and the Properties of Liquids. 569 



happen — that the empirical relation is of such a form that 

 the relative value of the constants may be varied over a 

 considerable range without affecting the agreement of the 

 relation with the facts. In that case, slight errors in the 

 data used may give rise to constants which are far from 

 being equal to those deduced theoretically. The proper way, 

 therefore, to test whether the theoretical constants fit in 

 with the facts is to assume that they do and then determine 

 whether the constants which are to be the same for each 

 substance (numerical factors) approximately fulfil that 

 condition. In cannot be too strongly emphasized in this 

 kind of work that starting out with some law and deducing 

 relations from it, their good or bad agreement with the facts 

 may in part be due to the mathematical form of the relations 

 in connexion with the experimental errors of the quantities 

 involved. 



Van der Waals has proposed the equation \=C ( 1— ™ ) 



for the surface tension and applied it to the facts *. It was 

 found that D is very nearly the same for the substances 

 examined, viz., ethyl oxide, benzene, methyl formate, chloro- 

 benzene, carbon-tetrachloride, being equal to about 1*23 ; 

 while the values found for C were 57*68, 69*02, 64*57, 67*14, 

 and 64*71, respectively. Assuming D constant the equation 

 is obtained by putting 



in the general equation for the surface tension ; which gives 



\ m / 



where b is a constant. The values of C for the above 

 substances are thus proportional to 9*6 XlO -3 , 12 x 10~ 3 , 

 9*8 x 10" 3 , 10 9 x 10* 3 , and 10*6 x 10" 3 , respectively. These 

 values are approximately proportional to those given by 

 Van der Waals. 

 If we put 



*.-!»('-€-•■■) 



the equation for the surface tension becomes 



»-K5f (v^(^ro-s- • ■ ■)• 



* Zeitsch. f. pliys. Chemie, xiii. p. 716 (1894). 



