

ADDITIONS TO THE THEORY. SECOND APPLICATION 93 



depends on the shape of the pole-pieces. The induction-flux is pro- 

 duced by the algebraical resultant of the exciting ampere-turns and 

 of these counter-ampere-turns. 



(2) A transverse reaction producing a flux which closes itself trans- 

 versely in the pole-pieces, without penetrating the field-windings 

 and having a numerical value equal to 



N 9 



wherein L'= a coefficient. 



This resolution, of which the validity has been shown else- 

 where, takes into account the lag, since the current intervenes by 

 its two components (active and reactive) with respect to the E.M.F. 

 of the motor. [The words " active " and "reactive" are here taken 

 relatively to an E.M.F. induced with open circuit. The phase-angle 

 thus obtained is therefore slightly different from that which would be 

 found at the terminals.] It also takes into account the saturation 

 of the fields, since the resultant flux of the fields is calculated from 

 the ampere-turns themselves, by reference to an excitation-curve 

 obtained experimentally. 



As to the transverse flux, it is substantially independent of the satura- 

 tion, because the reluctance of the magnetic circuit through which 

 it finds its path is substantially constant. That is why L r can be con- 

 sidered constant. 



With this assumption, it is easy to establish a new diagram for 

 synchronous motors which will take these reactions into account. It 

 will be sufficient to segregate the motor-reactances. Let and x equal 

 the impedance and the reactance, respectively, of the generator and 

 of the line, and of the magnetic leakage of the motor; and let R equal 

 the resistance of the circuit, including the motor-resistance. (The 

 generator-impedance may be neglected when the current is taken 

 from a distribution-system.) Let 2 equal the effective motor E.M.F., 

 i.e., the E.M.F. produced by the resultant fields of the field and 

 armature ampere-turns. 



The generator E.M.F. E\ will be equal to the resultant of the following 

 three components: First, the effective counter E.M.F., A 2 O=e 2 , \\ith 

 its sign reversed; second, the transverse reaction E.M.F. A 2 B=toL'I w 



with its sign reversed and having a phase-lead of ahead of e 2 ', and, 



2 



