

1894.] Dissociation of the Molecules of Liquids. 181 



Addendum. 



Since the foregoing pages were written, Professor van der Waals 

 has published a long memoir on the " Thermodynamic Theory of 

 Capillarity on the Assumption of Continuous Change of Density " 

 (' Zeitschrif t fur physikalische Chemie,' vol. 13, pp. 657 725). On 

 the main part of his work I have no criticism to offer; but on 

 p. 714, he states some objections to the method previously employed 

 by Ramsay and Shields in calculating the factor of association x. 

 These remarks are fully justified, as will have been seen from the 

 preceding pages of this paper ; but in the formula which he suggests 

 to replace it, he makes an assumption which, at first sight, is no less 

 untenable than our assumption that the factor of association, x, does 

 not vary with temperature. In placing the factor of association as 

 equal to unity at temperatures near the critical temperature, he 

 obtains the formula 



. _ 



7 (Mi;) 1 



and, inasmuch as this assumption is apparently very nearly true for 

 methyl and ethyl alcohols and for acetic acid, the numbers he gives 

 are nearly identical with those in the last table of this paper. But 

 they differ in the case of water, and x, according to him, is equal to 

 1-9, instead of to 1707. 



The formula given by him on p. 716 to calculate 7 yields remark- 

 ably good results. In fact, if 7 be calculated for ether at 89'8, a 

 result is obtained identical with that found. This result was unfore- 

 seen by van der Waals, for the value for 7, 30*65, was not given by 

 us at that low temperature in our previous paper. 



Professor van der Waals, however, makes two criticisms which 

 appear to me to be hardly justified. The first refers to a correction 

 applied by us in order to allow for the capillarity in the wider, yet 

 still narrow, tube in which the capillary tube stood. He thinks that 

 this correction would be affected by the curvature of the meniscus 

 not being the same at high as at low temperatures. The remark is 

 certainly true ; but as the alteration in height due to altered curva- 

 ture of meniscus would be well within the range of experimental 

 error, it is negligible. The second criticism deals, with the capil- 

 larity near the critical point, and van der Waals states that the 

 simple formula, applicable to narrow tubes, no longer holds when 

 the capillary rise is only a few times greater than the radius of the 

 tube. This objection would be justified were it not that the 

 capillary heights are nearly a linear function of the temperature ; 

 and with non-dissociating liquids, which he is here considering, 



