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rid of. The fact that the upper regions of the air from which the drops start
are colder than those through which they descend, might, as has been sup-
posed, cause the drop to grow by condensing vapour in the air through which
it passes but, as was shown by Mr Baxendell*, only to a very small extent,
and one the limit of which may be easily estimated.

Suppose the drop to start having a weight w^ and a temperature t l} and
on reaching the earth to have a temperature t 2 . Then the increase in the
quantity of heat in the drop would be ( 2 1) MI nearly. This heat would be

rt/l

developed by the condensation of a weight of water (t 2 ^) * nearly ; so

that, even supposing 2 t l = 100 F., which it could not possibly be, the
increase in the weight of the drop could not be one-tenth.

It is obvious also that the drop would not have parted with its heat to
the air it passes through ; for it is assumed to be colder than this air.
Therefore the only way in which it could have parted with its heat would
have been by radiation. Some heat might be lost in this way, but only a
very small amount, and one of which an approximate estimate may be made.
For after the drop had acquired a considerable size, say one-hundredth of a
foot in diameter, the time occupied in its descent would be very small.
Assume this to be one minute ; and assume that during this time the drop
is 100 degrees hotter than the surrounding objects, although this is of
course far beyond what could possibly be. According to the most accurate
data the amount of heat it would then lose would not be sufficient to condense
^Q of a grain of water*f- an altogether inappreciable amount when com-
pared with the weight of the drop, which would be nearly the quarter of a
grain.

* Memoirs of the Lit. and Phil. Soc. of Manchester, Vol. i., 3rd Series, p. 399.

f The surface of a drop whose diameter is -05 ft. is '000314 sq. ft. Now if the temperature of
the surrounding objects be zero Centigrade, and the temperature of the drop be 60 Centigrade,
then, assuming the radiation from the surface of the drop to be the same as the radiation from
the surface of glass, we have (see Balfour Stewart on Heat, p. 228) :

/?= 10 (16-00770-1)^,



220 ON THE MANNER IN WHICH RAINDROPS [29

It appears clear, therefore, that the only way in which a falling drop can
grow is by the aggregation to itself of the particles of moisture in the air ;
and the only way in which it can encounter these is by its downward motion
through this air.

Such a means of growth is amply sufficient to account for the size of rain-
drops or of hailstones.

If we suppose all the vapour which a body of saturated air at 60 F.
would contain, over and above what it would contain at 30, to be changed
into a fog or cloud, then, if a particle, after commencing to descend, aggre-
gated to itself all the water suspended in the volume of air through which it
swept, the diameter of the drop after passing through 2000 feet* would be
more than an eighth of an inch, and after passing through 4000 feet a
quarter of an inch, and so on ; so that in passing through 8000 feet of such
cloud it would acquire a diameter of half an inch. Now, as clouds must
often contain more water than what is here supposed, there is no difficulty in
explaining the size of the drops. The difficulty is rather the other way, in
explaining why the drops are not sometimes larger than they are.

There are, however, two reasons why raindrops do not acquire the full size
which might be expected on the above assumptions.

where R is the heat radiated from the surface A in one minute, the unit being the heat required
to raise 1000 grains of water 1 C. This gives

R=6A,
or R= -002 nearly.

Now if R' be the same quantity of heat, the unit being the heat required to raise one grain
1 Fahr.,



= 3-6.

This is equivalent to the latent heat of condensation of '0036 grain of water.
Again, let w be the weight of the drop ; then

w = 7000 x 62-5 x^irr 3
= '21 or nearly grain.

* If a; be the diameter of the drop after descending a distance h, and p the volume of water
suspended in a unit volume of air, then the increase of volume of the drop in descending a
distance dh is given by



X=-h.

Hence, if p = -00001 , x - -000005/* ;

and if x = -01, 7; = 2000 feet.



29] AND HAILSTONES ARE FORMED. 221

In the first place, the drop will not aggregate to itself all the particles in
front of it. Some of these will be swept away sideways by the diverging
current of air ; and the smaller the particles are the more will this be the
case. This is, of course, true for hail as well as for rain.

The second reason applies only to rain, and explains why it is that hail-
stones sometimes acquire magnitudes never approached by raindrops.

A drop retains its form simply by the surface-tension of the water ; and
as this is the same whatever may be the size of the drop, its power to hold
the drop together diminishes as the size of the drop increases, whereas the
velocity and consequent tendency of the air to disturb the shape of the drop
increase with its size. Hence it must eventually arrive at such a size that it
can no longer hold together, but will be blown to pieces by the rush of air past
it. This action may be seen in a waterfall or a fountain, where, in passing
through the air, a solid column of water is separated into drops not larger
than large raindrops.

The same reasoning does not hold for hailstones, which are held together
by the adhesion of the particles throughout their entire mass, and whose
compactness and strength increase with their size. It is, however, the case
that the smaller end of the stone, where the texture is looser, appears to be
blown off in its subsequent descent, especially when the stones acquire a
larger size.

It seems, therefore, that, so far as the growth of a drop or a stone is con-
cerned, the particles it overtakes in its downward path are a necessary and
sufficient cause ; but the origin of the drops and stones requires further ex-
planation. Why should some of the particles in a cloud be larger than the
others, as it is necessary for them to be in order that they may commence a
more rapid descent ?

A cloud does not always rain ; and hence it would seem that in their
normal condition the particles of a cloud are all of the same size and have no
internal motion, and that the variation of size is due to some irregularity or
disturbance in the cloud.

Such irregularity would result when a cloud is cooling by radiation from
its upper surface. The particles on the top of the cloud being more exposed
would radiate faster than those below them ; and hence they would condense
more vapour and grow more rapidly in size. They would therefore descend
and leave other particles to form the top of the cloud. In this way we should
have in embryo a continuous succession of drops.

Eddies in the cloud also form another possible cause of the origin of drops
and stones. Whenever the direction of motion of a portion of the cloud is not



222 ON THE FORMATION OF RAINDROPS AND HAILSTONES. [29

straight, the suspended particles will have more or less motion through the
air. And if, as in an eddy, the motion of the cloud varies from point to point
both in direction and magnitude, then the motion of the particles through the
air will also vary, and they may overtake one another and, combining, form
larger particles or drops in embryo.

Whatever may be the cause of the variation in the size of the particles
which form the cloud, we may know from observations on fogs that such
variations do exist. In fogs we have particles of all sizes, from those which
are too fine to be seen even by the aid of a microscope, and which will remain
suspended for hours without any appreciable descent, up to such a size that
they can be easily detected with the naked eye, and descend with a very
appreciable velocity so as to form a drizzle. When a coarse mist, such as
this, is superimposed over a fine mist, then rain must ensue if the particles
are water, and hail if they are ice.

Although, as has been shown, a raindrop cannot add considerably to its
volume by condensing the vapour from the air through which it passes ; the
reverse of this is not the case. The raindrop may be diminished by evapora-
tion. Whenever a raindrop falls through dry air (that is, air of which the
dew-point is below the temperature), evaporation might, and would, go on to
almost any extent, and the size of the drops be diminished until they entirely
vanished, the heat for evaporation being supplied from the air, which would
be warmer than the drop.

The case of snow differs from that of hail. The snow crystals are clearly
formed by the condensation of vapour, and not by the mere aggregation of
particles of ice. In this case the latent heat developed in condensation is
probably dissipated by radiation, the shape and smallness of the crystals
causing them to descend very slowly, and so affording time for the radia-
tion to produce an effect.

But even in snow we see the effect of aggregation. The individual
crystals never acquire a large size. But in their descent, the larger ones
overtaking the smaller, they form into flakes. In this case the aggregation
may be seen taking place. If when large flakes of snow are falling fast with-
out wind, the eye be fixed on a large Hake as high as it can at first be per-
ceived, and follow this flake in its subsequent descent, it may sometimes be
seen to overtake another flake and combine with it, the two descending
together.

For continuation see p. 223.



30.



ON THE FORMATION OF HAILSTONES, RAINDROPS, AND

SNOWFLAKES.

[From the Sixth Volume of the Third Series of " Memoirs of the Literary
and Philosophical Society of Manchester." Session 1877-78.]

(Head October 30, 1877.)

THIS communication forms a continuation of the paper I read before this
Society on the 31st of October, 1876, "On the Manner in which Raindrops
and Hailstones are formed*."

To the contents of this paper I shall have to refer continually ; hence, in
order to render what I have to say intelligible, it may be well for me to
recapitulate some of the leading points in my former paper. The chief
purpose of the paper was to explain the manner in which the minute cloud-
particles aggregated so as to form raindrops and hailstones.

Aggregation resulting from the more rapid Descent of the larger

Particles.

I commenced by pointing out that, as the suspended particles of water or
ice which constitute a cloud are all descending with velocities which increase
with their size, the larger particles will descend faster than the others, and will
consequently overtake those immediately beneath them ; with these they will
combine so as to form still larger particles, which will move with greater
velocity and, more quickly overtaking the particles in front of them, will add
to their size at an increasing rate. And I then proceeded to consider how far
this was a sufficient as well as a necessary cause of the phenomena of hail
and rain. One of the most important points on which my arguments were
based was

* See p. 214.



224 ON THE FORMATION OF HAILSTONES, [30

The Shape and Structure of ordinary Hailstones.

On close observation I had found, what had previously been noticed by
other observers, that the shape of an ordinary hailstone is not what it at first
sight appears to be. They are not spheres more or less imperfect, but more
or less imperfect cones or pyramids with rounded bases, like the sectors of
spheres the conical surface being striated, the striae radiating from the vertex
of the cone.

In texture the hailstones have the appearance of being an aggregation of
minute particles of ice fitting closely together, but without any crystallization
such as that seen in the snowflake ; while, on careful observation, it is seen
that they are denser and firmer towards their bases or spherical sides than
near the vertex of the cone, which latter often appears to have been broken
off in their descent.

As I explained, it seemed to me that this form and structure was exactly
such as would result from the manner of aggregation which I had supposed.
When a particle which ultimately forms the vertex of the cone starts on its
downward career and encounters other particles, these adhere to its lower face.
The mass, therefore, grows in thickness downwards ; and as some of the
particles strike the face so close to the edge that they overhang, the lower
face continually grows broader, and a conical form is given to the mass
above.

When a particle first starts, it moves slowly, and the force with which
it meets the other particles is slight, and consequently its texture is loose ;
but as it increases in size and velocity, it strikes the particles which it over-
takes with greater force, and so drives them into a more compact mass.

Assuming that the temperature at which hailstones are formed is not
greatly below 32, the particles must actually freeze together. For the effect
of squeezing two pieces of ice together at or near the temperature of 32 is
to cause them to thaw at those points where the pressure is greatest, at which
points they freeze again as soon as the pressure is removed.

In illustration of the force with which the particles strike the face of the
hailstone, I instanced the action of the particles of sand in Mr Tilghman's
sand-blast used for cutting glass and other hard materials.

I also reverted to the possibility of making

Artificial Hailstones,

by blowing a stream of frozen fog against a small object, making, as it were,
the cloud to rise up and meet the stone instead of the stone falling through
the cloud.



30] RAINDROPS, AND SNOWFLAKES. 225

I had not, however, then overcome the difficulty of obtaining such a
stream of frozen fog ; but I gave two sketches of plaster stones, which, as far
as their shape and the striated appearance of their surface were concerned,
closely resembled hailstones, and which plaster stones had been obtained by
blowing some finely-divided plaster of Paris against small splinters of wood
by means of a jet of steam.

In the discussion which followed my paper Dr Crompton suggested

The Ether Spray,

such as is used in surgery, as a means of obtaining a frozen fog. And shortly
after the Meeting I tried this ether spray, using an instrument such as
surgeons use. But although I found that the spray would freeze anything
such as a small tube of water, I could get no deposit of ice particles on the
outside of any object. I varied the form of the apparatus, but with no better
success ; and for the time I abandoned the attempt.

What the cause of this failure was I do not precisely know ; but I attribute
it to some excess of alcohol in the ether then used, which was not methylated
ether. That this might have been the cause occurred to me about two
months ago. I then determined to try again, and combine a spray of water
with that of ether. I now obtained the lightest ether which Messrs
Mottershead & Co. could supply. The specific gravity of this was '717 ;
and it was made from methylated spirit.

With this, somewhat to my surprise, I at once obtained a deposit of ice
even without the water spray, and with the same apparatus I had previously
used ; it was not, however, until I used the combined spray of water and
ether that I obtained anything resembling a hailstone in appearance. But
the first time I used this combination I obtained a small but well-shaped
hailstone on the end of a match which I held pointed towards the spray.

The next time I tried, however, on another day, I did not succeed so well
with the water as without it : when using the water spray the deposit of ice
was wet or half melted, while without the water I obtained a hailstone in
much the same manner as I had obtained before with the water.

This difference in the results on the two occasions was at once explained
by the different states of the air ; for on the first occasion it had been cold
and dry, whereas on the second it was warm and saturated. With the dry air
the ether spray reduced the temperature so far below 32 that the particles
of ice did not freeze together ; the force of impact was not sufficient to cause
them to thaw in the first instance ; and hence the water spray was necessary
to keep this temperature from falling too low ; whereas with the warm
o. R. 15



226 ON THE FORMATION OF HAILSTONES, [30

saturated air the ether did not reduce the temperature of the air and the
vapour it contained much below 32, and consequently, when the water spray
was added, the water was only partially frozen.

I subsequently improved the apparatus so as to be able to regulate the
supply of water and ether to the condition of the air.

The Apparatus.

This is shown in the accompanying sketch. It consists of a brass tube
half an inch in diameter, one end of which is connected with bellows capable
of maintaining a constant pressure of about eighteen inches of water ; on the
other end of the tube is a cap, over the end of which is a flat plate or
diaphragm having a central opening an eighth of an inch in diameter, which
forms the aperture for the blast. Entering through the sides of the main
brass tube are two small brass tubes which reach to within half an inch of the
plate, and into the ends of which are sealed fine glass capillary tubes, the
glass being very thin ; these protrude just through the middle of the
aperture, the one about one-sixteenth of an inch and the other one thirty-
second. Through these tubes the water and ether are separately introduced
into the blast to form the spray ; and it is mainly on the adjustment of these
tubes that the efficiency of the apparatus depends. It is essential that the
ether-tube should be slightly the longest ; otherwise the ends become stopped
with ice ; and I find it better that the ether-tube should be somewhat larger
than the water-tube. The bore of the tubes must be very small : but this is
not sufficient ; for unless the glass is very thin the spray will not be finely
divided. Both the ether and water are forced through the tubes from bottles
by connecting the interiors of these bottles with the bellows ; and the quan-
tities of ether and water are regulated either by raising or lowering the
bottles or by means of the cocks in the pipes.

The tube is fixed in an ordinary retort-stand so that the blast is vertical.
If, then, a small splinter of wood is held downwards pointing into the spray,
a lump of ice forms on the end of the splinter ; and this lump has all the
appearance of the hailstone. It is quite white and opaque ; it is conical in
form, and has a rounded base and striated surface.

In this way I have formed stones from half to three-quarters of an inch in
diameter. When, however, the stones are growing large, it is necessary to
move this splinter so as to expose in succession all parts of the face of the stone
to the more direct action of the spray.

When using this apparatus in a warm room, I have found it best to fix a
pad of blotting-paper over the jet at a height of ten or twelve inches. The
surface of this pad is cooled by the spray and prevents radiation from the



30]



RAINDROPS, AND SNOWFLAKES.



227



ceiling, which otherwise tends to melt the top of the stone. For a similar
reason I have found it well to surround the blast with a wide cylinder or




inverted cone of paper, which keeps off radiation without interfering with the
action of the jet.

By sticking several splinters of wood pointing downwards into the pad, a
number of stones may be made at once.

In the accompanying sketch (p. 228) are shown a medium-sized stone, as well
as one of the largest stones, attached to the splinters of wood. The surface of
the cone where continuous is truly conical, or rather pyramidal ; but the sur-
face is broken, as it were, by steps ; and a very marked fact is that all the
continuous surfaces have the same vertex; and hence the different conical

152



228



ON THE FORMATION OF HAILSTONES,



[30



surfaces to which they belong have not the same vertical angle, the surface
being exactly such as would be acquired by the fragments of a sphere so con-
stituted that the fracture tended to follow radial lines.





Owing to the radiation of the surfaces from a common vertex and the
steps which occur between the vertex and the base, the angle of the conical
surface of the stone is greater near the vertex than near the base. Thus the
smaller stones appear less elongated than those which are larger.

The fact that in the sketches of actual stones, which I gave in my last
paper, I showed the steps as less pronounced and the angles as larger than
they are in the artificial stones, is probably owing in some measure to
my having formed my ideas from the observation of favourable specimens
chosen from amongst those which fell. The larger angles were probably
also, in part, owing to the smaller size of the actual hailstones, which were
not much more than one-fourth of an inch across. But I think that it is
important to notice that the somewhat imperfect way in which the outside
layers in the surface of the artificial stones are continued may be owing to the
narrowness of the jet of air, which, on striking the stone, tends to diverge
laterally rather than to flow upwards past the sides of the stone, as it would
do if the jet were broader, or as the air must do when the stone is falling
through it.

The rate at which stones can be formed depends on the amount of water
which can be introduced into the spray, the larger stones taking from one to
two minutes. At first sight this may seem to be somewhat slow ; but the
following estimate tends to show that the artificial are probably formed more
quickly than the actual stones.

The speed of the jet of air at the point at which the stones are formed
is nearly equal to that at which the larger stones would fall through the
air. This is shown by the fact that if a large stone becomes accidentally



30] RAINDROPS, AND SNOWFLAKES. 229

detached from its splinter of wood it rather falls than rises, but when this
happens with smaller stones they are driven up by the force of the blast.

I find that the speed of the blast varies from 150 to 200 feet per second,
i.e. from one to two miles a minute. The larger stones, therefore, traverse
from one to three miles of frozen spray. So that if we imagine a cloud as
dense as the spray, it would have to be from one to three miles thick in
order that the stones might, in falling through it, attain the size of the
artificial stones ; and considering that the stones would only gradually acquire
a speed equal to that of the blast, the time occupied in falling through the
cloud would, in all probability, be very considerable, at least from five to ten
minutes, after the stone had acquired a sensible size.

As regards the proportion which the density of spray bears to that of a
cloud, a comparison may be made from the fact that when working in
saturated air at a temperature of 60 or 70 F., the condensation of vapour
supplied sufficient ice to form the spray ; and since it is probable that the
dense summer clouds, from which hail is formed, result from the cooling of
air from temperatures nearly, if not quite, equal to this, there is probably no
great difference in the density of the clouds and the spray.



Snow Crystals.

I have not yet had an opportunity of examining the texture of these
artificial stones under the microscope ; but to all appearance they consist of
an aggregation of small spherical particles of ice ; and it seems worthy of
notice that, while nothing like a snow crystal appears ever to be produced in
the ether spray, the moment the blast is stopped the end of the ether-tube
becomes covered with ice, which often assumes the form of snow crystals.

This appears to indicate the character of the difference between those
conditions which result in snow and those which result in hail.

When the cloud-particles are formed at or above the temperature of 32,
and then freeze, owing to cooling by expansion or otherwise, the particles as
they freeze retain their spherical form. This is what happens in the spray.

On the other hand, when saturated air at a temperature below 32 is still
further cooled, the deposit of the vapour will be upon ice, and will take the
form of snow crystals.

The aggregation of the snow crystals into flakes is, as I have pointed out
in my previous paper, accounted for by the larger crystals overtaking the
smaller crystals in their descent, and the still more rapid descent of the flakes
as they increase in size.



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