198 Dr. E. Bout y on the Magnetization of Steel by Currents. 



been conducted with the view of studying the variation of 

 these functions. 



Tempered bars furnish analogous results, provided that only 

 bars of the same temper be considered. For them the values 

 of Aj and A 2 are lower than for natural bars: the value of B x 

 for the temper which I used becomes equal to £, and remains 

 constant whatever the intensity of the magnetizing force may 

 be. But the value of B 2 increases with the intensity of that 



force ; its value commences at ., _ g . and amounts to \ for the 



13-75 7 8 



most intense magnetizing forces employed by me. These 



results are of the same sort as those obtained for the values of 



d= jy- in section I. 

 B 2 



Let us now pass to the inductions to be derived from the 



direct results obtained from the study of the moments, relative 



to the distribution. If it be admitted that the quantity of free 



magnetism contained in a slice of the thickness du, situated at 



a distance u from the centre of any bar of the series studied, 



may be represented by the formula 



£2 — e 2 



the magnetic moment y will be represented by formula (1). 

 The same letters in the two formulae refer to the same quan- 

 tities. 



Inversely we admit with Biot* that, if the magnetic mo- 

 ments verify formula (1), the distributions are conformable to 

 formula (2). The foregoing experiments supply the values of 

 the constants A and B characteristic of the distribution. 



To explain to ourselves exactly the physical character of 

 these constants, let us consider the case of a bar of infinite 

 length. In this case the distribution will be represented, 

 starting from the end of the bar as origin, by the formula 



z=Aa 2 l3e-P u = ABae-a u (2 a) 



If A alone be varied, the distribution-curve will remain similar 

 to itself, its form will not be modified ; this is what happens 

 in the case of the temporary magnetization produced by cur- 

 rents of different intensity. If, on the contrary, we make B 



* This inference is not a necessary one a 'priori. An infinity of differ- 

 ent magnetic distributions may be imagined, giving the same values of the 

 magnetic moments; but formula (2) having been verified directly by 

 various observers, the mode of reasoning we have borrowed from Biot may 

 be with perfect security employed. 



