298 
C. T, E. WILSON ON CONDENSATION OF WATER VAPOUR 
Super saturation recpdred to produce the sensitive tint. 
At first sight it might seem that when the expansion is so great that a very large 
number of drojjs begin to grow before it is completed, the maximum supersaturation 
must be much less than is obtained by calculation according to the above method. 
It is difficult, however, to understand the constancy of the results obtained in the 
observations of the colour phenomena unless the supersaturation resulting from 
expansion of a given amount is always the same in spite of the variations which there 
must be in the rate of expansion. If the maximum supersaturation be independent 
of variations in the rate of expansion, it must be because the maximum supersatura¬ 
tion reached does not differ much from what would result from an infinitely rapid 
expansion. 
This is, perhaps, not very surprising if we consider how little time the drops have 
to grow before the expansion is completed. To produce the sensitive tint in air 
Po/Ui must be made equal to 1‘420. It is only while vjv-^ is increasing from 1’38 to 
T42, that the number of drops in process of formation is at all considerable, that is, 
when the piston has already completed nine-tenths of its journey. Now the piston 
must be moving with constantly increasing velocity ; the whole distance moved by 
the piston amounts to less than 1'5 centimetres; the time taken to travel the last 
tenth of this, that is, less than 1‘5 millimetres, must therefore be very short. We 
have seen that the time taken to travel the whole distance is itself very short. The 
growth of the drops too, as has already been pointed out, cannot be very rapid. It 
is quite likely therefore that even when they are very numerous, the quantity of 
water which separates out upon them before the expansion is complete may be too 
small to diminish appreciably the final supersaturation reached. 
The supersaturation required to produce the sensitive tint in air is calculated below. 
q. 
a,. 
TTj. 
ro/i'i- 
7- 
oje.,- 
b- 
ifi 
II 
20 '’ 
29.9 
17-39 
1-420 
1-41 
1 - 1.55 
- 19-2 
1 
1-07 9-9 
1 
On the numher of the drops. 
It is possible to obtain some information as to the number of the drops formed for 
a certain range of siqiersaturation from the colour phenomena. For from the colours 
we ought to be able to deduce the size of the full-grown drops, and the total quantity 
of water which condenses in consequence of the corresponding expansion may be 
calculated. With the exceedingly dense fogs with which we are now dealing there 
is no doubt that the water which condenses on the walls will be small in quantity 
