On an Exi:>eri mental Modification of van der Wants ^ Equation. 129 
The improvement effected by this modification is strikingly shown in 
Fig. 2. The reduced vapour-pressures from equations (1) and (9) are 
plotted, together with the experimental curves for isopentane and methyl 
alcohol. If the law of corresponding states were rigorously obeyed the 
last two curves would be coincident ; as long as such differences as these 
occur it is obviously impossible to represent the thermal behaviour of 
different substances by a single equation, and all that one can do is to 
construct an equation for a fictitious substance to serve as a type from 
which particular substances deviate more or less according to their 
molecular complexity. This is what Kameklingh Onnes has done in 
deducing his "mean empirical reduced equation." Equation (9) seems, 
at least in so far as vapour-pressures are concerned, to be as good a type 
as can be found to represent both normal (isopentane) and abnormal 
(methyl alcohol) substances ; it gives a much closer quantitative estimate 
than the unmodified equation, while, at the same time, it retains all the 
essential features of the original. 
From the following table it will be seen that the modified equation is 
in good agreement with the van der Waals empirical vapour-pressure 
law — 
log^=/(l-|) (16) 
as long as the temperature is not too low, and that the value of / at the 
critical point, 3*04, is not far from the corresponding values for such 
typically normal substances as carbon dioxide, 2-97, and isopentane, 2-95. 
The unmodified equation, on the other hand, as was previously shown,! 
gives values for / which deviate greatly from constancy, while the critical 
value is 1-72. 
Table III. 
/. 
^. 
/• 
/• 
0-496 
3-23 
0-725 
3-07 
0-892 
304 
0-549 
3-18 
0-762 
3-06 
0-920 
3 04 
0-598 
3-14 
0-797 
3-05 
0-948 
3-04 
0-643 
3-11 
0-830 
304 
0-975 
3-04 
0-685 
3-09 
0-861 
3-04 
1-000 
* The carbon dioxide carve is coincident with this, 
t Loc. cit. 
