462 J. WUlard Gibhs — Geophysical Research. 



d log p/d log t for saturated vapor at the critical state. The 

 units of temperature and pressure fall out of this expression. 

 If Van der Waals ? Law were exact, the value of this expres- 

 sion for all substances would be 4. Actual values seem to be 

 much higher than this. Suppose we had a table of these 

 values for a considerable number of substances. Will these 

 values or a large part of them be identical ? In any case we 

 can probably find several substances which have nearly the 

 same values. We may then ask whether, or how far, these 

 substances, which have the same limiting values d log p/d log t, 

 have similar relations between p, t, and v. This would per- 

 haps be most easily tested by finding whether p/p c is the same 

 function of t/t c for the saturated vapor of the several sub- 

 stances (t c and p c denote t and p for the critical state) ; and 

 this again would be sufficiently and most easily tested by a few 

 particular . cases (for each substance), as t/t c = 9/10 or 8/10, 

 etc. 



In this way we might decide whether the general (or quasi- 

 general) equation has three independent constants (which is all 

 that Van der Waals' theory of " corresponding states " allows) 

 or four or more than four. Uncritically we might push the 

 inquiry further, if there are more than four, but with rapidly 

 increasing difficulties of various kinds, and with diminishing 

 value of the results obtained, since the most simple results are 

 the most valuable. 



Incidentally, such an investigation would enable us to dis- 

 tinguish those substances which are typical from those which 

 are exceptional or " abnormal." 



