292 Dr. S. P. Thompson on the Formula of the 



be the diacritical value of the same for the given magnet ; let 

 $ be the intensity of the field, or the strength of the pole, or 

 the magnetic moment, or the integral of the magnetic induc- 

 tion, and <I> its maximum value; then 



This being the general equation of the electromagnet, it 

 remains to be shown how excessively simple become the 

 equations of the various kinds of dynamo. 



3. Equations of the Series-wound Dynamo. 



If A is the "equivalent area " of the coils of the armature, 

 and H the average strength of the field in which it turns, the 

 number of lines of force cut in each quadrant is AH ; hence 

 the average electromotive force at the speed n is 



E=4wAH . . (1) 



But h=yA, 



and, writing B = 4AY, and remembering that, if 2R be the 

 sum of the resistances in the circuit, E/2R=? (by Ohm's 

 law), we get 



._ nB ., 



But Y being the maximum value of H, it is obvious that nB 

 is the maximum value that E could possibly have (at that 

 speed) even if the magnets were separately excited to satura- 

 tion. Hence wB/XR is the maximum value that i could have 

 if the magnets were thus separately saturated and the arma- 

 ture, driven at speed n, were in a circuit the total resistance 

 of which was equal to 2R. Adopting Frolich's notation here, 

 we will write as i this current; and as it is important to 

 distinguish the current generated under such conditions, I 

 propose to call it the " maximal " current*. The equation of 

 the series dynamo now becomes 



i = i-i/; (2) 



or, multiplying each term by SR, 



E=E-E', (3) 



* The maximal current must not be confused with the maximum cur- 

 rent. The latter would be obtained by rotating the armature in the 

 saturated field at a very high speed in a circuit of resistance so small that 

 the current did just not fuse the conductors. The maxim al current is that 

 obtained at speed n in circuit of resistance 2R when the magnets are 

 separately excited to saturation. 



