58 On the Theory of Dynamo-electrical Machines. 



moment M to the magnetizing force exerted by the fixed elec- 

 tromagnet upon the iron core. We will call this magnitude 

 N, and define it by the fact that we represent the magnetic 

 moment which the current in the rotating coil would by itself 

 produce in the iron core, by the formula 



I+7N' 



The magnitude N thus defined must obviously be proportional 

 to the current-strength in the rotating coil, which in the two 

 halves is together equal to i, so that we can put 



N=Bi ; ....... . (13) 



in which B is a constant for each machine. 



If, now, both those magnetizing forces act simultaneously on 

 the iron core, a more powerful magnetism must be excited in 

 it. In order to express the magnetic moment P of this mag- 

 netism, we must first of all form the resultant of M and N, 

 which is represented by \/M 2 + N 2 . If we form an expression 

 quite analogous to the above expression, this magnitude must 

 be used both in the numerator and denominator instead of the 

 values M and 1ST, by which we should get 



p ^ (Vm 2 +n 2 



=S l+7V / M 2 + N 2 ' 



Now it has been remarked above, that the expression by 

 which, on Frolich's plan, we have represented the depend- 

 ence of the magnetic moment on the effective magnetizing 

 force, can only be regarded as approximate, and this holds 

 particularly for the form of the numerator. As now the 

 occurrence of the root \/M 2 + N 2 in the numerator makes the 

 expression somewhat inconvenient for calculation, it may be 

 permitted somewhat to simplify the numerator. Of the two 

 magnetizing forces one is exerted directly by the current, and 

 is therefore simply proportional to the current-strength i. The 

 other is also exerted indirectly by the current ; for this pro- 

 duces the magnetism of the fixed electromagnet, which in turn 

 exerts the force in question. Hence the degree of accuracy 

 of the expression will not be appreciably diminished if, instead 

 of that root which represents the force, we introduce a value 

 proportional to the current-strength i in the numerator of Ihe 

 fraction, and thereby give this the same form as the numerator 

 of the fraction occurring in equation (12). The equation, 

 then, which serves to determine P is as follows : — 



"l+# y J 





