Mathias and the Critical Density. 295 



a being negative in these and all affier cases (for both formulae), 

 whilst /3 is positive in the first two cases but negative in the 

 last two. 



For normal pentane it will be seen that there is absolutely 

 no indication of curvature, so that /3 = ; for the alcohols, on 

 the other hand, the curvature (in the same direction as that 

 for propyl acetate) is so pronounced that a fourth term, yt 3 , 

 has to be introduced into the formula to reproduce the data. 



The values of a and of ^ [the ratio of the actual to the 



theoretical density at the critical point] are given for the five 

 substances; those for methyl alcohol are very high, 1*142 and 

 4*521 respectively. 



It is remarkable that as the curvature changes in such a 

 manner that /3 passes from a positive value, through zero, to _ 



a negative value, a and j^ regularly increase. It is espe- 



-L" c 



cially remarkable that for normal pentane, for which /3 = 0, the 



value of =ry (3*765) is almost exactly that which may be 



taken as normal for substances whose molecules undergo no 

 dissociation or polymerization. (The ratio given by van der 



Waals is ~ = 2*6, but, as shown by Guye and by Heilborn, if 

 o 



we accept 0. E. Meyer's correction for the relation between 



b in the formula of van der Waals and the space actually 



occupied by the molecules, this number should be multiplied 



by ^2, which would give 3*77.) 



That being so, we may perhaps take the normal value of a 

 to be about 0*93. 



It seems unnecessary to give the differences of the ob- 

 served mean densities from those calculated from the formula 

 J) t = D + ott at intervals of ten degrees for each of the thirty 

 substances, but in Table 1. I have given the values of D , 



*Xl0 6 , a, jrf , rp — 3*770, the difference between the ob- 

 served and calculated mean density at 0°, and lastly A 

 (Thorpe and Riicker). 



The substances are arranged in ascending order of -prf, 



and it will be noticed that there is, on the whole, a distinct 

 tendency for a to rise ; thus the values of a on the one side 

 of normal pentane are, with one exception (stannic chloride), 

 lower than '931, and those on the other side are, again with 

 one exception (fluorbenzene), higher. 



