Prof. Rankine on the Dynamical Theory of Heat. 195 



thermometric heat consists in molecular motions (as was shown 

 in a paper of mine of the same date). 



For the purposes of the present paper, it is unnecessary to 

 state the second law of the mechanical action of heat in its most 

 abstract form. It will be sufficient to state the form which it 

 takes when applied to a perfect thermo-dynamic engine : viz. — 



In a perfect thermo-dynamic engine, receiving heat at a higher 

 absolute temperature and rejecting heat at a lower absolute tempe- 

 rature, the quantity of heat which disappears in the production of 

 an equivalent quantity of mechanical zoork is, to the ivhole quantity 

 of heat expended, as the difference of the two absolute temperatures 

 is to the higher absolute temperature. That ratio is the efficiency 

 of the engine. 



Mr. Gill erroneously represents as consequences of the dyna- 

 mical theory of heat, two propositions which are contradictory of 

 this law. The first of these is that, by the aid of a perfect regene- 

 rator, the whole of the heat rejected in a perfect thermo-dynamic 

 air-engine might be transferred back to the air, so as to make 

 its efficiency unity — in other words, to cause the whole heat 

 expended to disappear in producing mechanical work. So far 

 from this being a consequence of the dynamical theory of .heat, 

 it is in direct contradiction to the second law of that theory ; 

 according to which the efficiency of a thermo-dynamic engine 

 cannot be increased beyond a certain function of the tempera- 

 tures between which it works, by a regenerator or by any other 

 contrivance whatsoever. In a paper published in the Philoso- 

 phical Transactions for 1854, I have shown that, according to 

 the dynamical theory of heat, the proper function of a rege- 

 nerator is to save some of the heat which would otherwise be 

 wasted in engines which do not fulfil the conditions of greatest 

 economy required by the second law, and that, in an engine 

 which does fulfil those conditions, the use of a regenerator is 

 nugatory. 



The second instance in which Mr. Gill, through not consider- 

 ing the second law, erroneously represents the consequences of 

 the Dynamical Theory of Heat, is where he alleges that, " accord- 

 ing to the dynamical theory, a common non-condensing steam- 

 engine, working without expansion, utilizes only about -^ of the 

 theoretical power of the steam. By the addition of condensa- 

 tion the efficiency is doubled, or the engine gives off ^n useful 

 effect." 



No such consequences have ever been deduced from the dyna- 

 mical theory of heat. In the numerous examples of the theore- 

 tical calculation of the efficiency of steam-engines which have 

 been published since 1849 in the writings of various authors, it 

 has been shown" that the efficiency of an ordinary non-expansive 



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