162 PROCEEDINGS OF THE AMERICAN ACADEMY, 



IV. 



If further investigation and further accordance with observed facts 

 prove that the principle of thermal pressure, which has been here shown 

 to possess a high degree of probability, is in fact an exact and universal 

 law of nature, then there are few physico-chemical phenomena in which 

 thermal pressure is not one of the most important determining factors ; 

 yet it would be premature to attempt at present any general application 

 of the new theory. But there is oue field in which the view here advo- 

 cated is in direct conflict with a well-known and fruitful theory, — j;he 

 theory of van der Waals. We shall, therefore, consider briefly the rela- 

 tions of thermal pressure to the equation of condition of liquids and gases 

 and the van der Waals formula. 



Equations (4) and (10) give at once a general equation of condition 



for all substances, 



^ nRT ^ RT 



V 



or P= a, (16) 



where n is the total number of gram molecules in the volume V, and a, 

 the attractive pressure, is the only quantity which is not immediately 

 determined. It is probably, in most cases, a complicated function of 

 volume and also of temperature. 



Equation (16) is directly opposed to the theory of van der Waals, in 

 that it does not recognize the influence upon the pressure of the so-called 

 covolume, but, on the other hand, it in no way contradicts the validity of 

 the equation of van der Waals considered as a purely empirical formula ; 

 for if that equation is regarded merely as a statement of experimental 

 observation, it may be written as well in some other form. For example, 

 instead of 



V — b v^ ' 

 the second term might be expanded, and the equation written, 



V^ y3 yi I .,,2 



It would then be in the form of equation (16), in which 



b b' b^ \ a 



„ / b i-^ P \ 



r - -f -3 + ^ . . . 



i?r. „,„,.... . , 



This form of a would be of significance only in case the equation of 

 van der Waals were perfectly accurate ; as a matter of fact, no one has 



