|GARVER] THE RANGE OF MOLECULAR ACTION $5 
where &’ is the vapour-pressure at the-convex surface of a liquid drop of 
radius r, © the vapour-pressure for a plane surface, 9 the vapour den- 
sity, Y the surface-tension and p the liquid density. From this equa- 
tion we can calculate the ratio w'/@ for any assumed value of r and 
substitute the result in (A) and calculate the value of Ar. 
To facilitate the computation and the testing of the constancy of 
r for different values of r, the equation may be considerably simplified. 
For brevity write Ar/r = x, and for the value of x, when r = 1, 
write ¢. Then we have 
1 x\2 f tet lee leas Ziv 
log (= == Zoe ( : *) = 4+ —x? + XIE ..)- Y EG) 
a €\l—-x 3 5 por 


Now when r = 1 and x = ©, all the powers of x above the first will 
vanish, as may easily be tested. Hence, when r = 1 
Y P 
Cel Cel Riese fat I oe a ee (D) 
2po 
(r = 1) 
In order to test the agreement of the two functions, the geometric and 
the dynamic, for all values of r, we may write (C) in the form 
a Ar I(t Needle AN NE - 
CURE: ne = + Es Re AO (E) 
2p0r r Saat a i 
which, if identical, should be true for all values of r if Ar is independent 
ee | : ANT ; 
of r. Inspection shows that all values of —— less than 1/10 cannot 
affect the third significant figure; and since Ar is seldom larger than 
107 cm. values of r may vary between o and j(—° em. without ap- 
preciable change in the value of ¢. For values of r less than three or 
four times the range of molecular action, ¢, the two functions begin to 
diverge slowly, differing by nearly 10 per cent when ¢/r = 1/2. As 
previously pointed out this may indicate a change in the average den- 
sity of the surface as the drops become almost of molecular dimensions 
when the film, or surface portion, becomes an appreciable part of the 
whole drop. The practical constancy of € and its practical independence 
of the size of the drop of liquid, lead us to conclude that it represents a 
characteristic property of the substance only slightly dependent upon 
the curvature which enables us to determine its value. 
