170 SYNCHRONOUS MOTORS 



take n\n\ =p\q\\ and m\n\ represents and measures the total 

 ampere-turns made necessary by the armature-current. In like 

 manner, m-wi represents the corresponding ampere-turns required 

 for the motor OAz at the output indicated. 



To the two values on'i, and on' 2, of the total ampere-turns, cor- 

 respond electromotive forces ', and equal, respectively, to AVi' 

 and N2 r n2, on the total characteristic. These e.m.f.'s (which are 

 those that would appear if the current / ceased suddenly to pass 

 through the alternators), correspond, in the present case, to what we 

 term internal electromotive forces in the case of Joubert's theory. 

 By measuring off (Fig. 84) from 0, along OAz and OA i, distances 

 OK\ and OK2, respectively equal to these e.m.f.'s, we obtain two 

 vectors which replace, in the " two-reactions " theory, the vectors 

 OA\ and OA-z in the diagram obtained with Joubert's theory. 



It is seen that, in consequence of saturation, these vectors are, 

 in general, shorter than OA i and OAz\ but this is not a necessary 

 result, because it is possible to design an alternator in which the 

 transverse reaction would be very small, by reducing the width of 

 the pole-pieces, and which could, consequently, lead to a length for 

 OA\ less than OK\, at least so long as the saturation of the field- 

 magnets is low. 



For the sake of simplicity Lt has been assumed constant at all 

 loads, because the influence of the air-path is generally prepondera- 

 ting in the transverse magnetic circuit, contrary to what is true for 

 the principal circuit ; but those who may wish greater refinement can 

 take into account the slight variations of L t with the load-conditions 

 of the alternator, and they can also replace the perpendicular straight 

 lines ABi and A#2 by curves comprised between these straight lines 

 and segments of circles. In this way allowance can be made for 

 the fact that, in certain cases, the transverse reaction may not raise 

 the voltage at the terminals as much as when the pole-pieces are 

 wide. This complication of the diagram does not materially increase 

 its precision and it is therefore preferable to use the simpler theoret- 

 ical diagram. 



The circles of constant power of the old diagram are to be replaced 

 here by lines, which are drawn by points. To obtain these lines, 

 the values of '2 are drawn or determined for a large number of 

 positions of A 2 and for the corresponding power-outputs, and each 

 power- value is indicated near the point AI corresponding to it. 

 When the entire diagram has been in this way covered by a sufficiently 



