or Centrifugal Theory of Elasticity. 417 



of variation of temperature in the two operations. It shows that 

 the proportion of the original latent heat of expansion finally 

 transformed into expansive power^ is a function of the tempei-a- 

 tures alone, and is therefore independent of the nature of the 

 body employed. 



Equation (28) includes Carnot's law as a particular case. Let 

 the limits of variation of temperature and volume be made inde- 

 finitely small. Then 



^ T — K 'I\ 



and dividing by drdY, 



dp__l_d(^ 



dr T—K dV ' 

 This differential equation is also an immediate consequence of 

 equation (25). 



If ^ be put for ■ —, and JM for -Tyr, it becomes identical 



J T — ^/C CI V 



with the equation by which Professor William Thomson expresses 

 Carnot's law^ as deduced by him and by ]\I. Clausius from the 

 principle, that it is impassvble to transfer heat from a colder to a 

 hotter body, without expenditure of mechanical poiver. 



The investigation which I have now given is identical in prin- 

 ciple with that in the fifth section of my paper on the Mechanical 

 Action of Heat, but the I'esult is expressed in a more compre- 

 hensive form. 



Equation (28), like (25), (26) and (27), is applicable to a 

 mixture composed of any number of different substances, in any 

 proportions, provided the tempei'ature, the pressure, and the 



coefficients -y-, -r^ are the same throughout the mass. 

 dT dr'- 



(12.) Apparent Specific Heat. — The general value of apparent 



specific heat of unity of weight is 



agreeing with eqration (13) of my previous paper. 



The value in each particular case depends on the mode of 

 variation of volume with temperature. Specific heat at constant 

 volume is 



Kv=fe + (T-«)(i^+/g./v). . . (30) 

 When the pressure is constant, we must have 



