292 Dr. S. Young on the Law of Cailletet and 



Now the law of! Cailletet and Mathias lias been found to 

 hold good for a considerable number of substances from the 

 boiling-point to the critical point ; and M. Mathias, making 

 the very natural assumption that the law may be relied upon 

 at lower temperatures, calculates the value of a from the 

 mean densities below the boiling-point. If the critical tem- 

 perature is known, the critical density is then calculated as 

 before; but for most substances the critical temperature has 

 not been directly determined ; and M. Mathias discusses the 

 methods, notably that of Thorpe and Riicker, that have been 

 suggested for calculating this constant. 



M. Mathias shows that if, in Thorpe and Riicker's formula 



A = 2, then it follows that a = l. 



He further shows how, if a = l, it would be possible to 

 ascertain both the critical density and the critical temperature 

 by a geometrical method. In most cases, however, A differs 

 sensibly from 2 and a from unity, and the geometrical method 

 is then inapplicable ; neither can the critical temperature be 

 calculated with sufficient accuracy by employing the value of 

 A, 1*995, adopted by Thorpe and Riicker. 



It occurred to me that A, though not quite the same for 

 different substances, might possibly be related to the compo- 

 sition in some simple way; and I have therefore calculated its 

 value (taking 0° and the boiling-point under normal pressure 

 as the two temperatures) for the thirty compounds referred to 

 in this paper ; these constants are given in Table I. Unfor- 

 tunately there does not seem to be a sufficiently marked con- 

 nexion between the values of A and the composition to be of 

 much practical use. 



M. Mathias arrives at the conclusion — which, I think (except 

 for a few special cases), is quite justified — that it is necessary 

 to make a direct determination of the critical temperature. 



M. Mathias then proceeds to the examination of experi- 

 mental data derived from various sources. The critical tem- 

 perature, the vapour-pressures, and the densities of liquid 

 chlorine have been very carefully determined by Knietsch ; 

 and M. Mathias has calculated the densities of the saturated 

 vapour below the boiling-point ( — 33°'6), and finds that the 

 constancy of both a and D c are apparently extremely satis- 

 factory; but the value of a ("7675) is very far from unity. 

 The value of D c is *5782; but it may be pointed out that the 

 ratio of this to the theoretical density at the critical tempe- 



