﻿602 Dr. A. Ferguson on the Boiling- Points and 



calculated from equation (v.) and the differences between 

 the observed and calculated values. The remaining columns 

 show the results of similiar computations using equations (i.), 

 (ii.), and (iii.)- 



A fair idea may be obtained of the relative accuracy of 

 the various formulae by computing the average error, regard- 

 less of sign. Thus 



for range n = 7 to n = 16, average error, W = 0°* 7 1 , 



("average error, R=:l o, 03, 



for rangen=4 to 71 = 17-5 „ „ Y = 0°-58, 



(. „ „ F = 0°-64. 



Thus it appears that, over the range taken, the new formula 

 is more accurate than either (i.) or (ii.), and, whilst having 

 the advantage of not being a difference formula, is only 

 slightly less exact than that of Young. Further, the dif- 

 ferences between the calculated and observed values are 

 much the same in magnitude at any point of the range. 



We now turn to the consideration of the relation between 

 critical temperature and constitution. Granted sufficient 

 exact experimental data, it would not be a difficult task to 

 find directly various empirical relations connecting critical 

 temperature and molecular weight in the normal paraffins. 

 In the present paper an indirect method is followed, which 

 will be seen in the sequel to lead to results of a fairly high 

 order of accuracy, while several interesting relationships 

 will be elucidated by the way, which would be obscured by 

 the direct method of attack. 



It has long been known that different substances are ap- 

 proximately in " corresponding states" as far as temperature 

 is concerned, when at their boiling-points (under normal 

 pressure) ; were this exactly true, the ratio of the critical 

 temperature to the boiling-point, when measured on the 

 absolute scale, would be a constant for all substances. Now 

 while it is the case that this ratio does not vary very greatly 

 for substances whose boiling-points are so diverse as those of 

 oxygen and aniline, there is, nevertheless, a slight variation, 

 and this variation is, for the normal paraffins, a perfectly 

 regular one. Calling the ratio 6 c /0 for any given paraffin R, 

 and the corresponding number of carbon atoms in the 

 molecule n, it can be shown graphically that the relation 

 between log R and log n is very accurately linear, leading 

 therefore to the relation 



Jxn^=h, (vii.) 



where g and h are constants. For the normal paraffins the 



