438 Mr. W. J. M. Rankine on the Mechanical Theory of Heat. 



[These formulae are approximative only ; but their deviation 

 from accuracy is inappreciably small in practice.] 

 The following table shows the results : — 



In the paper already referred to, I have shown that the pro- 

 bable range of error in the theoretical determination of the 

 specific heats of air is about ^^y th or /^th of their amount ; an 

 uncertainty which originates chiefly in the determination of the 

 velocity of sound. The agreement, therefore, of the theoretical 

 with the experimental results in the foregoing table is as close 

 as the uncertainty of the data will permit. 



M. Regnault's experiments also prove a fact, of vital import- 

 ance both in the theory of heat and in the laws of its practical 

 application to the production of motive power, viz. that the 

 specific heat of air does not sensibly vary between —30° and 

 -f 225° Centigrade ; and therefore that equal numbers of degrees 

 on the scale of the air-thermometer represent equal quantities of 

 heat. This fact, which had already been rendered probable by 

 the experiments of Messrs. Joule and Thomson on the thermic 

 phsenomena of air rushing through small apertures, is favourable 

 to the adoption, as a means of deducing the laws of heat from 

 mechanical principles, of the hypothesis that the elasticity of 

 heat is due to the centrifugal force of molecular vortices, by 

 deduction from which hypothesis the fact had been anticipated. 



Its most important consequence, as regards the application of 

 heat to produce motive power, is the following formula for the 

 maximum proportion of the total heat expended which can be 

 converted into mechanical work by any thermo-dynamic machine, 

 receiving heat at the maximum temperature Tj, and giving it out 

 at the minimum temperature Tg, a formula deduced from the 

 hypothesis in question in the Transactions of the Royal Society 

 of Edinbui-gh, vol. xx. pp. 207, 438. 



Let Hj be the mechanical equivalent of the total heat received 

 by the machine at the temperature Tj ; 



Hg that of the heat given out at the temperature Tg ; 



E = H, — Hj the maximum mechanical effect of the machine; 



K the temperature corresponding to absolute privation of heat ; 



