632 CONSTANTS OF MAGNETISATION. 



of the tangent is a, and it is an asymptote to the right line y=i. 

 We get thus at this general property that the magnetic moment m 

 is first proportional to the magnetising force and tends towards a 

 maximum. The intensity of magnetisation is proportional to m, 

 and may be represented by b(i-e~ a ^ > ); it follows that 





The initial value of the coefficient of magnetisation k will be equal 



to the ratio 7 , and will diminish to zero. 

 a 



Lamont's formula represents very exactly the phenomena observed 

 by Joule, and generally those which correspond to magnetising forces 

 so great that we have exceeded the first elements of the curve of 

 inverse curvature. 



Instead of using an experimental formula, which has the incon- 

 venience of greatly complicating calculations in practice, the mag- 

 netic moment may be represented, as Frohlich has shown,* by the 

 branch of a hyperbola under the condition of having the same 

 tangent at the origin and the same asymptote as Lamont's expo- 

 nential curve. We shall have then 



m a<t> a<b 

 , r . or * 



Miillerf found that for a soft iron bar of diameter d, the mag- 

 netic moment M corresponding to a field </> is pretty exactly 

 represented by an empirical expression of the form 



M = Cd* arc tan 



in which A and C are constants; but this formula corresponds 

 solely to the particular case of a bar magnetised by a much 

 shorter coil placed at the centre. It has not then a general 

 character, but it also indicates a maximum of magnetisation ; and 

 the narrower the bar, the more rapidly is this maximum attained. 



* FR6HLICH. Electrotechnixte Zeitschrift, Vol. II., p. 134. 1881. 



t MULLER. Pogg. Ann., Vol. LXXIX., p. 337, 1850; Vol. LXXXII., p. 181, 1851. 



