64 



Profs. Ayrton and Perry on the 



as we did in our original paper, since, although the results so 

 obtained for critical speed, &c, cannot be used directly with- 

 out correction in actual practice, these equations are sufficiently 

 accurate to show whether or not a certain combination is a 

 possible or an impossible one for obtaining a certain required 

 result. 



If E be the back E.M.F. in the armature of a motor at a 

 speed of n revolutions, if p be a term depending on the 

 permanent magnetism in the iron of the field-magnet, S the 

 current passing round the series-coil, and Z the current round 

 the shunt-coil, we have 



E=n(p±qS±tZ) (1) 



The signs + or — in the two terms being used as the series- 

 and the shunt- currents respectively help or oppose the perma- 

 nent magnetism. 



If s and z be the resistances of the series- and shunt-coils 

 respectively, a the resistance of the armature, and A the 

 current round the armature, we have in the case of what has 

 been called a short shunt (fig. 1), 



E = Z^-Aa, (2) 



and in the case of what has been called a long shunt (fig. 2), 



ft = Zz-A(a + s); (3) 



Fig. 1. 



Fiar. 2. 



V_-^ 



and in both cases, if C be the constant current supplied to the 

 motor, 



C = A + Z (4) 



Now, remembering that in the case of a short shunt (fig. 1), 

 C is equal to S, equations (1), (2), and (4) lead to 



n{p±qC±t (C-A)}=(C-A)s-Aa; . . (5) 



and in the case of a long shunt (fig. 2) , remembering that C 



