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



in the The'orie Me'canique de la Chaleur of Verdet*. ' Yet it 

 remained a mere mathematical abstraction until its significance 

 was pointed out three or four years ago by Siemens. 



(5) Further, if the motor be not a " perfect " one, but one 

 whose intrinsic efficiency, or efficiency per se, is known, the 

 actual mechanical work performed by the motor can be repre- 

 sented on the diagram by simply retrenching from the rect- 

 angle GrLCH the fraction of work lost in friction &c. Simi- 

 larly, in the case where the electric energy expended has 

 been generated in a dynamo-electric machine whose intrinsic 

 efficiency is known, the total mechanical work expended can 

 be represented by adding on to the area A F H D the propor- 

 tion spent on useless friction &c. To make the diagram still 

 more expressive, we may divide the area K G- H D into slices 

 proportional to the several resistances of the circuit ; and the 

 areas of these several slices will represent the heat wasted in 

 the respective parts of the circuit. These points are exempli- 

 fied in fig. 4, which represents the transmission of power 

 between two dynamos, each supposed to have an intrinsic effi- 

 ciency of 80 per cent., each having 500 ohms resistance, 

 working through a line of 1000 ohms resistance, the electro- 

 motive force of the machine used as generator being 2400 

 volts, and the counter electromotive force of the machine used 

 as motor being 1600 volts. 



The entire upper area repre- 

 sents the total mechanical work 

 expended. Call this 100, and it 

 is expended as follows : — a = 20, 

 lost by friction &c. in the generator; 

 fr=6§, lost in heating generator; 

 c = 13^-, lost in heating line-wires; 

 d=6§, lost in heating motor; 

 0=1O§, lost in friction in the 

 motor; w = 42§ is the percentage 

 realized as useful mechanical work. 



(6) The advantage derived in the case of the electric trans- 

 mission of power from the employment of very high electro- 

 motive forces in the two machines is also deducible from the 

 diagram. 



Let fig. 3, given above, be taken as representing the case 

 where E is 100 volts and e 80 volts. Now suppose the resist- 

 ances of the circuit to remain the same while E is increased to 

 200 volts and e to 180 volts. (This can be accomplished by 

 increasing the speed of both machines to the requisite degrees.) 

 E — e is still 20 volts, and the current will be the same as 

 before. Fig. 5 represents this state of things. The square 

 * Verdet, CEuvres, t. ix. p. 174. 



Fig. 4. 



«- 



JV 



e 



b 



c \d 







v' 







/ 



/ 



/ 



/ 





uy 



