252 Mr. W. J. M. Rankine on the Mechanical Action of Heat. 



pressures. The heat emitted is evidently 



Ho=(to-'c){</)(Vc,To)-<^(Vd,To)}. . . (c) 



Fourth operation. The body, being prevented from receiving 

 or emitting heat, is compressed until it recovers its original 

 temperature Tj, volume V, and pressure Pa; the locus of the 

 pressures being DA. During this operation, the same condi- 

 tions must be fulfilled as in the second operation ; therefore 



'\Jr being the same function as in equation {b) . 



By comparing equations {b) and {d), we obtain the relation 

 which must subsist between the four volumes to which the body 

 is successively brought in order that the maximum effect may 

 be obtained from the heat. It is expressed by the equation 



«^(Vb,T,)-c/,(Va, T,)=C^(Vc,To)-</,(Vo, To). . (64) 



From this and equations («) and (c), it appears that 



K^^. («^) 



That is to say, tvhen no heat is employed in producing variations 

 of temperature, the ratio of the heat received to the heat emitted 

 by the ivorking body of an expansive machine is equal to that of 

 the absolute temperatures of reception and emission, each diminished 

 by the constant k, which is the same for all substances. 



Hence let 



n=H,-Ho 



denote the maximum amount of power which can be obtained 

 out of the total heat H, in an expansive machine working between 

 the temperatures t, and Tq. Then 



^ = ^11:^ (66) 



Jij r^ — K 



being the law which has been enunciated in article 42, and 

 which is deduced entirely from the principles already laid down 

 in the Introduction and first Section of this paper. 



The value of the constant k is unknown; and the nearest 

 approximation to accuracy which we can at present make is, to 

 neglect it in calculation as being very small as compared with r*. 



* Subsequent investigations, founded chiefly on the experiments of 

 Messrs. Joule and Thomson on the thermic phsenomena of currents of 

 elastic fluids, have shown that the constant k, as anticipated in the text, is 

 actually very small, if not altogether inappreciable. Its approximate values, 

 computed from these experiments, range from 0° to about 2° Centigrade ; 

 the discrepancies being too small to affect materially the computation of 

 the power of engines. 



