﻿90 Prof. R. Threlfall on an Approximate Method 



to calculate the forces tending to draw the ends of the iron 

 ring together when the strength of current flowing in the 

 magnetizing circuit and the data of winding are given. 

 § 2. The position established by Maxwell is as follows : — 



(1) The laws of magnetic force are such that magnetic 

 forces may be regarded as the expression of a state of stress 

 in the magnetic medium. 



(2) The medium is stable under such a distribution of 

 stresses. 



(3) A series of expressions may be found for the stresses 

 at any point in the magnetic field. 



§ 3. Maxwell's investigation does not explicitly include the 

 case of a body with inconstant permeability; but I cannot find 

 that this in any way vitiates the argument. Professor J. J. 

 Thomson shows (' Applications of Dynamics to Physics and 

 Chemistry,' § 33) that Maxwell's results may be considered 



as being derived from the existence of a term ~— HB in the 



Lagrangian function for unit volume of a magnetic field. If 

 the permeability is a function of the induction, however, in 



any part of the field, the more general expression ^— fH<£B 



must be substituted for the above and the results modified 

 accordingly. I have not succeeded in doing this. It appears, 

 therefore, that Maxwell's system as applied to iron does not 

 cover all the ground, because a modification must be intro- 

 duced on account of the inconstancy of the permeability, and 

 also on account of the Villari effect as shown by Professor 

 Thomson. There may also be other undiscovered additions 

 to make. 



§ 4. A great step is necessary to pass from Maxwell's 

 position — that magnetic forces may be regarded as the ex- 

 pression of stresses in the field — to the position that magnetic 

 forces are such an expression. There is all the difference that 

 exists between a theory and a fact. 



Everything, however, tends to show that the fact is that 

 the theory is probably true so far as it goes, and we will 

 therefore provisionally adopt it, and see first what additional 

 hypotheses are necessary. It is obvious . at once that the 

 stresses are " stresses in a medium," while the forces are 

 mechanical forces acting on matter. We must therefore 

 consider that the medium is " attached " to matter so as to 

 allow the stresses to appear as forces. Now the stresses in 

 the medium depend on the nature of the matter which is 

 permeated by the medium. Thus in the cut anchor-ring 



