142 ELEMENTS OF ELECTRICAL ENGINEERING. 



The two machines, A and B, in Figs. 122 and 123 are in 

 series with each other in regard to the circuit formed by the two 

 machines, and this circuit formed by the two machines is the only 

 circuit at present to be considered. The electromotive force which 

 tends to produce current in this circuit is at each instant equal 

 to the algebraic sum* of the electromotive forces of the respective 

 machines. Therefore, if the machines are in synchronism, that 

 is, if their electromotive forces have the same frequency, the total 

 electromotive force which tends to produce current in the circuit 

 may be represented in the clock diagram as the resultant E of 

 the two lines A and B which represent the electromotive forces 



of the respective machines, 

 as shown in Fig. 124. In 

 this diagram < is the phase 

 difference between A, and 

 B, and this angle remains 

 constant in value so long 

 as the two machines A and 

 B run exactly in synchron- 

 ism. If, however, one ma- 

 chine runs momentarily 

 faster than the other, the 

 value of <f> will change. It is evident that $ can have any 

 value whatever, except in so far as it may be kept within certain 

 limits by the action of the two machines on each other. For 

 the present we will consider that the angle < can have any value 

 from zero to 360. 



The resultant electromotive force E produces in the circuit 

 of the two machines a current / of which the value is 



= - 



and which lags degrees behind E in phase where 6 is the 

 angle whose tangent is X\ R, that is, 



* The electromotive force of each machine is here considered to be positive when 

 it acts in a chosen direction around the circuit formed by the two machines. 



