J. Willard Gibbs — Geophysical Research. 461 



Akt. XLIV. — Certain Suggestions by J. Willard Gibbs on 



Geophysical Research. 



Note. — Some years ago when I was interested in physical 

 geology and after some progress had been made, I endeavored to 

 secure the cooperation of Prof. J. W. Gibbs on the theoretical 

 side, hoping to carry out the experimental part suggested 

 myself. Prof. Gibbs entered into the project cordially and wrote 

 out for me a plan of attack. Unfortunately, and to my lasting 

 regret, circumstances beyond my control made it impossible for 

 me to live up to my part of the project, and the scheme proved 

 barren of results. 



The suggestions of Gibbs are given below. They must be 

 read with a time allowance for the intervening years and with 

 the reservation that Gibbs, who was chary of print, would not 

 probably have published them himself. On the other hand, I do 

 not feel justified in withholding what Gibbs counseled on a sub- 

 ject in which he was so admirably qualified to judge, from those 

 who may be interested in geophysical research. Cakl Barus. 



A good deal of work has been spent in the endeavor to find 

 equations which shall represent the relations^?, t, v, for vari- 

 ous substances. It would be very pleasant to have such an 

 equation, but it is doubtful whether the relation can be repre- 

 sented by any simple formula. 



Now instead of comparing the relation in any given case 

 with an analytical formula, one may compare the relations for 

 different substances with each other. Van der Waals has 

 given an algebraic equation which would make the law similar 

 for all substances, in this sense, that by measuring the t, p, v, 

 for different substances in different units, the numerical expres- 

 sion of the relation becomes identical for all substances. Now 

 Yan der Waals' law gives only a very rough approximation. 

 But it is worthy, I think, of much effort to find out whether, 

 or with what degree of approximation, and within what limits, 

 and with what exceptions, the actual laws for different sub- 

 stances are similar in the sense defined above. And if not 

 similar, to find how many degrees of variation there are, in 

 addition to the three connected with the measure of tempera- 

 ture, pressure and volume. In other words, to find how many 

 independent constants there are in the general formula, i. e., 

 in a formula sufficiently general to be so called. Certain cases 

 would probably remain, which would naturally be regarded as 

 exceptional or " abnormal." 



The method to be followed would appear in the course of 

 the investigation, but we might commence as follows. Sup- 

 pose we find for various substances the limiting values of 



