of the Law of Efficiency of an Electric Motor. 129 



Kg. 5. 



K G H D which repre- 

 sents the heat-waste is 

 the same size as before; 

 but the energy spent is 

 twice as great, and the 

 useful work done is 

 more than twice as 

 great as previously. 

 High electromotive 

 force therefore means 

 not only a greater 

 quantity of power 

 transmitted," but a 

 higher efficiency of 

 transmission also. The 

 efficiency of the system 



in the case of fig. 3 B l c 



was 80 per cent; in the case of fig. 5 it is 90 (the dynamos 

 used being supposed "perfect"); and whilst double energy is 

 expended, the useful return has risen in the ratio of 9 to 4. 



(7) So far it has been supposed that the resistance of the 

 system is a constant quantity. But it is possible to construct 

 diagrams in which changes of resistance are taken into 

 account. All that is necessary is to vary the scale of the 

 diagram, the linear unit of scale being chosen inversely pro- 

 portional to the square root of the total resistance. This will 

 make the areas of the diagrams inversely proportional to the 

 resistances in the different cases, as required by the law that 



IT 2 

 the energy of the current is proportional to p-« 



An example in which this rule is applied is the following. 

 It can be shown that the power transmitted and efficiency of a 

 transmitting system are increased by doubling the number of 

 coils in the armatures of the machines. This is not at first sight 

 self-evident; for though, cceteris paribus, this doubles the elec- 

 tromotive force of the machines, it also doubles their resistances. 

 Let fig. 6 be the diagram for a trans- 

 mitting system, where e = fE, and 

 in which these values are both going 

 to be doubled by doubling the num- 

 ber of armature-coils. There are 

 two cases to consider: — (a) first, 

 where the line-resistance is very 

 small compared with that of the 

 two machines; (b) second, where 

 the line-resistance is very large 

 compared with that of the two machines. 



Fig. 6. 



