165 



The ratio of the Real Specific Heats of any pair of substances is 

 the same at all temperatures. 



Symbolically, let r denote the temperature of a body ; x, the tem- 

 perature of absolute privation of heat : |(, a function of the nature, 

 and possibly of the density of the body. Then the quantity of heat 

 in unity of weight may be expressed thus — 



If this notation be introduced into the expression for the greatest 

 proportion of heat convertible into mechanical power by an expansive 

 engine, it becomes 



that is to say, this ratio is a function merely of the temperatures of 

 receiving heat, r^, and of emitting heat, r^, and independent of the 

 nature of the body. This is Carnofs Theorem, as modified by Messrs 

 Clausius and Thomson. The expression for the latent heat of ex- 

 pansion becomes 



J <^ P 



= . __ d V, in Prof. Thomson's notation. 

 fJL dr ' 



Hence, in Professor Thomson's notation, 



which, being introduced into the formulse of the first sub-section, re- 

 produces all his forniulse. 



In the Third Suh^Sectio7i, the author points out the consequences 

 peculiar to the Hypothesis of Molecular Vortices (that is to say, of 

 whirling eddies in elastic atmospheres surrounding atomic nuclei) ; 

 an hypothesis, the first outline of which was given by Sir Humphry 

 Davy, and which the author adopted, with modifications and additions, 

 as the basis of his investigations in the first five sections of this 

 paper, in two papers on the Centrifugal Theory of Elasticity, and in 

 other papers, with a view to the deduction of the laws of heat and 

 elasticity from the principles of mechanics. After pointing out the 

 resemblances and difi'erences between this hypothesis and that of 

 Molecular Collisions proposed by Messrs Herapath and Waterston, 

 and remarking that the Hypothesis of Molecular Vortices, besides re- 



O 2 



