VARIATION OF MOLECULAR SURFACE-ENERGY WITH TEMPERATURE. 659 
density diminishes; and he discovered that the decrease in length of column 
supported, is approximately proportional to the rise of temperature. For water, he 
found that if the surface-tension, or coefficient of capillarity at 0° C., be placed equal 
to 1, the variation with temperature between 0° and 100° C. may be expressed with 
fair accuracy by the equation y=l — 0’00191L 
Frankenheim was the first to point out that at a certain high temperature, differing 
for each liquid, the capillary ascent would cease; and he suggested that the state 
observed by Cagniard de la Tour, now knov/n as the critical point, should be that 
temperature. 
Brunner, in 1847 (‘Pogg. Ann.,’ vol. 70, p. 514), and Wolff, in 1857 (‘Ann, 
Chim. Phys,’ (3), vol. 49, p. 230), also found proportionality between capillary ascent' 
and temperature; they observed, however, that such proportionality did not always 
hold. The next researches on this subject in order of time were by P. Schiff 
(‘Annalen,’ vol. 223, p. 47), in 1884; but as he measured the capillary heights at 
only two temperatures, no conclusion can be drawn from his work relative to the 
question. Moreover, the capillary rise was measured with the surface of the liquid in 
contact with air, and not with its own vapour. 
The problem was again experimentally attacked by Eotvos {loc. cit.), in 1886. 
Starting with Van der Waal’s definition that corresponding states for diflerent 
liquids are those at which 
/ 1 \ Yl _ _ P'iXl 
^ ^ W “ “ ibTs ’ 
(where V^ and Vg are the molecular volumes of two saturated vapours; Vi and Vg; 
those of their liquids in contact with saturated vapours; and corresponding 
pressures; and T^ and Tg, corresponding temperatures on the absolute scale), he 
reasons as follows :— 
For a surface on which n molecules lie, the pressure of the vapour on that surface 
is npp)p, since # is proportional to the mean linear distance between the molecules. 
On the other hand, the surface-tension across a line of m molecules is myiVp. The 
first force may be measured in dynesper square centimetre, the latter, in dynes per 
Imear centimetre. The corresponding expressions for another liquid are npp):^ and 
Eotvos next assumes that bodies which are in corresponding states should possess 
similar mechanical properties, especially those which relate to the forces which act 
between their parts, and to their energies. On this assumption, he imagines pro¬ 
portionality between yv*, the surface-energy, and the product pv the volume-energy ; 
and combining the relations given above, he obtains 
