1892.] and aniiual and vegetable life. 7 



of different metals, joined together at P. Let a feeble electric 



current enter the system at A, and after crossing the junction P, 



leave at B ; and suppose that the current tends to cool the 



junction, but that by absorbing heat from external objects the 



temperature of the whole system is kept constantly equal to 0. 



Then the quantity of heat Q, absorbed by the system in any 



period, is positive ; and therefore Carnot's principle is not satisfied 



Q 

 in the form ^ < 0. If, however, we extend the system so that 



it includes all bodies traversed by the current, Carnot's principle 

 becomes applicable. 



It is now clear that an animal cannot be compared to an 

 electro-magnetic engine, and that Carnot's principle cannot be 

 expected to apply unless we take account of the flux of matter. 

 In the case of the animal body, our system must therefore be 

 chosen to contain, in addition to the living animal, a sufficient 

 quantity of air, water, food, soil, &c. ; so that, in the changes 

 we wish to investigate, the system contains the same matter. 

 When this is done, it will be found that Carnot's principle applies. 

 But even when our system is properly chosen, we cannot speak 

 of the ' efficiency ' unless the cycle of operations is complete. If 

 the cycle is incomplete, we must take account of the change of 

 entropy ; and it will be presently seen that there is something 

 which may easily be mistaken for ' efficiency.' 



If, for example, a system undergoes a reversible operation, 

 at the constant temperature 6, during which the energy and 

 entropy change from U^ and (f>^ to U^ and (j)^, respectively, the 

 heat given out will be equal to 6 (^^ — ^J, and therefore the 

 work done by the system will be tl^— tl^— 6 (^^ — (^^. Here 

 there is nothing which can be called ' efficiency,' if we use the 

 word strictly according to the definition ; but the ratio of the 

 work done to the loss of energy is 



This quantity may have any value Ave please. If no sensible 

 amount of heat is lost or gained, it will be practically equal to 

 unity ; and the work obtained from the system will be equal to 

 the energy lost by it. 



Now if the same amount of energy had been lost from the 

 system entirely in the form of heat, and the heat so obtained 

 had been used to work a Carnot's perfectly reversible engine 

 between the temperatures 6' and 6", the work obtained would 

 have been 



