VAKIATION OF MOLECULAR SURFACE-ENERGY WITH TEMPERATURE. 649 
The modification to be introduced into the equation y (Mr)* = k{t — d) in order 
to secure concordance at temperatures (or values of r) higher than those represented 
by the point C on the figure will be considered later. 
In calculating the results of experiment, we have assumed with Eotvos that 
(Mr)* = s; for the surface of a liquid conceived to be contained in a cubical vessel is 
obviously a square on tlie line representing the cube-root of its volume. Such an 
assumption, if molecular volumes be employed, gives a comparison of surfaces on 
which are distributed equal numbers of molecules, and permits of comparison between 
different liquids. * 
f 
2 . Proof of the Validity of the Equation y (Mr)* = k(t — d). 
The data necessary in order to calculate the molecular surface-energy of a liquid 
are ; (1) the height to which the liquid rises in a capillary tube of known diameter ; 
(2) the density of the liquid at the temperature of observation ; (3) the molecular 
weight of the liquid examined. These data will be found on p. 667, et. seq. 
The licjuids examined were : (l) ethyl oxide or ether ; (2) methyl alcohol; (3) ethyl 
alcohol ; the specific orthobaric volumes of these liquids at tenqoeratures from that 
of the atmosphere to their critical temperatures were determined by Eamsay and 
Young (‘Phil. Trans.,’ 1887, A., 87 ; 313; 1886, A., 313); (4) methyl formate; and 
(5) ethyl acetate; the constants for these two liquids were kindly communicated to 
us by Young, as they are not yet published; (6) carbon tetrachloride; (7) benzene ; 
and (8) chlorobenzene, examined by Young (‘ Trans. Chem. Soc.,’ 1891, p. 932 ; 1889, 
p. 504 ; and 1891, p. 134) ; and acetic acid {ibid., 1886, p. 790 ; and 1891, p. 909). 
These are at present the only liquids for which such data are available, and therefore 
they are the only ones of which the surface-energy and its variation with temperature 
can be determined. 
They divide into two groups ; to the first group belong ether, methyl formate, and 
ethyl acetate, carbon tetrachloride, benzene, and chlorobenzene. These liquids may 
be termed normal liquids, inasmuch as their behaviour resembles that of a normal gas. 
The second group comprises acetic acid and the alcohols ; and these displaj- properties 
which, as will afterwards be shown, make it more than likely that their molecules 
coalesce to form aggregates, as temperature falls, as indeed is known to be the case 
with acetic acid, even in the state of gas. 
The first of these groups has the advantage of comprising liquids differing widely 
from each other chemically; they are therefore specially suitable for testing the truth 
It Fas been assumed that the distribution of molecules on the surface of a liquid is such that the 
average distance between any two molecules on the surface is equal to that in the interior. We can 
give no proof of the correctness of this assumption, save to refer to the results of this investigation 
which appear to justify it. 
MDCCCXCIII.—A. 4 O 
