Theory of Dynamo-electrical Machines. 57 



a very great current-strength it approaches a limiting value. 

 This ratio is expressed by Frolich* by an equation which, with 

 some non-essential changes in the notation, is as follows : — 



M=m (!2) 



1 + az 



in which M is the magnetic moment, and A and a are 

 constants. I do not think that the ratio of the magnetic 

 moment is hereby presented in the best manner ; but for our 

 immediate purpose, in which, owing to the many accessory 

 circumstances which refuse to lend themselves to an exact 

 determination, only approximately correct results can be ob- 

 tained, it seems to me admissible to apply this equation, which 

 is remarkable for its simplicity. 



For a very small current-strength the remanent magnetism 

 present in the iron, and arising from the previous magnetiza- 

 tion, has to be taken into account. This is of no importance 

 for calculations referring to machines at full work; but it is an 

 essential requisite for the first production of the current in the 

 starting of the machine, and for this reason we shall return to 

 it. For the present we may disregard it, and simply retain 

 equation (12). 



We must now consider further the magnetism of the iron core 

 of the rotating coil. This magnetism is more complicated for 

 the determination ; for, as already mentioned in § 1, it results 

 from two magnetic forces, which are exerted by the fixed elec- 

 tromagnet and by the current which traverses the rotating 



coil. 



The first force is proportional to the magnetic moment M 

 of the fixed electromagnet, and if it alone acted, would pro- 

 duce in the iron core a magnetic moment that could be repre- 

 sented by the expression 



CM 

 1 + 7 M> 



in which C and 7 are constants ; an expression quite cor- 

 responding to that by which we represented the magnetic 

 moment in the fixed electromagnet resulting from the current L 

 The second force, whose direction is perpendicular to the first, 

 would, if it alone acted, produce a magnetic moment which must 

 be also represented by an expression of the form just given. 

 We must, however, replace M by another magnitude which 

 stands in the same relation to the magnetizing force exerted by 

 the current in the coil on the iron core, as does the magnetic 



* Electrotechn. Zeifschrift des Berliner Eleetrotechnischer Vereins. ii. 

 p. 139 (1881). 



