Prof. Thomson on the Dynamical Theory of Heat. 169 



sions. Such of these as are independent of Joule's principle 

 (expressed by equation (2) of § 20), being also independent of 

 the truth or falseness of Garnet's contrary assumption regarding 

 the pei-raanence of heat, are common to his theory and to the 

 dynamical theory ; and some of the most important of them* 

 have been given by Carnot himself, and other writers who 

 adopted his principles and mode of reasoning without modifica- 

 tion. Other )-emarkable conclusions on the same subject might 



have been drawn from the equation -^ — -^- = 0, expressing 



Carnot's assumption (of the truth of which experimental tests 

 might have been thus suggested) ; but I am not aware that any 

 conclusion deducible from it, not included in Carnot's expres- 

 sion for the motive power of heat through finite ranges of tem- 

 perature, has yet been actually obtained and published. 



45. The recent writings of Rankine and Clausius contain 

 some of the consequences of the fundamental principle of the 

 dynamical theory (expressed in the first fmidamental proposition 

 above) regarding physical properties of various substances; 

 among which may be mentioned especially a very remarkable 

 discovery regarding the specific heat of saturated steam (inves- 

 tigated also in this paper in § 58 below), made independently 

 by the two authors, and a property of water at its freezing-point, 

 deduced from the corresponding investigation regarding ice and 

 water under pressure by Clausius ; according to which he finds 

 that, for each -^^q° Cent, that the solidifying point of water is 

 lowered by pressure, its latent heat, which under atmospheric 

 pressure is 79, is diminished by -081. The investigations of 

 both these writers involve fundamentally various hypotheses 

 which may be qv may not be found by experiment to be ap- 

 proximately true ; and which render it difficult to gather from 

 their writings what part of their conclusions, especially with 

 reference to air and gases, depend merely on the necessary prin- 

 ciples of the dynamical theory. 



46. In the remainder of this paper, the two fundamental pro- 

 positions, expressed by the equations 



dm dN 1 dp ,^, „ 



-dT'l^^ilt • • • (2)of§20, 



and 1 dp 



^=ll'i' (3) of §21, 



are applied to establish ])roperties of the specific heats of any 



substance whatever ; and then special conclusions are deduced 



for the case of a iluid following strictly the "gaseous laws" of 



* See above, § 22. 



