ADDITIONS TO THE THEOKY. SECOND APPLICATION 95 



/herein Ni equals the exciting ampere-turns, and /equals the function 

 which defines the law of variation of the induced E.M.F. with the 

 total inducing ampere-turns (this law being defined, in practice, by 

 means of a curve). The ampere-turns of the armature are, in fact, 

 demagnetizing, whenever I d lags behind 2, i-e., when the point A\ 

 is at the right of the axis BY; and they are, on the contrary, magnetiz- 

 ing, when A i is at the left. 



The segments zl w and zl d again measure, in magnitude and in 

 )hase, the active and reactive amperes by reference to some suitable 



:ale; and the phase-angles (lags) are measured from the line BY, 

 which serves as axis of reference. 



The output is the sum of the outputs corresponding to the currents 

 I w and I d . The induced E.M.F. is composed of the E.M.F. 2, pro- 

 duced by the direct field, and of the E.M.F. (u)L'I w ), produced by the 

 field of transverse reaction. The first is in phase with I w and the second 

 with I d . We therefore have 



The diagram therefore gives us again all the conditions of operation 

 of the motor without material increase in complication. 1 



First Application of Corrected Diagram. Determination of 

 Reactive Current as a Function 1 * of the Excitation, with Constant 

 Active Current. The preceding diagram enables us easily to find 

 the values of the reactive current as a function of the excitation and of 

 the active current, by the additional assistance of the excitation-curve 

 for open circuit, either obtained experimentally or else predetermined 

 by calculation. This curve (Fig. 45) gives, for each value, F, of the 

 ampere-turns, the corresponding induced E.M.F. 



1 The problem is really much more complex, especially when the load 

 changes suddenly, since the effect on the field-flux due to the armature-reac- 

 tion does not then appear as fast as the change of armature-current. The 

 flux may indeed remain constant for several seconds, even if the armature-cur- 

 rent changes considerably. Hence, for sudden changes of load the phenomenon is 

 largely governed by the true self-induction of the armature only. Thus, the 

 armature-reactance may be only from i per cent to 3 per cent, whereas, for 

 slowly changing loads, it would be equal to the synchronous reactance, say, 

 40 per cent. Therefore, machines which have good mutual induction between 

 field and armature, such as high-speed motors and turbogenerators, may be 

 unstable if the line-loss is great and if the load changes suddenly. The 

 remedy in such cases is to install external reactances. E. J. B. 



