5 2 4 SCIENCE PROGRESS 



In the case of the first ten gases mentioned in the preceding 

 table, the molecular weights calculated from the values of A* 

 given agree well with those derived from the International 

 Table of Atomic Weights but considerable discrepancies occur 

 in the case of the remaining gases. 



Another equation deduced by Berthelot (6) should also be 

 mentioned, as it has given rise to some misunderstanding. The 

 equation is 



_l_ d(n-p) 9 / _6\ 

 TTv- dn ~ lzSeV ~ 6>) 



in which 77-, v and 6 denote the " reduced " pressure, volume and 

 abs. temperature of a gas {i.e. these magnitudes expressed as 

 fractions of the critical values). This equation is only valid 



when it is indefinitely small; in other words A — - only gives 



the slope of the compressibility curve at A (figs. 1 and 2). 

 This point has escaped the notice of Guye and his collaborators, 

 who quote the above equation in its equivalent form (at o°C.) 



T /6T 2 x 



A = o"ob0257S — = ( — =5 - 1 ) 



Pc W3 2 ' 



and refer to it as Berthelot's indirect formula for A\. Such is, 

 of course, not the case; the formula refers only to the limiting 

 value of AjJ when both p a and p b approach zero, a value 

 considerably smaller than A|. 



It was by utilising this formula that Rayleigh (12) reduced 

 his compressibility measurements to the values at o° C. 



The Molecular Volume Method 



The method of molecular volumes was chronologically the 

 first of the methods described in this article (2). It will be 

 seen that while in principle it may be identified with the method 

 of limiting densities, yet with respect to the experimental data 

 necessary, viz. densities and critical constants, it resembles the 

 method of critical constants. Unlike the latter, however, it is 

 not a deduction from van der Waals' equation empirically 

 modified but rests on the broader basis of the Theorem of 

 Corresponding States. 



The account here given is, in substance, that contained 

 in Leduc's latest memoir on the subject (21). The pressure, 

 molecular volume and absolute temperature of a perfect gas, 



