Title: The Splash of a Drop
Author: Worthington, A. M. (Arthur Mason), 1852-1916
Language: English
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  _THE ROMANCE OF SCIENCE_

  THE SPLASH OF A DROP


  BY
  PROF. A.M. WORTHINGTON, M.A., F.R.S.


  _Being the reprint of a Discourse delivered at the Royal Institution
  of Great Britain, May 18, 1894._

  PUBLISHED UNDER THE DIRECTION OF THE GENERAL
  LITERATURE COMMITTEE.


  LONDON:
  SOCIETY FOR PROMOTING CHRISTIAN KNOWLEDGE,
  NORTHUMBERLAND AVENUE, CHARING CROSS, W.C.;
  43, QUEEN VICTORIA STREET, E.C.
  BRIGHTON: 129, NORTH STREET.
  NEW YORK: E. & J.B. YOUNG & CO.
  1895.



THE SPLASH OF A DROP



INSTANTANEOUS PHOTOGRAPHS OF THE SPLASH OF A WATER-DROP FALLING ABOUT 16
INCHES INTO MILK.

[Illustration: Time after contact = ·0262 sec.]

[Illustration: Time after contact = ·0391 sec.]

[Illustration: Time after contact = ·101 sec.]



THE SPLASH OF A DROP


The splash of a drop is a transaction which is accomplished in the
twinkling of an eye, and it may seem to some that a man who proposes to
discourse on the matter for an hour must have lost all sense of
proportion. If that opinion exists, I hope this evening to be able to
remove it, and to convince you that we have to deal with an exquisitely
regulated phenomenon, and one which very happily illustrates some of the
fundamental properties of fluids. It may be mentioned also that the
recent researches of Lenard in Germany and J.J. Thomson at Cambridge, on
the curious development of electrical charges that accompanies certain
kinds of splashes, have invested with a new interest any examination of
the mechanics of the phenomenon. It is to the mechanical and not to the
electrical side of the question that I shall call your attention this
evening.

The first well-directed and deliberate observations on the subject that
I am acquainted with were made by a school-boy at Rugby some twenty
years ago, and were reported by him to the Rugby Natural History
Society. He had observed that the marks of accidental splashes of
ink-drops that had fallen on some smoked glasses with which he was
experimenting, presented an appearance not easy to account for. Drops of
the same size falling from the same height had made always the same
kind of mark, which, when carefully examined with a lens, showed that
the smoke had been swept away in a system of minute concentric rings and
fine striæ. Specimens of such patterns, obtained by letting drops of
mercury, alcohol, and water fall on to smoked glass, are thrown on the
screen, and the main characteristics are easily recognized. Such a
pattern corresponds to the footprints of the dance that has been
performed on the surface, and though the drop may be lying unbroken on
the plate, it has evidently been taking violent exercise, and were our
vision acute enough we might observe that it was still palpitating after
its exertions.

A careful examination of a large number of such footprints showed that
any opinion that could be formed therefrom of the nature of the motion
of the drop must be largely conjectural, and it occurred to me about
eighteen years ago to endeavour by means of the illumination of a
suitably-timed electric spark to watch a drop through its various
changes on impact.

The reason that with ordinary continuous light nothing can be
satisfactorily seen of the splash, is not that the phenomenon is of such
short duration, but because the changes are so rapid that before the
image of one stage has faded from the eye the image of a later and quite
different stage is superposed upon it. Thus the resulting impression is
a confused assemblage of all the stages, as in the photograph of a
person who has not sat still while the camera was looking at him. The
problem to be solved experimentally was therefore this: to let a drop of
definite size fall from a definite height in comparative darkness on to
a surface, and to illuminate it by a flash of exceedingly short duration
at any desired stage, so as to exclude all the stages previous and
subsequent to the one thus picked out. The flash must be bright enough
for the image of what is seen to remain long enough on the eye for the
observer to be able to attend to it, and even to shift his attention
from one part to another, and thus to make a drawing of what is seen. If
necessary the experiment must be capable of repetition, with an exactly
similar drop falling from exactly the same height, and illuminated at
exactly the same stage. Then, when this stage has been sufficiently
studied, we must be able to arrange with another similar drop to
illuminate it at a rather later stage, say 1/1000 second later, and in
this way to follow step by step the whole course of the phenomenon.

The apparatus by which this has been accomplished is on the table before
you. Time will not suffice to explain how it grew out of earlier
arrangements very different in appearance, but its action is very simple
and easy to follow by reference to the diagram (Fig. 1).

AA´ is a light wooden rod rather longer and thicker than an ordinary
lead pencil, and pivoted on a horizontal axle O. The rod bears at the
end A a small deep watch-glass, or segment of a watch-glass, whose
surface has been smoked, so that a drop even of water will lie on it
without adhesion. The end A´ carries a small strip of tinned iron, which
can be pressed against and held down by an electro-magnet CC´. When the
current of the electro-magnet is cut off the iron is released, and the
end A´ of the rod is tossed up by the action of a piece of india-rubber
stretched catapult-wise across two pegs at E, and by this means the drop
resting on the watch-glass is left in mid-air free to fall from rest.

[Illustration: FIG. 1.]

BB´ is a precisely similar rod worked in just the same way, but carrying
at B a small horizontal metal ring, on which an ivory timing sphere of
the size of a child's marble can be supported. On cutting off the
current of the electro-magnet the ends A´ and B´ of the two levers are
simultaneously tossed up by the catapults, and thus drop and sphere
begin to fall at the same moment. Before, however, the drop reaches the
surface on which it is to impinge, the timing sphere strikes a plate D
attached to one end of a third lever pivoted at Q, and thus breaks the
contact between a platinum wire bound to the underside of this lever and
another wire crossing the first at right angles. This action breaks an
electric current which has traversed a second electro-magnet F (Fig. 2),
and releases the iron armature N of the lever NP, pivoted at P, thus
enabling a strong spiral spring G to lift a stout brass wire L out of
mercury, and to break at the surface of the mercury a strong current
that has circulated round the primary circuit of a Ruhmkorff's induction
coil; this produces at the surface of the mercury a bright
self-induction spark in the neighbourhood of the splash, and it is by
this flash that the splash is viewed. The illumination is greatly helped
by surrounding the place where the splash and flash are produced by a
white cardboard enclosure, seen in Fig. 2, from whose walls the light is
diffused.

[Illustration: FIG. 2.]

It will be observed that the time at which the spark is made will depend
upon the distance that the sphere has to fall before striking the plate
D, for the subsequent action of demagnetizing F and pulling the wire L
out of the mercury in the cup H is the same on each occasion. The modus
operandi is consequently as follows:--The observer, sitting in
comparative but by no means complete darkness, faces the apparatus as it
appears in Fig. 2, presses down the ends A´B´ of the levers first
described, so that they are held by the electro-magnet C (Fig. 1); then
he presses the lever NP down on the electro-magnet F, sets the timing
sphere and drop in place, and then by means of a bridge between two
mercury cups, short-circuits and thus cuts off the current of the
electro-magnet C. This lets off drop and sphere, and produces the flash.
The stage of the phenomenon that is thus revealed having been
sufficiently studied by repetition of the experiment as often as may be
necessary, he lowers the plate D a fraction of an inch and thus obtains
a later stage. Not only is any desired stage of the phenomenon thus
easily brought under examination, but the apparatus also affords the
means of measuring the time interval between any two stages. All that
is necessary is to know the distance that the timing sphere falls in the
two cases. Elementary dynamics then give us the interval required. Thus,
if the sphere falls one foot and we then lower D 1/4 inch, the interval
between the corresponding stages will be about ·0026 second.

Having thus described the apparatus, which I hope shortly to show you in
action, I pass to the information that has been obtained by it.

This is contained in a long series of drawings, of which a selection
will be presented on the screen. The First Series that I have to show
represents the splash of a drop of mercury 0·15 inch in diameter that
has fallen 3 inches on to a smooth glass plate. It will be noticed that
very soon after the first moment of impact, minute rays are shot out in
all directions on the surface. These are afterwards overflowed or
united, until, as in Fig. 8, the outline is only slightly rippled. Then
(Fig. 9) main rays shoot out, from the ends of which in some cases
minute droplets of liquid would split off, to be left lying in a circle
on the plate, and visible in all subsequent stages. By counting these
droplets when they were thus left, the number of rays was ascertained to
have been generally about 24. This exquisite shell-like configuration,
shown in Fig. 9, marks about the maximum spread of the liquid, which,
subsiding in the middle, afterwards flows into an annulus or rim with a
very thin central film, so thin, in fact, as often to tear more or less
irregularly. This annular rim then divides or segments (Figs. 14, 15,
16) in such a manner as to join up the rays in pairs, and thus passes
into the 12-lobed annulus of Fig. 16. Then the whole contracts, but
contracts most rapidly between the lobes, the liquid then being driven
into and feeding the arms, which follow more slowly. In Fig. 21 the end
of this stage is reached, and now the arms continuing to come in, the
liquid rises in the centre; this is, in fact, the beginning of the
rebound of the drop from the plate. In the case before us the drops at
the ends of the arms now break off (Fig. 25), while the central mass
rises in a column which just fails itself to break up into drops, and
falls back into the middle of the circle of satellites which, it will be
understood, may in some cases again be surrounded by a second circle of
the still smaller and more numerous droplets that split off the ends of
the rays in Fig. 9. The whole of the 30 stages described are
accomplished in about 1/20 second, so that the average interval between
them is about 1/600 second.


FIRST SERIES.

[Illustration: 1]

[Illustration: 2]

[Illustration: 3]

[Illustration: 4]

[Illustration: 5]

[Illustration: 6]

[Illustration: 7]

[Illustration: 8]

[Illustration: 9]

[Illustration: 10]

[Illustration: 11]

[Illustration: 12]

[Illustration: 13]

[Illustration: 14]

[Illustration: 15]

[Illustration: 16]

[Illustration: 17]

[Illustration: 18]

[Illustration: 19]

[Illustration: 20]

[Illustration: 21]

[Illustration: 22]

[Illustration: 23]

[Illustration: 24]

[Illustration: 25]

[Illustration: 26]

[Illustration: 27]

[Illustration: 28]

[Illustration: 29]

[Illustration: 30]

It should be mentioned that it is only in rare cases that the
subordinate drops seen in the last six figures, are found lying in a
very complete circle after all is over, for there is generally some
slight disturbing lateral velocity which causes many to mingle again
with the central drop, or with each other. But even if only half or a
quarter of the circle is left, it is easy to estimate how many drops,
and therefore how many arms there have been. It may be mentioned that
sometimes the surface of the central lake of liquid (Figs. 14, 15, 16,
17) was seen to be covered with beautiful concentric ripples, not shown
in the figures.

The question now naturally presents itself, Why should the drop behave
in this manner? In seeking the answer it will be useful to ask ourselves
another question. What should we have expected the drop to do? Well, to
this I suppose most people would be inclined, arguing from analogy with
a solid, to reply that it would be reasonable to expect the drop to
flatten itself, and even very considerably flatten itself, and then,
collecting itself together again, to rebound, perhaps as a column such
as we have seen, but not to form this regular system of rays and arms
and subordinate drops.

Now this argument from analogy with a solid is rather misleading, for
the forces that operate in the case of a solid sphere that flattens
itself and rebounds, are due to the bodily elasticity which enables it
not only to resist, but also to recover from any distortion of shape or
shearing of its internal parts past each other. But a liquid has no
power of recovering from such internal shear, and the only force that
checks the spread, and ultimately causes the recovery of shape, is the
_surface tension_, which arises from the fact that the surface layers
are always in a state of extension and always endeavouring to contract.
Thus we are at liberty when dealing with the motions of the drop to
think of the interior liquid as not coherent, provided we furnish it
with a suitable elastic skin. Where the surface skin is sharply curved
outwards, as it is at the sharp edge of the flattened disc, there the
interior liquid will be strongly pressed back. In fact the process of
flattening and recoil is one in which energy of motion is first expended
in creating fresh liquid surface, and subsequently recovered as the
surface contracts. The transformation is, however, at all moments
accompanied by a great loss of energy as heat. Moreover, it must be
remembered that the energy expended in creating the surface of the
satellite drops is not restored if these remain permanently separate.
Thus the surface tension explains the recoil, and it is also closely
connected with the formation of the subordinate rays and arms. To
explain this it is only necessary to remind you that a liquid cylinder
is an unstable configuration. As you know, any fine jet becomes beaded
and breaks into drops, but it is not necessary that there should be any
flow of liquid along the jet; if, for example, we could realize a rod of
liquid of the shape and size of this cylindrical ruler that I hold in my
hand, and liberate it in the air, it would not retain its cylindrical
shape, but would segment or divide itself up into a row of drops
regularly disposed according to a definite and very simple numerical
law, viz. that the distances between the centres of contiguous drops
would be equal to the circumference of the cylinder. This can be shown
by calculation to be a consequence of the surface tension, and the
calculation has been closely verified by experiment. If the liquid
cylinder were liberated on a plate, it would still topple into a regular
row of drops, but they would be further apart; this was shown by
Plateau. Now imagine the cylinder bent into an annulus. It will still
follow the same law,[1] _i.e._ it will topple into drops just as if it
were straight. This I can show you by a direct experiment. I have here a
small thick disc of iron, with an accurately planed face and a handle at
the back. In the face is cut a circular groove, whose cross section is a
semi-circle. I now lay this disc face downwards on the horizontal face
of the lantern condenser, and through one of two small holes bored
through to the back of the disc I fill the groove with quicksilver. Now,
suddenly lifting the disc from the plate, I release an annulus of
liquid, which splits into the circle of very equal drops which you see
projected on the screen. You will notice that the main drops have
between them still smaller ones, which have come from the splitting up
of the thin cylindrical necks of liquid which connected the larger drops
at the last moment.

Now this tendency to segment or topple into drops, whether of a straight
cylinder or of an annulus, is the key to the formation of the arms and
satellites, and indeed to much that happens in all the splashes that we
shall examine. Thus in Fig. 12 we have an annular rim, which in Figs. 13
and 14 is seen to topple into lobes by which the rays are united in
pairs, and even the special rays that are seen in Fig. 9 owe their
origin to the segmentation of the rim of the thin disc into which the
liquid has spread. The proceeding is probably exactly analogous to what
takes place in a sea wave that curls over in calm weather on a slightly
sloping shore. Any one may notice how, as it curls over, the wave
presents a long smooth edge, from which at a given instant a multitude
of jets suddenly shoot out, and at once the back of the wave, hitherto
smooth, is seen to be furrowed or "combed." There can be no doubt that
the cylindrical edge topples into alternate convexities and concavities;
at the former the flow is helped, at the latter hindered, and thus the
jets begin, and special lines of flow are determined. In precisely the
same way the previously smooth circular edge of Fig. 8 topples, and
determines the rays and lines of flow of Fig. 9.

Before going on to other splashes I will now endeavour to reproduce a
mercury splash of the kind I have described, in a manner that shall be
visible to all. For this purpose I have reduplicated the apparatus which
you have seen, and have it here so arranged that I can let the drop fall
on to the horizontal condenser plate of the lantern, through which the
light passes upwards, to be afterwards thrown upon this screen. The
illuminating flash will be made inside the lantern, where the arc light
would ordinarily be placed. I have now set a drop of mercury in
readiness and put the timing sphere in place, and now if you will look
intently at the middle of the screen I will darken the room and let off
the splash. (The experiment was repeated four or five times, and the
figures seen were like those of Series X.) Of course all that can be
shown in this way is the outline, or rather a horizontal section of the
splash; but you are able to recognize some of the configurations already
described, and will be the more willing to believe that a momentary view
is after all sufficient to give much information if one is on the alert
and has acquired skill by practice.

The general features of the splash that we have examined are not merely
characteristic of the liquid mercury, but belong to all splashes of a
liquid falling on to a surface which it does not wet, provided the
height of fall or size of the drop are not so great as to cause complete
disruption,[2] in which case there is no recovery and rebound. Thus a
drop of milk falling on to smoked glass will, if the height of fall and
size of drop are properly adjusted, give forms very similar to those
presented by a drop of mercury. The whole course of the phenomenon
depends, in fact, mainly on four quantities only: (1) the size of the
drop; (2) the height of fall; (3) the value of the surface tension; (4)
the viscosity of the liquid.

The next series of drawings illustrates the splash of a drop of water
falling into water.

In order the better to distinguish the liquid of the original drop from
that into which it falls, the latter was coloured with ink or with an
aniline dye, and the drop itself was of water rendered turbid with
finely-divided matter in suspension. Finally drops of milk were found to
be very suitable for the purpose, the substitution of milk for water not
producing any observable change in the phenomenon.

In Series II. the drop fell 3 inches, and was 1/5 inch in diameter.

[In most of the figures of this and of succeeding series the central
white patch represents the original drop, and the white parts round it
represent those raised portions of the liquid which catch the light. The
numbers under each figure give the time interval in seconds from the
occurrence of the first figure, or of the figure marked [Tau] = 0.]


SERIES II.

_The Splash of a Drop, followed in detail by Instantaneous
Illumination._

Diameter of Drop, 1/5 inch. Height of Fall, 3-1/5 inches.

[Illustration: 1

[Tau] = 0 sec.]

[Illustration: 2

[Tau] = 0 sec.]

[Illustration: 3

[Tau] = ·0097 sec.]

[Illustration: 4

[Tau] = ·0392 sec.]

[Illustration: 5

[Tau] = ·0392 sec.]

[Illustration: 6]

[Illustration: 7

[Tau] = ·0979 sec.]

[Illustration: 8

[Tau] = ·1095 sec.]

[Illustration: 9

[Tau] = ·167 sec.]

It will be observed that the drop flattens itself out somewhat, and
descends at the bottom of a hollow with a raised beaded edge (Fig. 2).
This edge would be smooth and circular but for the instability which
causes it to topple into drops. As the drop descends the hollow becomes
wider and deeper, and finally closes over the drop (Fig. 3), which,
however, soon again emerges as the hollow flattens out, appearing first
near, but still below the surface (Fig. 4), in a flattened, lobed form,
afterwards rising as a column somewhat mixed with adherent water, in
which traces of the lobes are at first very visible.

The rising column, which is nearly cylindrical, breaks up into drops
before or during its subsequent descent into the liquid. As it
disappears below the surface the outward and downward flow causes a
hollow to be again formed, up the sides of which an annulus of milk is
carried, while the remainder descends to be torn again a second time
into a vortex ring, which, however, is liable to disturbance from the
falling in of the drops which once formed the upper part of the
rebounding column.

It is not difficult to recognize some features of this splash without
any apparatus beyond a cup of tea and a spoonful of milk. Any drinker of
afternoon tea, after the tea is poured out and before the milk is put
in, may let the milk fall into it drop by drop from one or two inches
above it. The rebounding column will be seen to consist almost entirely
of milk, and to break up into drops in the manner described, while the
vortex ring, whose core is of milk, may be seen to shoot down into the
liquid. But this is better observed by dropping ink into a tumbler of
clear water.

Let us now increase the height of fall to 17 inches. Series III.
exhibits the result. All the characteristics of the last splash are
more strongly marked. In Fig. 1 we have caught sight of the little
raised rim of the hollow before it was headed, but in Fig. 2 special
channels of easiest flow have been already determined. The number of
ribs and rays in this basket-shaped hollow seemed to vary a good deal
with different drops, as also did the number of arms and lobes seen in
later figures, in a somewhat puzzling manner, and I made no attempt to
select drawings which are in agreement in this respect. It will be
understood that these rays contain little or none of the liquid of the
drop, which remains collected together in the middle. Drops from these
rays or from the larger arms and lobes of subsequent figures are often
thrown off high into the air. In Figs. 3 and 4 the drop is clean gone
below the surface of the hollow, which is now deeper and larger than
before. The beautiful beaded annular edge then subsides, and in Fig. 5
we see the drop again, and in Fig. 6 it begins to emerge. But although
the drop has fallen from a greater height than in the previous splash,
the energy of the impact, instead of being expended in raising the same
amount of liquid to a greater height, is now spent in lifting a much
thicker adherent column to about the same height as in the last splash.
There was sometimes noticed, as seen in Fig. 9, a tendency in the water
to flow up past the milk, which, still comparatively unmixed with water,
rides triumphant on the top of the emergent column. The greater relative
thickness of this column prevents it splitting into drops, and Figs. 10
and 11 show it descending below the surface to form the hollow of Fig.
12, up the sides of which an annular film of milk is carried (Figs. 12
and 13), having been detached from the central mass, which descends to
be torn again, this time centrally into a well-marked vortex ring.


SERIES III.

_The Splash of a Drop, followed in detail by Instantaneous
Illumination._

Diameter of Drop, 1/5 inch. Height of Fall, 1 ft. 5 in.

[Illustration: 1

[Tau] = 0 sec.]

[Illustration: 2

[Tau] = ·0314 sec.]

[Illustration: 3

[Tau] = ·0317 sec.]

[Illustration: 4

[Tau] = ·0389 sec.]

[Illustration: 5

[Tau] = ·0498 sec.]

[Illustration: 6

[Tau] = ·0551 sec.]

[Illustration: 7

[Tau] = ·0759 sec.]

[Illustration: 8

[Tau] = ·0901 sec.]

[Illustration: 9]

[Illustration: 10]

[Illustration: 11]

[Illustration: 12

[Tau] = ·295 sec.]

[Illustration: 13]

[Illustration: 14]

If we keep to the same size of drop and increase the fall to something
over a yard, no great change occurs in the nature of the splash, but the
emergent column is rather higher and thinner and shows a tendency to
split into drops.

When, however, we double the volume of the drop and raise the height of
fall to 52 inches, the splash of Series IV. is obtained, which is
beginning to assume quite a different character. The raised rim of the
previous series is now developed into a hollow shell of considerable
height, which tends to close over the drop. This shell or dome is a
characteristic feature of all splashes made by large drops falling from
a considerable height, and is extremely beautiful. In the splash at
present under consideration it does not always succeed in closing
permanently, but opens out as it subsides, and is followed by the
emergence of the drop (Fig. 8). In Fig. 9 the return wave overwhelms the
drop for an instant, but it is again seen at the summit of the column in
Fig. 10.


SERIES IV.

_The Splash of a Drop, followed in detail by Instantaneous
Illumination._

Diameter of Drop, 1/4 inch. Height of Fall, 4 ft. 4 in.

[Illustration: 1

[Tau] = 0 sec.]

[Illustration: 2

[Tau] = ·0021 sec.]

[Illustration: 3

[Tau] = ·0042 sec.]

[Illustration: 4

[Tau] = ·0165 sec.]

[Illustration: 5

[Tau] = ·0206 sec.]

[Illustration: 6

[Tau] = ·0443 sec.]

[Illustration: 7

[Tau] = ·0482 sec.]

[Illustration: 8

[Tau] = ·0595 sec.]

[Illustration: 9

[Tau] = ·0707 sec.]

[Illustration: 10]

[Illustration: 11]

But on other occasions the shell or dome of Figs. 4 and 5 closes
permanently over the imprisoned air, the liquid then flowing down the
sides, which become thinner and thinner, till at length we are left with
a large bubble floating on the water (see Series V.). It will be
observed that the flow of liquid down the sides is chiefly along
definite channels, which are probably determined by the arms thrown up
at an earlier stage. The bubble is generally creased by the weight of
the liquid along these channels. It must be remembered that the base of
the bubble is in a state of oscillation, and that the whole is liable to
burst at any moment, when such figures as 6 and 7 of the previous series
will be seen.

[Illustration: SERIES V.

_The Splash of a Drop, followed in detail by Instantaneous
Illumination._

The Size of Drop and Height of Fall are the same as before, but the
hollow shell (see figs. 4 and 5 of the previous Series) does not succeed
in opening, but is left as a bubble on the surface. This explains the
formation of bubbles when _big_ rain-drops fall into a pool of water.]

Such is the history of the building of the bubbles which big rain-drops
leave on the smooth water of a lake, or pond, or puddle. Only the bigger
drops can do it, and reference to the number at the side of Fig. 5 of
Series IV. shows that the dome is raised in about two-hundredths of a
second. Should the domes fail to close, or should they open again, we
have the emergent columns which any attentive observer will readily
recognize, and which have never been better described than by Mr. R.L.
Stevenson, who, in his delightful _Inland Voyage_, speaks of the surface
of the Belgian canals along which he was canoeing, as thrown up by the
rain into "an infinity of little crystal fountains."

Very beautiful forms of the same type indeed, but different in detail,
are those produced by a drop of water falling into the lighter and more
mobile liquid, petroleum.

It will now be interesting to turn to the splash that is produced when a
solid sphere, such as a child's marble, falls into water.

I found to my great surprise that the character of the splash, at any
rate up to a height of 4 or 5 feet, depends entirely on the state of the
surface of the sphere. A polished sphere of marble about 0·6 of an inch
in diameter, rubbed very dry with a cloth just beforehand and dropped
from a height of 2 feet into water, gave the figures of Series VI., in
which it is seen that the water spreads over the sphere so rapidly, that
it is sheathed with the liquid even before it has passed below the
general level of the surface. The splash is insignificantly small and of
very short duration.[3] If the drying and polishing be not so perfect,
the configurations of Series VII. are produced; while if the sphere be
roughened with sandpaper, or _left wet_, Series VIII. is obtained, in
which it will be perceived that, as was the case with the liquid drop,
the water is driven away laterally, forming the ribbed basket-shaped
hollow, which, however, is now prolonged to a great depth, the drop
being followed by a cone of air, while the water seems to find great
difficulty in wetting the surface completely. Part of this column of air
was carried down at least 16 inches, and then only detached when the
sphere struck the bottom of the vessel.


SERIES VI., VII.

_Splash of a Solid Sphere (a marble 1/2 inch in diameter falling 2 feet
into water)._

[Illustration: SERIES VI.

When the sphere is _dry_ and _polished_.]

[Illustration: SERIES VII.

When the sphere is _not_ well _dried_ and _polished_.]

[Illustration: SERIES VIII.

_The Splash of a Solid Sphere_--(continued.)

When the sphere is _rough_ or _wet_.]

[Illustration: SERIES IX.

_The Splash of a Solid Sphere_--(continued.)

When the sphere is rough or wet, and falls above 5 feet.]

Figs. 6 and 7 show the crater falling in, but this did not always
happen, for the walls often closed over the hollow exactly as in Figs. 4
and 5 of Series IV. Meanwhile the long and nearly cylindrical portion
below breaks up into bubbles which rise quickly to the surface.

By increasing the fall to 5 feet we obtain the figures of Series IX. The
tube of Fig. 1 corresponds to the dome of Series IV. and V., and is not
only elevated to a surprising height, but is also in the act of cleaving
(the outline being approximately that of the unduloid of M. Plateau).
Figs. 2 and 3 show the bubble formed by the closing up of this tube,
weighed down in the centre as in Figs. 5 and 6 of Series V. Similar
results were obtained with other liquids, such as petroleum and alcohol.

It is easy to show in a very striking manner the paramount influence of
the condition of the solid surface. I have here a number of similar
marbles; this set has been well polished by rubbing with wash leather. I
drop them one by one through a space of about 1 foot into this deep,
wide, cylindrical glass vessel, lighted up by a lamp placed behind it.
You see each marble enters noiselessly and with hardly a visible trace
of splash. Now I pick them out and drop them in again (or to save
trouble, I drop in the place of these other wet ones), everything is
changed. You see how the air is carried to the very bottom of the
vessel, and you hear the "phloisbos" of the bubbles as they
rise to the surface and burst. These dry but rough marbles behave in
much the same way.

Such are the main features of the Natural History of Splashes, as I made
it out between thirteen and eighteen years ago. Before passing on to the
photographs that I have since obtained, I desire to add a few words of
comment. I have not till now alluded to any imperfections in the timing
apparatus. But no apparatus of the kind can be absolutely perfect, and,
as a matter of fact, when everything is adjusted so as to display a
particular stage, it will happen that in a succession of observations
there is a certain variation in what is seen. Thus the configuration
viewed may be said to oscillate slightly about the mean for which the
apparatus is adjusted. Now this is due both to small imperfections in
the timing apparatus and to the fact that the splashes themselves do
actually vary within certain limits. The reasons are not very far to
seek. In the first place the rate of demagnetization of the
electro-magnets varies slightly, being partly dependent on the varying
resistance of the contacts of crossed wires, partly on the temperature
of the magnet, which is affected by the length of time for which the
current has been running. But a much more important reason is the
variation of the slight adhesion of the drop to the smoked watch-glass
that has supported it, and consequently of the oscillations to which, as
we shall see, the drop is subjected as it descends. Thus the drop will
sometimes strike the surface in a flattened form, at others in an
elongated form, and there will be a difference, not only in the time of
impact, but in the nature of the ensuing splash; consequently some
judgment is required in selecting a consecutive series of drawings. The
only way is to make a considerable number of drawings of each stage, and
then to pick out a consecutive series. Now, whenever judgment has to be
used, there is room for error of judgment, and moreover, it is
impossible to put together the drawings so as to tell a consecutive
story, without being guided by some theory, such as I have already
sketched, as to the nature of the motion and the conditions that govern
it. You will therefore be good enough to remember that this chronicle of
the events of a tenth of a second is not a mechanical record but is
presented by a fallible human historian, whose account, like that of
any other contemporary observer, will be none the worse for independent
confirmation. That confirmation is fortunately obtainable. In an attempt
made eighteen years ago to photograph the splash of a drop of mercury, I
was unable to procure plates sufficiently sensitive to respond to the
very short exposures that were required, and consequently abandoned the
endeavour. But in recent years plates of exquisite sensitiveness have
been produced, and such photographs as those taken by Mr. Boys of a
flying rifle bullet have shown that difficulties on the score of
sensitiveness have been practically overcome. Within the last few weeks,
with the valuable assistance of my colleague at Devonport, Mr. R.S.
Cole, I have succeeded in obtaining photographs of various splashes.
Following Prof. Boys' suggestion, we employed Thomas's cyclist plates,
or occasionally the less sensitive "extra-rapid" plates of the same
makers, and as a developer, Eikonogen solution of triple strength, in
which the plates were kept for about 40 minutes, the development being
conducted in complete darkness.

A few preliminary trials with the self-induction spark produced at the
surface of mercury by the apparatus that you have seen at work, showed
that the illumination, though ample for direct vision, was not
sufficient for photography. When the current strength was increased, so
as to make the illumination bright enough for the camera, then the spark
became of too great duration, for it lasted for between 4 and 5
thousandths of a second, within which time there was very perceptible
motion of the drop and consequent blurring. It was therefore necessary
to modify the apparatus so as to employ a Leyden-jar spark whose
duration was probably less than 10-millionths of a second. A very
slight change in the apparatus rendered it suitable for the new
conditions, but time does not permit me to describe the arrangements in
detail. It is, however, less necessary to do so as the method is in all
essentials the same as that described in this room two years ago by Lord
Rayleigh in connection with the photography of a breaking soap-film.[4]
I therefore pass at once to the photographs themselves.

The first two series (X. and XI.) may be described as shadow
photographs; they were obtained by allowing a drop of mercury to fall on
to the naked photographic plate itself, the illuminating spark being
produced vertically above it, and they give only a horizontal section of
the drop in various stages, revealing the form of the outline of the
part in contact with the plate, but of course telling nothing about the
shape of the parts above. The first series corresponds to a mercury
splash very similar to that first described, and the second to the
splash of a larger drop such as was not described. In each series, the
tearing of the thin central film to which allusion was made is well
illustrated. I think the first comment that any one would make is that
the photographs, while they bear out the drawings in many details, show
greater irregularity than the drawings would have led one to expect. On
this point I shall presently have something to say.


SERIES X.

(1) _Instantaneous Shadow Photographs (life size) of the Splash of a
Drop of Mercury falling 8 cm. on to the Photographic Plate._

[Illustration: 1

Actual size of the Drop, 4·83 mm.]

[Illustration: 2

[Tau] = 0]

[Illustration: 3]

[Illustration: 4]

[Illustration: 5]

[Illustration: 6]

[Illustration: 7

[Tau] = ·048 sec.]


SERIES XI.

(2) _Instantaneous Shadow Photographs (life size) of the Splash of a
Drop of Mercury falling 15 cm. on to Glass._

[Illustration: 1

Actual size, 4·83 mm. in diameter.]

[Illustration: 2

[Tau] = 0 sec.]

[Illustration: 3]

[Illustration: 4

4A

[Tau] = ·0032 sec.]

[Illustration: 5

[Tau] = ·0063 sec.]

[Illustration: 5A

[Tau] = ·0094 sec.]

[Illustration: 6

[Tau] = ·0134 sec.]

Comparing the first set of drawings (pp. 20-24) with the photographs of
Series X., it will be seen that

  Photograph 2 corresponds to drawing 4 or 5
      "      3     "             "    9
      "      4     "             "   18
      "      6     "             "   20
      "      7     "             "   24

but the irregularity of the last photograph almost masks the
resemblance.


SERIES XII.

_Engravings from Instantaneous Photographs (16/17 of the real size) of
the Splash of a Drop of Mercury, 4·83 mm. in diameter, falling 8·9 cm.
on to a hard polished surface._

[Illustration: 1]

[Illustration: 2

[Tau] = 0 sec.]

[Illustration: 3]

[Illustration: 4]

[Illustration: 5]

[Illustration: 6

[Tau] = ·0195 sec.]

Series XII. gives an objective view of a mercury splash as taken by the
camera. Only the first of this series shows any detail in the interior.
The polished surface of the mercury is, in fact, very troublesome to
illuminate, and this splash proved the most difficult of all to
photograph.

Series XIII. shows the splash of a drop of milk falling on to a smoked
glass plate, on which it runs about without adhesion just as mercury
would. Here there is more of detail. In Fig. 4 the central film is so
thin in the middle that the black plate beneath it is seen through the
liquid. In Fig. 8 this film has been torn.

Series XIV. exhibits the splash of a water drop falling into milk. The
first four photographs show the oscillations of the drop about a mean
spherical figure as it approaches the surface.

In the subsequent figures it will be noticed that the arms which are
thrown up at first, afterwards segment into drops which fly off and
subside (see Fig. 8), to be followed by a second series which again
subside (Fig. 11), to be again succeeded by a third set. In fact, so
long as there is any downward momentum the drop and the air behind it
are penetrating the liquid, and so long must there be an upward flow of
displaced liquid. Much of this flow is seen to be directed into the arms
along the channels determined by the segmentation of the annular rim.
This reproduction of the lobes and arms time after time on a varying
scale goes far to explain the puzzling variations in their number which
I mentioned in connection with the drawings. I had not, indeed,
suspected this, which is one of the few new points that the photographs
have so far revealed.[5]


SERIES XIII.

_Engravings of Instantaneous Photographs (16/17 of the real size) of the
Splash of a Drop of Milk falling 20 cm. on to smoked glass._

[Illustration: 1]

[Illustration: 2

[Tau] = 0 sec.]

[Illustration: 3

[Tau] = ·0025 sec.]

(It was not found possible to reproduce satisfactorily the missing
figures of this series.)

[Illustration: 7

[Tau] = ·0128 sec.]

[Illustration: 8

[Tau] = ·0149 sec.]

[Illustration: 9

[Tau] = ·0149 sec.]


SERIES XIV.

_Engravings of Instantaneous Photographs of the Splash of a Drop of
Water falling 40 cm. into Milk._

Scale about 6/10 of actual size.

[Illustration: 1]

[Illustration: 2]

[Illustration: 3]

[Illustration: 4

[Tau] = 0 sec.]

[Illustration: 5]

[Illustration: 6

[Tau] = ·0056 sec.]

[Illustration: 7

[Tau] = ·0163 sec.]

[Illustration: 8]

[Illustration: 9

[Tau] = ·0182 sec.]

[Illustration: 10

[Tau] = ·0197 sec.]

[Illustration: 11

[Tau] = ·0262 sec.]

[Illustration: 12

[Tau] = ·0391 sec.]

[Illustration: 13

[Tau] = ·0514 sec.]

[Illustration: 14

[Tau] = ·0601 sec.]

[Illustration: 15]

[Illustration: 16

[Tau] = ·080 sec.]

[Illustration: 17]

[Illustration: 18

[Tau] = ·101 sec.]

With respect to these photographs,[6] the credit of which I hope you
will attribute firstly to the inventors of the sensitive plates, and
secondly to the skill and experience of Mr. Cole, I desire to add that
they are, as far as we know, the first really detailed objective views
that have been obtained with anything approaching so short an exposure.

Even Mr. Boys' wonderful photographs of flying bullets were after all
but shadow-photographs, and did not so strikingly illustrate the
extreme sensitiveness of the plates, and I want you to distinguish
between such and what (to borrow Mr. F.J. Smith's phrase) I call an
"objective view."

It remains only to speak of the greater irregularity in the arms and
rays as shown by the photographs. The point is a curious and interesting
one. In the first place I have to confess that in looking over my
original drawings I find records of many irregular or unsymmetrical
figures, yet in compiling the history it has been inevitable that these
should be rejected, if only because identical irregularities never
recur. Thus the mind of the observer is filled with an ideal splash--an
"Auto-Splash"--whose perfection may never be actually realized.

But in the second place, when the splash is nearly regular it is very
difficult to detect irregularity. This is easily proved by projecting
on the screen with instantaneous illumination such a photograph as that
of Series X., Fig. 6. My experience is that most persons pronounce what
they have seen to be a regular and symmetrical star-shaped figure, and
they are surprised when they come to examine it by detail in continuous
light to find how far this is from the truth. Especially is this the
case if no irregularity is suspected beforehand. I believe that the
observer, usually finding himself unable to attend to more than a
portion of the rays in the system, is liable instinctively to pick out
for attention a part of the circumference where they are regularly
spaced, and to fill up the rest in imagination, and that where a ray may
be really absent he prefers to consider that it has been imperfectly
viewed.

This opinion is confirmed by the fact that in several cases, I have
been able to observe with the naked eye a splash that was also
simultaneously photographed, and have made the memorandum "quite
regular," though the photograph subsequently showed irregularity. It
must, however, be observed that the absolute darkness and other
conditions necessary for photography are not very favourable for direct
vision.

And now my tale is told, or rather as much of it as the limits of the
time allowed me will permit. I think you will agree that the phenomena
are very beautiful, and that the subject, commonplace and familiar
though it is, has yet proved worthy of an hour's attention.


THE END.


_Richard Clay & Sons, Limited, London & Bungay._


FOOTNOTES:

[1] See Worthington on the "Spontaneous Segmentation of a Liquid
Annulus," _Proceedings Royal Society_, No. 200, p. 49 (1879).

[2] Readers who wish a more detailed account of a greater variety of
splashes are referred to papers by the author. _Proceedings Royal
Society_, vol. xxv. pp. 261 and 498 (1877); and vol. xxxiv. p. 217
(1882).

[3] Photographs obtained since this was written show that much may
happen after the stages here traced.

[4] A detailed account of the optical, mechanical, and electrical
arrangements employed, written by Mr. Cole, will be found in _Nature_,
vol. i., p. 222 (July 5, 1894).

[5] The black streaks, seen especially in Figs. 11, 15, and 16, are due
to particles of lamp-black carried down by the drop from the surface of
the smoked watch-glass on which it rested.

[6] Three of these photographs, viz. Nos. 11, 12, and 17, are reproduced
full size, as a frontispiece, by a _photographic_ process, to enable the
reader to form a more correct idea than can be gathered from the
engravings, of the amount of detail actually obtained, though even in
these reproductions much is inevitably lost.



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_Some Chief Truths of Religion._

     By the late Rev. EDWARD L. CUTTS, D.D., Author of "St. Cedd's
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_Thoughts for Men and Women._

     THE LORD'S PRAYER. By EMILY C. ORR. Post 8vo. _Limp cloth_, 1_s._


_Thoughts for Working Days._

     Original and Selected. By EMILY C. ORR. Post 8vo. _Limp cloth_,
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_Time Flies; a Reading Diary._

     By the late CHRISTINA G. ROSSETTI. Post 8vo. _Cloth boards_, 3_s._
     6_d._


_Turning Points of English Church History._

     By the late Rev. EDWARD L. CUTTS, D.D. Crown 8vo. _Cloth boards_,
     3_s._ 6_d._


_Turning Points of General Church History._

     By the late Rev. E.L. CUTTS, D.D., Author of "Pastoral Counsels."
     Crown 8vo. _Cloth boards_, 4_s._


_Verses._

     By the late CHRISTINA G. ROSSETTI. Printed on hand-made paper.
     Small Post 8vo. _Cloth_, 3_s._ 6_d._


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