230 FORMATION OF HAILSTONES, RAINDROPS, AND SNOWFLAKES. [30
As regards the formation of raindrops, I have nothing to add to what was
contained in my last paper. The same explanation obviously applies to both
hail and rain ; and any doubt which may have been left by the less direct
arguments in my former paper will, I venture to think, have been removed
by the verification of my predictions in the production of artificial hailstones
so closely resembling in all particulars those formed by nature. In conclusion,
I would thank Dr Crompton for the suggestion of the means by which I have
been able to produce these stones.
ON THE INTERNAL COHESION OF LIQUIDS AND THE
SUSPENSION OF A COLUMN OF MERCURY TO A HEIGHT
MORE THAN DOUBLE THAT OF THE BAROMETER.
[From the Sixth Volume of the Third Series of " Memoirs of the Manchester
Literary and Philosophical Society." Session 1877-78.]
(Read October 30, 1877.)
THE ease with which, under ordinary circumstances, the different portions
of liquid may be separated, is a fact of such general observation that the
inability of liquids like water to offer any considerable resistance to rupture
appears to have been tacitly accepted as an axiom. In no work on Hydro-
statics does it appear that the possibility of water existing in a state of
tension is so much as considered ; and suction is always described as being
solely attributable to the pressure of the atmosphere.
The limit, of 32 feet or thereabouts, to the height to which water can be
raised by suction in the common pump, and the sinking of the mercury in
the barometer-tube (leaving the Torricellian vacuum above) until the column
.is at most only 31 inches (sufficient to balance the highest pressure of the
atmosphere), are phenomena so well known as to be almost household words
with us. It is not, therefore, without some fear of encountering simple
incredulity that I venture to state
The Object of this Communication.
In the first place my purpose is to show that certain facts, already fully
established, afford grounds for believing that almost all liquids, and par-
ticularly mercury and water, are capable of offering resistance to rupture
232 ON THE INTERNAL COHESION OF LIQUIDS. [31
commensurate with the resistance offered by solid materials. In the second
place, I have to describe certain experimental results which, as far as they
go, completely verify these conclusions and subvert the general ideas previously
mentioned as to the limits to the height to which mercury can be suspended
in a tube, or water raised by suction. And, in conclusion, I shall endeavour
to explain the nature of the circumstances which have resulted in the practical
limits to these phenomena.
The Separation of Liquids is not caused by Rupture.
Although the smallness of the force generally requisite to separate a mass
of liquid into parts leads to the supposition that the parts of the liquid have
but little coherence, it may be seen on close examination that this supposition
is not altogether legitimate ; for such separation of a liquid as we ordinarily
observe takes place at the surface of the liquid, is caused by an indentation
or running-in of the surface, and not by an internal rupture or simultaneous
separation over any considerable area. Thus when we see a stream of liquid
break up to drops, the drops separate gradually by the contraction of the
necks joining them, as shown in fig. 1, and not suddenly as in fig. 2. And
Fig. l. Fig. 2.
the ease with which portions of a liquid may be separated by the forcing or
drawing in of the surface affords no ground for assuming that the liquid is
without coherence, any more than does the ease with which we may cut a
piece of string, cloth, or metal with sharp shears, or even tear some of these
bodies by beginning at an edge, prove that they are without strength to resist
great force when these are applied uniformly so as to call forth the resistance
of all the parts of the body simultaneously. It is true that under certain
circumstances we observe the internal rupture of liquid whenever bubbles
are formed, as when water is boiled ; but under these circumstances we have
no means of estimating the forces which cause the internal rupture : they
are molecular in their action ; and, for all we know, they may be very con-
siderable. Having thus pointed out that the ease of separation of the parts
of a mass of liquid does not even imply a want of cohesion on the part of the
liquid, I shall now point out that we have in common phenomena.
31] ON THE INTERNAL COHESION OF LIQUIDS. 233
Evidence of Considerable Cohesion.
These are, for the most part, what are considered minor phenomena ; they
are confined to the surface of the liquid and are included under what is
called " capillarity," or " surface-tension."
The phenomena of capillarity or surface-tension have recently attracted a
great deal of attention ; and many important facts concerning them have
been clearly elucidated, some of which bear directly on my present subject.
Of the phenomena I may instance the suspension of drops of water, the
rising of water up small tubes, the tendency of bubbles to contract, and the
spherical form assumed by small fragments of mercury.
These phenomena and others are found to be explained by the fact that
the surface of these liquids is always under a slight but constant tension, as
if enclosed in a thin elastic membrane.
No satisfactory explanation as to the cause of this surface-tension has, I
believe, been as yet found ; but the fact itself is proved beyond all question.
It is a molecular phenomenon ; and in order to offer any explanation as
to its cause, it would be necessary to adopt some hypothesis respecting the
molecular constitution of the liquid. Such an explanation making the
surface-tension to arise from the cohesion of the molecules of the liquid is,
I believe, possible ; but this is beside my present purpose, which will be
completely served by showing that
The Surface-tension proves the existence of Cohesion.
To prove this requires no molecular hypothesis ; but, before proceeding, it
may be well to define clearly the term cohesion.
Cohesion in a liquid is here to be understood as a property which enables
the fluid to resist any tendency to cause internal separation of its parts any
tendency to draw it asunder ; or, more definitely, it is the property which
enables a liquid to resist a tension or negative pressure.
Let us suppose a mass of liquid without internal cohesion. Then any
external action tending to enlarge the capacity within the bounding surface
of the liquid would at once cause the interior of the liquid to open, and a
hollow would be formed within the liquid without any resistance on the part
of the liquid. Such a condition is inconsistent with surface-tension ; for the
tension of the surface of the internal hollow would tend to contract the
hollow ; and since the interior of the hollow is supposed to be empty, there
234 ON THE INTERNAL COHESION OF LIQUIDS. [31
could be no resistance to the tendency of the surface to contract, such as that
offered by the pressure of the gas within an ordinary bubble. Hence any
force that might, under the circumstances, balance the surface-tension and
keep open the hollow must be supplied by the suction or cohesion of the
liquid outside. Q. E. D.
Again, the intensity of the cohesion is determined by the intensity of the
surface-tension and the smallness of the least possible opening over the surface
on which tension exists.
So far as has yet been determined by experiment, it has been found that
the surface-tension is independent of the curvature of the surface is constant
for the same liquid. Assuming that this is the case, it follows that the
intensity of the force necessary to keep a spherical bubble or opening from
contracting (whether this force arises from the pressure of the gas within the
bubble or the cohesive traction of the liquid within the opening) is equal to
twice the intensity of the surface-tension divided by the radius of the sphere.
Hence the cohesive tension must be equal to twice the surface-tension of the
liquid divided by the diameter of the smallest opening for which the surface-
tension exists. Q. E. D.
It immediately follows from the foregoing proposition, that no matter
how small the surface-tension may be, if it is finite even when the opening is
infinitely small, then the cohesion of the liquid must be infinitely great. For,
if the liquid were continuous, in its origin the opening must always be
infinitely small ; and hence to cause such an opening would require infinite
That the cohesion is infinitely great is not probable, to say the least.
Hence it is improbable that the surface-tension remains finite when the
opening becomes infinitely small. As has already been stated, it has been
found that the surface-tension is constant, or nearly so, under ordinary cir-
cumstances; but it has never been measured for bubbles of very small
diameter, and there appears to be every probability that, when the size of the
bubble comes to be of the same order of small quantity as the dimensions of
a molecule, the surface-tension must diminish rapidly with the size of the
If this is the case, then we have a limit to the cohesion, although it is
probably very great for most liquids, something like the cohesion of solid
matter of the same kind. That is to say, it is probable that it would require
nearly as great intensity pf stress to rupture fluid as it would to rupture
solid mercury, or as great tension to rupture water as to rupture ice.
31] ON THE INTERNAL COHESION OF LIQUIDS. 235
The Effect of Vapour.
Nothing has yet been said about the effect of the pressure of vapour
within the bubbles in balancing the surface-tension. It may, however, be
shown that this can be of no moment. Even supposing that the tension of
the vapour within the opening of the liquid were equal to the tension due to
the temperature under ordinary circumstances, this would be inappreciable.
So that, unless the tension of vapour within small openings were much
greater than that in larger openings for the same temperature, its effect
might be neglected ; and so far from this being the case, Sir William
Thomson has shown that the pressure of the vapour within a bubble at any
particular temperature diminishes with the size of the opening. Hence it is
clear that this vapour can have no effect on the result a conclusion verified
by the now well-known fact that water may be raised to a temperature high
above 212 without passing into steam.
Experimental Verification necessary.
This line of reasoning has been apparent to me now for several years.
I find notes on some of the principal points which I made in 1873 ; and for
several years I have pointed out the conclusions arrived at as regards the
probable cohesion of water to the students in the engineering class at Owens
College. I have, however, hitherto refrained from publishing my views,
because I had no definite experimental results to appeal to in confirmation of
them. Experimental indications of such a cohesive force were not wanting,
but they were not definite. And although methods of making definite
experiments have often occupied my thoughts, certain difficulties, which
turn out to have been somewhat imaginary, kept me from trying the
It had always appeared to me that, in order to subject the interior of
a liquid mass to tension, it would be necessary to, as it were, hold the surface
of the liquid at all points to prevent its contracting. To accomplish this, it
was necessary to have the liquid in a vessel, to the surface of which the liquid
would adhere as water adheres to glass. The experiment which I had con-
ceived would have been equivalent to a vertical glass tube more than 34 feet
long, closed at the upper end and open at the lower, so that when the tube
was full of water the column would be higher than the pressure of the
atmosphere would maintain, and hence could only be maintained by the
cohesion of the water. The difficulty of such an experiment, however,
appeared to be great. It was clear that if mercury could be substituted for
water this difficulty would be much reduced ; but then mercury does not
236 ON THE INTERNAL COHESION OF LIQUIDS. [31
readily adhere to glass, and the ordinary method of making barometers
seemed to disprove the possibility of making it adhere.
It was only on the 2nd of this month that an accidental phenomenon at
once afforded me the experimental proof for which I had been looking.
The phenomenon was observed in a mercurial vacuum-gauge (a siphon
gauge which admitted a column of mercury 31 inches long). Before the
mercury was introduced the tube had been wetted with sulphuric acid, a few
drops of which covered the mercury on both ends of the column.
The gauge had been in constant use as a vacuum-gauge for three weeks ;
and, probably owing to the action of the acid on the mercury, a little gas had
been generated between the mercury and the closed end of the tube, sufficient
to cause the column to sink to 27^ when the barometer stood at 29. To get
rid of this air, the tube was removed from its situation and placed in such a
position that the bubble of air passed along the tube and escaped, the open
end of the tube being entirely free. Before the tube was tilted in this way,
the unbalanced column was 27|- inches long. When tilted, the mercury ran
back right up to the end of the tube as the bubble of air passed out. On
erecting the tube again, the mercury remained up to the end of the tube,
except about one-eighth of an inch, which was filled with sulphuric acid. The
unbalanced column of mercury was therefore 31 inches long. At first the
full significance of this phenomenon was not recognized; but in order to
ascertain that the tube was cleared of air, it was moved gently up and down
to see if the mercury clicked, as it usually does when the tube is free from air,
but the mercury did not move in the tube. The rapidity of the oscillation
was thereupon increased until it became a violent shake, and, as the mercury
still remained firm, it was clear that some very powerful force was holding it
in its place. The tube being in a vertical position, was then left in order
that the barometer might be consulted. This was standing at 29 inches.
After a few seconds, when the gauge was again examined, the column no
longer reached the end of the tube, but stood at 29 inches. As it was singular
that the mercury should have quietly settled down after having resisted such
violent shaking, the tube was again inclined until the mercury and acid came,
apparently, up to the end of the tube ; but this time on the erection of the
tube the mercury at once settled down. That is to say, it settled down
gradually as the tube was erected. At first what appeared to be a very small
bubble opened in the sulphuric acid ; and this enlarged as the top of the
tube was raised. On again inclining the tube until it was horizontal, and
examining it closely, a minute bubble could be seen in the acid, and it was
this bubble which expanded as the tube was erected, and so allowed the
31] ON THE INTERNAL COHESION OF LIQUIDS. 237
mercury to descend. To get rid of this bubble, the tube was turned down so
as to allow the bubble to pass along the tube ; but, owing to its small size, it
did not pass many inches along the tube before it became fixed between the
mercury and the glass. When the bubble came to a standstill at about six
inches from the end of the tube, the gauge was again erected ; the bubble
immediately began to move back, but so slowly that it was some seconds
before it entered the region of no pressure. During this interval the mercury
remained up to the end of the tube ; but the bubble, as soon as it neared the
top of the tube, expanded and rapidly rose to the top of the tube, leaving the
column at 29 inches. This operation having been repeated several times, it
became quite evident that it was this small bubble which, either by rising up
the tube or being generated at the top, had caused the mercury in the first
instance to sink. As the bubble would not pass out by itself, the tube was
tilted so as to allow a larger bubble of air to enter ; and having been left
standing for about twelve hours to allow the small bubble to unite with the
larger one, it was again tilted so as to allow the air to pass out. When this
was done the mercury again remained firmly against the end of the tube and
did not descend when violently shaken. The open end of the tube was then
connected with an air-pump and exhausted until the pressure within it fell
to about four inches of mercury. This operation occupied some seconds ; but
all this time the mercury did not move from the end of the tube ; but
eventually the column opened near the bottom of the tube and a large
bubble appeared, which rose up the tube, the mercury falling past the
opening. That the breaking of the column so near the bottom of the tube
was owing to the presence at that point of a small bubble of air was almost
proved by the fact that, on readmitting the air to the open end of the tube
and inclining the tube to see if it was free from air, there was found a minute
bubble which played exactly the same part as the small bubble which had
been previously examined.
At the instant previous to the rupture of the column at the bottom of
the tube, there must at the top of the tube have been an unbalanced tension
or negative pressure equal to 27 inches of mercury ; and this tension did not
break the continuity of the column. Hence I had a proof that the cohesion
within the mercury and the sulphuric acid as well as the adhesion of the
sulphuric acid to the mercury and the glass is sufficient to resist this very
In the hope of improving the experiments, another gauge was constructed,
the tube being $ of an inch in internal diameter and 35 inches high. Into
this tube mercury and sulphuric acid were introduced, as in the first tube.
238 ON THE INTERNAL COHESION OF LIQUIDS. [31
But on trying to get rid of the small bubbles of air, it was found impossible
to do so, as bubbles were continually generated. Hence it appeared that the
three weeks during which the mercury and sulphuric acid in the first tube
had remained in contact had had an important influence on the result.
Failing in this attempt, it occurred to me to try if water would answer the
purpose as well as sulphuric acid. Having in my possession an old vacuum-
gauge with a column three inches long, which had originally been wetted
with sulphuric acid, but into which a considerable quantity of water had
accidentally been introduced, I carefully allowed all the air to escape, and
then applied a mercurial air-pump to the open end of the gauge, and
exhausted as far as the pump would draw. The mercury did not descend.
As I could apply no further tension, I shook the gauge up and down ; but
still the mercury remained unmoved. I then tapped the gauge smartly on
the side; the mercury then fell three inches, until it was level. Having
succeeded so far, I extracted the mercury and sulphuric acid from the 35-inch
gauge and introduced some water without washing the tube, and, having
boiled the water in the tube, again introduced the mercury.
Having extracted all the air, I found no difficulty in making the gauge
to stand up to the 35 inches without any immediate tendency to fall. On
applying the air-pump to the open end the mercury several times remained
up until the exhaustion had proceeded so far that when it fell from 22 to
28 inches, and when the rupture took place it was accompanied by a loud
click. I could not on that occasion get the mercury to withstand complete
exhaustion ; but after leaving the gauge with the mercury suspended for
24 hours at 35 inches, I was able to exhaust the open end of the tube as far
as the pump would draw, without bringing the mercury down ; so that I had
a column of 35 inches of mercury suspended by the cohesion of the liquids.
There was no reason to suppose that this was the limit or anywhere near
the limit. It was clearly possible to suspend a longer column ; but as the
length of the column increased so would the difficulty of getting rid of the
disturbing causes, and I determined to rest satisfied with the 35 inches ; but
in order to see if this could be maintained, I obtained a gauge 60 inches long,
which would leave 30 inches above the pressure of the atmosphere.
The difficulty of getting rid of the air in this tube sufficiently to allow of
the mercury standing 60 inches was very considerable. Before filling the
tube it was rinsed out with concentrated sulphuric acid, then twice washed
with distilled water, and then water put in and boiled in the tube. Then
sufficient mercury was introduced to fill the long leg and the bend, so that
the column, when complete, was 59 inches long, the barometer being at 29'5.
After the tube had been tilted several times so as to allow the air to pass
out, the mercury would be suspended as the tube was slowly re-erected, until
ON THE INTERNAL COHESION OF LIQUIDS.
it had attained an elevation of 40, 50, or sometimes the full height of
60 inches (as shown in fig. 3), but only for a few seconds. When the mercury
fell, if the column broke anywhere near the top of the tube, it gave way with
a loud click. But this was by no means always the case. The mercury
would sometimes separate nearly 30 inches down the tube ; and then the
appearance of the upper portion falling was very singular : the upper portion
of the column remained intact ; and a stream of mercury fell from its under
surface, as shown in fig. 4, breaking up into globules as it came into contact
with the lower portion, with a loud rattling noise. I was unable to get the
column in the tube thus filled to maintain itself for more than twenty or
thirty seconds, which failure was clearly due to the presence of air ; for after
the mercury had fallen a small quantity of air was always found to collect
above it. Sometimes, when on inclining the tube the liquid again reached
the top, the bubble which remained was so small as to be scarcely visible,
although subject to no pressure other than the surface-tension; but its
presence always became apparent instantly on erecting the tube. In no case
was it possible, after the mercury had once fallen, to get it to remain up to
any considerable height above that due to the pressure of the atmosphere
until the bubble of air collected had been allowed to pass out,
240 ON THE INTERNAL COHESION OF LIQUIDS. [31
The tube was then again emptied, washed, and filled with glycerine.
This behaved much in the same manner as the water; but the difficulty of
getting rid of the air was greater.
Similar results were obtained when very dilute ammonia-liquid was tried.
The tube was then again carefully washed, first with water, and then
several times with concentrated sulphuric acid. The mercury was subjected
to nitric acid, washed arid dried, and then filtered into a bottle of sulphuric
acid, from which it was poured into the tube, some acid passing in with the
mercury. When first introduced into the tube a few small bubbles could be
seen rising between the mercury and the tube and passing up through the
sulphuric acid into the vacuum above ; but after it had stood for five or six
hours no bubbles were perceived, the surface of the mercury against the tube
being perfectly clear ; nevertheless, on erecting the tube, the mercury would
not rise above the height of the barometer, and air was always found to have
collected above the mercury. Water was then introduced so as to dilute the
acid ; then the mercury was suspended as before, for a few seconds only. The
tube was then placed in a position with the closed end lowest, so that the air
and water might ascend towards the end and pass out ; and after being in
this position for some hours, when it was again erected the column remained
It was thereupon again lowered and left to drain for forty-eight hours.
On being again erected, the mercury was still suspended. The tube has
since been carried in a more or less horizontal position some three miles to
the Society's rooms in order that I might exhibit this phenomenon. If it
has not been affected by the shaking, you will see a suspended column of
mercury some fifty-nine inches high, or twenty-nine inches above the height
due to the atmosphere*.