20 SYNCHRONOUS MOTORS 



is sufficient, therefore, to apply the reasoning to one of the circuits 

 only, and to multiply the power by the number of circuits. 



It should be noted, moreover, that, in these motors, the pulsations 

 of the power derived from the different circuits, occurring at different 

 intervals, compensate each other, from the standpoint of the total 

 power, which becomes constant. This is easily shown by taking the 

 sum of the powers. For example, in a three-phase motor, the pulsa- 

 tions at the instant itut will have the form 



(f) \ 

 2a>tf j; 



/ 27T\ 



A sin \.2<jjty I; 



/ M 



A sin I 2ajtr ). 



V 2 3 / 



It is known that the sum of the sines of three angles differing from 

 each other by 120 is identically equal to zero. Therefore the" result- 

 ant" pulsation is equal to zero. The same thing would be true for 

 any number whatever of equidistant and symmetrical phases. 



The result is that the torque is constant (to a sufficient degree of 

 approximation for this theory, which neglects the higher harmonics 

 of the field-distortions), whereas, in a single-phase motor, it undergoes 

 heavy periodical variations. In the latter case, the inertia of the armature 

 plays the role of a flywheel storing and restoring energy twice during 

 each period; but if the inertia is insufficient, the velocity of the armature 

 will experience slight variations which will greatly interfere with the 

 stability of operation. Polyphase motors are, in this respect, superior 

 to single-phase motors; they are also superior to them in being lighter 

 for a given output (less weight per kilo-volt-ampere) and also in 

 having higher efficiency. 



Graphical Representation of Operative Conditions. Blakesley's 

 Method. Mr. Blakesley was the first to apply Fresnel's method of 

 vectors to the study 9f alternating currents. 1 



The following principles constitute the basis of Fresnel's method: 



i. Any sinusoidal function can be represented in magnitude and 

 in phase by a vector, or a segment of a right line, whose length is pro- 

 portional to the amplitude of the function and whose phase is meas- 

 ured by an angle reckoned from some other vector serving as a point 

 of origin. 



' Blakesley, Alternating Currents of Electricity, 1885 



