Distributions of Electricity, Magnetism and Galvanism, 195 



heat that would* be generated by the expenditure of the same 

 amount of work on mere friction. 



The same considerations are applicable to the magnetization 

 of a piece of steel ; mth this difference, that, according to the 

 hardness of the steel, the magnetization which it receives in the 

 nearest position will be more or less permanent ; and if there be 

 any demagnetization after removal from the magnet, it will be 

 much less complete than in the case of soft iron, and that heat 

 will be necessarily generated both during the magnetization 

 which takes place during the gradual approach, and in the sub- 

 sequent demagnetization. Further, by putting together a num- 

 ber of pieces of steel, each separately magnetized, a complete 

 magnet will be fornied, of which the mechanical value wall be 

 equal to the sum of the mechanical values of its parts, increased 

 or diminished by the amount of work spent or gained in bringing 

 them together. 



Upon the principles which have been explained, the author 

 has investigated the mechanical value of any conceivable distri- 

 bution of magnetism in any kind of substance. The result, 

 which cannot be well expressed except in mathematical language, 

 is as follows : — ^ 



/ j l\(^dx dy dr + ^ / / / 1^^^^ dy dz, 



where 11 denotes the resultant magnetic force at any internal or 

 external point {x, y, z), q the intensity of magnetization at a 

 point [x, y, z) of the magnet, and X, a quantity depending on the 

 nature of the substance at this point. 



The integral constituting the first term of this expression in- 

 cludes the whole of the magnetized substance, and expresses 

 the sum of the separate mechanical values of the distributions 

 in all the parts obtained by infinitely minute division along the 

 lines of magnetization. The second term expresses the amount 

 of work that would have to be spent to put these parts together, 

 were they given 6e])arately, each mth the exact magnetization 

 that it is to have when in its place in the whole. If the sub- 

 stance be perfectly free in its si;sceptibility for magnetization 

 or demagnetization, X, will be such a function of the inductive 

 capacity, that if a ball of similar substance be placed in a mag- 

 netic field where 'ie force is F, the intensity of the magnetiza- 

 tion induced in it will be 



47r 



