the sphere, then the 

 conditions to be fulfilled are, that the interior and exterior potential should coincide at the 



" See Prof. Thomson, on the Theory of Magnetic Induction, 

 Phil. Mag, March, 1851. The inductive capacity of the sphere, 

 according to that paper, is the ratio of the quantity of magnetic 



induction (not the intensity) within the sphere to that without. 



1 k' 3jt' 

 It is therefore equal to j S -r- = S7 — y according to our notation. 



