IN THE PRESENCE OP DUST-FREE AIR AND OTHER GASES. 
305 
rapidity as the supersaturation is increased, reaching in air, oxygen, or nitrogen 
probably many millions per cubic centimetre under a tenfold supersaturation. In 
the other gases the observations in the colour phenomena necessary for this estimate 
were not made. There is no indication in these experiments of any limit to the 
number of drops which could be formed by sufficiently increasing the supersaturation. 
It is possible to make an approximate calculation of the size of the smallest drops 
which would be able to grow in vapour supersaturated to any given extent. 
The formula given by Lord Kelvin* for the effect of curvature of a surface upon 
the pressure of the saturated vapour in contact with it only applies, in its original 
form, to cases where the curvature is not sufficiently great to make the density of 
the vapour over the curved surface differ more than very slightly from that over a 
flat surface. Here we wish to calculate the curvature necessary to make the 
equilibrium density of the vapour from four to eight times that over a flat surface. 
If we assume that the supersaturated vapour obeys Boyle’s law, and that the 
surface tension retains its ordinary value in the case of the very small drops with 
which we are dealing, there is no difficulty in seeing how the formula must be 
modified to allow of its being extended to such cases as the present. Both of these 
conditions are, unfortunately, likely to be far from being satisfied. 
If we make these assumptions, the formula becomes, when the density of the 
vapour is as in the present case small compared with that of the liquid, identical 
with that obtained in a different way by R. v. Helmholtz,! 
1 P 
2T 
Rs0r 
where is the vapour pressure in contact with drops of radius r, P that over a flat 
surface at the same temperature 0; T is the surface-tension, s the density of the 
liquid, and R the constant in the equation 'p\p = Rd. Since Boyle’s law is assumed 
to hold, p/p is equal to the ratio of the corresponding densities, that is, to what 
is here called the supersaturation S. We thus obtain for the radius of the diops 
just in equilibrium 
2T 
~ log, S ’ 
since s in the case of water is equal to unity. R for water vapour is equal 
to 4-6 X 10". 
The results of the application of this formula are here given. 
* ‘ Proc. Roy. See.,’ Edin., VII., p. 63 (1870). 
t ‘ Wied. Ann.,’ sxvii., p. 508 (1886). 
2 R 
MDCCCXCVII.—A. 
