GENERAL PRINCIPLES ,OF SYNCHRONOUS MOTORS 21 



2. The addition or subtraction of sinusoidal functions may be made 

 on the graph by a geometrical addition or subtraction of the vectors 

 of these functions. 



3. The mean product of two functions is equal to the work done 

 by one of the vectors on the other, i.e. it is equal to the area of the 

 triangle constructed on vectors which are equal to the effective values 

 of the variables, or to half this area when the triangle is constructed 

 with the amplitudes of the sinusoidal functions. 



This method, with which the reader is supposed to be familiar, 

 has been applied by Blakesley to the problem of synchronous motors 

 in the following manner: 



Let us represent the amplitudes of the E.M.F.'s. of the generator 

 and of the motor, E 1 V 2, and E 2 V 2, re- 

 spectively, by means of two vectors, 

 OA and OB, (Fig. 12), having between 

 them the angle x + 6. These E.M.F.'s 

 are approximately opposed to each other, 

 as we have seen in what precedes. 



Let OB' be equal but opposed to OB^ 

 The E.M.F. ev/z, which is the resultant 

 of EiV 2 and E 2 ^2, will be represented 

 by the vector B'A which is equal to the 

 resultant of OA and OB. 



Let us again designate by 7- the 

 phase-angle between the current and 

 the resultant E.M.F. denned by the re- 

 lation 



tan r =-, 



and let this angle be drawn with respect to the point A . The direction 

 CA will represent the current which is in phase. Let CA be the pro- 

 jection of B'A . We will have 



\/2 



or 



CA 



'' R ' 



The length of CA is therefore proportional to 7. 



