Fiff. 7. 



130 Prof. S. P. Thompson on the Graphic Representation 



{a) In the former case, where we neglect the resistance of 

 the line, we must draw a diagram diminishing the linear unit 



of scale to —j= of its value. But as on this scale we are going 



to represent doubled electromotive forces, the actual figure 

 will have to be ^/2 times as large as fig. 6. Draw, then, the 

 fig. 7, taking as side of the 

 square a line equal to the dia- 

 gonal of fig. 6, and we obtain 

 a diagram in which, while the 

 efficiency is the same as before, 

 the actual quantity of work 

 effected in unit time is doubled. 

 For the areas representing re- 

 spectively energy expended, work 

 done, and heat- waste are in fig. 7 

 double of those in fig. 6. But 

 no such case can occur in prac- 

 tice, as the line must have some resistance. Then doubling 

 the number of coils of the machines will not cut down the scale 

 so greatly as we have supposed; and the work transmitted will 

 be more than doubled. Further, if the number of coils on the 

 machine used as motor be a little more than doubled, a higher 

 efficiency will be attained; since then the area of the square 

 K Gr H D will be further diminished, while the scale on which 

 the diagram is drawn will only be very slightly diminished. 

 If diminished, as shown by the dotted lines, so that e — E has 

 the same value as before, the efficiency will be a little less than 

 doubled, the power transmitted remaining as at first. 

 (b) If the case where 



Fig. 8. 



180 



the line-resistance is very 

 great as compared with 

 the resistances of the 

 machines be taken, we i6o 

 find that doubling the 

 number of the coils of 

 the two machines will 

 double their respective 

 electromotive forces, 

 without altering appre- 

 ciably the total resistance 

 or the scale of the dia- 

 gram. To represent this 

 change relatively to fig. 

 6, we must reconstruct 

 that figure, doubling its linear dimensions each way, as in fig. 8. 



