Liquid Spheres — Molecular Diameters. 887 



The temperature coefficient of surface tension has been 

 assumed to be constant down to 0° A, and in accordance 

 with the reasons given in the case of water we have regarded 

 the surface tension T m about a free molecule equal to T , 

 in the empirical formula T e = T o — 'B0. However, the tem- 

 perature coefficient is only approximately constant, and 

 consequently T m or T is only approximately determined. 

 These data have been taken from the ordinary tables and are- 

 subject to question in some cases. Especially in the case of 

 mercury, where L was determined by Youn<>- in 1910, there 

 is a probability that the vapour of mercury involved in the- 

 determination was not altogether of dissociated molecules. 

 For example, if the spheres of the mercury vapour contain 

 32 molecules, the real value of L is seen from Table I. to be 

 498/(498-340-5) or 3-16 times the value in the Table III. ; 

 and consequently the value of N would be 



(3-16) 3 x-21xl0 23 or 6*64 x 10 23 , 



which agrees with that we know. 



But the greatest discrepancy is seen in the case of ether, 

 chloroform, nitrogen, oxygen, and benzene. The values of N, 

 however, are very uniform and equal to about one-fifth of 

 the true value. One contributing cause may be in the high 

 vapour pressures common to all of these substances. But 

 the chief cause lies in the use of p g instead of p , which in 

 the absence of sufficient data could not be even approxi- 

 mately estimated. So far as we have evidence, p increases 

 for the liquid quite rapidly as 6 decreases, suddenly increases 

 at solidification, and continues to increase more slowly for 

 the solid down to 0° A. It seems to be quite possible that 

 for these substances the value of p would be double the 

 value used ; in which case, as N increases with the square 

 of p e , the values of N would approximate to the true value. 

 For mercury the value 14* 25 for p was obtained on the 

 supposition that the temperature coefficient of expansion of 

 the liquid remained constant through the solid down to 0° A. 



In the case of the alcohols, from considerations in regard 

 to the arrangement of the atoms in the molecule the idea has 

 arisen that the free molecule is not spherical, especially as 

 one of the elements is carbon. If this be so, two such 

 molecules coming into contact would give up less of their 

 enveloping area than they would if they were spherical and 

 coalesced in the same manner as. two liquid drops. At first 

 they would resemble two solid particles adhering, and after- 

 wards the combined mass would gradually become spherical 

 as more molecules were included in the enclosure. It would, 



