vee 
198 RICHARD THRELFALL. 
chapter “On Energy and Stress in the Magnetic Field,”—(Elec- 
tricity and Magnetism, Vol. 11., §§. 641 — 644)—-with the follow- 
ing results :— 
§1. Theoretical considerations.—The problem for solution in its 
simplest form is as follows: “Given an iron anchor-ring uniformly 
wound and interrupted at one point by an air gap of any given 
dimensions, to calculate the forces tending to draw the ends of the 
iron ring together when the strength of current flowing in the 
magnetising circuit and the data of winding are given.” 
2. The position established by Maxwell is as follows :— 
(i.) 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. 
(ii.) The medium is stable under such a distribution of stresses. 
(i1i.) 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 can not 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 _ H Bin 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 < = Ws H d B must be substituted for the above and the 
results modified accordingly. 1 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 introduced 
on account of the inconstancy of the permeability, and also on 
account of the Villari effect as shewn by Prof. 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 expression of stresses 
in the field, to the position that magnetic forces are such an 
