Density, Temperature, and Pressure of Substances. 337 



The above series of equations are the general fundamental 

 equations connecting T, pi, and p 2 , for a liquid in contact 

 A>ith its saturated vapour. Since they also contain p c and 

 T c , they are the fundamental equations for determining these 

 quantities from any convenient data. The equations we have 

 been discussing, obtained by equating different formulae 

 for the internal latent heat, will readily be recognized as 

 belonging to this type of equations. 



Making use of: the above result, the equation for the latent 

 heat may be written 



when B is a constant which is the same for all liquids at 

 corresponding states. It can then be easily shown * by 

 means of this equation that L = L ?7, where L is the latent 

 heat at the absolute zero, and rj is a constant which is the 

 same for all liquids at corresponding states ; which establishes 

 the required result in the case of the internal latent heat. 



By means of: the foregoing results and thermodynamics 

 the law of corresponding states can be established for the 

 pressure^? of the saturated vapour of a liquid. If the value 

 of L from the former of the above two latent heat equations 

 is substituted in Clapeyron's equation, it can be reduced to 

 the form 



, /n \7/3 T 



where W is the same for all liquids at corresponding tempe- 

 ratures. At the critical point the right-hand side becomes 

 zero, and since p x is finite at the critical point, W must also 



m /m 



become zero. The limiting value of the ratio .^ 



may be written p G . V c , where V c is a numerical constant, and 

 the equation at the critical point becomes 



Combining this equation with the above equation we have 



-•Mr--t 



or p = n 4c p c , where n 4 is the same for corresponding tempera- 

 tures, which is the required result. 



* Phil. Ma*. June 1910, p. 845. 

 t Phil. Mag. Dec. 1009, p. 908. 



