120 Dr. E. Bouty on the Magnetization of Steel by Currents. 



tion * a fictitious superficial distribution of polar (austral and 

 boreal) magnetism may be substituted, which replaces it in 

 respect of all the actions exerted by the magnet exteriorly to 

 its mass. This is the distribution usually studied since 

 Coulomb ; and the knowledge of it is sufficient as long as 

 the magnet is not disunited. 



In the second place, when the practical case of a bar 

 magnetized regularly is considered, it is observed that the 

 magnetic distribution of the bar is limited to two regions, 

 equal in quantity and of opposite signs, occupying the two 

 extremities. We may suppose each of these masses condensed 

 in its centre of gravity ; and the bar will then be replaced by 

 two magnetic poles of which the masses are m and — m, and 

 the distance of the one from the other a quantity \"\. 



Lastly, in regard to the actions at infinite distance one 

 magnet differs from another by one element only, which is 

 designated under the name of magnetic moment, and of which 

 the rational measure, in the case of a regular bar, is the pro- 

 duct mX of the quantity of magnetism of each pole by their 

 distance. Such is the term of this analysis. 



The methods to which recourse is had for the experimental 

 study of magnets are of two kinds : the one sort, utilizing 

 action at contact or at minute distance, are employed for 

 determining the magnetic distribution : their employment is 

 tedious and laborious, and their application subject to special 

 theoretical difficulties. The others, founded upon action at 

 very great distances, furnish in a manner as simple as it is 

 accurate the measurement of the magnetic moment. 



I purpose in this investigation to apply these latter methods 

 to the study of the distribution. Biot has already set the 

 example of this kind of research, by combining in a mathe- 

 matical formula (subsequently connected by Green with the 



* See, in the Journal de Physiqw., tome ii. p. 297, my article " Sur les 

 distributions fictives d'electricite et de magnetisnie," &c. 



f Physically we may, with M. Jamin, consider a bar as a "bundle of 

 indefinitely thin magnets having their poles at their extremities. This 

 bundle, embraced by the mean section of the bar as by a ring, expands 

 on the two sides its oppositely named poles, which form the superficial 

 distribution. This synthesis amounts to replacing the unknown distri- 

 bution of the magnetic elements by the equivalent solenoidal distribution 

 (see Thomson's memoirs), and is perfectly legitimate from the mathema- 

 tical point of view. It has the advantage of addressing the imagination, 

 and of giving a precise physical meaning to all the quantities met with in 

 the analytical study of magnets. Thus the power m of the pole of a bar 

 measures the number of files (rows) of magnetic elements comprised in 

 it; and the distance X is the mean length of the files, reckoned in the 

 direction of the axis : it may be called the reduced or magnetic length of 

 the bar. 



