whence 



620 Mr. Rankine on the Centrifugal Theory of Elasticity, 



t(i)=««=<i+g+(^5^) h (10) 



(a>')''-2(o,')K) + (a>"') \ 



^ 27^ + ^"-J 



Now because [a') = — t ^(u=i)=0, 

 which may be represented by ^; . . (10 A) 



F(D, 6) being a quantity which becomes continually less as the 

 density becomes less and the heat greater. The complete ex- 

 pression for the elasticity of a gas is therefore, according to 

 equations (1), (8) and (lOA), 



P=;,+/(D)=^d(^+6)(1-F(D,^))+/(D); . (11) 



when each atom contains a quantity of heat measured by the 

 mechanical power coiTesponding to the velocity v in the weight 

 M, or 



according to equation (4) . 



Section III. Of Temperature, and of real Specific Heat, 



(15.) The definition of temperature consists of two parts : — 

 first, the definition of that condition of two portions of matter 

 when they are said to be at the same temperature ; and second, 

 the definition of the measure of differences of temperature. 



Two bodies are said to be at the same temperature, when there 

 is no tendency for one to become hotter by abstracting heat from 

 the other; that is to say (calling the two bodies A andB), when 

 there is either no tendency to transmission of heat between them, 

 or when A transmits as much heat to B as B does to A. Now 

 it is known by experiment, that any surface or other thing which 

 aflfects the transmission of heat being placed between B and A, 

 has exactly the same influence upon the same quantity of heat 

 passing in either direction ; therefore to produce equilibrium of 

 temperature between A and B, the powers of their atoms to com- 

 municate heat must be equal. 



