212 ON FARADAY'S LINES OF FORCE. 



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



have 



n J &t a 6. O 



R = a and = -r, - = , &c. , 



' 



so that at the. surface 



^ a 6, 6, 

 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 j^ = I, and 6j is infi- 

 nitely distant along the axis of x, and E = 0. 



The value p outside the sphere becomes then 



and inside p = 0. 



II. On the effect of a paramagnetic or diamagnetic sphei'e 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 x is 



, d /m 

 ' dx 



(m\ , x 



= Im -j . 

 \r) r 1 



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.) 



* See Prof. Thomson, on the Theory of Magnetic Induction, Phil. Mag. March, 1851. The induc- 

 tive capacity of the sphere, according to that paper, is the ratio of the quantity of magnetic induction 



1 V Sk' 



(not the inlenrity) within the sphere to that without It is therefore equal to jB-^= -^7 r/ accord- 

 ing to our notation. 



