Magnetomotive Force. 211 



its absence its centre of symmetry would have had. The fall 

 of potential on approaching the body is greater than in the 

 undisturbed state. This gives rise to stream-line problems, 

 which are the same as those ordinarily dealt with. 



We see that, in such a field, no new lines of force can be 

 developed in any circuit ; for the action of the uniform mag- 

 netomotive force on the opposite portions of the circuit is the 

 same in amount and opposite in direction. 



We may use the known solutions to obtain the permeability 

 of a sphere, by which we mean the ratio of the number of 

 lines of force through its equatorial section to the number 

 through the same section in air. This is 3 for a sphere of 

 infinite conductivity. This is deduced by Stefan in a recent 

 number of Wiedemann's Annalen, xvii. p. 956. It can also 

 be obtained from fig. 4, p. 489, of the Reprint of Sir William 

 Thomson's Papers, by comparing the square of the ordinate of 

 the outside line inflected so as just to meet the sphere with 

 the square of the radius of the sphere. This gives 



(1-375 x;/2) 2 = 3-001. 

 In both these cases the solution only refers to the case of a 

 uniform field of infinite extent, which excludes circuits (as 

 remarked above). I shall presently examine this excluded case. 



In the meantime an important point may here be noticed. If 

 we calculate the magnetization of a sphere of infinite conducti- 

 vity by the usual formula (Maxwell, vol. ii. p. 65), we obtain the 

 number 3/(4tt). Now if we seek to deduce the permeability 

 from this by the usual formula fi= (1 + 4-rf), we find the num- 

 ber 4 instead of 3 as given by the above investigations. This 

 obviously arises from the formula being based on the hypo- 

 thesis that the " magnetizing force" penetrates unchanged 

 through the body, and is to be added to the distribution of 

 stream-lines which has been determined. It is very difficult 

 to admit this. Our point of view, according to which the 

 magnetizing agent is a magnetomotive force and not a field 

 intensity, removes this difficulty; and the formula for /jl re- 

 duces to/^ = 47r&, which gives 3, as before, in the present case. 



We can obtain a more general approximate solution for the 

 case of a sphere subjected to a magnetomotive force such that 

 the sphere forms part of circuits through which the force acts, 

 in a form suitable for experimental verification. 



Let a coil be wound on a reel having a cylindrical opening 

 within. Length of reel = diameter of sphere = diameter of 

 cylindrical opening. Then magnetic circuits will be formed 

 passing through the sphere and linked once with each turn of 

 the coil. It will be near enough for the present purpose to 

 assume that the lines of force radiate at right angles from the 



