464 
MR. T. H. LABY ON THE SUPER,SATURATION AND 
If c is the radius of a drop (with charge e) which is in equilibrium with the saturated 
vapour, and a its radius when in equilibrium with the vapour at a pressure^, then 
lie io g ,£ = 2n(i-x 3 )A, 
where x = c/a. 
For water at 10° C. we have It = 4‘62 x 10 6 , c — 3 - 05 x 10 -8 cm., cr = 1, 
T = 74 dynes/cm., so that for it 
logio (pfP) = l ' 61x (l-® 3 )- 
The graph of this function (which is typical of the organic vapours as well) is given 
in fig. 5, where p/P, the supersaturation, is the ordinate, and the abscissa is the 
Os 
Fig. 5. Radius of charged drop in equilibrium with water vapour at various pressures. 
radius of the drop with a vapour pressure p. It will be seen that as p/ P increases 
from a very small value to 1, the size of the drop changes very little. When p/\ P is 
5’8, its maximum value, the radius of the drop is F6c. Any further increase in p/P 
makes the drop grow to a very large size, or visible condensation takes place. The 
AB portion of the curve represents unstable equilibrium, for a increases as p/P 
diminishes. For condensation to take place, p/P must be slightly greater than its 
value at A, which is the value of p/P in the above equation when x(l— a? 3 ) is a 
maximum, i.e., when l-4.n 3 = 0, or x = 0'63 and jc (l-x 3 ) = 0'472. 
Thus the value of p/P given by the expression 
lo gio (p/P) = 
1 2T 
2‘3 Rdecr 
x (l-.x 3 ) = 0-41 
T 
PbOccr 
is the least value which will cause condensation. 
1 he values p>/P which the equation gives are stated below for a number of esters, 
acids, and alcohols. T, the surface tension, was found at the required temperature by 
plotting Ramsay and Shield s, and Ramsay and Aston’s* values of T at different 
temperatures; straight lines were nearly always obtained from which the required 
* Loc. cit. 
