494, REPORT—1904, 
It will be seen that in every case there is a decided rise in the value of A as 
the series is ascended, but that the rise is relatively smallest when the comparison 
is made at the particular reduced temperature chosen. At higher reduced tempe- 
ratures, however, it would be relatively much greater, since it is very marked at 
the critical point, where the reduced temperature =1. The rise is also compara- 
tively small at the common temperature 0°, but the comparison would not be 
satisfactory if a higher common temperature, say 150°, were chosen, because the 
coefficients of expansion differ considerably: at 150° the values of A would be 
8 75, 13:45, and 15°38 respectively. 
In the case of nine of the lower esters the values of A are by no means con- 
stant, whether the comparison be made at 0°, at the boiling-point, or at the critical 
point, The eleven values of A vary in the three methods between 16:34 and 18°21, 
20:84 and 23°42, 54:3 and 61-7 respectively; but there is not a regular rise with 
increase of molecular weight. 
Both Kopp and Schroder compared the molecular volumes of compounds at 
their boiling-points under normal pressure, but they deduced quite different values 
for the atomic volumes of carbon and hydrogen; it is clear, however, that as A 
varies considerably no values whatever for C and H could give accurate results, 
even in the case of true homologues. 
Traube makes the comparison at a common temperature, usually 15°, and takes 
into consideration both the actual volumes of the molecules and the co-volume, 
which he assumes to have the same value, 24:5 (1+ at), where a= 1/273, for all 
substances. He calculates definite values for the atomic volumes of C and H. at 
a given temperature; thus, at 15°,C=9°9 and H=3:1, or CH,=16:1, so that 
here again the difference for CH, at a given temperature should be constant, 
It does not appear to me that the problem has yet been completely solved, 
although Trauhe’s method of calculation generally gives much better results than 
those of Kopp and Schroder. 
Comparison of Boiling-points at a Series of Equal Pressures, 
The results of this comparison are often exceedingly simple if the two sub- 
stances compared are very closely related, and if there is no molecular association 
in either case. Taking, for example, chlorobenzene and bromobenzene, it is found 
that the ratio of the boiling-points (on the absolute scale of temperature) under 
equal pressures is constant whatever the pressure may be, or 
1, _ Ts. 1.0590. 
T; Ts 
A similar result is obtained with the other halogen derivatives of benzene, 
with ethyl bromide and ethyl iodide, with ethyl acetate and propyl acetate, and 
some other pairs of esters; but in some cases of close relationship—for example, 
with ethyl formate and ethyl acetate—the ratio is not quite constant, and the 
formula becomes a= a5 + ¢e(T,—T’,), where c has a very low value [0:0000417 
for these two esters. When there is no close relationship, but the molecules are 
not associated, the value of ¢ is usually larger—for example, 0:0001185 for carbon 
disulphide and ethy! bromide. 
Lastly, when there is no close relationship and the molecules of one or both 
substances are associated, the formula = = = +ce(T;—T’;) may no longer hold, 
B B 
and a third term may be required, thus: = = = + ¢e(T, —T’,)+d(Ts—T’,)?; or, 
B B 
in any case, the value of ¢ becomes much higher, as with benzene and ethyl 
alcohol [¢ = 0:0008030] or sulphur and carbon disulphide [¢ = 0:0006845]. 
