218 
Proceedings of the Royal Society of Edinburgh. [Sess. 
calculate the expansion in the test-flask. To simplify matters and save 
calculations, an easier method, however, was adopted. The capacity of 
the expander barrel was carefully measured with water, and found to 
contain 4'6 c.c. per cm. of stroke. If the capacity of the test-flask and 
tubes was 460' c.c., then 1 cm. of stroke would give 1 per cent, of expansion 
of the air in the flask. In these tests a smaller flask was generally used, 
as it enabled the tests to be made more quickly and only half the 
quantity of air was used. It held about 400 c.c. of water. The flask was 
first filled with water, then 216 c.c. were measured out; this with 14 c.c. in 
the tubes makes 230 c.c. to be operated on, so that when the slide is put 
at 1 cm. on the scale the expansion is 2 per cent. In writing the above 
degree of expansion we may either use the ordinary mathematical ex- 
pression of u 2 /u 1 = 1*02, or we may write T -|-o or or simply 2 per cent. 
The latter seems to be the simplest with our new apparatus, and will be 
adopted in what follows. 
Though we can easily get definite degrees of expansion, we cannot by 
any means get such definite degrees of supersaturation. First, because 
we can only get very slight degrees of saturation while there is any 
dust in the air, however great the expansion may be, since the amount 
of condensing surface presented by the cloud particles prevents it. Second, 
the size of the vessel has a great effect even when there are no nuclei 
present. If the vessel be only 2 or 3 centimetres in diameter, the air 
is rapidly heated by its walls, and also rapidly unburdens itself of the 
vapour to the nearest surfaces. This diffusion of vapour, I have previ- 
ously shown (loc. cit.), takes place with very great rapidity. Third, 
the rate of expansion is an important factor, and in small vessels is of 
very great importance ; but even in large vessels it has a considerable 
effect. The exchanges of heat between the air and the walls of the vessel 
and the diffusion of the vapour take place so quickly that it is only when 
the expansion is instantaneous and the air dustless that the calculated 
supersaturation can be attained. All decrease in the rate of expansion 
means lower supersaturation, even in dustless air, and this is particularly 
the case where high supersaturations are required. For instance, if we 
use an ordinary air-pump to expand the air, we find that the length 
of stroke required to produce condensation on ions is never the same in 
two tests, because we cannot make the successive expansions at the same 
rate ; and the wire-drawing effect of the valve further complicates matters. 
For this reason there is no valve in the expander used in these tests, and 
the air, instead of having to pass through a valve of about 1 or 2 mm. 
diameter, has an opening of 6 mm. The expander has the disadvantage, 
