24 



KUKTHOMOTIYK KnlK'K AND (TKKENT. 



The easiest way to obtain the sum of the projections of 

 two such lines as E r E { is to draw one of them (say E r ) from 

 the end of the other (E { ) (see Fig. 10), so that the arrows of 

 the two lines point in the same direction. The horizontal 

 projection of E { is then Oe l9 and the horizontal projection 

 of E T is e l % Since the projection of E r is measured from 

 right to left, instead of from left to right, it must be considered 

 negative, and thus the sum of the two projections is Oe.>. But 

 Oe., is the same as the projection of the line E joining the 



10 20 30 40 50 



SCALE OF VOLTS 

 FK;. 9. !'!<;. 10. 



ItKSUI/rANT AND COMPONENT K[,KCTIK)M()TI \ K KoilCES. 



free ends of E r and E,. E is, however, the diagonal of 

 the parallelogram whose sides are E,. and E { , the line E, 

 Fig. 10, is, in fact, the same as E in Fig. 9. Hence the 

 instantaneous value of the resultant of the two varying 

 quantities is the instantaneous value of the diagonal of the 

 parallelogram of which the quantities form the sides. 



The result just obtained is of the greatest practical 

 importance, and shows that, when represented by vectors, 

 two electromotive forces or two currents may be combined 

 together in exactly the same way as may the forces or velocities 

 illustrated in mechanics by straight lines, which are combined 

 to form single resultant forces or velocities by the law of 

 the parallelogram of forces. 



A similar rule to this may therefore be given in the follow- 

 ing terms. The resultant of two currents or electromotive 



