580 Dr. R. D. Kleeman on Molecular Attraction 



formulae deduced from the law of attraction is not obtained, 

 this may be due in some cases to the molecules of the sub- 

 stance under consideration being polymerized, and the 

 necessary factors of the molecular weight, etc., taking this 

 into account not having been introduced. 



The Fundamental Relations. 

 Traube * has shown that the molecular volume of a molecule 

 in a liquid at the absolute zero is proportional to £ Vwi- The 

 molecular volume at any temperature of a liquid may there- 

 fore, according to the law of corresponding states, be written 



= -SvS, (7) 



pi n \ 



where it is a universal constant. If we substitute for — in 



m 



equations (3) (4) (5) (6) from equation (7) we obtain expres- 

 sions for T, jt?,L, and X, in terms of m 1 ,?i 1 ,n 2 ,n 3 , and w 4 , and T c ,p c , 

 > ,L , in terms of ?%. This shows that we need not look for any 

 further fundamental relations connecting the above quantities 

 than the equations (3), (4), (5), (6), (7), for we could not 

 expect the expression for the critical constants of a substance 

 to involve fewer and more fundamental quantities than the 

 atomic weights of a molecule. Equation (7) expresses an 

 independent fundamental law, and equations (3), (4), (5) and 

 (6) are obtained from the law of attraction between molecules 

 given at the beginning of the paper and the laws of thermo- 

 dynamics. But it is found that the equations obtained on 

 making the above substitution agree only roughly with the 

 facts. This is due partly to the law of Traube being only 

 approximately true, strictly it should be written 



where @ is a constant which depends probably on the consti- 

 tution of the molecule. If the more general law of attraction 

 is used in deducing equations (3), (4), (5) and (6), and a and 

 ft are determined from some of the experimental data, a much 

 better agreement with the facts is at once obtained. The 

 values of p c , T c , and p c would then for example be propor- 

 tional to 



' and 



respectively. 



* Pkijs. Zeit. Oct. 1909, p. 667. 



,7/3 



