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



supposed that the whole of the heat actually absorbed in the 

 cycle of operations is converted into useful work; and in this 

 case the efficiency is the ratio of the heat absorbed to the total 

 heat expended. As is well known, this efficiency of the per- 

 fect heat-engine can be expressed as a function of two absolute 

 temperatures, namely those respectively of the heater and of 

 the refrigerator of the engine. Carnot's engine is also ideally 

 reversible ; that is to say, capable of reconverting mechanical 

 work into heat. 



The mathematical law of efficiency of a perfect electric 

 engine illustrated in the above construction is an equally ideal 

 case. And the efficiency can also be expressed, when the 

 constants of the case are given, as a function of two electro- 

 motive forces. We shall return to this comparison a little later. 



The Law of Maximum Rate of Working (Jacobi) . 



(3) Let us next consider the area Gr L C H of the diagram 

 (fig. 2), which represents the work utilized in the motor. The 

 value of this area will vary with the posi- 

 tion of the point G, and will be a maximum 

 when Gr is midway between B and D ; for 

 of all rectangles that can be inscribed in 

 the triangle BOD, the square will have 

 maximum area (fig. 2). But if G is 

 midway between B and D, the rectangle 

 G L C H will be exactly half the area of 

 the rectangle AFHD; or, the useful 

 work is equal to half the energy ex- 

 pended. When this is the case, the 



counter electromotive force reduces the current to half the 

 strength it would have if the motor were at rest; which is 

 Jacobi's law of the efficiency of a motor doing work at its 

 greatest possible rate. 



Law of Maximum Efficiency. 



(4) Again, consider these two rectangles when the point G 

 moves indefinitely near to D (fig. 3). Fig. 3. 

 We know from common geometry that 

 the rectangle G L C H is equal to the 

 rectangle A F G K. The area (square) 

 K G H D, which is the excess of A F H D 

 over A F G K, represents therefore the 

 electric energy which is wasted in heat- 

 ing the resistances of the motor. That 

 the efficiency should be a maximum the 

 heat-waste must be a minimum. The 



