1077 



present, but I will point out that the appreciably larger values of s, 

 which are given for associating substances by Sydney Young, may 

 be perfectly accounted for with this value of .? = 3,77. 



Sydney Young (Proceedings Physical Society of Londen July 1894) 

 gives s := o for acetic acid, .v = 4,52 for methyl alcohol, 5 = 4,02 

 for ethyl alcohol, etc. 



For associating substances a modification must be applied in the 

 formula for Dk, which we have given above, namely in the value 

 of M. Let there l)e present l—.t'k single molecules, and xjc double 

 molecules, then the molecular weight present in the critical state 

 =: il/i (1 — a:jc)-{-M^Xk and M], being ='2Af^, the molecular weight 

 := J/j (1 + xjc). Hence we get : 



The ratio between the critical density and that which would be 



found when the laws of Boyle Gay-Lussac were followed, is 



therefore greater for two reasons. First because of the existence 



of the quantity ,Vfc, and secondly on account of the existence of 



6'^1. And Sydney Young's value for acetic acid, viz. 5, is the 



product .'? (l-\-X};). And assuming again 3.77 for s, we determine 



5 

 1 -[- xjc = — - or 1 -|- d'k = 1,324. But we are onl}^ sure ot this 



value of Ai-, if we may assume s = 3,77 also in this case. And 



though this is probable, a priori, because the value of s, deviating 



8 

 from — , the value obtained when /; is put invariable, only depends 



o 



on the way in which b decreases, yet it seemed desirable to me 

 to investigate this more closely. For this purpose I have examined 

 the equation of state for an associating substance more accurately. 

 It has the form : 



RT a^ 

 V — 6;;. u 



The numerator, which would be equal to RyTM^i^l — x)-\' R^TM^x 

 may be written in this simple form, because M^R^T= M.Ji^T. 



