Theory of Dynamo-electrical Machines. 131 



which the dependence of the current-strength on the conduc- 

 tivity is apparent, and that on account of the members affected 

 by the factors p, a, and X, they increase more slowly than v, 

 which is important with high values of v. 



§ 13. The Starting of the Machine. 



It has been pointed out in the previous paragraphs that the 

 equation (36), even by using the upper sign, and in corre- 

 spondence therewith the equation (40), for no values of v, gives 

 negative values of i, which are inadmissible. But this cannot 

 be understood to mean that the chief equation from which 

 we have started (that is II. a) gives untrustworthy results for 

 small velocities of rotation. We must rather remember that 

 this equation gave us first the equation (31), from which, only 

 on dividing by i did we arrive at the equation of the second 

 degree, the solution of which is given in (36). If we had not 

 divided by i, we should have had, instead of an equation of 

 the second degree, one of the third degree, which, besides the 

 roots given in (36), would have had the root i = 0. We must 

 consider this value null of i as a value satisfying the chief 

 equation ; and it is this which we must apply in the interval in 

 which the two other values are untrustworthy. 



Hence, if even with small velocities of rotation we wished to 

 hold rigidly to the chief equation given in (II. a), we should 

 arrive at the following results. For small velocities of rotation 

 the machine gives no current, but its action begins at a certain 

 velocity of rotation; and now as this increases, there is an in- 

 crease in the current-strength which is in a finite ratio to the 

 differences of the velocity. This corresponds in fact to expe- 

 rience with such approximation that the interval in which the 

 machine is inactive has received a special name, the first few 

 turns having been called the dead turns. 



It must not, however, be regarded as strictly correct to apply 

 equation (II. a) even with small velocities of rotation, but, at 

 any rate with velocities in which that equation would indicate 

 no current, we must take into account the remanent magnetism 

 in the iron of the fixed electromagnet arising from the previous 

 magnetization. 



In deducing the above chief equations we have defined the 

 magnetic moment of the fixed electromagnet by the equation 



M= -**-„ 



1+ai 



For small values of i this equation would give correspondingly 

 small values of M, and for i=0 the value M = 0. But if a 

 certain magnetization is present in the iron before the action 



K2 



