288 



substance, a constant co-efficient, and, according to another definition, 

 are proportional to the tendencies of heat to disappear in producing 

 mechanical effects. These definitions are substantially equivalent. 

 The recent experiments of Messrs Joule and Thomson have confirmed 

 the anticipation, that absolute temperatures, as thus defined, agree 

 with those measured by the variation of pressure of a perfect gas ; 

 they have also proved, what could only be conjectured before, that 

 the absolute zeros of heat and of gaseous pressure sensibly coincide. 

 The authoi', from a revision of M. Regnault's experiments on the 

 elasticity of gases, concludes the most probable value of the absolute 

 temperature of melting ice to be — 



274° Centigrade = 493°-2 Fahrenheit. 



Messrs Joule and Thomson, from their experiments on the coolino- 

 of gases by free expansion, deduce the value — 



273°-7 Centigrade = 492'-66 Fahrenheit. 



The difference between those values is practically inappreciable. 



A Thermodynamic Function is a function of the condition of a 

 substance, such that the heat absorbed by the substance during any 

 small variation of condition represented, in units of work, by the 

 product of the corresponding variation of the thermodynamic func- 

 tion into the absolute temperature. A thermodynamic function con- 

 sists of two parts- The first is connected with the heat stored up as 

 actual heat in the substance, and is simply the product of the real 

 specific heat by the hyperbolic logarithm of the absolute temperature. 

 The second is what has been employed in the previous sections of the 

 paper, and in a paper on the centrifugal theory of elasticity, under 

 the name of Heat-potential, being a function the product of whose 

 variation into the absolute temperature represents heat converted 

 into mechanical work. 



The complete value of the thermodynamic function for a given 

 substance is, 



pd:? 



*=Hhyp. log. T+J ^dV, 



where U is the real specific heat, r the absolute temperature, P the 

 pressure, and V the volume ; and the fundamental equation of the 

 mechanical action of heat, previously given in various forms, may be 

 expressed as follows : — 



