622 
MESSRS. T. E. THORPE AND J. W. RODGER ON THE RELATIONS 
C. Comparisons of Viscosity Magnitudes at Temperatures of Equal Slope. 
On comparing the viscosity curves of those substances which gave the best 
physico-chemical relationships at the boiling-point, it was at once seen that the general 
shape of these curves towards the boiling-point was practically the same. If tangents 
were drawn to the curves at points corresponding with the boiling-points of the liquids, 
the inclinations of the tangents to the axes, that is the slopes of the curves, varied hut 
little. On the other hand, the curves for liquids such as the alcohols or the lowest 
members of homologous series, which gave little indication of physico-chemical 
relationships, had invariably a different shape. The entire course of these curves was 
indeed exceptional, and the inclinations of tangents drawn at the boiling-point were 
markedly different from those of the majority of substances. It seemed probable, 
therefore, that the discrepancies were related to this difference in the value of the 
slopes, and that if the temperatures of comparison were chosen so as to eliminate this 
difference better relationships might be obtained. This idea led to the adoption of 
temperatures of equal slope as comparable temperatures, and indeed apart altogether 
from considerations such as the above, which refer to the particular case of viscosity, 
much may be said from a theoretical point of view in favour of employing such 
temperatures for physico-chemical comparisons in general. To begin with, at the 
temperature of equal slope, the effect of temperature upon the ju’operty examined is 
the same for different substances. In the case of viscosity, for instance, dy](dt, or the 
rate at which viscosity is being altered by the temperature, has the same value for all 
the liquids, and this equality might be taken as sufficient justification for supposing 
that at temperatures of equal slope the substances, so far as viscosity is concerned, are 
in comparable states. Another argument which may be advanced in favour of such a 
method of treatment is that the comparable temperatures are chosen by means of a 
study of the effect of temperature on the property actually examined. The main 
objection which can be urged against the boiling-point as a comparable temperature 
even rvhen, as in the case of such a property as density, it gives comparatively definite 
stoichiometric relationships is that these relationships may not be general. If a 
pressure other than the atmospheric is employed at wdiich to determine the boiling- 
point and density the relationships initially obtained may no longer hold. Whether 
they hold or not can only be decided by a study, not only of the effect of temperature 
on density, the property under consideration, but also of the effect of temperature on 
vapour pressure, a property which, at first sight at least, need not be connected with 
density. If, however, comparable temperatures be chosen, as in the case of slope, by 
a study of the property considered, the generality of the relationships obtained can 
be ascertained without the study of other properties of the substances. Moreover it 
is possible to devise a system of choosing slopes such that the relationships obtained 
at any series of slojies chosen in this way shall be the same as those obtained at any 
