Supplement to “ Nature,” April 14, 1923 xi 
ice forms when the relative humidity over water 
is 82 per cent., which means that if water and 
_ ice are simultaneously present the relative humidity 
of the air relative to the ice is 121 per cent., t.e. it 
is 21 per cent. supersaturated. Thus if a few drops 
become converted into ice they are in a highly super- 
saturated atmosphere, and so will grow rapidly at the 
expense of the water drops. Meteorologists generally 
- consider that — 20° C. is about the limit at which large 
water particles can exist without changing into ice. 
Let us consider a region in the atmosphere through 
which there is an ascending current of air. The air is 
supposed to have a temperature of 20° C., and a relative 
humidity of about 50 per cent. at the ground. As the air 
rises, at first its temperature is reduced by 1° C. for 
each 100 metres of ascent. Hence by the time it has 
risen 1000 metres its temperature will have been reduced 
to 10° C., and it will have reached its dew point. Here 
the cloud level begins. As it rises still further its 
temperature continues to decrease, but not so rapidly 
as before, because the condensation of water vapour 
releases the latent heat of vaporisation. It reaches 0° C. 
at a height of 3000 metres. Hence the region between 
Iooo and 3000 metres contains only drops of water. 
As the air rises above 3000 metres the temperature falls 
still lower, but the water particles do not freeze at once, 
they remain super-cooled. We may assume that at 
—20° C., which is reached at about 6000 metres, the 
super-cooled drops solidify and the remaining part of 
the cloud above this level is composed of snow alone. 
There will not be a sharp division between the region 
of super-cooled water and the region of snow. For a 
certain distance ice crystals and super-cooled water will 
be mixed together. Such conditions are very unstable, 
and from considerations of the vapour pressure alone 
the ice particles grow rapidly, because the vapour over 
super-cooled water is highly supersaturated with respect 
to ice. In addition, the slightest contact between ice 
and super-cooled water causes the latter to solidify at 
once. The original ice particle will therefore quickly 
grow in size and, if the ascending current is not too large, 
will commence to fall. It has, however, to fall through 
3000 metres of super-cooled water drops, and in doing 
so grows appreciably in size. As each super-cooled 
water particle strikes the ice it solidifies, and also 
imprisons a certain amount of air, so that by the time 
the ice particle reaches the bottom of the super-cooled 
region it is simply a ball of soft white ice without any 
sign of regular crystalline structure. 
If the descent through the super-cooled region has 
been fairly rapid the temperature of the ice ball will be 
considerably below the freezing point when it arrives 
in the region where the temperature is o° C., and the 
cloud particles are not super-cooled. As it continues 
its way downwards it receives a considerable addition 
of water: in the first place, by direct deposition, because 
it is colder than the air ; and, secondly, by collision with 
the water particles. This water covers the surface of 
the cold ice ball with a uniform layer of liquid which 
quickly freezes into clear solid ice, with little or no 
imprisoned air. Finally the ice escapes from the bottom 
of the cloud, and falls to the ground as a hailstone. 
When hailstones are split open to show their internal 
structure we can nearly always see the inner soft 
white mass of ice which was collected while the stones 
were in the super-cooled region, surrounded by a layer 
of clear transparent ice formed by the freezing of the 
water deposited when the stone was passing through 
the non-super-cooled region. 
This simple explanation of the formation of a hail- 
stone was not considered satisfactory at first, because 
it was considered that hailstones produced in this way 
must necessarily be small. Trabert calculated that 
if a hailstone started to fall from a height of 2 kilo- 
metres, and swept up all the water it met on its way 
down, its radius would grow only by 2 millimetres. 
But Trabert left many things out of consideration, as 
pointed out by Wegener. In the first place, he started 
his hailstone much too low in the atmosphere; he 
should have started it from a height nearer 8 kilo- 
metres than 2. Secondly, he neglected the effect 
of the ascending currents. We know that there are 
violent ascending currents during thunder-storms, in 
which alone hailstones are formed. The ascending 
currents may be so violent that even large hailstones 
will not be able to fall through them, but they are all 
the time falling rapidly relatively to the air, and there- 
fore sweeping water out of it. 
The velocity with which a hailstone falls through 
still air at atmospheric pressure is 
v=1246/r cm./sec. 
If, therefore, the velocity of the ascending current were 
ro metres per second, the hailstone could not commence 
to fall until it had a radius of 0-64 cm. It would then 
commence to fall very slowly as its size grew larger, but 
it would all the time be moving relatively to the air at 
a greater rate than ro metres a second. Thus the 
effective height through which it would fall would be 
very great in comparison with the actual height. 
It must also be remembered that with such an 
ascending current no water could fall in the form of 
rain ; all the water would be retained in the cloud, the 
water content of which could be very large indeed, thus 
giving large quantities of water to be swept up by the 
hailstone. When we also take into account that a 
hailstone is generally very much colder than the sur- 
rounding saturated air, so that the deposition of 
