VOLTAGE REGULATION OF THE ALTERNATOR. 123 



C and D may be represented by the four equidistant vectors A, 

 B, C and D in the clock diagram Fig. 1 10. 



Fig. 110. 



If the windings in all of the slots in Fig. 1 09 are connected in 

 series as a single distributed winding, the effective value of the 

 electromotive force produced by the combined winding will be 

 the vector sum of A, B, C and D y as shown by the line E in 

 Fig. no, in which the lines A, B f , O and D' form a portion 

 of a regular polygon of which E is the chord. If the angular dis- 

 tance between A and B, B and C and so on, is small, the lines 

 A, B', C' and D 1 form sensibly the arc of a circle of which E 

 is the chord, and the angle subtended by the arc is the phase dif- 

 ference between A and D. 



If the electromotive forces A, B, C and D were in phase with 

 each other, that is if all of the armature conductors were concen- 

 trated in / slots, the effective value of E could be calculated from 

 the formula IT j (21/2) x pQZn abvolts, and it would be equal to 

 the arithmetical sum (not the vector sum) of A, B, C and D ; 

 that is, the value of E would be represented by the length of the 

 arc AB'C'D' in Fig. no. In fact, however, E is represented 

 by the length of the chord, so that 7r/(2i/2) X pQZn must be 

 multiplied by the ratio chord /arc to give the correct value of E, 

 the chord and arc being such as to subtend an angle equal to the 

 phase difference between the electromotive forces induced in those 

 armature conductors which lie in the most distant slots of a 



