8 Dr. S. P. Thompson on the Law of the 



pendent line of thought, and who has gone much further 

 than Lamont in bringing in the additional consideration of the 

 forces resisting the orientation of the molecules. Lamont's 

 theory is, briefly, that the permeability of the iron diminishes 

 as the permeation increases, being at every stage of the 

 magnetization proportional to the deficit of saturation. He 

 assumes that for every bar there is a certain maximum of 

 magnetization, to which it could only attain under the in- 

 fluence of an infinitely great magnetizing force ; and that the 

 permeability of the bar is at every stage of the magnetization 

 proportional to the difference between the actual magnetization 

 and the possible magnetization. This is, in other words, as 

 if in every bar there were room for only a certain limited 

 number of magnetic lines of force, and that, when any lesser 

 number have been induced in it, the susceptibility of the bar 

 to the reception of additional lines is proportional to the room 

 yet left for them in the bar. Lamont's theory is expressed as 

 follows : Let the magnetism present at any stage be called m, 

 and let the maximum magnetism be called M. Then the 

 amount which the bar can still take up is M — m; and it is 

 to this that the permeability dmjdos is proportional. Here x 

 may be understood, as itself proportional to the number of 

 ampere-turns of the exciting current ; and we may write 



where h is a constant depending on the units employed, and 

 on the initial value of the permeability of the magnetic circuit 

 when m = 0. Integrating we obtain 



M— m=Ae-** } 



where A is a constant of integration. But when x = 0, 

 m = also ; whence A = M, giving 



m=M(l — €"**), 



which is Lamont's formula. 



Lamont also develops this expression in ascending powers 

 of kx, 



'-"^-fe+ifo- > 



and he then makes the remark that it may be approximately 

 represented by the simpler, but empirical expression 



_ flMa? 



m- 



