Density, Temperature, and Pressure of Substances. 331 



The value of b is best; obtained from this equation by 

 applying it to a case when all the quantities it contains are 

 known except b. 



We may substitute p 2 for p l in the above equations. It can 



then be easily shown that at the absolute zero -£f = — co . 



Let us express the quantities p lt p 2 , and T in terms of 

 their critical values thus, p ] =p c n 1 , p 2 =p c n 2 , T = T C « 3 , and 

 substitute in equation (1). The equation reduces to 



£ 3 log^=r.f-nf, (3) 



which, it will be seen, is independent of the nature of the liquid 

 under consideration, Since p L and p 2 are each a function of 

 T, and n l and n 2 therefore each a function of n 3 , it follows 

 that for equal values of n 3 for a number of substances, n x and 

 n 2 will each have equal values. The equation thus demon- 

 strates the theory of corresponding states, and gives a relation 

 between the quantities n u n 2 , n- d . The corresponding state 

 of substances, it will be shown later, has its fundamental 

 reason in the occurrence of the function in the general law 

 of attraction between molecules which has the same value for 

 all substances at corresponding temperatures. 



In a previous paper* we have established the relation 



E(^— p^) = Tlogt- 1 , where E is a constant depending only 



P2 



on the nature of the liquid. This equation, like equation (1), 

 represents two different formulae for the latent heat equated. 

 It was found to agree very well with the facts. The value 

 of E, when the logarithm in the equation is taken to the 

 base 10, was shown to be given by 



258-8 ( S vV) 2 



m 4/ 3/) 2/3 



A different expression for E can be obtained in the same 

 way as was obtained for B. Writing p 2 = xpi, the value of E 

 at the critical temperature is 



f-Tlog^l - 



T c 



or 



2/of ^2 x 2*303 



■da-*) 



* Phil. Mag. Oct. 1910, pp. 686-687. 

 Z 2 



