456 
MR. T. H. LABY ON THE SUPERSATURATION AND 
finally at 0 2 before drops 
liquid at 0 2 , so that 
are formed to the pressure of vapour over plane surface of 
S 
1 e x 
TT i 0 2 l\ 
IT2 0\ '^2 
( 2 ) 
where tt x is the saturated pressure of the vapour at the temperature 0 X , and tt 2 at 0 2 . 
The expansion decreases tt x , to tt 1 . v x /v 2 , and the temperature falls in the ratio 0 2 /0 x . 
In deducing the above formula, and in using it to calculate supersaturations, it is 
assumed (a) that the final temperature when a mixture of air and vapour expands is 
given by the relation (I), and (b) that Boyle’s and Charles’ laws hold for the 
vapour. The assumption that Boyle’s and Charles’ laws hold for the vapours 
named on p. 455 seems unavoidable,* since the experimental data do not exist which 
would enable the supersaturations to be calculated without assuming these laws. 
Consider assumption (a): for it to be true, the expansions must be (1) adiabatic, 
and (2) the formula 0 2 = 0 X (v x /v 2 ) 1 ' m ~ 1 must hold for the mixtures of ah' and organic 
vapour used. 
(l) The expansion is believed to be adiabatic on these grounds : Wilson has most 
carefully tested the matter, using two very different apparatus, one of which had no 
piston. The piston of the other was light and the expansion must have been very 
rapid, certainly more rapid than in the first. The mean of a number of experiments, 
using air and water vapour gave with each apparatus the same value, 1*252, for the 
expansion which caught the natural ions present. The writer’s result for this point 
was 1'256, both at the beginning and the end of his experiments. Let 0 2 be 
the final temperature in these three experiments, if the mean expansion (D253) 
were adiabatic, and let the rise of temperature due to the ingress of heat by 
convection, conduction, and radiation from the walls of the expansion vessel in the 
different conditions of the three experiments be p, q, r. The actual final tempe¬ 
ratures would then be 0 2 +p, 0 2 + q, d,+ r, but since in each case these were the 
temperatures at which condensation just began, they were experimentally the same. 
Thus p, q, r are too small to be observed, and the expansions were adiabatic. 
Further, Wilson found v x /v 2 — 1'38 for fog-like condensation with air and water, and 
the writer’s apparatus gave 1*376. In these two experiments we have the same final 
temperature, that necessary for fog-like condensation. The same final temperature is, 
however, only obtained from equal expansions of 1*38 in different apparatus, when the 
expansions are not only adiabatic, but are such that the whole lowering of temperature 
* T° supply evidence that Boyle’s and Charles’ laws are applicable to supersaturated vapours would 
mean a separate and difficult research. I can think of no direct solution. Professor Thomson’s deter¬ 
mination of - e, the charge on a negative ion, is an indirect test of the applicability of these laws in the 
case considered, for in that method of determining — e the quantity of water condensed by an expansion in 
ionised air and water vapour is calculated by an application of the gas laws. Dr. H. A. Wilson’s method 
for — e does not assume those laws. The results of the two methods could be compared. They agree 
when water vapour is used. Both are subject to large errors. 
