Density, Temperature, and Pressure of Substances. 339 

 quantities p, p^ p 2 , T, may be written 



The law of corresponding states can also be proved for all 

 possible states of matter. From thermodynamics we have 



(dQA =T /^ 



\dp / T const. \dT/p con st. 



where dQ is the amount of heat given out by a 

 mass of matter of volume v at a temperature T, when the 

 pressure changes by dp. Now Q=jdu + w, where u is the 

 internal energy of the substance. The internal energy we 

 will take (as usual) equal to the internal heat of evaporation 

 at constant temperature into a vacuum. According to the 

 formula for the latent heat used in a previous part of the 

 paper (deduced from the law of molecular attraction"), this is 

 for unit mass equal to 



where x& is the distance of separation of the molecules of the 

 matter and p its density. This expression for the internal 

 energy we will write for shortness HO/A 3 , where 



m 7/3 • 



We have then 



/dQ\ dv r JdH ,., 4n dp\ 



Let us express the quantities p, v, and T in terms of their 

 critical values thus 



p — $p c , V = CLV C , T = /3T C . 

 The above equation may then be written 



["+*•(§) + ^(^)i(^r-g H )]r^S)/ 



or - — 775 =E, where 1) and E are functions of *, j3 } and <£. 



P'eVe' J 



