APPENDIX A 



IF Eq. (A} on page 16 be solved completely for i, the solution 

 will include a transient exponential term depending upon the point 

 of the E.M.F. cycle at which the circuit is closed. It is a well-known 

 fact that this transient term becomes negligible a short time after 

 the circuit is closed, and that when the impressed E.M.F. is sinu- 

 soidal the current i will settle down to a sinusoidal form. 



In the present case both of the active E.M.F. 's (ei and 62) are 

 assumed sinusoidal and of the same frequency; their resultant is there- 

 fore sinusoidal as will be the current produced thereby. Then all the 

 variables involved are sinusoidal and may be represented by vectors 

 in such a manner as to indicate clearly their phase-relations. 



A< 



Referring to Fig. A, draw OC, to designate by its length and 

 direction the phase and magnitude of the internal or induced E.M.F. 

 E\ of the generator, and OA to designate in a similar manner the 

 internal or induced E.M.F. 2 of the motor. Then the resultant 

 or vector-sum of EI and 2 will be E, designated by the line OB. 



The horizontal line OX is taken arbitrarily as the zero of phase, 1 



1 In Fig. A the instantaneous values of the various variables (e.g., e\ and e^ 

 are given by the vertical projections of the corresponding vectors (multiplied 

 by \fi)i as the latter revolve counter-clockwise at constant angular velocity, 

 o) = 2icw, where n = cycles per second. The diagram is shown at the instant t =0. 



283 



