Electromagnet and the Laio of the Dynamo, 9 



which is identical in form with the expression known as 

 Frolich's. Now, writing k for a/M, 



Wcx 



m=- =— , 



l + hc' 



and expanding this in ascending powers, we get 



m = Mfoc(l — foc + AV— ). 



Neglecting the fourth and higher terms, it will be seen 

 that the formulae are very nearly equal for all small values of 

 k%, and are identical for the value 



/ex — — -, 

 W 



or when the actual magnetism has about '456 of the value it 

 would have under an infinite magnetizing force. For larger 

 values of the magnetizing force the values of m calculated by 

 the empirical formula are slightly greater than those calcu- 

 lated by the exponential formula. 



None of these formulae render any account of a phenomenon 

 noticed in many cases where an electromagnet is magnetized 

 with gradually ascending magnetic forces, namely, a concavity 

 in the early part of the curve of magnetization, the per- 

 meability apparently becoming greater after a certain degree 

 of magnetization has been attained. The researches of 

 Chwolson and of Siemens seem to show that this apparent 

 increase in the permeability (which is not observed with de- 

 scending magnetic forces) is due to non-homogeneity, and to 

 the resistance of some of the molecules to magnetization. 

 Bosanquet's theory may be taken in connection with the 

 recent observations of Rowland, Warburg, Ewing, and Hop- 

 kinson on this subject, which, however, is of no great im- 

 portance here since the apparent maximum of permeability is 

 attained in most cases at a much lower degree of magnetization 

 than that at which the dynamo is actually worked. 



The very close agreement between the observed values of 

 current and potential of the dynamo and those calculated by 

 the equations based upon Frolich's formula, proves that 

 nowhere within the working range do the actual values of 

 the magnetization differ sensibly from those calculated by the 

 Frolich formula. That is to say this formula may be taken 

 as something more than a first approximation to the true law 

 of the electromagnet for all degrees of saturation of the 

 magnets employed in practice, and may be taken as a first 

 approximation for all degrees of saturation beyond that 

 usually attained. 



