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



and a and b are constants (for the normal paraffins a = 37* 38, 

 b — 0'5. The boiling-points in this, and in all other cases 

 considered, are supposed to be measured at a pressure of 

 760 mm.). 



This formula represents the observed facts with fair 

 accuracy over a limited range, but does not lend itself well 

 to extrapolation. The reason lies in the fact that the formula, 

 as is obvious, assumes a linear relation between log 6 and 

 log M, which is by no means the case, as the graph of these 

 quantities shows a slight, but quite distinct, curvature. In 

 this case, therefore, as in all other cases in which a straight 

 line is assumed to coincide with a limited portion of a curve 

 of slight curvature, the agreement between calculated and 

 observed quantities is very good over the mid-portion of the 

 range chosen, but the differences become more and more 

 marked the further one extrapolates beyond either the upper 

 or lower limit of the range chosen. 



The formula given by Kamage, 



<?=a[M(l-2-»)]», (ii.) 



where a is Walker's constant, and n the number of carbon 

 atoms in the molecule, gives notably improved results for 

 the lower paraffins. But above decane or thereabouts, the 

 factor 2~ n becomes neolioible. and the formula then becomes 

 identical with Walker's, equally implying a linear relation 

 between log and log M, which relation, as is seen by the 

 curve between these quantities, is only approximately fulfilled. 

 From n=14 onwards, the difference between theory and 

 experiment becomes steadily greater. 



The formula proposed by Young is of a different type. 

 If A be the difference between the boiling-point 6 of any 

 homologue and that next above it in the series, then 



A = W7o> (i 11 -) 



where for the normal paraffins (and for certain other series), 

 c = 144-86 and ^ = '0148. Thus the boiling-point of any 

 paraffin can be calculated, provided that of the homologue 

 next below it be known. This restriction apart, the formula 

 gives very consistent results, and the observed and calcu- 

 lated results do not show, at the upper and lower limits of 

 the range considered, that tendency to a gradually increasing 

 divergence so characteristic of those formulae which assume 

 approximate coincidence between a straight line and a curve. 

 It should be noticed in passing, as we shall have need to 

 use the principle later, that equation (iii.) is really a dif- 

 ferential equation. Young's A is really the change in 



