356 Mr. Rankine 07i the Hrjpothesis of Molecular Vortices, 



mean density; Q the quantity of heat in unity of weight, that 

 is to say, the vis viva of the molecular revolutions, which, accord- 

 ing to the hypothesis, give rise to the expansive pressure depend- 

 ing on heat; and let P denote the total expansive pressure. 

 Theu 



P = F(V,Q)+/(V) (1) 



In this equation, F(V, Q) is the pressure of the atomic atmo- 

 spheres at the surfaces called their boundaries, which varies witli 

 the centrifugal force of the molecular vortices as well as with the 

 mean density ; and /(V) is a portion of pressure due to the mu- 

 tual attractions and repulsions of distinct atoms, and varying with 

 the number of atoms in a given volume only. If the above equa- 

 tion be differentiated with respect to the hyperbolic logarithm 

 of the density, we obtain the coefficient of elasticity of volume 



where tJ denotes the cubic compressibility. 



The latter portion of this coefficient, — .j^f(V), consists of 



T" 



two parts, one of which gives rise to rigidity, or elasticity of 

 figure, as well as to elasticity of volume, while the other gives 

 rise to elasticity of volume only. The ratio of each of those 

 parts to their sum must be a function of the heat, the former 

 part being greater, and the latter less, as the atomic atmosphere 

 is more concentrated round the nucleus ; that is to say, as the 

 heat is less ; but their sum, so far as elasticity of volume is con- 

 cerned, is a function of the density only. 



That is to say, let the total coefficient of elasticity of volume 

 be denoted thus, 



i=J + c/,{C„C„C3), .... (IB) 



C„ Co, Cg being coefficients of rigidity round the three axes of 

 elasticity, and J a coefficient of fluid elasticity ; then 



J = -^^F(V,Q)-t(V,Q).^/(V) ^ 



V" T 



c^(C„C„C3)=-(l-V^(V,Q)).A/(V) 



T 



For the present, we have to take into consideration that por- 



(IC) 



