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A STUDY OF SPLASHES
_BY THE SAME AUTHOR._
* * * * *
A FIRST COURSE OF PHYSICAL LABORATORY
PRACTICE.
CONTAINING 264 EXPERIMENTS.
_With Illustrations. Crown 8vo, 4s. 6d._
* * * * *
DYNAMICS OF ROTATION.
AN ELEMENTARY INTRODUCTION TO RIGID DYNAMICS.
_Crown 8vo, 4s. 6d._
* * * * *
LONGMANS, GREEN, AND CO.
LONDON, NEW YORK, BOMBAY, AND CALCUTTA.
[Illustration: Permanent Splashes left where a Projectile has
entered an Armour-plate. [_See page 120._]
A STUDY OF SPLASHES
BY
A. M. WORTHINGTON
C.B., M.A., F.R.S.
HEADMASTER AND PROFESSOR OF PHYSICS
AT
THE ROYAL NAVAL ENGINEERING COLLEGE, DEVONPORT
WITH 197 ILLUSTRATIONS FROM INSTANTANEOUS PHOTOGRAPHS
LONGMANS, GREEN, AND CO.
39 PATERNOSTER ROW, LONDON
NEW YORK, BOMBAY, AND CALCUTTA
1908
_All rights reserved_
DEDICATED
TO
THE NATURAL HISTORY SOCIETY OF RUGBY SCHOOL
AND ITS FORMER PRESIDENT
ARTHUR SIDGWICK
IN REMEMBRANCE OF THE ENCOURAGEMENT
GIVEN TO THE EARLY OBSERVATIONS MADE IN BOYHOOD
BY MY OLD SCHOOL-FRIEND
H. F. NEWALL
FROM WHICH THIS STUDY SPRANG.
PREFACE
This publication is an attempt to present in a form acceptable to the
general reader the outcome of an inquiry conducted by the aid of
instantaneous photography, which was begun about fourteen years ago. The
author, in 1894, had occasion to lecture at the Royal Institution on the
"Splash of a Drop," of which he had already made a somewhat prolonged
study. That lecture, which was subsequently reprinted in the "Romance of
Science" series by the Society for Promoting Christian Knowledge, dealt
largely with the splash of a drop falling on a solid plate, with which
the present volume is not concerned. At the close of the lecture were
exhibited for the first time a few photographs of some of the phenomena
now dealt with, which the author had just succeeded in taking with the
help of his friend Mr. R. S. Cole. The success of the photographs and
the additional information they afforded led to a long photographic
investigation, which formed the subject of two papers[A] in the
_Transactions_ of the Royal Society. Except for two magazine
articles,[B] the results of this work have not been presented to the
general public. Moreover, in the illustrations printed by the Royal
Society much of the beauty of the original photographs was lost in the
reproduction, or was sacrificed in a selection of which the only object
was the elucidation of points of technical scientific interest.
If the present volume is so fortunate as to find many readers among the
general public, as the author hopes it may, especially among the young
whose eyes are still quick to observe, and whose minds are eager, it
will be on account of admiration for the exquisite beauty of some of the
forms assumed, of surprise at the revelation of so much where so little
was expected, and because of the peculiar fascination that is always
felt in following any gradually changing natural phenomenon, in which
the sequence of events can, partly at any rate, be anticipated and
understood.
For the sake of serious students of Physics who may be interested in
unexpected phenomena of fluid motion, all references that seem necessary
have been given in footnotes, and it may be mentioned that the later
photographs of Series I and those of Series I-a and III, have not been
previously published, and afford new information on certain points.
In taking these photographs the author has been much helped by his
friends Dr. G. B. Bryan and Mr. G. F. Page.
A. M. W.
TAVISTOCK, _Sept. 18, 1907_.
[Added _March 1, 1908_.] A slight delay in the publication of this book
has afforded the opportunity of obtaining the new and quite unexpected
information given in the supplementary chapter.
CONTENTS
PAGE
CHAPTER I
PRELIMINARY--METHODS OF OBSERVATION AND APPARATUS 1
CHAPTER II
THE SPLASH OF A DROP--LOW FALL 15
CHAPTER III
PRINCIPLES INVOLVED 32
CHAPTER IV
THE SPLASH CONTINUED 41
CHAPTER V
HIGHER FALLS--BUBBLE-BUILDING 53
CHAPTER VI
BELOW THE SURFACE 69
CHAPTER VII
THE TWO KINDS OF SPLASHES OF SOLID SPHERES 73
CHAPTER VIII
THE TRANSITION FROM THE SMOOTH OR "SHEATH" SPLASH
TO THE ROUGH OR "BASKET" SPLASH 95
CHAPTER IX
THE EXPLANATION OF THE CAUSE OF DIFFERENCE BETWEEN
THE TWO SPLASHES 108
CHAPTER X
CONCLUSION 118
CHAPTER XI
(SUPPLEMENTARY)
A NEW PHENOMENON THAT APPEARS WITH AN INCREASE IN
THE VELOCITY OF ENTRY OF A ROUGH SPHERE 121
FOOTNOTES:
[A] "Impact with a Liquid Surface," by Worthington and Cole. _Phil.
Trans. Roy. Soc._, A 193, 1897, and A 255, 1900.
[B] _Pearson's Magazine_, July and August, 1898.
A STUDY OF SPLASHES
CHAPTER I
PRELIMINARY--METHODS OF OBSERVATION AND APPARATUS
There will be but few of my readers who have not, in some heavy shower
of rain, beguiled the tedium of enforced waiting by watching, perhaps
half-unconsciously, the thousand little crystal fountains that start up
from the surface of pool or river; noting now and then a surrounding
coronet of lesser jets, or here and there a bubble that floats for a
moment and then vanishes.
It is to this apparently insignificant transaction, which always has
been and always will be so familiar, and to others of a like nature,
that I desire to call the attention of those who are interested in
natural phenomena; hoping to share with them some of the delight that I
have myself felt, in contemplating the exquisite forms that the camera
has revealed, and in watching the progress of a multitude of events,
compressed indeed within the limits of a few hundredths of a second, but
none the less orderly and inevitable, and of which the sequence is in
part easy to anticipate and understand, while in part it taxes the
highest mathematical powers to elucidate.
In these modern days of kinematographs and snapshot cameras it might
seem an easy matter to follow, by the aid of photography, even a
splashing drop. But in reality the task is not so simple, for the
changes of form that take place in a splash are far too rapid to come
within reach of any ordinary kinematograph, and even the quickest
photographic shutter is also much too slow, so that it is necessary to
have recourse to the far shorter exposure of a suitable electric spark.
The originals of the photographs which illustrate this book were
taken by means of a spark, whose duration was certainly less than
three-millionths of a second, an interval of time which bears to a whole
second about the same proportion as a day to a thousand years.
In order to obtain the photographs, advantage was taken of the fact that
whatever be the sequence of events in any particular splash, this
sequence will be exactly repeated every time that a falling drop strikes
the surface under exactly the same conditions, and the problem to be
solved was, therefore, as follows:--To cause a drop of definite size to
fall from a definite height in absolute darkness so as to strike the
surface of the liquid into which it falls at a spot towards which is
directed a photographic camera with uncovered lens, and armed with an
exceptionally sensitive plate, and to illuminate the drop at the instant
that it just touches the surface by a flash of such excessively short
duration that no appreciable change of form can take place while the
drop is illuminated.
This gives us a photograph of the earliest stage. The plate must then be
removed and a fresh one substituted; a second drop, of exactly the same
size, must be let fall from exactly the same place, and photographed in
just the same way, but the flash must now be so timed as to take place
at a slightly later stage of the splash, say, one-thousandth of a second
later. The photographic plate must be then again removed and a third
substituted, on which a still later stage is to be depicted, and in this
way the phenomenon can be followed step by step.
By adopting this process, and not attempting to follow the same
individual splash throughout, we avoid two great difficulties: (1) the
necessity of shifting our photographic plate or film through a distance
equal to the breadth of the whole picture every five hundredth or
thousandth of a second (if we wish to obtain pictures of stages so near
together as this); and (2) the difficulty of obtaining brilliant flashes
of light of sufficiently short duration at these very short intervals.
For these we substitute two other difficulties: (1) that of delivering
the drops exactly as required; and (2) that of timing the flash on each
occasion within one or two thousandths of a second, so as to pick out
the exact stage we wish to photograph.
I will now describe how these two problems have been solved.
It is easy enough to arrange for the production of small drops of almost
exactly equal size. They may be allowed to fall one by one at a steady
rate from the end of a fine glass tube connected to a vessel in which
the liquid is maintained at a constant level, as in Fig. 1, or they may
be squeezed out slowly as required by means of a syringe held in a clip
as in Fig. 2. Any required number of these small drops can be caught,
and allowed to run together if a larger drop is to be experimented with.
[Illustration: FIG. 1]
[Illustration: FIG. 2]
If the liquid used is mercury, the drops may be caught in any little
glass cup such as a deeply concave watch-glass; but other liquids, such
as water or milk, would wet the glass and stick to it.
If, however, the inside surface of the watch-glass be first carefully
smoked in the flame of a candle, then even water or milk will roll over
it without sticking, and the drop thus made up will retain a spheroidal
form, and can be conveyed to the place of observation in the dark room,
where it is transferred to the "dropping cup."
This consists of a similar, deep, smoked watch-glass (W)--see Plate
I--supported on the end of a small horizontal lever, a light cylindrical
rod of about the dimensions of an ordinary uncut lead pencil, pivoted
about a horizontal axle near the end to which the watch-glass is
attached. The other end is armed with a small light piece of iron (I)
and is held in position by means of an electro-magnet (M), against the
action of a spring. On cutting off the current from the electro-magnet
the spring, acting as a catapult, tosses up the longer arm of the lever
and thus removes the watch-glass from below the drop (D), which is left
unsupported in mid-air, so that it falls from a definite fixed distance
into a bowl of water placed below it, towards the surface of which the
camera (C) is directed. This solves problem number one. Of course, if we
wish to observe the splash of a solid sphere, there is no need to smoke
the surface of the watch-glass. Indeed, the sphere may be more
conveniently supported on a small ring.
Now for the production and timing of the flash. Two large Leyden jars
(JJ) are provided, and charged by an electrical machine on their inner
coats, one positively and one negatively. Stout wires lead from the
outer coats to the dark room, and terminate in a spark-gap (S) between
magnesium terminals close over the surface of the water in the bowl just
mentioned. If the inner coats are now connected together, the positive
and negative charges unite with a dazzling flash and a simultaneous
discharge and flash takes place between the two outer coats across the
spark-gap in the dark room.
This latter is the illuminating spark; we have now to time it correctly.
For this purpose it is arranged that the discharge shall be effected by
means of a falling metal sphere (T) which I shall call the timing
sphere, which passes between two terminals S and S connected one to the
inside of one jar and one to the inside of the other. These terminals
are just too far apart for a spark to leap across, till the timing
sphere passes between them and thus shortens the gap; then the discharge
takes place, with its accompanying flash in the dark room.
The release of the timing sphere is effected by an arrangement of lever
and spring controlled by an electro-magnet exactly similar to that which
releases the drop in the dark room, and the two electro-magnets _are on
the same electric circuit_, so that the drop and timing sphere _are
released simultaneously_. But while the drop always falls the same
distance, the height through which the timing sphere has to fall before
producing discharge can be adjusted at will, and to great nicety, by
moving its releasing-lever up or down a vertical support with a scale
attached.
If, for example, a particular stage of the splash is photographed when
the timing sphere falls just four feet to the gap, then by raising its
releasing-lever about two-fifths of an inch, the laws of falling bodies
tell us that we shall postpone the flash by just one-thousandth of a
second, and the next photograph will accordingly reveal a stage just so
much later.
[Illustration: PLATE I
Arrangement of apparatus for photographing splashes.
LABORATORY
E is the electrical machine.
J J are the Leyden jars whose inner coats are connected to the
sparking knobs S S.
L is the lever for releasing the timing sphere T.
C is the catapult.
I is the light strip of iron held down by the electro-magnet M.
DARK ROOM
D is the drop resting on the smoked watch-glass W.
M is the electro-magnet holding down the lever against the
action of the catapult, by means of the thin strip of iron
I.
C is the camera directed towards the liquid L into which the
drop will fall.
S is the spark-gap between magnesium terminals connected to the
outer coats of the Leyden jars.
R is the concave mirror.]
It ought still to be mentioned that to make the utmost use of the
illuminating power of the spark, it is necessary to place close behind
it a little concave mirror (R), by means of which a compact beam of
rays, which would otherwise have been wasted, is directed to the
required spot. By this addition we imitate, in miniature, the
search-light of a man-of-war.
* * * * *
As with all experimental devices, the precision attainable with this
arrangement is limited by several circumstances. In the first place, the
demagnetization of the iron cores of the electro-magnets, when the
current is cut off, is not truly instantaneous, and the time required
depends on the strength of the magnetizing current and on the
temperature of the iron, which in turn will depend on the length of time
for which the current has been running. This variation would be of no
importance if the two magnets were exactly alike and the springs of
exactly equal strength, conditions which can be nearly but not perfectly
fulfilled.
[Illustration: PLATE II
Photographs taken to test the accuracy of the "timing."
1 2 3 4 5]
A more important source of uncertainty arises from the fact that the
time at which the spark takes place depends partly on the magnitude of
the + and - charges which have been allowed to accumulate on the
discharging knobs connected to the two Leyden jars, for when these
charges are larger, then the spark will be longer and will take place
earlier and before the timing sphere has reached the mid-position. The
charging has therefore to be carefully watched by means of the
indications of a suitable electrometer, and the timing sphere must on
each occasion be released when the charges have just reached the right
value. But even this does not entirely suffice, for the passage of the
spark depends also partly on the state of the surface of the knobs,
which cannot be kept at any high degree of polish.
Still, when care is taken to keep the conditions as nearly as possible
constant, neither of these sources of error is serious, and the reader
can judge for himself of the accuracy of the timing from the photographs
given on Plate II, in which a solid sphere was let fall in the dark room
past a metre scale. The timing sphere was arranged, in the first four
photographs, to illuminate it at the same stage in its fall, after a
descent of thirty centimetres; if the timing had been perfect the sphere
would appear on each occasion at the same mark on the scale.
It will be observed that in the first, second, and fourth photographs
the falling sphere is almost accurately bisected by the long line of the
three-inch mark on the right-hand edge of the scale. The greatest
difference of position being just about one millimetre (as read off the
left-hand scale), which would correspond to an error of about 1/2700 of
a second. But the third photograph is earlier, showing the sphere 4.5
millimetres higher up, a distance which implies an error of just 1/600
of a second.
A fifth photograph was then taken, with the timing arranged so as to
illuminate the sphere one centimetre higher up, and it will be seen that
if we compare this with No. 3, the error is again only one millimetre.
Thus Nos. 3 and 5 agree very closely, but disagree with Nos. 1, 2, and 4
by about 1/600 of a second.
The photographs themselves supply the reason. For there happens to be
visible on each an (out-of-focus) image of the spark, and this image is
very much the same in 1, 2 and 4, but much larger and brighter in 3 and
5, showing that the knobs were then more highly charged, which would
account for the spark occurring a little too early.
But when we are watching the splash made by the fall of a liquid drop,
instead of a solid sphere, there is a new and more serious source of
difficulty. For the drop as it lies on the smoked glass cup is not
perfectly spherical, but is flattened by its own weight, as shown in
Fig. 3, and on the sudden removal of the supporting cup it oscillates
between an oval form, elongated vertically, and a flattened form (see
Fig. 4). These oscillations are unavoidable, and their extent will
depend partly on the amount of adhesion between the smoked surface and
the drop, and as this adhesion is never entirely absent and is variable,
depending partly on the length of time that the drop has been lying in
the cup, it follows that the drop will always receive a slight tug
downwards at starting, which will be greater on some occasions than on
others. On this account not only will the time taken to reach the water
vary slightly, but the drop will strike it sometimes when elongated and
sometimes when flattened, and the resulting splash will be affected by
this circumstance.
[Illustration: FIG. 3]
[Illustration: FIG. 4]
The four photographs on the next page were taken in succession in order
to afford the reader an opportunity of judging for himself the sort of
accuracy attainable when a liquid drop was concerned.
The fall was 30 centim., and the greatest discrepancy is 4.8
millimetres, corresponding to 1/560 of a second. Thus even here the
error does not amount to two-thousandths of a second.
[Illustration: Photographs taken to test the timing of a falling
drop.
1 2 3 4]
With higher falls the timing sphere is moving more quickly past the
discharging knobs, and the error due to a longer or shorter spark is
correspondingly less, so that it appears safe to say that the accuracy
of the timing was such that, when all precautions were taken, any
desired stage could be picked out within two-thousandths of a second.
It is not however pretended that the precautions necessary for the most
accurate timing were always taken, especially in the earlier Series of
Photographs, for the main object of the experiments was to find out
what happened, and only incidentally to ascertain exactly how long it
took to happen, and there is no doubt that on some occasions, through
the smoke-film being allowed to wear away, adhesions to the dropping cup
occurred, with a corresponding disturbance of the timing, before the
defect was noticed and remedied.
[Illustration: FIG. 5
Photograph of the edge of a rapidly whirling disc.]
It remains to mention, for the sake of those interested in photography,
that notwithstanding the sensitiveness of the plates and the brilliance
of the illuminating spark, its duration was so short that the negatives
were always "under-exposed."[C] I have mentioned that the effective
duration of the spark was less than three-millionths of a second. The
evidence for this is the accompanying photograph (Fig. 5), taken of a
cardboard disc when rotating at a rate of fifty-three turns per second;
the disc was 22 cm. in diameter, and had been roughly graduated round
the edge with pen and ink. The photograph of the part that was in focus
shows no perceptible blurring of the edge of the marks, and with a lens,
a blurring of one-tenth of a millimetre would be easily detectable.
Since the edge was moving at a rate of 36.5 metres per second (about 78
miles per hour), the time taken to traverse one-tenth of a millimetre
would be rather less than three-millionths of a second. Hence we may
conclude that the illumination did not last so long as this.
The weakness of the negatives was met by a prolonged development of
about forty minutes in a saturated solution of eikonogen. This forbade
the use of any artificial light, and all the photographic processes had
to be conducted in absolute darkness. To avoid the tedium of long
waiting in the dark room, a light-tight tray was constructed, in which
several developing dishes could be placed, and the whole brought out
into the daylight and suitably rocked. In this way ten or twelve
photographs could be developed simultaneously.
It may be worth while to mention here that the bright spark given by
breaking the _primary_ circuit of an induction coil at the surface of
mercury was found to be of much too long duration to be useful for the
purposes of splash-photography.
FOOTNOTES:
[C] The plates which I have mostly used have been Thomas's A 1
ordinary.