PKOrESSOR TuOMSON On the Distribution of Electricity. 283 



After a very short time bas elapsed with the piece of soft iron at a great 

 distance from the magnet, it will have lost, as is well known, all or 

 nearly all the magnetization which it had acquired temporarily in the 

 neighbourhood of the magnet ; and in this short time some energy, equi- 

 valent to that of the magnetization lost, must have been produced. Mr- 

 Joule's experiments show that this energy consists of heat, which is gene- 

 rated during the demagnetization of the iron ; and we infer the remark- 

 able conclusion, that at the end of the process, which has been described, 

 or of any motion of a piece of soft iron in the neighbourhood of a mag- 

 net, from a certain position and back to the same, the iron will be as 

 much the warmer than it was at the beginning, as it would have been 

 without any magnetic action, if it had received the 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, with 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 subsequent 

 demagnetization. Further, by putting together a number of pieces of 

 steel, each separately magnetized, a complete magnet will be formed, of 

 which the mechanical value will be equal to the sum of the mechanical 

 values of its parts, increased or diminiohed by the amount of work spent 

 or gained in bringing them together. 



Upon the principles which have been explained, the author has investi- 

 gated the mechanical value of any conceivable distribution of magnetism, 

 in any kind of substance. The result, which cannot be well expressed, 

 except in mathematical language, is as follows: — 



00 

 fffrfdxdydz + ^fff R'^dzdydz 



00 



where 11 denotes the resultant magnetic force at any internal or external 

 point (x, y, z), of the intensity of magnetization at a point {x, y, s), of 

 the magnet, and a a quantity depending on the nature of the substance 

 at this point. 



The integral constituting the first term of this expression, includes 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 separately, each with the exact magnetiz- 

 ation that it is to have when in its place in the whole. If the substance 

 be perfectly free in its susceptibility for magnetization or demagnetization. 



