x Supplement to ‘ Nature,” April 14, 1923 

(b) As the drops get larger the rate of fall tends to a 
constant value of about 8 metres a second. 
(c) Drops for which r =o-25 cm. have the most rapid 
fall, larger drops fall more slowly. 
Lenard has given the reason for (¢). He showed that 
the friction on the air causes deformation of the drops, 
so that instead of retaining the shape of spheres they 
become flattened out, thus presenting an increased re- 
sistance to the air through which they are falling. This 
deformation becomes appreciable when the radius of 
a drop is about o-2 cm. and then increases rapidly as the 
drop grows larger. When the radius is about 0-25 cm. 
and the drop is falling at the rate of 8 metres a second, 
any further increase in volume produces a greater 
flattening, and instead of the velocity being increased it 
is slightly decreased. When the size of the drop is 
such that if it were not flattened it would have a 
diameter of about half a centimetre, 7 =0-25 cm., the 
drop becomes very unstable, and all drops larger than 
this quickly break up into a number of smaller drops, 
which of course fall more slowly. This means that 
raindrops can never fall through air at a greater 
velocity than 8 metres a second. Small drops fall 
slower than this, and large drops flatten out as soon as 
they are falling at 8 metres a second, and then soon 
break up into smaller drops. 
In the above all the velocities have been given for air 
at normal pressure. If, however, the pressure is less, all 
the results are the same, except that the velocities must 
be increased in the proportion ,/B/ ./P, in which B is the 
normal pressure and P the actual pressure. 
Dines has found that in Europe the quantity of 
vapour in air is always very small. If the whole water 
vapour in the atmosphere on an average summer day 
were precipitated it would only give a total rainfall of 
o-80 in. The greatest amount ever measured on a 
summer day in Europe would only give 1-5 in. of 
rain, and of course the quantity is much less in winter. 
How then can we have rainfall of several inches of 
rain in the course of an hour or so? The answer is 
simple ; the ascending currents which are necessary to 
cause precipitation carry with them their own water 
vapour to supply the rainfall. An ascending current of 
air which is saturated at 10° C. (50° F.) needs only an 
upward velocity of 1 metre a second to carry with it 
sufficient vapour to give a rainfall of more than 1 inch 
per hour, so that there is no difficulty in explaining the 
greatest rate of rainfall ever experienced in the tropics. 
There are many ways in which the air is caused to 
rise in the atmosphere ; ascending currents up to many 
metres a second are possible, and do occur in the atmo- 
sphere. Let us think of air rising at about 10 cm. per 
second, which is the order of the upward velocity of the 
air in depressions. At a certain height cloud particles 

form as already described. These have a radius of about 
o-oor cm. and fall relatively to the air at 1-3 cm. per sec., 
hence they are carried upwards with the air, but the 
base of the cloud remains at the same height because 
new cloud particles are constantly being formed at that 
height. As the air rises the cloud particles grow in 
size, because water is being condensed on them, and they 
lag more and more behind the air. Drops with a 
radius of o-oo2 cm. are falling as rapidly as the air is 
rising, and therefore remain stationary, while drops of 
0-007 cm. are falling at the rate of one metre a second, 
and therefore fall through the rising air and appear at 
the earth’s surface as rain. It is obvious that this 
process will continue as long as the ascending currents 
continue, and in this way we get the continuous steady 
rain with which we are so familiar in this country. 
The rate of rainfall will increase as the upward 
velocity of the ascending air increases until the upward 
velocity becomes greater than 8 metresasecond. When 
this occurs no water can fall through the ascending air 
for the reason already explained. All water condensed 
in such an upward current—and it will be a very large 
amount —is carried upwards until the upward air 
velocity falls below 8 metres a second, as it is bound to 
do at some height owing to lateral spreading out. Here 
water accumulates in large amounts. It is the sudden 
cessation of the upward velocity in such an ascending 
current which gives rise to the so-called cloud-bursts, 
for when the sustaining current stops the accumulated 
water falls just as though the cloud had literally burst. 
The accumulated water while it is suspended in the 
air is constantly going through the process of coalescing 
into large drops, which at once become deformed and 
broken up again into small drops. Every time a drop 
breaks there is a separation of electricity, and this is 
probably the chief source of electricity in a thunder- 
storm. This explains why thunder-storms are asso- 
ciated with heavy rainfall and do not occur in polar 
regions where there is no rain. 
Hail.—I have already explained how the small liquid 
cloud particles are carried upwards with the ascending 
air, but as the air rises its temperature constantly falls, 
and there must come a point in the ascent when the 
temperature falls befow the freezing point. The cloud 
particles do not immediately turn into ice. As a 
matter of fact it is not an easy matter to freeze perfectly 
pure water, and water can remain liquid at temperatures 
far below the freezing point. Observations made on 
mountains and in balloons and aeroplanes have proved 
conclusively that cloud particles remain liquid at 
temperatures so low as —20° C. How far small drops 
can be super-cooled before they solidify we do not 
know, but super-cooled drops are in a very unstable 
state. From Table II. we see that at —20° C. 
Ee 
— 
