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SOAP-BUBBLES

AND THE

FORCES WHICH MOULD THEM.

[Illustration: Experiment for showing by intermittent light the
apparently stationary drops into which a fountain is broken up by the
action of a musical sound. (_See_ page 109.)]




SOAP-BUBBLES

AND THE

FORCES WHICH MOULD THEM.

_BEING A COURSE OF THREE LECTURES_

DELIVERED IN THE THEATRE OF THE LONDON
INSTITUTION ON THE AFTERNOONS OF DEC. 30, 1889,
JAN. 1 AND 3, 1890, BEFORE A JUVENILE AUDIENCE.

BY

C. V. BOYS, A.R.S.M., F.R.S.,

ASSISTANT PROFESSOR OF PHYSICS AT THE ROYAL COLLEGE OF SCIENCE, SOUTH
KENSINGTON.

PUBLISHED UNDER THE DIRECTION OF THE GENERAL LITERATURE COMMITTEE.

SOCIETY FOR PROMOTING CHRISTIAN KNOWLEDGE,
LONDON: NORTHUMBERLAND AVENUE, W.C.;
43, QUEEN VICTORIA STREET, E.C.
BRIGHTON: 129, NORTH STREET.
New York: E. & J. B. YOUNG & CO.
1896.


TO

G. F. RODWELL,

THE FIRST

SCIENCE-MASTER APPOINTED AT MARLBOROUGH COLLEGE,

_This Book is Dedicated_

BY THE AUTHOR

AS A TOKEN OF ESTEEM AND GRATITUDE,

AND IN THE HOPE THAT

IT MAY EXCITE IN A FEW YOUNG PEOPLE SOME SMALL

FRACTION OF THE INTEREST AND ENTHUSIASM WHICH

HIS ADVENT AND HIS LECTURES AWAKENED

IN THE AUTHOR, UPON WHOM THE LIGHT

OF SCIENCE THEN SHONE FOR

THE FIRST TIME.




PREFACE.


I would ask those readers who have grown up, and who may be disposed to
find fault with this book, on the ground that in so many points it is
incomplete, or that much is so elementary or well known, to remember
that the lectures were meant for juveniles, and for juveniles only.
These latter I would urge to do their best to repeat the experiments
described. They will find that in many cases no apparatus beyond a few
pieces of glass or india-rubber pipe, or other simple things easily
obtained are required. If they will take this trouble they will find
themselves well repaid, and if instead of being discouraged by a few
failures they will persevere with the best means at their disposal, they
will soon find more to interest them in experiments in which they only
succeed after a little trouble than in those which go all right at
once. Some are so simple that no help can be wanted, while some will
probably be too difficult, even with assistance; but to encourage those
who wish to see for themselves the experiments that I have described, I
have given such hints at the end of the book as I thought would be most
useful.

I have freely made use of the published work of many distinguished men,
among whom I may mention Savart, Plateau, Clerk Maxwell, Sir William
Thomson, Lord Rayleigh, Mr. Chichester Bell, and Prof. Rücker. The
experiments have mostly been described by them, some have been taken
from journals, and I have devised or arranged a few. I am also indebted
to Prof. Rücker for the use of various pieces of apparatus which had
been prepared for his lectures.




SOAP-BUBBLES, AND THE FORCES WHICH MOULD THEM.


I do not suppose that there is any one in this room who has not
occasionally blown a common soap-bubble, and while admiring the
perfection of its form, and the marvellous brilliancy of its colours,
wondered how it is that such a magnificent object can be so easily
produced.

I hope that none of you are yet tired of playing with bubbles, because,
as I hope we shall see during the week, there is more in a common bubble
than those who have only played with them generally imagine.

The wonder and admiration so beautifully portrayed by Millais in a
picture, copies of which, thanks to modern advertising enterprise, some
of you may possibly have seen, will, I hope, in no way fall away in
consequence of these lectures; I think you will find that it will grow
as your knowledge of the subject increases. You may be interested to
hear that we are not the only juveniles who have played with bubbles.
Ages ago children did the same, and though no mention of this is made by
any of the classical authors, we know that they did, because there is an
Etruscan vase in the Louvre in Paris of the greatest antiquity, on which
children are represented blowing bubbles with a pipe. There is however,
no means of telling now whose soap they used.

It is possible that some of you may like to know why I have chosen
soap-bubbles as my subject; if so, I am glad to tell you. Though there
are many subjects which might seem to a beginner to be more wonderful,
more brilliant, or more exciting, there are few which so directly bear
upon the things which we see every day. You cannot pour water from a jug
or tea from a tea-pot; you cannot even do anything with a liquid of any
kind, without setting in action the forces to which I am about to
direct your attention. You cannot then fail to be frequently reminded of
what you will hear and see in this room, and, what is perhaps most
important of all, many of the things I am going to show you are so
simple that you will be able without any apparatus to repeat for
yourselves the experiments which I have prepared, and this you will find
more interesting and instructive than merely listening to me and
watching what I do.

There is one more thing I should like to explain, and that is why I am
going to show experiments at all. You will at once answer because it
would be so dreadfully dull if I didn't. Perhaps it would. But that is
not the only reason. I would remind you then that when we want to find
out anything that we do not know, there are two ways of proceeding. We
may either ask somebody else who does know, or read what the most
learned men have written about it, which is a very good plan if anybody
happens to be able to answer our question; or else we may adopt the
other plan, and by arranging an experiment, try for ourselves. An
experiment is a question which we ask of Nature, who is always ready to
give a correct answer, provided we ask properly, that is, provided we
arrange a proper experiment. An experiment is not a conjuring trick,
something simply to make you wonder, nor is it simply shown because it
is beautiful, or because it serves to relieve the monotony of a lecture;
if any of the experiments I show are beautiful, or do serve to make
these lectures a little less dull, so much the better; but their chief
object is to enable you to see for yourselves what the true answers are
to questions that I shall ask.

[Illustration: Fig. 1.]

Now I shall begin by performing an experiment which you have all
probably tried dozens of times. I have in my hand a common camel's-hair
brush. If you want to make the hairs cling together and come to a point,
you wet it, and then you say the hairs cling together because the brush
is wet. Now let us try the experiment; but as you cannot see this brush
across the room, I hold it in front of the lantern, and you can see it
enlarged upon the screen (Fig. 1, left hand). Now it is dry, and the
hairs are separately visible. I am now dipping it in the water, as you
can see, and on taking it out, the hairs, as we expected, cling
together (Fig. 1, right hand), because they are wet, as we are in the
habit of saying. I shall now hold the brush in the water, but there it
is evident that the hairs do not cling at all (Fig. 1, middle), and yet
they surely are wet now, being actually in the water. It would appear
then that the reason which we always give is not exactly correct. This
experiment, which requires nothing more than a brush and a glass of
water, then shows that the hairs of a brush cling together not only
because they are wet, but for some other reason as well which we do not
yet know. It also shows that a very common belief as to opening our eyes
under water is not founded on fact. It is very commonly said that if you
dive into the water with your eyes shut you cannot see properly when you
open them under water, because the water gums the eyelashes down over
the eyes; and therefore you must dive in with your eyes open if you wish
to see under water. Now as a matter of fact this is not the case at all;
it makes no difference whether your eyes are open or not when you dive
in, you can open them and see just as well either way. In the case of
the brush we have seen that water does not cause the hairs to cling
together or to anything else when under the water, it is only when taken
out that this is the case. This experiment, though it has not explained
why the hairs cling together, has at any rate told us that the reason
always given is not sufficient.

I shall now try another experiment as simple as the last. I have a pipe
from which water is very slowly issuing, but it does not fall away
continuously; a drop forms which slowly grows until it has attained a
certain definite size, and then it suddenly falls away. I want you to
notice that every time this happens the drop is always exactly the same
size and shape. Now this cannot be mere chance; there must be some
reason for the definite size, and shape. Why does the water remain at
all? It is heavy and is ready to fall, but it does not fall; it remains
clinging until it is a certain size, and then it suddenly breaks away,
as if whatever held it was not strong enough to carry a greater weight.
Mr. Worthington has carefully drawn on a magnified scale the exact shape
of a drop of water of different sizes, and these you now see upon the
diagram on the wall (Fig. 2). These diagrams will probably suggest the
idea that the water is hanging suspended in an elastic bag, and that the
bag breaks or is torn away when there is too great a weight for it to
carry. It is true there is no bag at all really, but yet the drops take
a shape which suggests an elastic bag. To show you that this is no
fancy, I have supported by a tripod a large ring of wood over which a
thin sheet of india-rubber has been stretched, and now on allowing water
to pour in from this pipe you will see the rubber slowly stretching
under the increasing weight, and, what I especially want you to notice,
it always assumes a form like those on the diagram. As the weight of
water increases the bag stretches, and now that there is about a pailful
of water in it, it is getting to a state which indicates that it cannot
last much longer; it is like the water-drop just before it falls away,
and now suddenly it changes its shape (Fig. 3), and it would immediately
tear itself away if it were not for the fact that india-rubber does not
stretch indefinitely; after a time it gets tight and will withstand a
greater pull without giving way. You therefore see the great drop now
permanently hanging which is almost exactly the same in shape as the
water-drop at the point of rupture. I shall now let the water run out by
means of a syphon, and then the drop slowly contracts again. Now in this
case we clearly have a heavy liquid in an elastic bag, whereas in the
drop of water we have the same liquid but no bag that is visible. As the
two drops behave in almost exactly the same way, we should naturally be
led to expect that their form and movements are due to the same cause,
and that the small water-drop has something holding it together like the
india-rubber you now see.

[Illustration: Fig. 2.]

[Illustration: Fig. 3.]

Let us see how this fits the first experiment with the brush. That
showed that the hairs do not cling together simply because they are wet;
it is necessary also that the brush should be taken out of the water, or
in other words it is necessary that the surface or the skin of the water
should be present to bind the hairs together. If then we suppose that
the surface of water is like an elastic skin, then both the experiments
with the wet brush and with the water-drop will be explained.

Let us therefore try another experiment to see whether in other ways
water behaves as if it had an elastic skin.

I have here a plain wire frame fixed to a stem with a weight at the
bottom, and a hollow glass globe fastened to it with sealing-wax. The
globe is large enough to make the whole thing float in water with the
frame up in the air. I can of course press it down so that the frame
touches the water. To make the movement of the frame more evident there
is fixed to it a paper flag.

Now if water behaves as if the surface were an elastic skin, then it
should resist the upward passage of the frame which I am now holding
below the surface. I let go, and instead of bobbing up as it would do if
there were no such action, it remains tethered down by this skin of the
water. If I disturb the water so as to let the frame out at one corner,
then, as you see, it dances up immediately (Fig. 4). You can see that
the skin of the water must have been fairly strong, because a weight of
about one quarter of an ounce placed upon the frame is only just
sufficient to make the whole thing sink.

This apparatus which was originally described by Van der Mensbrugghe I
shall make use of again in a few minutes.

[Illustration: Fig. 4.]

I can show you in a more striking way that there is this elastic layer
or skin on pure clean water. I have a small sieve made of wire gauze
sufficiently coarse to allow a common pin to be put through any of the
holes. There are moreover about eleven thousand of these holes in the
bottom of the sieve. Now, as you know, clean wire is wetted by water,
that is, if it is dipped in water it comes out wet; on the other hand,
some materials, such as paraffin wax, of which paraffin candles are
made, are not wetted or really touched by water, as you may see for
yourselves if you will only dip a paraffin candle into water. I have
melted a quantity of paraffin in a dish and dipped this gauze into the
melted paraffin so as to coat the wire all over with it, but I have
shaken it well while hot to knock the paraffin out of the holes. You
can now see on the screen that the holes, all except one or two, are
open, and that a common pin can be passed through readily enough. This
then is the apparatus. Now if water has an elastic skin which it
requires force to stretch, it ought not to run through these holes very
readily; it ought not to be able to get through at all unless forced,
because at each hole the skin would have to be stretched to allow the
water to get to the other side. This you understand is only true if the
water does not wet or really touch the wire. Now to prevent the water
that I am going to pour in from striking the bottom with so much force
as to drive it through, I have laid a small piece of paper in the sieve,
and am pouring the water on to the paper, which breaks the fall (Fig.
5). I have now poured in about half a tumbler of water, and I might put
in more. I take away the paper but not a drop runs through. If I give
the sieve a jolt then the water is driven to the other side, and in a
moment it has all escaped. Perhaps this will remind you of one of the
exploits of our old friend Simple Simon,

    "Who went for water in a sieve,
    But soon it all ran through."

But you see if you only manage the sieve properly, this is not quite so
absurd as people generally suppose.

[Illustration: Fig. 5.]

If now I shake the water off the sieve, I can, for the same reason, set
it to float on water, because its weight is not sufficient to stretch
the skin of the water through all the holes. The water, therefore,
remains on the other side, and it floats even though, as I have already
said, there are eleven thousand holes in the bottom, any one of which is
large enough to allow an ordinary pin to pass through. This experiment
also illustrates how difficult it is to write real and perfect nonsense.

You may remember one of the stories in Lear's book of Nonsense Songs.

    "They went to sea in a sieve, they did,
      In a sieve they went to sea:
    In spite of all their friends could say,
    On a winter's morn, on a stormy day,
      In a sieve they went to sea.

              *    *    *

    "They sailed away in a sieve, they did,
      In a sieve they sailed so fast,
    With only a beautiful pea-green veil,
    Tied with a riband by way of a sail,
      To a small tobacco-pipe mast;"

And so on. You see that it is quite possible to go to sea in a
sieve--that is, if the sieve is large enough and the water is not too
rough--and that the above lines are now realized in every particular
(Fig. 6).

[Illustration: Fig. 6.]

I may give one more example of the power of this elastic skin of water.
If you wish to pour water from a tumbler into a narrow-necked bottle,
you know how if you pour slowly it nearly all runs down the side of the
glass and gets spilled about, whereas if you pour quickly there is no
room for the great quantity of water to pass into the bottle all at
once, and so it gets spilled again. But if you take a piece of stick or
a glass rod, and hold it against the edge of the tumbler, then the water
runs down the rod and into the bottle, and none is lost (Fig. 7); you
may even hold the rod inclined to one side, as I am now doing, but the
water runs down the wet rod because this elastic skin forms a kind of
tube which prevents the water from escaping. This action is often made
use of in the country to carry the water from the gutters under the roof
into a water-butt below. A piece of stick does nearly as well as an iron
pipe, and it does not cost anything like so much.

[Illustration: Fig. 7.]

I think then I have now done enough to show that on the surface of
water there is a kind of elastic skin. I do not mean that there is
anything that is not water on the surface, but that the water while
there acts in a different way to what it does inside, and that it acts
as if it were an elastic skin made of something like very thin
india-rubber, only that it is perfectly and absolutely elastic, which
india-rubber is not.

You will now be in a position to understand how it is that in narrow
tubes water does not find its own level, but behaves in an unexpected
manner. I have placed in front of the lantern a dish of water coloured
blue so that you may the more easily see it. I shall now dip into the
water a very narrow glass pipe, and immediately the water rushes up and
stands about half an inch above the general level. The tube inside is
wet. The elastic skin of the water is therefore attached to the tube,
and goes on pulling up the water until the weight of the water raised
above the general level is equal to the force exerted by the skin. If I
take a tube about twice as big, then this pulling action which is going
on all round the tube will cause it to lift twice the weight of water,
but this will not make the water rise twice as high, because the larger
tube holds so much more water for a given length than the smaller tube.
It will not even pull it up as high as it did in the case of the smaller
tube, because if it were pulled up as high the weight of the water
raised would in that case be four times as great, and not only twice as
great, as you might at first think. It will therefore only raise the
water in the larger tube to half the height, and now that the two tubes
are side by side you see the water in the smaller tube standing twice as
high as it does in the larger tube. In the same way, if I were to take a
tube as fine as a hair the water would go up ever so much higher. It is
for this reason that this is called Capillarity, from the Latin word
_capillus_, a hair, because the action is so marked in a tube the size
of a hair.

[Illustration: Fig. 8.]

Supposing now you had a great number of tubes of all sizes, and placed
them in a row with the smallest on one side and all the others in the
order of their sizes, then it is evident that the water would rise
highest in the smallest tube and less and less high in each tube in the
row (Fig. 8), until when you came to a very large tube you would not be
able to see that the water was raised at all. You can very easily
obtain the same kind of effect by simply taking two square pieces of
window glass and placing them face to face with a common match or small
fragment of anything to keep them a small distance apart along one edge
while they meet together along the opposite edge. An india-rubber ring
stretched over them will hold them in this position. I now take this
pair of plates and stand it in a dish of coloured water, and you at once
see that the water creeps up to the top of the plates on the edge where
they meet, and as the distance between the plates gradually increases,
so the height to which the water rises gradually gets less, and the
result is that the surface of the liquid forms a beautifully regular
curve which is called by mathematicians a rectangular hyperbola (Fig.
9). I shall have presently to say more about this and some other curves,
and so I shall not do more now than state that the hyperbola is formed
because as the width between the plates gets greater the height gets
less, or, what comes to the same thing, because the weight of liquid
pulled up at any small part of the curve is always the same.

[Illustration: Fig. 9.]

If the plates or the tubes had been made of material not wetted by
water, then the effect of the tension of the surface would be to drag
the liquid away from the narrow spaces, and the more so as the spaces
were narrower. As it is not easy to show this well with paraffined glass
plates or tubes and water, I shall use another liquid which does not wet
or touch clean glass, namely, quicksilver. As it is not possible to see
through quicksilver, it will not do to put a narrow tube into this
liquid to show that the level is lower in the tube than in the
surrounding vessel, but the same result may be obtained by having a wide
and a narrow tube joined together. Then, as you see upon the screen, the
quicksilver is lower in the narrow than in the wide tube, whereas in a
similar apparatus the reverse is the case with water (Fig. 10).

[Illustration: Fig. 10.]

I want you now to consider what is happening when two flat plates partly
immersed in water are held close together. We have seen that the water
rises between them. Those parts of these two plates, which have air
between them and also air outside them (indicated by the letter _a_ in
Fig. 11), are each of them pressed equally in opposite directions by the
pressure of the air, and so these parts do not tend to approach or to
recede from one another. These parts again which have water on each side
of each of them (as indicated by the letter _c_) are equally pressed in
opposite directions by the pressure of the water, and so these parts do
not tend to approach or to recede from one another. But those parts of
the plates (_b_) which have water between them and air outside would,
you might think, be pushed apart by the water between them with a
greater force than that which could be exerted by the air outside, and
so you might be led to expect that on this account a pair of plates if
free to move would separate at once. But such an idea though very
natural is wrong, and for this reason. The water that is raised between
the plates being above the general level must be under a less pressure,
because, as every one knows, as you go down in water the pressure
increases, and so as you go up the pressure must get less. The water
then that is raised between the plates is under a less pressure than the
air outside, and so on the whole the plates are pushed together. You can
easily see that this is the case. I have two very light hollow glass
beads such as are used to decorate a Christmas tree. These will float in
water if one end is stopped with sealing-wax. These are both wetted by
water, and so the water between them is slightly raised, for they act in
the same way as the two plates, but not so powerfully. However, you will
have no difficulty in seeing that the moment I leave them alone they
rush together with considerable force. Now if you refer to the second
figure in the diagram, which represents two plates which are neither of
them wetted, I think you will see, without any explanation from me, that
they should be pressed together, and this is made evident by experiment.
Two other beads which have been dipped in paraffin wax so that they are
neither of them wetted by water float up to one another again when
separated as though they attracted each other just as the clean glass
beads did.

[Illustration: Fig. 11.]

If you again consider these two cases, you will see that a plate that is
wetted tends to move towards the higher level of the liquid, whereas one
that is not wetted tends to move towards the lower level, that is if the
level of the liquid on the two sides is made different by capillary
action. Now suppose one plate wetted and the other not wetted, then, as
the diagram imperfectly shows, the level of the liquid between the
plates _where it meets_ the non-wetted plate is higher than that
outside, while where it meets the wetted plate it is lower than that
outside; so each plate tends to go away from the other, as you can see
now that I have one paraffined and one clean ball floating in the same
water. They appear to repel one another.

You may also notice that the surface of the liquid near a wetted plate
is curved, with the hollow of the curve upwards, while near a non-wetted
plate the reverse is the case. That this curvature of the surface is of
the first importance I can show you by a very simple experiment, which
you can repeat at home as easily as the last that I have shown. I have a
clean glass bead floating in water in a clean glass vessel, which is
not quite full. The bead always goes to the side of the vessel. It is
impossible to make it remain in the middle, it always gets to one side
or the other directly. I shall now gradually add water until the level
of the water is rather higher than that of the edge of the vessel. The
surface is then rounded near the vessel, while it is hollow near the
bead, and now the bead sails away towards the centre, and can by no
possibility be made to stop near either side. With a paraffined bead the
reverse is the case, as you would expect. Instead of a paraffined bead
you may use a common needle, which you will find will float on water in
a tumbler, if placed upon it very gently. If the tumbler is not quite
full the needle will always go away from the edge, but if rather
over-filled it will work up to one side, and then possibly roll over the
edge; any bubbles, on the other hand, which were adhering to the glass
before will, the instant that the water is above the edge of the glass,
shoot away from the edge in the most sudden and surprising manner. This
sudden change can be most easily seen by nearly filling the glass with
water, and then gradually dipping in and taking out a cork, which will
cause the level to slowly change.

So far I have given you no idea what force is exerted by this elastic
skin of water. Measurements made with narrow tubes, with drops, and in
other ways, all show that it is almost exactly equal to the weight of
three and a quarter grains to the inch. We have, moreover, not yet seen
whether other liquids act in the same way, and if so whether in other
cases the strength of the elastic skin is the same.

You now see a second tube identical with that from which drops of water
were formed, but in this case the liquid is alcohol. Now that drops are
forming, you see at once that while alcohol makes drops which have a
definite size and shape when they fall away, the alcohol drops are not
by any means so large as the drops of water which are falling by their
side. Two possible reasons might be given to explain this. Either
alcohol is a heavier liquid than water, which would account for the
smaller drop if the skin in each liquid had the same strength, or else
if alcohol is not heavier than water its skin must be weaker than the
skin of water. As a matter of fact alcohol is a lighter liquid than
water, and so still more must the skin of alcohol be weaker than that of
water.

[Illustration: Fig. 12.]

We can easily put this to the test of experiment. In the game that is
called the tug-of-war you know well enough which side is the strongest;
it is the side which pulls the other over the line. Let us then make
alcohol and water play the same game. In order that you may see the
water, it is coloured blue. It is lying as a shallow layer on the bottom
of this white dish. At the present time the skin of the water is pulling
equally in all directions, and so nothing happens; but if I pour a few
drops of alcohol into the middle, then at the line which separates the
alcohol from the water we have alcohol on one side pulling in, while we
have water on the other side pulling out, and you see the result. The
water is victorious; it rushes away in all directions, carrying a
quantity of the alcohol away with it, and leaves the bottom of the dish
dry (Fig. 13).

[Illustration: Fig. 13.]

This difference in the strength of the skin of alcohol and of water, or
of water containing much or little alcohol, gives rise to a curious
motion which you may see on the side of a wine-glass in which there is
some fairly strong wine, such as port. The liquid is observed to climb
up the sides of the glass, then to gather into drops, and to run down
again, and this goes on for a long time. This is explained as
follows:--The thin layer of wine on the side of the glass being exposed
to the air, loses its alcohol by evaporation more quickly than the wine
in the glass. It therefore becomes weaker in alcohol or stronger in
water than that below, and for this reason it has a stronger skin. It
therefore pulls up more wine from below, and this goes on until there is
so much that drops form, and it runs back again into the glass, as you
now see upon the screen (Fig. 14). There can be no doubt that this
movement is referred to in Proverbs xxiii. 31: "Look not thou upon the
wine when it is red, when it giveth his colour in the cup, when it
moveth itself aright."

If you remember that this movement only occurs with strong wine, and
that it must have been known to every one at the time that these words
were written, and used as a test of the strength of wine, because in
those days every one drank wine, then you will agree that this
explanation of the meaning of that verse is the right one. I would ask
you also to consider whether it is not probable that other passages
which do not now seem to convey to us any meaning whatever, may not in
the same way have referred to the common knowledge and customs of the
day, of which at the present time we happen to be ignorant.

[Illustration: Fig. 14.]

Ether, in the same way, has a skin which is weaker than the skin of
water. The very smallest quantity of ether on the surface of water will
produce a perceptible effect. For instance, the wire frame which I left
some time ago is still resting against the water-skin. The buoyancy of
the glass bulb is trying to push it through, but the upward force is
just not sufficient. I will however pour a few drops of ether into a
glass, and simply pour the vapour upon the surface of the water (not a
drop of _liquid_ is passing over), and almost immediately sufficient
ether has condensed upon the water to reduce the strength of the skin to
such an extent that the frame jumps up out of the water.

There is a well-known case in which the difference between the strength
of the skins of two liquids may be either a source of vexation or, if we
know how to make use of it, an advantage. If you spill grease on your
coat you can take it out very well with benzine. Now if you apply
benzine to the grease, and then apply fresh benzine to that already
there, you have this result--there is then greasy benzine on the coat to
which you apply fresh benzine. It so happens that greasy benzine has a
stronger skin than pure benzine. The greasy benzine therefore plays at
tug-of-war with pure benzine, and being stronger wins and runs away in
all directions, and the more you apply benzine the more the greasy
benzine runs away carrying the grease with it. But if you follow the
directions on the bottle, and first make a ring of clean benzine round
the grease-spot, and then apply benzine to the grease, you then have the
greasy benzine running away from the pure benzine ring and heaping
itself together in the middle, and escaping into the fresh rag that you
apply, so that the grease is all of it removed.

There is a difference again between hot and cold grease, as you may see,
when you get home, if you watch a common candle burning. Close to the
flame the grease is hotter than it is near the outside. It has therefore
a weaker skin, and so a perpetual circulation is kept up, and the grease
runs out on the surface and back again below, carrying little specks of
dust which make this movement visible, and making the candle burn
regularly.

You probably know how to take out grease-stains with a hot poker and
blotting-paper. Here again the same kind of action is going on.

A piece of lighted camphor floating in water is another example of
movement set up by differences in the strength of the skin of water
owing to the action of the camphor.

I will give only one more example.

If you are painting in water-colours on greasy paper or certain shiny
surfaces the paint will not lie smoothly on the paper, but runs together
in the well-known way; a very little ox-gall, however, makes it lie
perfectly, because ox-gall so reduces the strength of the skin of water
that it will wet surfaces that pure water will not wet. This reduction
of the surface tension you can see if I use the same wire frame a third
time. The ether has now evaporated, and I can again make it rest against
the surface of the water, but very soon after I touch the water with a
brush containing ox-gall the frame jumps up as suddenly as before.

It is quite unnecessary that I should any further insist upon the fact
that the outside of a liquid acts as if it were a perfectly elastic skin
stretched with a certain definite force.

Suppose now that you take a small quantity of water, say as much as
would go into a nut-shell, and suddenly let it go, what will happen? Of
course it will fall down and be dashed against the ground. Or again,
suppose you take the same quantity of water and lay it carefully upon a
cake of paraffin wax dusted over with lycopodium which it does not wet,
what will happen? Here again the weight of the drop--that which makes it
fall if not held--will squeeze it against the paraffin and make it
spread out into a flat cake. What would happen if the weight of the drop
or the force pulling it downwards could be prevented from acting? In
such a case the drop would only feel the effect of the elastic skin,
which would try to pull it into such a form as to make the surface as
small as possible. It would in fact rapidly become a perfectly round
ball, because in no other way can so small a surface be obtained. If,
instead of taking so much water, we were to take a drop about as large
as a pin's head, then the weight which tends to squeeze it out or make
it fall would be far less, while the skin would be just as strong, and
would in reality have a greater moulding power, though why I cannot now
explain. We should therefore expect that by taking a sufficiently small
quantity of water the moulding power of the skin would ultimately be
able almost entirely to counteract the weight of the drop, so that very
small drops should appear like perfect little balls. If you have found
any difficulty in following this argument, a very simple illustration
will make it clear. Many of you probably know how by folding paper to
make this little thing which I hold in my hand (Fig. 15). It is called a
cat-box, because of its power of dispelling cats when it is filled with
water and well thrown. This one, large enough to hold about half a pint,
is made out of a small piece of the _Times_ newspaper. You may fill it
with water and carry it about and throw it with your full power, and the
strength of the paper skin is sufficient to hold it together until it
hits anything, when of course it bursts and the water comes out. On the
other hand, the large one made out of a whole sheet of the _Times_ is
barely able to withstand the weight of the water that it will hold. It
is only just strong enough to allow of its being filled and carried, and
then it may be dropped from a height, but you cannot throw it. In the
same way the weaker skin of a liquid will not make a large quantity take
the shape of a ball, but it will mould a minute drop so perfectly that
you cannot tell by looking at it that it is not perfectly round every
way. This is most easily seen with quicksilver. A large quantity rolls
about like a flat cake, but the very small drops obtained by throwing
some violently on the table and so breaking it up appear perfectly
round. You can see the same difference in the beads of gold now upon the
screen (Fig. 16). They are now solid, but they were melted and then
allowed to cool without being disturbed. Though the large bead is
flattened by its weight, the small one appears perfectly round. Finally,
you may see the same thing with water if you dust a little lycopodium on
the table. Then water falling will roll itself up into perfect little
balls. You may even see the same thing on a dusty day if you water the
road with a water-pot.

[Illustration: Fig. 15.]

[Illustration: Fig. 16.]

If it were not for the weight of liquids, that is the force with which
they are pulled down towards the earth, large drops would be as
perfectly round as small ones. This was first beautifully shown by
Plateau, the blind experimentalist, who placed one liquid inside another
which is equally heavy, and with which it does not mix. Alcohol is
lighter than oil, while water is heavier, but a suitable mixture of
alcohol and water is just as heavy as oil, and so oil does not either
tend to rise or to fall when immersed in such a mixture. I have in front
of the lantern a glass box containing alcohol and water, and by means of
a tube I shall slowly allow oil to flow in. You see that as I remove the
tube it becomes a perfect ball as large as a walnut. There are now two
or three of these balls of oil all perfectly round. I want you to notice
that when I hit them on one side the large balls recover their shape
slowly, while the small ones become round again much more quickly. There
is a very beautiful effect which can be produced with this apparatus,
and though it is not necessary to refer to it, it is well worth while
now that the apparatus is set up to show it to you. In the middle of the
box there is an axle with a disc upon it to which I can make the oil
adhere. Now if I slowly turn the wire and disc the oil will turn also.
As I gradually increase the speed the oil tends to fly away in all
directions, but the elastic skin retains it. The result is that the ball
becomes flattened at its poles like the earth itself. On increasing the
speed, the tendency of the oil to get away is at last too much for the
elastic skin, and a ring breaks away (Fig. 17), which almost
immediately contracts again on to the rest of the ball as the speed
falls. If I turn it sufficiently fast the ring breaks up into a series
of balls which you now see. One cannot help being reminded of the
heavenly bodies by this beautiful experiment of Plateau's, for you see a
central body and a series of balls of different sizes all travelling
round in the same direction (Fig. 18); but the forces which are acting
in the two cases are totally distinct, and what you see has nothing
whatever to do with the sun and the planets.

[Illustration: Fig. 17.]

[Illustration: Fig. 18.]

We have thus seen that a large ball of liquid can be moulded by the
elasticity of its skin if the disturbing effect of its weight is
neutralized, as in the last experiment. This disturbing effect is
practically of no account in the case of a soap-bubble, because it is so
thin that it hardly weighs anything. You all know, of course, that a
soap-bubble is perfectly round, and now you know why; it is because the
elastic film, trying to become as small as it can, must take the form
which has the smallest surface for its content, and that form is the
sphere. I want you to notice here, as with the oil, that a large bubble
oscillates much more slowly than a small one when knocked out of shape
with a bat covered with baize or wool.

The chief result that I have endeavoured to make clear to-day is this.
The outside of a liquid acts as if it were an elastic skin, which will,
as far as it is able, so mould the liquid within it that it shall be as
small as possible. Generally the weight of liquids, especially when
there is a large quantity, is too much for the feebly elastic skin, and
its power may not be noticed. The disturbing effect of weight is got rid
of by immersing one liquid in another which is equally heavy with which
it does not mix, and it is hardly noticed when very small drops are
examined, or when a bubble is blown, for in these cases the weight is
almost nothing, while the elastic power of the skin is just as great as
ever.




LECTURE II.


I did not in the last lecture by any direct experiment show that a
soap-film or bubble is really elastic, like a piece of stretched
india-rubber.

A soap-bubble consisting, as it does, of a thin layer of liquid, which
must have of course both an inside and an outside surface or skin, must
be elastic, and this is easily shown in many ways. Perhaps the easiest
way is to tie a thread across a ring rather loosely, and then to dip the
ring into soap water. On taking it out there is a film stretched over
the ring, in which the thread moves about quite freely, as you can see
upon the screen. But if I break the film on one side, then immediately
the thread is pulled by the film on the other side as far as it can go,
and it is now tight (Fig. 19). You will also notice that it is part of a
perfect circle, because that form makes the space on one side as great,
and therefore on the other side, where the film is, as small, as
possible. Or again, in this second ring the thread is double for a short
distance in the middle. If I break the film between the threads they are
at once pulled apart, and are pulled into a perfect circle (Fig. 20),
because that is the form which makes the space within it as great as
possible, and therefore leaves the space outside it as small as
possible. You will also notice, that though the circle will not allow
itself to be pulled out of shape, yet it can move about in the ring
quite freely, because such a movement does not make any difference to
the space outside it.

[Illustration: Fig. 19.]

[Illustration: Fig. 20.]

[Illustration: Fig. 21.]

[Illustration: Fig. 22.]

I have now blown a bubble upon a ring of wire. I shall hang a small ring
upon it, and to show more clearly what is happening, I shall blow a
little smoke into the bubble. Now that I have broken the film inside the
lower ring, you will see the smoke being driven out and the ring lifted
up, both of which show the elastic nature of the film. Or again, I have
blown a bubble on the end of a wide pipe; on holding the open end of the
pipe to a candle flame, the outrushing air blows out the flame at once,
which shows that the soap-bubble is acting like an elastic bag (Fig.
21). You now see that, owing to the elastic skin of a soap-bubble, the
air inside is under pressure and will get out if it can. Which would you
think would squeeze the air inside it most, a large or a small bubble?
We will find out by trying, and then see if we can tell why. You now
see two pipes each with a tap. These are joined together by a third pipe
in which there is a third tap. I will first blow one bubble and shut it
off with the tap 1 (Fig. 22), and then the other, and shut it off with
the tap 2. They are now nearly equal in size, but the air cannot yet
pass from one to the other because the tap 3 is turned off. Now if the
pressure in the largest one is greatest it will blow air into the other
when I open this tap, until they are equal in size; if, on the other
hand, the pressure in the small one is greatest, it will blow air into
the large one, and will itself get smaller until it has quite
disappeared. We will now try the experiment. You see immediately that I
open the tap 3 the small bubble shuts up and blows out the large one,
thus showing that there is a greater pressure in a small than in a large
bubble. The directions in which the air and the bubble move is indicated
in the figure by arrows. I want you particularly to notice and remember
this, because this is an experiment on which a great deal depends. To
impress this upon your memory I shall show the same thing in another
way. There is in front of the lantern a little tube shaped like a U half
filled with water. One end of the U is joined to a pipe on which a
bubble can be blown (Fig. 23). You will now be able to see how the
pressure changes as the bubble increases in size, because the water will
be displaced more when the pressure is more, and less when it is less.
Now that there is a very small bubble, the pressure as measured by the
water is about one quarter of an inch on the scale. The bubble is
growing and the pressure indicated by the water in the gauge is
falling, until, when the bubble is double its former size, the pressure
is only half what it was; and this is always true, the smaller the
bubble the greater the pressure. As the film is always stretched with
the same force, whatever size the bubble is, it is clear that the
pressure inside can only depend upon the curvature of a bubble. In the
case of lines, our ordinary language tells us, that the larger a circle
is the less is its curvature; a piece of a small circle is said to be a
quick or a sharp curve, while a piece of a great circle is only slightly
curved; and if you take a piece of a very large circle indeed, then you
cannot tell it from a straight line, and you say it is not curved at
all. With a part of the surface of a ball it is just the same--the
larger the ball the less it is curved; and if the ball is very large
indeed, say 8000 miles across, you cannot tell a small piece of it from
a true plane. Level water is part of such a surface, and you know that
still water in a basin appears perfectly flat, though in a very large
lake or the sea you can see that it is curved. We have seen that in
large bubbles the pressure is little and the curvature is little, while
in small bubbles the pressure is great and the curvature is great. The
pressure and the curvature rise and fall together. We have now learnt
the lesson which the experiment of the two bubbles, one blown out by the
other, teaches us.

[Illustration: Fig. 23.]

[Illustration: Fig. 24.]

A ball or sphere is not the only form which you can give to a
soap-bubble. If you take a bubble between two rings, you can pull it
out until at last it has the shape of a round straight tube or cylinder
as it is called. We have spoken of the curvature of a ball or sphere;
now what is the curvature of a cylinder? Looked at sideways, the edge of
the wooden cylinder upon the table appears straight, _i. e._ not curved
at all; but looked at from above it appears round, and is seen to have a
definite curvature (Fig. 24). What then is the curvature of the surface
of a cylinder? We have seen that the pressure in a bubble depends upon
the curvature when they are spheres, and this is true whatever shape
they have. If, then, we find what sized sphere will produce the same
pressure upon the air inside that a cylinder does, then we shall know
that the curvature of the cylinder is the same as that of the sphere
which balances it. Now at each end of a short tube I shall blow an
ordinary bubble, but I shall pull the lower bubble by means of another
tube into the cylindrical form, and finally blow in more or less air
until the sides of the cylinder are perfectly straight. That is now done
(Fig. 25), and the pressure in the two bubbles must be exactly the same,
as there is a free passage of air between the two. On measuring them you
see that the sphere is exactly double the cylinder in diameter. But
this sphere has only half the curvature that a sphere half its diameter
would have. Therefore the cylinder, which we know has the same curvature
that the large sphere has, because the two balance, has only half the
curvature of a sphere of its own diameter, and the pressure in it is
only half that in a sphere of its own diameter.

[Illustration: Fig. 25.]

I must now make one more step in explaining this question of curvature.
Now that the cylinder and sphere are balanced I shall blow in more air,
making the sphere larger; what will happen to the cylinder? The cylinder
is, as you see, very short; will it become blown out too, or what will
happen? Now that I am blowing in air you see the sphere enlarging, thus
relieving the pressure; the cylinder develops a waist, it is no longer a
cylinder, the sides are curved inwards. As I go on blowing and enlarging
the sphere, they go on falling inwards, but not indefinitely. If I were
to blow the upper bubble till it was of an enormous size the pressure
would become extremely small. Let us make the pressure nothing at all at
once by simply breaking the upper bubble, thus allowing the air a free
passage from the inside to the outside of what was the cylinder. Let me
repeat this experiment on a larger scale. I have two large glass rings,
between which I can draw out a film of the same kind. Not only is the
outline of the soap-film curved inwards, but it is exactly the same as
the smaller one in shape (Fig. 26). As there is now no pressure there
ought to be no curvature, if what I have said is correct. But look at
the soap-film. Who would venture to say that that was not curved? and
yet we had satisfied ourselves that the pressure and the curvature rose
and fell together. We now seem to have come to an absurd conclusion.
Because the pressure is reduced to nothing we say the surface must have
no curvature, and yet a glance is sufficient to show that the film is so
far curved as to have a most elegant waist. Now look at the plaster
model on the table, which is a model of a mathematical figure which also
has a waist.

[Illustration: Fig. 26.]

Let us therefore examine this cast more in detail. I have a disc of card
which has exactly the same diameter as the waist of the cast. I now hold
this edgeways against the waist (Fig. 27), and though you can see that
it does not fit the whole curve, it fits the part close to the waist
perfectly. This then shows that this part of the cast would appear
curved inwards if you looked at it sideways, to the same extent that it
would appear curved outwards if you could see it from above. So
considering the waist only, it is curved both towards the inside and
also away from the inside according to the way you look at it, and to
the same extent. The curvature inwards would make the pressure inside
less, and the curvature outwards would make it more, and as they are
equal they just balance, and there is no pressure at all. If we could in
the same way examine the bubble with the waist, we should find that this
was true not only at the waist but at every part of it. Any curved
surface like this which at every point is equally curved opposite ways,
is called a surface of no curvature, and so what seemed an absurdity is
now explained. Now this surface, which is the only one of the kind
symmetrical about an axis, except a flat surface, is called a catenoid,
because it is like a chain, as you will see directly, and, as you know,
_catena_ is the Latin for a chain. I shall now hang a chain in a loop
from a level stick, and throw a strong light upon it, so that you can
see it well (Fig. 28). This is exactly the same shape as the side of a
bubble drawn out between two rings, and open at the end to the air.[1]

[Illustration: Fig. 27.]

[Illustration: Fig. 28.]

[Footnote 1: If the reader finds these geometrical relations too
difficult to follow, he or she should skip the next pages, and go on
again at "We have found...." p. 77.]

Let us now take two rings, and having placed a bubble between them,
gradually alter the pressure. You can tell what the pressure is by
looking at the part of the film which covers either ring, which I shall
call the cap. This must be part of a sphere, and we know that the
curvature of this and the pressure inside rise and fall together. I have
now adjusted the bubble so that it is a nearly perfect sphere. If I blow
in more air the caps become more curved, showing an increased pressure,
and the sides bulge out even more than those of a sphere (Fig. 29). I
have now brought the whole bubble back to the spherical form. A little
increased pressure, as shown by the increased curvature of the cap,
makes the sides bulge more; a little less pressure, as shown by the
flattening of the caps, makes the sides bulge less. Now the sides are
straight, and the cap, as we have already seen, forms part of a sphere
of twice the diameter of the cylinder. I am still further reducing the
pressure until the caps are plane, that is, not curved at all. There is
now no pressure inside, and therefore the sides have, as we have
already seen, taken the form of a hanging chain; and now, finally, the
pressure inside is less than that outside, as you can see by the caps
being drawn inwards, and the sides have even a smaller waist than the
catenoid. We have now seen seven curves as we gradually reduced the
pressure, namely--

     1. Outside the sphere.

     2. The sphere.

     3. Between the sphere and the cylinder.

     4. The cylinder.

     5. Between the cylinder and the catenoid.

     6. The catenoid.

     7. Inside the catenoid.

[Illustration: Fig. 29.]

Now I am not going to say much more about all these curves, but I must
refer to the very curious properties that they possess. In the first
place, they must all of them have the same curvature in every part as
the portion of the sphere which forms the cap; in the second place, they
must all be the curves of the least possible surface which can enclose
the air and join the rings as well. And finally, since they pass
insensibly from one to the other as the pressure gradually changes,
though they are distinct curves there must be some curious and intimate
relation between them. This though it is a little difficult, I shall
explain. If I were to say that these curves are the roulettes of the
conic sections I suppose I should alarm you, and at the same time
explain nothing, so I shall not put it in that way; but instead, I shall
show you a simple experiment which will throw some light upon the
subject, which you can try for yourselves at home.

[Illustration: Fig. 30.]

I have here a common bedroom candlestick with a flat round base. Hold
the candlestick exactly upright near to a white wall, then you will see
the shadow of the base on the wall below, and the outline of the shadow
is a symmetrical curve, called a hyperbola. Gradually tilt the candle
away from the wall, you will then notice the sides of the shadow
gradually branch away less and less, and when you have so far tilted the
candle away from the wall that the flame is exactly above the edge of
the base,--and you will know when this is the case, because then the
falling grease will just fall on the edge of the candlestick and splash
on to the carpet,--I have it so now,--the sides of the shadow near the
floor will be almost parallel (Fig. 30), and the shape of the shadow
will have become a curve, known as a parabola; and now when the
candlestick is still more tilted, so that the grease misses the base
altogether and falls in a gentle stream upon the carpet, you will see
that the sides of the shadow have curled round and met on the wall, and
you now have a curve like an oval, except that the two ends are alike,
and this is called an ellipse. If you go on tilting the candlestick,
then when the candle is just level, and the grease pouring away, the
shadow will be almost a circle; it would be an exact circle if the flame
did not flare up. Now if you go on tilting the candle, until at last the
candlestick is upside down, the curves already obtained will be
reproduced in the reverse order, but above instead of below you.

You may well ask what all this has to do with a soap-bubble. You will
see in a moment. When you light a candle, the base of the candlestick
throws the space behind it into darkness, and the form of this dark
space, which is everywhere round like the base, and gets larger as you
get further from the flame, is a cone, like the wooden model on the
table. The shadow cast on the wall is of course the part of the wall
which is within this cone. It is the same shape that you would find if
you were to cut a cone through with a saw, and so these curves which I
have shown you are called conic sections. You can see some of them
already made in the wooden model on the table. If you look at the
diagram on the wall (Fig. 31), you will see a complete cone at first
upright (A), then being gradually tilted over into the positions that I
have specified. The black line in the upper part of the diagram shows
where the cone is cut through, and the shaded area below shows the true
shape of these shadows, or pieces cut off, which are called sections.
Now in each of these sections there are either one or two points, each
of which is called a focus, and these are indicated by conspicuous
dots. In the case of the circle (D Fig. 31), this point is also the
centre. Now if this circle is made to roll like a wheel along the
straight line drawn just below it, a pencil at the centre will rule the
straight line which is dotted in the lower part of the figure; but if we
were to make wheels of the shapes of any of the other sections, a pencil
at the focus would certainly not draw a straight line. What shape it
would draw is not at once evident. First consider any of the elliptic
sections (C, E, or F) which you see on either side of the circle. If
these were wheels, and were made to roll, the pencil as it moved along
would also move up and down, and the line it would draw is shown dotted
as before in the lower part of the figure. In the same way the other
curves, if made to roll along a straight line, would cause pencils at
their focal points to draw the other dotted lines.

[Illustration: Fig. 31.]

We are now almost able to see what the conic section has to do with a
soap-bubble. When a soap-bubble was blown between two rings, and the
pressure inside was varied, its outline went through a series of forms,
some of which are represented by the dotted lines in the lower part of
the figure, but in every case they could have been accurately drawn by a
pencil at the focus of a suitable conic section made to roll on a
straight line. I called one of the bubble forms, if you remember, by its
name, catenoid; this is produced when there is no pressure. The dotted
curve in the second figure B is this one; and to show that this catenary
can be so drawn, I shall roll upon a straight edge a board made into the
form of the corresponding section, which is called a parabola, and let
the chalk at its focus draw its curve upon the black board. There is the
curve, and it is as I said, exactly the curve that a chain makes when
hung by its two ends. Now that a chain is so hung you see that it
exactly lies over the chalk line.

All this is rather difficult to understand, but as these forms which a
soap-bubble takes afford a beautiful example of the most important
principle of continuity, I thought it would be a pity to pass it by. It
may be put in this way. A series of bubbles may be blown between a pair
of rings. If the pressures are different the curves must be different.
In blowing them the pressures slowly and _continuously_ change, and so
the curves cannot be altogether different in kind. Though they may be
different curves, they also must pass slowly and continuously one into
the other. We find the bubble curves can be drawn by rolling wheels made
in the shape of the conic sections on a straight line, and so the conic
sections, though distinct curves, must pass slowly and continuously one
into the other. This we saw was the case, because as the candle was
slowly tilted the curves did as a fact slowly and insensibly change from
one to the other. There was only one parabola, and that was formed when
the side of the cone was parallel to the plane of section, that is when
the falling grease just touched the edge of the candlestick; there is
only one bubble with no pressure, the catenoid, and this is drawn by
rolling the parabola. As the cone is gradually inclined more, so the
sections become at first long ellipses, which gradually become more and
more round until a circle is reached, after which they become more and
more narrow until a line is reached. The corresponding bubble curves are
produced by a gradually increasing pressure, and, as the diagram shows,
these bubble curves are at first wavy (C), then they become straight
when a cylinder is formed (D), then they become wavy again (E and F),
and at last, when the cutting plane, _i. e._ the black line in the upper
figure, passes through the vertex of the cone the waves become a series
of semicircles, indicating the ordinary spherical soap-bubble. Now if
the cone is inclined ever so little more a new shape of section is seen
(G), and this being rolled, draws a curious curve with a loop in it; but
how this is so it would take too long to explain. It would also take too
long to trace the further positions of the cone, and to trace the
corresponding sections and bubble curves got by rolling them. Careful
inspection of the diagram may be sufficient to enable you to work out
for yourselves what will happen in all cases. I should explain that the
bubble surfaces are obtained by spinning the dotted lines about the
straight line in the lower part of Fig. 31 as an axis.

As you will soon find out if you try, you cannot make with a soap-bubble
a great length of any of these curves at one time, but you may get
pieces of any of them with no more apparatus than a few wire rings, a
pipe, and a little soap and water. You can even see the whole of one of
the loops of the dotted curve of the first figure (A), which is called a
nodoid, not a complete ring, for that is unstable, but a part of such a
ring. Take a piece of wire or a match, and fasten one end to a piece of
lead, so that it will stand upright in a dish of soap water, and project
half an inch or so. Hold with one hand a sheet of glass resting on the
match in middle, and blow a bubble in the water against the match. As
soon as it touches the glass plate, which should be wetted with the soap
solution, it will become a cylinder, which will meet the glass plate in
a true circle. Now very slowly incline the plate. The bubble will at
once work round to the lowest side, and try to pull itself away from the
match stick, and in doing so it will develop a loop of the nodoid, which
would be exactly true in form if the match or wire were slightly bent,
so as to meet both the glass and the surface of the soap water at a
right angle. I have described this in detail, because it is not
generally known that a complete loop of the nodoid can be made with a
soap-bubble.

[Illustration: Fig. 32.]

[Illustration: Fig. 33.]

We have found that the pressure in a short cylinder gets less if it
begins to develop a waist, and greater if it begins to bulge. Let us
therefore try and balance one with a bulge against another with a waist.
Immediately that I open the tap and let the air pass, the one with a
bulge blows air round to the one with a waist and they both become
straight. In Fig. 32 the direction of the movement of the air and of the
sides of the bubble is indicated by arrows. Let us next try the same
experiment with a pair of rather longer cylinders, say about twice as
long as they are wide. They are now ready, one with a bulge and one with
a waist. Directly I open the tap, and let the air pass from one to the
other, the one with a waist blows out the other still more (Fig. 33),
until at last it has shut itself up. It therefore behaves exactly in the
opposite way that the short cylinder did. If you try pairs of cylinders
of different lengths you will find that the change occurs when they are
just over one and a half times as long as they are wide. Now if you
imagine one of these tubes joined on to the end of the other, you will
see that a cylinder more than about three times as long as it is wide
cannot last more than a moment; because if one end were to contract ever
so little the pressure there would increase, and the narrow end would
blow air into the wider end (Fig. 34), until the sides of the narrow end
met one another. The exact length of the longest cylinder that is
stable, is a little more than three diameters. The cylinder just becomes
unstable when its length is equal to its circumference, and this is
3-1/7 diameters almost exactly.

[Illustration: Fig. 34.]

I will gradually separate these rings, keeping up a supply of air, and
you will see that when the tube gets nearly three times as long as it is
wide it is getting very difficult to manage, and then suddenly it grows
a waist nearer one end than the other, and breaks off forming a pair of
separate and unequal bubbles.

If now you have a cylinder of liquid of great length suddenly formed and
left to itself, it clearly cannot retain that form. It must break up
into a series of drops. Unfortunately the changes go on so quickly in a
falling stream of water that no one by merely looking at it could follow
the movements of the separate drops, but I hope to be able to show to
you in two or three ways exactly what is happening. You may remember
that we were able to make a large drop of one liquid in another, because
in this way the effect of the weight was neutralized, and as large drops
oscillate or change their shape much more slowly than small, it is more
easy to see what is happening. I have in this glass box water coloured
blue on which is floating paraffin, made heavier by mixing with it a
bad-smelling and dangerous liquid called bisulphide of carbon.

[Sidenote: _See Diagram at the end of the Book._

Fig. 35.]

The water is only a very little heavier than the mixture. If I now dip a
pipe into the water and let it fill, I can then raise it and allow drops
to slowly form. Drops as large as a shilling are now forming, and when
each one has reached its full size, a neck forms above it, which is
drawn out by the falling drop into a little cylinder. You will notice
that the liquid of the neck has gathered itself into a little drop which
falls away just after the large drop. The action is now going on so
slowly that you can follow it. Fig. 35 contains forty-three consecutive
views of the growth and fall of the drop taken photographically at
intervals of one-twentieth of a second. For the use to which this figure
is to be put, see page 149. If I again fill the pipe with water, and
this time draw it rapidly out of the liquid, I shall leave behind a
cylinder which will break up into balls, as you can easily see (Fig.
36). I should like now to show you, as I have this apparatus in its
place, that you can blow bubbles of water containing paraffin in the
paraffin mixture, and you will see some which have other bubbles and
drops of one or other liquid inside again. One of these compound bubble
drops is now resting stationary on a heavier layer of liquid, so that
you can see it all the better (Fig. 37). If I rapidly draw the pipe out
of the box I shall leave a long cylindrical bubble of water containing
paraffin, and this, as was the case with the water-cylinder, slowly
breaks up into spherical bubbles.

[Illustration: Fig. 36.]

[Illustration: Fig. 37.]

[Illustration: Fig. 38.]

Having now shown that a very large liquid cylinder breaks up regularly
into drops, I shall next go the other extreme, and take as an example an
excessively fine cylinder. You see a photograph of a spider on her
geometrical web (Fig. 38). If I had time I should like to tell you how
the spider goes to work to make this beautiful structure, and a great
deal about these wonderful creatures, but I must do no more than show
you that there are two kinds of web--those that point outwards, which
are hard and smooth, and those that go round and round, which are very
elastic, and which are covered with beads of a sticky liquid. Now there
are in a good web over a quarter of a million of these beads which catch
the flies for the spider's dinner. A spider makes a whole web in an
hour, and generally has to make a new one every day. She would not be
able to go round and stick all these in place, even if she knew how,
because she would not have time. Instead of this she makes use of the
way that a liquid cylinder breaks up into beads as follows. She spins a
thread, and at the same time wets it with a sticky liquid, which of
course is at first a cylinder. This cannot remain a cylinder, but breaks
up into beads, as the photograph taken with a microscope from a real web
beautifully shows (Fig. 39). You see the alternate large and small
drops, and sometimes you even see extra small drops between these again.
In order that you may see exactly how large these beads really are, I
have placed alongside a scale of thousandths of an inch, which was
photographed at the same time. To prove to you that this is what
happens, I shall now show you a web that I have made myself by stroking
a quartz fibre with a straw dipped in castor-oil. The same alternate
large and small beads are again visible just as perfect as they were in
the spider's web. In fact it is impossible to distinguish between one of
my beaded webs and a spider's by looking at them. And there is this
additional similarity--my webs are just as good as a spider's for
catching flies. You might say that a large cylinder of water in oil, or
a microscopic cylinder on a thread, is not the same as an ordinary jet
of water, and that you would like to see if it behaves as I have
described. The next photograph (Fig. 40), taken by the light of an
instantaneous electric spark, and magnified three and a quarter times,
shows a fine column of water falling from a jet. You will now see that
it is at first a cylinder, that as it goes down necks and bulges begin
to form, and at last beads separate, and you can see the little drops as
well. The beads also vibrate, becoming alternately long and wide, and
there can be no doubt that the sparkling portion of a jet, though it
appears continuous, is really made up of beads which pass so rapidly
before the eye that it is impossible to follow them. (I should explain
that for a reason which will appear later, I made a loud note by
whistling into a key at the time that this photograph was taken.)

[Illustration: Fig. 39.]

[Illustration: Fig. 40.]

Lord Rayleigh has shown that in a stream of water one twenty-fifth of an
inch in diameter, necks impressed upon the stream, even though
imperceptible, develop a thousandfold in depth every fortieth of a
second, and thus it is not difficult to understand that in such a stream
the water is already broken through before it has fallen many inches. He
has also shown that free water drops vibrate at a rate which may be
found as follows. A drop two inches in diameter makes one complete
vibration in one second. If the diameter is reduced to one quarter of
its amount, the time of vibration will be reduced to one-eighth, or if
the diameter is reduced to one-hundredth, the time will be reduced to
one-thousandth, and so on. The same relation between the diameter and
the time of breaking up applies also to cylinders. We can at once see
how fast a bead of water the size of one of those in the spider's web
would vibrate if pulled out of shape, and let go suddenly. If we take
the diameter as being one eight-hundredth of an inch, and it is really
even finer, then the bead would have a diameter of one sixteen-hundredth
of a two-inch bead, which makes one vibration in one second. It will
therefore vibrate sixty-four thousand times as fast, or sixty-four
thousand times a second. Water-drops the size of the little beads, with
a diameter of rather less than one three-thousandth of an inch, would
vibrate half a million times a second, under the sole influence of the
feebly elastic skin of water! We thus see how powerful is the influence
of the feebly elastic water-skin on drops of water that are sufficiently
small.

I shall now cause a small fountain to play, and shall allow the water as
it falls to patter upon a sheet of paper. You can see both the fountain
itself and its shadow upon the screen. You will notice that the water
comes out of the nozzle as a smooth cylinder, that it presently begins
to glitter, and that the separate drops scatter over a great space (Fig.
41). Now why should the drops scatter? All the water comes out of the
jet at the same rate and starts in the same direction, and yet after a
short way the separate drops by no means follow the same paths. Now
instead of explaining this, and then showing experiments to test the
truth of the explanation, I shall reverse the usual order, and show one
or two experiments first, which I think you will all agree are so like
magic, so wonderful are they and yet so simple, that if they had been
performed a few hundred years ago, the rash person who showed them might
have run a serious risk of being burnt alive.

[Illustration: Fig. 41.]

[Illustration: Fig. 42.]

You now see the water of the jet scattering in all directions, and you
hear it making a pattering sound on the paper on which it falls. I take
out of my pocket a stick of sealing-wax and instantly all is changed,
even though I am some way off and can touch nothing. The water ceases
to scatter; it travels in one continuous line (Fig. 42), and falls upon
the paper making a loud rattling noise which must remind you of the rain
of a thunder-storm. I come a little nearer to the fountain and the water
scatters again, but this time in quite a different way. The falling
drops are much larger than they were before. Directly I hide the
sealing-wax the jet of water recovers its old appearance, and as soon
as the sealing-wax is taken out it travels in a single line again.

Now instead of the sealing-wax I shall take a smoky flame easily made by
dipping some cotton-wool on the end of a stick into benzine, and
lighting it. As long as the flame is held away from the fountain it
produces no effect, but the instant that I bring it near so that the
water passes through the flame, the fountain ceases to scatter; it all
runs in one line and falls in a dirty black stream upon the paper. Ever
so little oil fed into the jet from a tube as fine as a hair does
exactly the same thing.

[Illustration: Fig. 43.]

I shall now set a tuning-fork sounding at the other side of the table.
The fountain has not altered in appearance. I now touch the stand of the
tuning-fork with a long stick which rests against the nozzle. Again the
water gathers itself together even more perfectly than before, and the
paper upon which it falls is humming out a note which is the same as
that produced by the tuning-fork. If I alter the rate at which the water
flows you will see that the appearance is changed again, but it is never
like a jet which is not acted upon by a musical sound. Sometimes the
fountain breaks up into two or three and sometimes many more distinct
lines, as though it came out of as many tubes of different sizes and
pointing in slightly different directions (Fig. 43). The effect of
different notes could be very easily shown if any one were to sing to
the piece of wood by which the jet is held. I can make noises of
different pitches, which for this purpose are perhaps better than
musical notes, and you can see that with every new noise the fountain
puts on a different appearance. You may well wonder how these trifling
influences--sealing-wax, the smoky flame, or the more or less musical
noise--should produce this mysterious result, but the explanation is not
so difficult as you might expect.

I hope to make this clear when we meet again.




LECTURE III.


At the conclusion of the last lecture I showed you some curious
experiments with a fountain of water, which I have now to explain.
Consider what I have said about a liquid cylinder. If it is a little
more than three times as long as it is wide, it cannot retain its form;
if it is made very much more than three times as long, it will break up
into a series of beads. Now, if in any way a series of necks could be
developed upon a cylinder which were less than three diameters apart,
some of them would tend to heal up, because a piece of a cylinder less
than three diameters long is stable. If they were about three diameters
apart, the form being then unstable, the necks would get more pronounced
in time, and would at last break through, so that beads would be formed.
If necks were made at distances more than three diameters apart, then
the cylinder would go on breaking up by the narrowing of these necks,
and it would most easily break up into drops when the necks were just
four and a half diameters apart. In other words, if a fountain were to
issue from a nozzle held perfectly still, the water would most easily
break into beads at the distance of four and a half diameters apart, but
it would break up into a greater number closer together, or a smaller
number further apart, if by slight disturbances of the jet very slight
waists were impressed upon the issuing cylinder of water. When you make
a fountain play from a jet which you hold as still as possible, there
are still accidental tremors of all kinds, which impress upon the
issuing cylinder slightly narrow and wide places at irregular distances,
and so the cylinder breaks up irregularly into drops of different sizes
and at different distances apart. Now these drops, as they are in the
act of separating from one another, and are drawing out the waist, as
you have seen, are being pulled for the moment towards one another by
the elasticity of the skin of the waist; and, as they are free in the
air to move as they will, this will cause the hinder one to hurry on,
and the more forward one to lag behind, so that unless they are all
exactly alike both in size and distance apart they will many of them
bounce together before long. You would expect when they hit one another
afterwards that they would join, but I shall be able to show you in a
moment that they do not; they act like two india-rubber balls, and
bounce away again. Now it is not difficult to see that if you have a
series of drops of different sizes and at irregular distances bouncing
against one another frequently, they will tend to separate and to fall,
as we have seen, on all parts of the paper down below. What did the
sealing-wax or the smoky flame do? and what can the musical sound do to
stop this from happening? Let me first take the sealing-wax. A piece of
sealing-wax rubbed on your coat is electrified, and will attract light
bits of paper up to it. The sealing-wax acts electrically on the
different water-drops, causing them to attract one another, feebly, it
is true, but with sufficient power where they meet to make them break
through the air-film between them and join. To show that this is no
fancy, I have now in front of the lantern two fountains of clean water
coming from separate bottles, and you can see that they bounce apart
perfectly (Fig. 44). To show that they do really bounce, I have coloured
the water in the two bottles differently. The sealing-wax is now in my
pocket; I shall retire to the other side of the room, and the instant it
appears the jets of water coalesce (Fig. 45). This may be repeated as
often as you like, and it never fails. These two bouncing jets are in
fact one of the most delicate tests for the presence of electricity that
exist. You are now able to understand the first experiment. The
separate drops which bounced away from one another, and scattered in all
directions, are unable to bounce when the sealing-wax is held up,
because of its electrical action. They therefore unite, and the result
is, that instead of a great number of little drops falling all over the
paper, the stream pours in a single line, and great drops, such as you
see in a thunder-storm, fall on the top of one another. There can be no
doubt that it is for this reason that the drops of rain in a
thunder-storm are so large. This experiment and its explanation are due
to Lord Rayleigh.

[Illustration: Fig. 44.]

[Illustration: Fig. 45.]

The smoky flame, as lately shown by Mr. Bidwell, does the same thing.
The reason probably is that the dirt breaks through the air-film, just
as dust in the air will make the two fountains join as they did when
they were electrified. However, it is possible that oily matter
condensed on the water may have something to do with the effect
observed, because oil alone acts quite as well as a flame, but the
action of oil in this case, as when it smooths a stormy sea, is not by
any means so easily understood.

When I held the sealing-wax closer, the drops coalesced in the same way;
but they were then so much more electrified that they repelled one
another as similarly electrified bodies are known to do, and so the
electrical scattering was produced.

You possibly already see why the tuning-fork made the drops follow in
one line, but I shall explain. A musical note is, as is well known,
caused by a rapid vibration; the more rapid the vibration the higher is
the pitch of the note. For instance, I have a tooth-wheel which I can
turn round very rapidly if I wish. Now that it is turning slowly you can
hear the separate teeth knocking against a card that I am holding in the
other hand. I am now turning faster, and the card is giving out a note
of a low pitch. As I make the wheel turn faster and faster, the pitch of
the note gradually rises, and it would, if I could only turn fast
enough, give so high a note that we should not be able to hear it. A
tuning-fork vibrates at a certain definite rate, and therefore gives a
definite note. The fork now sounding vibrates 128 times in every second.
The nozzle, therefore, is made to vibrate, but almost imperceptibly, 128
times a second, and to impress upon the issuing cylinder of water 128
imperceptible waists every second. Now it just depends what size the jet
is, and how fast the water is issuing, whether these waists are about
four and a half diameters apart in the cylinder. If the jet is larger,
the water must pass more quickly, or under a greater pressure, for this
to be the case; if the jet is finer, a smaller speed will be sufficient.
If it should happen that the waists so made are anywhere about four
diameters apart, then even though they are so slightly developed that
if you had an exact drawing of them, you would not be able to detect the
slightest change of diameter, they will grow at a great speed, and
therefore the water column will break up regularly, every drop will be
like the one behind it, and like the one in front of it, and not all
different, as is the case when the breaking of the water merely depends
upon accidental tremors. If the drops then are all alike in every
respect, of course they all follow the same path, and so appear to fall
in a continuous stream. If the waists are about four and a half
diameters apart, then the jet will break up most easily; but it will, as
I have said, break up under the influence of a considerable range of
notes, which cause the waists to be formed at other distances, provided
they are more than three diameters apart. If two notes are sounded at
the same time, then very often each will produce its own effect, and the
result is the alternate formation of drops of different sizes, which
then make the jet divide into two separate streams. In this way, three,
four, or even many more distinct streams may be produced.

[Illustration: Fig. 46.]

I can now show you photographs of some of these musical fountains, taken
by the instantaneous flash of an electric spark, and you can see the
separate paths described by the drops of different sizes (Fig. 46). In
one photograph there are eight distinct fountains all breaking from the
same jet, but following quite distinct paths, each of which is clearly
marked out by a perfectly regular series of drops. You can also in these
photographs see drops actually in the act of bouncing against one
another, and flattened when they meet, as if they were india-rubber
balls. In the photograph now upon the screen the effect of this rebound,
which occurs at the place marked with a cross, is to hurry on the upper
and more forward drop, and to retard the other one, and so to make them
travel with slightly different velocities and directions. It is for this
reason that they afterwards follow distinct paths. The smaller drops had
no doubt been acted on in a similar way, but the part of the fountain
where this happened was just outside the photographic plate, and so
there is no record of what occurred. The very little drops of which I
have so often spoken are generally thrown out from the side of a
fountain of water under the influence of a musical sound, after which
they describe regular little curves of their own, quite distinct from
the main stream. They, of course, can only get out sideways after one or
two bouncings from the regular drops in front and behind. You can easily
show that they are really formed below the place where they first
appear, by taking a piece of electrified sealing-wax and holding it near
the stream close to the nozzle and gradually raising it. When it comes
opposite to the place where the little drops are really formed, it will
act on them more powerfully than on the large drops, and immediately
pull them out from a place where the moment before none seemed to exist.
They will then circulate in perfect little orbits round the sealing-wax,
just as the planets do round the sun; but in this case, being met by the
resistance of the air, the orbits are spirals, and the little drops
after many revolutions ultimately fall upon the wax, just as the planets
would fall into the sun after many revolutions, if their motion through
space were interfered with by friction of any kind.

There is only one thing needed to make the demonstration of the
behaviour of a musical jet complete, and that is, that you should
yourselves see these drops in their different positions in an actual
fountain of water. Now if I were to produce a powerful electric spark,
then it is true that some of you might for an instant catch sight of the
drops, but I do not think that most would see anything at all. But if,
instead of making merely one flash, I were to make another when each
drop had just travelled to the position which the one in front of it
occupied before, and then another when each drop had moved on one place
again, and so on, then all the drops, at the moments that the flashes of
light fell upon them, would occupy the same positions, and thus all
these drops would appear fixed in the air, though of course they really
are travelling fast enough. If, however, I do not quite succeed in
keeping exact time with my flashes of light, then a curious appearance
will be produced. Suppose, for instance, that the flashes of light
follow one another rather too quickly, then each drop will not have had
quite time enough to get to its proper place at each flash, and thus at
the second flash all the drops will be seen in positions which are just
behind those which they occupied at the first flash, and in the same
way at the third flash they will be seen still further behind their
former places, and so on, and therefore they will appear to be moving
slowly backwards; whereas if my flashes do not follow quite quickly
enough, then the drops will, every time that there is a flash, have
travelled just a little too far, and so they will all appear to be
moving slowly forwards. Now let us try the experiment. There is the
electric lantern sending a powerful beam of light on to the screen. This
I bring to a focus with a lens, and then let it pass through a small
hole in a piece of card. The light then spreads out and falls upon the
screen. The fountain of water is between the card and the screen, and so
a shadow is cast which is conspicuous enough. Now I place just behind
the card a little electric motor, which will make a disc of card which
has six holes near the edge spin round very fast. The holes come one
after the other opposite the hole in the fixed card, and so at every
turn six flashes of light are produced. When the card is turning about
21-1/2 times a second, then the flashes will follow one another at the
right rate. I have now started the motor, and after a moment or two I
shall have obtained the right speed, and this I know by blowing through
the holes, when a musical note will be produced, higher than the fork if
the speed is too high, and lower than the fork if the speed is too low,
and exactly the same as the fork if it is right.

To make it still more evident when the speed is exactly right, I have
placed the tuning-fork also between the light and the screen, so that
you may see it illuminated, and its shadow upon the screen. I have not
yet allowed the water to flow, but I want you to look at the fork. For a
moment I have stopped the motor, so that the light may be steady, and
you can see that the fork is in motion because its legs appear blurred
at the ends, where of course the motion is most rapid. Now the motor is
started, and almost at once the fork appears quite different. It now
looks like a piece of india-rubber, slowly opening and shutting, and now
it appears quite still, but the noise it is making shows that it is not
still by any means. The legs of the fork are vibrating, but the light
only falls upon them at regular intervals, which correspond with their
movement, and so, as I explained in the case of the water-drops, the
fork appears perfectly still. Now the speed is slightly altered, and, as
I have explained, each new flash of light, coming just too soon or just
too late, shows the fork in a position which is just before or just
behind that made visible by the previous flash. You thus see the fork
slowly going through its evolutions, though of course in reality the
legs are moving backwards and forwards 128 times a second. By looking at
the fork or its shadow, you will therefore be able to tell whether the
light is keeping exact time with the vibrations, and therefore with the
water-drops.

Now the water is running, and you see all the separate drops apparently
stationary, strung like pearls or beads of silver upon an invisible wire
(_see_ Frontispiece). If I make the card turn ever so little more
slowly, then all the drops will appear to slowly march onwards, and what
is so beautiful,--but I am afraid few will see this,--each little drop
may be seen to gradually break off, pulling out a waist which becomes a
little drop, and then when the main drop is free it slowly oscillates,
becoming wide and long, or turning over and over, as it goes on its way.
If it so happens that a double or multiple jet is being produced, then
you can see the little drops moving up to one another, squeezing each
other where they meet and bouncing away again. Now the card is turning a
little too fast and the drops appear to be moving backwards, so that it
seems as if the water is coming up out of the tank on the floor, quietly
going over my head, down into the nozzle, and so back to the
water-supply of the place. Of course this is not happening at all, as
you know very well, and as you will see if I simply try and place my
finger between two of these drops. The splashing of the water in all
directions shows that it is not moving quite so quietly as it appears.
There is one more thing that I would mention about this experiment.
Every time that the flashing light gains or loses one complete flash,
upon the motion of the tuning-fork, it will appear to make one complete
oscillation, and the water-drops will appear to move back or on one
place.

I must now come to one of the most beautiful applications of these
musical jets to practical purposes which it is possible to imagine, and
what I shall now show are a few out of a great number of the experiments
of Mr. Chichester Bell, cousin of Mr. Graham Bell, the inventor of the
telephone.

To begin with I have a very small jet of water forced through the nozzle
at a great pressure, as you can see if I point it towards the ceiling,
as the water rises eight or ten feet. If I allow this stream of water to
fall upon an india-rubber sheet, stretched over the end of a tube as big
as my little finger, then the little sheet will be depressed by the
water, and the more so if the stream is strong. Now if I hold the jet
close to the sheet the smooth column of liquid will press the sheet
steadily, and it will remain quiet; but if I gradually take the jet
further away from the sheet, then any waists that may have been formed
in the liquid column, which grow as they travel, will make their
existence perfectly evident. When a wide part of the column strikes the
sheet it will be depressed rather more than usual, and when a narrow
part follows, the depression will be less. In other words, any very
slight vibration imparted to the jet will be magnified by the growth of
waists, and the sheet of india-rubber will reproduce the vibration, but
on a magnified scale. Now if you remember that sound consists of
vibrations, then you will understand that a jet is a machine for
magnifying sound. To show that this is the case I am now directing the
jet on to the sheet, and you can hear nothing; but I shall hold a piece
of wood against the nozzle, and now, if on the whole the jet tends to
break up at any one rate rather than at any other, or if the wood or the
sheet of rubber will vibrate at any rate most easily, then the first few
vibrations which correspond to this rate will be imparted to the wood,
which will impress them upon the nozzle and so upon the cylinder of
liquid, where they will become magnified; the result is that the jet
immediately begins to sing of its own accord, giving out a loud note
(Fig. 47).

I will now remove the piece of wood. On placing against the nozzle an
ordinary lever watch, the jolt which is imparted to the case at every
tick, though it is so small that you cannot detect it, jolts the nozzle
also, and thus causes a neck to form in the jet of water which will grow
as it travels, and so produce a loud tick, audible in every part of
this large room (Fig. 48). Now I want you to notice how the vibration is
magnified by the action I have described. I now hold the nozzle close to
the rubber sheet, and you can hear nothing. As I gradually raise it a
faint echo is produced, which gradually gets louder and louder, until at
last it is more like a hammer striking an anvil than the tick of a
watch.

[Illustration: Fig. 47.]

[Illustration: Fig. 48.]

I shall now change this watch for another which, thanks to a friend, I
am able to use. This watch is a repeater, that is, if you press upon a
nob it will strike, first the hour, then the quarters, and then the
minutes. I think the water-jet will enable you all to hear what time it
is. Listen! one, two, three, four;... ting-tang, ting-tang;... one, two,
three, four, five, six. Six minutes after half-past four. You notice
that not only did you hear the number of strokes, but the jet faithfully
reproduced the musical notes, so that you could distinguish one note
from the others.

I can in the same way make the jet play a tune by simply making the
nozzle rest against a long stick, which is pressed upon a musical-box.
The musical-box is carefully shut up in a double box of thick felt, and
you can hardly hear anything; but the moment that the nozzle is made to
rest against the stick and the water is directed upon the india-rubber
sheet, the sound of the box is loudly heard, I hope, in every part of
the room. It is usual to describe a fountain as playing, but it is now
evident that a fountain can even play a tune. There is, however, one
peculiarity which is perfectly evident. The jet breaks up at certain
rates more easily than at others, or, in other words, it will respond to
certain sounds in preference to others. You can hear that as the
musical-box plays, certain notes are emphasized in a curious way,
producing much the same effect that follows if you lay a penny upon the
upper strings of a horizontal piano.

[Illustration: Fig. 49.]

Now, on returning to our soap-bubbles, you may remember that I stated
that the catenoid and the plane were the only figures of revolution
which had no curvature, and which therefore produced no pressure. There
are plenty of other surfaces which are apparently curved in all
directions and yet have no curvature, and which therefore produce no
pressure; but these are not figures of revolution, that is, they cannot
be obtained by simply spinning a curved line about an axis. These may be
produced in any quantity by making wire frames of various shapes and
dipping them in soap and water. On taking them out a wonderful variety
of surfaces of no curvature will be seen. One such surface is that known
as the screw-surface. To produce this it is only necessary to take a
piece of wire wound a few times in an open helix (commonly called
spiral), and to bend the two ends so as to meet a second wire passing
down the centre. The screw-surface developed by dipping this frame in
soap-water is well worth seeing (Fig. 49). It is impossible to give any
idea of the perfection of the form in a figure, but fortunately this is
an experiment which any one can easily perform.

[Illustration: Fig. 50.]

Then again, if a wire frame is made in the shape of the edges of any of
the regular geometrical solids, very beautiful figures will be found
upon them after they have been dipped in soap-water. In the case of the
triangular prism these surfaces are all flat, and at the edges where
these planes meet one another there are always three meeting each other
at equal angles (Fig. 50). This, owing to the fact that the frame is
three-sided, is not surprising. After looking at this three-sided frame
with three films meeting down the central line, you might expect that
with a four-sided or square frame there would be four films meeting each
other in a line down the middle. But it is a curious thing that it does
not matter how irregular the frame may be, or how complicated a mass of
froth may be, there can never be more than three films meeting in an
edge, or more than four edges, or six films, meeting in a point.
Moreover the films and edges can only meet one another at equal angles.
If for a moment by any accident four films do meet in the same edge, or
if the angles are not exactly equal, then the form, whatever it may be,
is unstable; it cannot last, but the films slide over one another and
never rest until they have settled down into a position in which the
conditions of stability are fulfilled. This may be illustrated by a very
simple experiment which you can easily try at home, and which you can
now see projected upon the screen. There are two pieces of window-glass
about half an inch apart, which form the sides of a sort of box into
which some soap and water have been poured. On blowing through a pipe
which is immersed in the water, a great number of bubbles are formed
between the plates. If the bubbles are all large enough to reach across
from one plate to the other, you will at once see that there are nowhere
more than three films meeting one another, and where they meet the
angles are all equal. The curvature of the bubbles makes it difficult to
see at first that the angles really are all alike, but if you only look
at a very short piece close to where they meet, and so avoid being
bewildered by the curvature, you will see that what I have said is true.
You will also see, if you are quick, that when the bubbles are blown,
sometimes four for a moment do meet, but that then the films at once
slide over one another and settle down into their only possible position
of rest (Fig. 51).

The air inside a bubble is generally under pressure, which is produced
by its elasticity and curvature. If the bubble would let the air pass
through it from one side to the other of course it would soon shut up,
as it did when a ring was hung upon one, and the film within the ring
was broken. But there are no holes in a bubble, and so you would expect
that a gas like air could not pass through to the other side.
Nevertheless it is a fact that gases can slowly get through to the other
side, and in the case of certain vapours the process is far more rapid
than any one would think possible.

[Illustration: Fig. 51.]

[Illustration: Fig. 52.]

Ether produces a vapour which is very heavy, and which also burns very
easily. This vapour can get to the other side of a bubble almost at
once. I shall pour a little ether upon blotting-paper in this bell jar,
and fill the jar with its heavy vapour. You can see that the jar is
filled with something, not by looking at it, for it appears empty, but
by looking at its shadow on the screen. Now I tilt it gently to one
side, and you see something pouring out of it, which is the vapour of
ether. It is easy to show that this is heavy; it is only necessary to
drop into the jar a bubble, and so soon as the bubble meets the heavy
vapour it stops falling and remains floating upon the surface as a cork
does upon water (Fig. 52). Now let me test the bubble and see whether
any of the vapour has passed to the inside. I pick it up out of the jar
with a wire ring and carry it to a light, and at once there is a burst
of flame. But this is not sufficient to show that the ether vapour has
passed to the inside, because it might have condensed in sufficient
quantity upon the bubble to make it inflammable. You remember that when
I poured some of this vapour upon water in the first lecture, sufficient
condensed to so weaken the water-skin that the frame of wire could get
through to the other side. However, I can see whether this is the true
explanation or not by blowing a bubble on a wide pipe, and holding it in
the vapour for a moment. Now on removing it you notice that the bubble
hangs like a heavy drop; it has lost the perfect roundness that it had
at first, and this looks as if the vapour had found its way in, but this
is made certain by bringing a light to the mouth of the tube, when the
vapour, forced out by the elasticity of the bubble, catches fire and
burns with a flame five or six inches long (Fig. 53). You might also
have noticed that when the bubble was removed, the vapour inside it
began to pass out again and fell away in a heavy stream, but this you
could only see by looking at the shadow upon the screen.

[Illustration: Fig. 53]

You may have noticed when I made the drops of oil in the mixture of
alcohol and water, that when they were brought together they did not at
once unite; they pressed against one another and pushed each other away
if allowed, just as the water-drops did in the fountain of which I
showed you a photograph. You also may have noticed that the drops of
water in the paraffin mixture bounced against one another, or if filled
with the paraffin, formed bubbles in which often other small drops, both
of water and paraffin, remained floating.

In all these cases there was a thin film of something between the drops
which they were unable to squeeze out, namely, water, paraffin, or air,
as the case might be. Will two soap-bubbles also when knocked together
be unable to squeeze out the air between them? This you can try at home
just as well as I can here, but I will perform the experiment at once. I
have blown a pair of bubbles, and now when I hit them together they
remain distinct and separate (Fig. 54).

[Illustration: Fig. 54.]

I shall next place a bubble on a ring, which it is just too large to get
through. In my hand I hold a ring, on which I have a flat film, made by
placing a bubble upon it and breaking it on one side. If I gently press
the bubble with the flat film, I can push it through the ring to the
other side (Fig. 55), and yet the two have not really touched one
another at all. The bubble can be pushed backwards and forwards in this
way many times.

[Illustration: Fig. 55.]

I have now blown a bubble and hung it below a ring. To this bubble I can
hang another ring of thin wire, which pulls it a little out of shape.
Since the pressure inside is less than that corresponding to a complete
sphere, and since it is greater than that outside, and this we can tell
by looking at the caps, the curve is part of one of those represented by
the dotted lines in C or E, Fig. 31. However, without considering the
curve any more, I shall push the end of the pipe inside, and blow
another bubble there, and let it go. It falls gently until it rests
upon the outer bubble; not at the bottom, because the heavy ring keeps
that part out of reach, but along a circular line higher up (Fig. 56). I
can now drain away the heavy drops of liquid from below the bubbles with
a pipe, and leave them clean and smooth all over. I can now pull the
lower ring down, squeezing the inner bubble into a shape like an egg
(Fig. 57), or swing it round and round, and then with a little care peel
away the ring from off the bubble, and leave them both perfectly round
every way (Fig. 58). I can draw out the air from the outer bubble till
you can hardly see between them, and then blow in, and the harder I
blow, the more is it evident that the two bubbles are not touching at
all; the inner one is now spinning round and round in the very centre
of the large bubble, and finally, on breaking the outer one the inner
floats away, none the worse for its very unusual treatment.

[Illustration: Fig. 56.]

[Illustration: Fig. 57.]

[Illustration: Fig. 58.]

There is a pretty variation of the last experiment, which, however,
requires that a little green dye called fluorescine, or better, uranine,
should be dissolved in a separate dish of the soap-water. Then you can
blow the outer bubble with clean soap-water, and the inner one with the
coloured water. Then if you look at the two bubbles by ordinary light,
you will hardly notice any difference; but if you allow sunlight, or
electric light from an arc lamp, to shine upon them, the inner one will
appear a brilliant green, while the outer one will remain clear as
before. They will not mix at all, showing that though the inner one is
apparently resting against the outer one, there is in reality a thin
cushion of air between.

Now you know that coal-gas is lighter than air, and so a soap-bubble
blown with gas, when let go, floats up to the ceiling at once. I shall
blow a bubble on a ring with coal-gas. It is soon evident that it is
pulling upwards. I shall go on feeding it with gas, and I want you to
notice the very beautiful shapes that it takes (Fig. 59, but imagine the
globe inside removed). These are all exactly the curves that a
water-drop assumes when hanging from a pipe, except that they are the
other way up. The strength of the skin is now barely able to withstand
the pull, and now the bubble breaks away just as the drop of water did.

[Illustration: Fig. 59.]

I shall next place a bubble blown with air upon a ring, and blow inside
it a bubble blown with a mixture of air and gas. It of course floats up
and rests against the top of the outer bubble (Fig. 60). Now I shall let
a little gas into the outer one, until the surrounding gas is about as
heavy as the inner bubble. It now no longer rests against the top, but
floats about in the centre of the large bubble (Fig. 61), just as the
drop of oil did in the mixture of alcohol and water. You can see that
the inner bubble is really lighter than air, because if I break the
outer one, the inner one rises rapidly to the ceiling.

[Illustration: Fig. 60.]

Instead of blowing the first bubble on a heavy fixed ring, I shall now
blow one on a light ring, made of very thin wire. This bubble contains
only air. If I blow inside this a bubble with coal-gas, then the
gas-bubble will try and rise, and will press against the top of the
outer one with such force as to make it carry up the wire ring and a
yard of cotton, and some paper to which the cotton is tied (Fig. 62);
and all this time, though it is the inner one only which tends to rise,
the two bubbles are not really touching one another at all.

[Illustration: Fig. 61.]

[Illustration: Fig. 62.]

I have now blown an air-bubble on the fixed ring, and pushed up inside
it a wire with a ring on the end. I shall now blow another air-bubble
on this inner ring. The next bubble that I shall blow is one containing
gas, and this is inside the other two, and when let go it rests against
the top of the second bubble. I next make the second bubble a little
lighter by blowing a little gas into it, and then make the outer one
larger with air. I can now peel off the inner ring and take it away,
leaving the two inner bubbles free, inside the outer one (Fig. 63). And
now the multiple reflections of the brilliant colours of the different
bubbles from one to the other, set off by the beautiful forms which the
bubbles themselves assume, give to the whole a degree of symmetry and
splendour which you may go far to see equalled in any other way. I have
only to blow a fourth bubble in _real_ contact with the outer bubble and
the ring, to enable it to peel off and float away with the other two
inside.

[Illustration: Fig. 63.]

We have seen that bubbles and drops behave in very much the same way.
Let us see if electricity will produce the same effect that it did on
drops. You remember that a piece of electrified sealing-wax prevented a
fountain of water from scattering, because where two drops met, instead
of bouncing, they joined together. Now there are on these two rings
bubbles which are just resting against one another, but not really
touching (Fig. 64). The instant that I take out the sealing-wax you see
they join together and become one (Fig. 65). Two soap-bubbles,
therefore, enable us to detect electricity, even when present in minute
quantity, just as two water fountains did.

[Illustration: Fig. 64.]

[Illustration: Fig. 65.]

We can use a pair of bubbles to prove the truth of one of the
well-known actions of electricity. Inside an electrical conductor it is
impossible to feel any influence of electricity outside, however much
there may be, or however near you go to the surface. Let us, therefore,
take the two bubbles shown in Fig. 56, and bring an electrified stick of
sealing-wax near. The outer bubble is a conductor; there is, therefore,
no electrical action inside, and this you can see because, though the
sealing-wax is so near the bubble that it pulls it all to one side, and
though the inner one is so close to the outer one that you cannot see
between them, yet the two bubbles remain separate. Had there been the
slightest electrical influence inside, even to a depth of a
hundred-thousandth of an inch, the two bubbles would have instantly come
together.

[Illustration: Fig. 66.]

There is one more experiment which I must show, and this will be the
last; it is a combination of the last two, and it beautifully shows the
difference between an inside and an outside bubble. I have now a plain
bubble resting against the side of the pair that I have just been using.
The instant that I take out the sealing-wax the two outer bubbles join,
while the inner one unharmed and the heavy ring slide down to the bottom
of the now single outer bubble (Fig. 66).

And now that our time has drawn to a close I must ask you whether that
admiration and wonder which we all feel when we play with soap-bubbles
has been destroyed by these lectures; or whether now that you know more
about them it is not increased. I hope you will all agree with me that
the actions upon which such common and every-day phenomena as drops and
bubbles depend, actions which have occupied the attention of the
greatest philosophers from the time of Newton to the present day, are
not so trivial as to be unworthy of the attention of ordinary people
like ourselves.




PRACTICAL HINTS.


I hope that the following practical hints may be found useful by those
who wish themselves to successfully perform the experiments already
described.


_Drop with India-rubber Surface._

A sheet of thin india-rubber, about the thickness of that used in
air-balls, as it appears _before_ they have been blown out, must be
stretched over a ring of wood or metal eighteen inches in diameter, and
securely wired round the edge. The wire will hold the india-rubber
better if the edge is grooved. This does not succeed if tried on a
smaller scale. This experiment was shown by Sir W. Thomson at the Royal
Institution.


_Jumping Frame._

This is easily made by taking a light glass globe about two inches in
diameter, such, for instance, as a silvered ball used to ornament a
Christmas-tree or the bulb of a pipette, which is what I used. Pass
through the open necks of the bulb a piece of wire about one-twentieth
of an inch in diameter, and fix it permanently and water-tight upon the
wire by working into the necks melted sealing-wax. An inch or two above
the globe, fasten a flat frame of thin wire by soldering, or if this is
too difficult, by tying and sealing-wax. A lump of lead must then be
fastened or hung on to the lower end, and gradually scraped away until
the wire frame will just be unable to force its way through the surface
of the water. None of the dimensions or materials mentioned are of
importance.


_Paraffined Sieve._

Obtain a piece of copper wire gauze with about twenty wires to the inch,
and cut out from it a round piece about eight inches in diameter. Lay it
on a round block, of such a size that it projects about one inch all
round. Then gently go round and round with the hands pressing the edge
down and keeping it flat above, until the sides are evenly turned down
all round. This is quite easy, because the wires can allow of the kind
of distortion necessary. Then wind round the turned-up edge a few turns
of thick wire to make the sides stiff. This ought to be soldered in
position, but probably careful wiring will be good enough.

Melt some paraffin wax or one or two paraffin candles of the best
quality in a clean flat dish, not over the fire, which would be
dangerous, but on a hot plate. When melted and clear like water, dip the
sieve in, and when all is hot quickly take it out and knock it once or
twice on the table to shake the paraffin out of the holes. Leave upside
down until cold, and then be careful not to scratch or rub off the
paraffin. This had best be done in a place where a mess is of no
consequence.

There is no difficulty in filling it or in setting it to float upon
water.


_Narrow Tubes and Capillarity._

Get some quill-glass tube from a chemist, that is, tube about the size
of a pen. If it is more than, say, a foot long, cut off a piece by
first making a firm scratch in one place with a three-cornered file,
when it will break at the place easily. To make very narrow tube from
this, hold it near the ends in the two hands very lightly, so that the
middle part is high up in the brightest part of an ordinary bright and
flat gas flame. Keep it turning until at last it becomes so soft that it
is difficult to hold it straight. It can then be bent into any shape,
but if it is wanted to be drawn out it must be held still longer until
the black smoke upon it begins to crack and peel up. Then quickly take
it out of the flame, and pull the two ends apart, when a long narrow
tube will be formed between. This can be made finer or coarser by
regulating the heat and the manner in which it is pulled out. No
directions will tell any one so much as a very little practice. For
drawing out tubes the flame of a Bunsen burner or of a blow-pipe is more
convenient; but for bending tubes nothing is so good as the flat gas
flame. Do not clean off smoke till the tubes are cold, and do not hurry
their cooling by wetting or blowing upon them. In the country where gas
is not to be had, the flame of a large spirit-lamp can be made to do,
but it is not so good as a gas-flame. The narrower these tubes are, the
higher will clean water be observed to rise in them. To colour the
water, paints from a colour-box must not be used. They are not liquid,
and will clog the very fine tubes. Some dye that will quite dissolve (as
sugar does) must be used. An aniline dye, called soluble blue, does very
well. A little vinegar added may make the colour last better.


_Capillarity between Plates._

Two plates of flat glass, say three to five inches square, are required.
Provided they are quite clean and well wetted there is no difficulty. A
little soap and hot water will probably be sufficient to clean them.


_Tears of Wine._

These are best seen at dessert in a glass about half filled with port. A
mixture of from two to three parts of water, and one part of spirits of
wine containing a very little rosaniline (a red aniline dye), to give it
a nice colour, may be used, if port is not available. A piece of the
dye about as large as a mustard-seed will be enough for a large
wine-glass. The sides of the glass should be wetted with the wine.


_Cat-Boxes._

Every school-boy knows how to make these. They are not the boxes made by
cutting slits in paper. They are simply made by folding, and are then
blown out like the "frog," which is also made of folded paper.


_Liquid Beads._

Instead of melting gold, water rolled on to a table thickly dusted with
lycopodium, or other fine dust, or quicksilver rolled or thrown upon a
smooth table, will show the difference in the shape of large and small
beads perfectly. A magnifying-glass will make the difference more
evident. In using quicksilver, be careful that none of it falls on gold
or silver coins, or jewellery, or plate, or on the ornamental gilding on
book-covers. It will do serious damage.


_Plateau's Experiment._

To perform this with very great perfection requires much care and
trouble. It is easy to succeed up to a certain point. Pour into a clean
bottle about a table-spoonful of salad-oil, and pour upon it a mixture
of nine parts by volume spirits of wine (not methylated spirits), and
seven parts of water. Shake up and leave for a day if necessary, when it
will be found that the oil has settled together by itself. Fill a
tumbler with the same mixture of spirit and water, and then with a fine
glass pipe, dipping about half-way down, slowly introduce a very little
water. This will make the liquid below a little heavier. Dip into the
oil a pipe and take out a little by closing the upper end with the
finger, and carefully drop this into the tumbler. If it goes to the
bottom, a little more water is required in the lower half of the
tumbler. If by chance it will not sink at all, a little more spirit is
wanted in the upper half. At last the oil will just float in the middle
of the mixture. More can then be added, taking care to prevent it from
touching the sides. If the liquid below is ever so little heavier, and
the liquid above ever so little lighter than oil, the drop of oil
perhaps as large as a halfpenny will be almost perfectly round. It will
not appear round if seen through the glass, because the glass magnifies
it sideways, but not up and down, as may be seen by holding a coin in
the liquid just above it. To see the drop in its true shape the vessel
must either be a globe, or one side must be made of flat glass.

Spinning the oil so as to throw off a ring is not material, but if the
reader can contrive to fix a disc about the size of a threepenny-piece
upon a straight wire, and spin it round without shaking it, then he will
see the ring break off, and either return if the rotation is quickly
stopped, or else break up into three or four perfect little balls. The
disc should be wetted with oil before being dipped into the mixture of
spirit and water.


_A Good Mixture for Soap-Bubbles._

Common yellow soap is far better than most of the fancy soaps, which
generally contain a little soap and a lot of rubbish. Castille soap is
very good, and this may be obtained from any chemist.

Bubbles blown with soap and water alone do not last long enough for many
of the experiments described, though they may sometimes be made to
succeed. Plateau added glycerine, which greatly improves the lasting
quality. The glycerine should be pure; common glycerine is not good, but
Price's answers perfectly. The water should be pure distilled water, but
if this is not available, clean rain-water will do. Do not choose the
first that runs from a roof after a spell of dry weather, but wait till
it has rained for some time, the water that then runs off is very good,
especially if the roof is blue slate or glass. If fresh rain-water is
not to be had, the softest water should be employed that can be
obtained. Instead of Castille soap, Plateau found that a pure soap
prepared from olive-oil is still better. This is called oleate of soda.
It should be obtained freshly prepared from a manufacturing chemist.
Old, dry stuff that has been kept a long time is not so good. I have
always used a modification of Plateau's formula, which Professors
Reinold and Rücker found to answer so well. They used less glycerine
than Plateau. It is best made as follows. Fill a clean stoppered bottle
three-quarters full of water. Add one-fortieth part of its weight of
oleate of soda, which will probably float on the water. Leave it for a
day, when the oleate of soda will be dissolved. Nearly fill up the
bottle with Price's glycerine and shake well, or pour it into another
clean bottle and back again several times. Leave the bottle, stoppered
of course, for about a week in a dark place. Then with a syphon, that
is, a bent glass tube which will reach to the bottom inside and still
further outside, draw off the clear liquid from the scum which will have
collected at the top. Add one or two drops of strong liquid ammonia to
every pint of the liquid. Then carefully keep it in a stoppered bottle
in a dark place. Do not get out this stock bottle every time a bubble is
to be blown, but have a small working bottle. Never put any back into
the stock. In making the liquid _do not warm or filter it_. Either will
spoil it. Never leave the stoppers out of the bottles or allow the
liquid to be exposed to the air more than is necessary. This liquid is
still perfectly good after two years' keeping. I have given these
directions very fully, not because I feel sure that all the details are
essential, but because it exactly describes the way I happen to make it,
and because I have never found any other solution so good. Castille
soap, Price's glycerine, and rain-water will almost certainly answer
every purpose, and the same proportions will probably be found to work
well.


_Rings for Bubbles._

These may be made of any kind of wire. I have used tinned iron about
one-twentieth of an inch in diameter. The joint should be smoothly
soldered without lumps. If soldering is a difficulty, then use the
thinnest wire that is stiff enough to support the bubbles steadily, and
make the joint by twisting the end of the wire round two or three times.
Rings two inches in diameter are convenient. I have seen that dipping
the rings in melted paraffin is recommended, but I have not found any
advantage from this. The nicest material for the light rings is thin
aluminium wire, about as thick as a fine pin (No. 26 to 30, B. W. G.),
and as this cannot be soldered, the ends must be twisted. If this is not
to be had, very fine wire, nearly as fine as a hair (No. 36, B. W. G.),
of copper or of any other metal, will answer. The rings should be wetted
with the soap mixture before a bubble is placed upon them, and must
always be well washed and dried when done with.


_Threads in Ring._

There is no difficulty in showing these experiments. The ring with the
thread may be dipped in the soap solution, or stroked across with the
edge of a piece of paper or india-rubber sheet that has been dipped in
the liquid, so as to form a film on both sides of the thread. A needle
that has also been wetted with the soap may be used to show that the
threads are loose. The same needle held for a moment in a candle-flame
supplies a convenient means of breaking the film.


_Blow out Candle with Soap-Bubble._

For this, the bubble should be blown on the end of a short wide pipe,
spread out at one end to give a better hold for the bubble. The tin
funnel supplied with an ordinary gazogene answers perfectly. This should
be washed before it is used again for filling the gazogene.


_Bubbles balanced against one another._

These experiments are most conveniently made on a small scale. Pieces of
thin brass tube, three-eighths or half an inch in diameter, are
suitable. It is best to have pieces of apparatus, specially prepared
with taps, for easily and quickly stopping the air from leaving either
bubble, and for putting the two bubbles into communication when
required. It should not be difficult to contrive to perform the
experiments, using india-rubber connecting tubes, pinched with spring
clips to take the place of taps. There is one little detail which just
makes the difference between success and failure. This is to supply a
mouth-piece for blowing the bubble, made of glass tube, which has been
drawn out so fine that these little bubbles cannot be blown out suddenly
by accident. It is very difficult, otherwise, to adjust the quantity of
air in such small bubbles with any accuracy. In balancing a spherical
against a cylindrical bubble, the short piece of tube, into which the
air is supplied, must be made so that it can be easily moved to or from
a fixed piece of the same size closed at the other end. Then the two
ends of the short tube must have a film spread over them with a piece of
paper, or india-rubber, but there must be _no_ film stretched across the
end of the fixed tube. The two tubes must at first be near together,
until the spherical bubble has been formed. They may then be separated
gradually more and more, and air blown in so as to keep the sides of the
cylinder straight, until the cylinder is sufficiently long to be nearly
unstable. It will then far more evidently show, by its change of form,
than it would if it were short, when the pressure due to the spherical
bubble exactly balances that due to a cylindrical one. If the shadow of
the bubbles, or an image formed by a lens on a screen, is then measured,
it will be found that the sphere has a diameter which is very accurately
double that of the cylinder.


_Thaumatrope for showing the Formation and Oscillations of Drops._

The experiment showing the formation of water-drops can be very
perfectly imitated, and the movements actually made visible, without any
necessity for using liquids at all, by simply converting Fig. 35 (at end
of book) into the old-fashioned instrument called a thaumatrope. What
will then be seen is a true representation, because the forms in the
figure are copies of a series of photographs taken from the moving drops
at the rate of forty-three photographs in two seconds.[2]

[Footnote 2: For particulars see _Philosophical Magazine_, September
1890.]

Obtain a piece of good card-board as large as the figure, and having
brushed it all over on one side with thin paste, lay the figure upon it,
and press it down evenly. Place it upon a table, and cover it with a few
thicknesses of blotting-paper, and lay over all a flat piece of board
large enough to cover it. Weights sufficient to keep it all flat may be
added. This must be left all night at least, until the card is quite
dry, or else it will curl up and be useless. Now with a sharp chisel or
knife, but a chisel if possible, cut out the forty-three slits near the
edge, accurately following the outline indicated in black and white, and
keeping the slits as narrow as possible. Then cut a hole in the middle,
so as to fit the projecting part of a sewing-machine cotton-reel, and
fasten the cotton-reel on the side away from the figure with glue or
small nails. It must be fixed exactly in the middle. The edge should of
course be cut down to the outside of the black rim.

Now having found a pencil or other rod on which the cotton-reel will
freely turn, use this as an axle, and holding the disc up in front of a
looking-glass, and in a good light, slowly and steadily make it turn
round. The image of the disc seen through the slit in the looking-glass
will then perfectly represent every feature of the growing and falling
drop. As the drop grows it will gradually become too heavy to be
supported, a waist will then begin to form which will rapidly get
narrower, until the drop at last breaks away. It will be seen to
continue its fall until it has disappeared in the liquid below, but it
has not mixed with this, and so it will presently appear again, having
bounced out of the liquid. As it falls it will be seen to vibrate as the
result of the sudden release from the one-sided pull. The neck which was
drawn out will meanwhile have gathered itself in the form of a little
drop, which will then be violently hit by the oscillations of the
remaining pendant drop above, and driven down. The pendant drop will be
seen to vibrate and grow at the same time, until it again breaks away as
before, and so the phenomena are repeated.

In order to perfectly reproduce the experiment, the axle should be
firmly held upon a stand, and the speed should not exceed one turn in
two seconds.

The effect is still more real if a screen is placed between the disc and
the mirror, which will only allow one of the drops to be seen.


_Water-drops in Paraffin and Bisulphide of Carbon._

All that was said in describing the Plateau experiment applies here.
Perfectly spherical and large drops of water can be formed in a mixture
so made that the lower parts are very little heavier, and the upper
parts very little lighter, than water. The addition of bisulphide of
carbon makes the mixture heavier. This liquid--bisulphide of carbon--is
very dangerous, and has a most dreadful smell, so that it had better not
be brought into the house. The form of a hanging drop, and the way in
which it breaks off, can be seen if water is used in paraffin alone, but
it is much more evident if a little bisulphide of carbon is mixed with
the paraffin, so that water will sink slowly in the mixture. Pieces of
glass tube, open at both ends from half an inch to one inch in diameter,
show the action best. Having poured some water coloured blue into a
glass vessel, and covered it to a depth of several inches with paraffin,
or the paraffin mixture, dip the pipe down into the water, having first
closed the upper end with the thumb or the palm of the hand. On then
removing the hand, the water will rush up inside the tube. Again close
the upper end as before, and raise the tube until the lower end is well
above the water, though still immersed in the paraffin. Then allow air
to enter the pipe very slowly by just rolling the thumb the least bit
to one side. The water will escape slowly and form a large growing drop,
the size of which, before it breaks away, will depend on the density of
the mixture and the size of the tube.

To form a water cylinder in the paraffin the tube must be filled with
water as before, but the upper end must now be left open. Then when all
is quiet the tube is to be rather rapidly withdrawn in the direction of
its own length, when the water which was within it will be left behind
in form of a cylinder, surrounded by the paraffin. It will then break up
into spheres so slowly, in the case of a large tube, that the operation
can be watched. The depth of paraffin should be quite ten times the
diameter of the tube.

To make bubbles of water in the paraffin, the tube must be dipped down
into the water with the upper end open all the time, so that the tube is
mostly filled with paraffin. It must then be closed for a moment above
and raised till the end is completely out of the water. Then if air is
allowed to enter slowly, and the tube is gently raised, bubbles of water
filled with paraffin will be formed which can be made to separate from
the pipe, like soap-bubbles from a "churchwarden," by a suitable sudden
movement. If a number of water-drops are floating in the paraffin in the
pipe, and this can be easily arranged, then the bubbles made will
contain possibly a number of other drops, or even other bubbles. A very
little bisulphide of carbon poured carefully down a pipe will form a
heavy layer above the water, on which these compound bubbles will remain
floating.

Cylindrical bubbles of water in paraffin may be made by dipping the pipe
down into the water and withdrawing it quickly without ever closing the
top at all. These break up into spherical bubbles in the same way that
the cylinder of liquid broke up into spheres of liquid.


_Beaded Spider-webs._

These are found in the spiral part of the webs of all the geometrical
spiders. The beautiful geometrical webs may be found out of doors in
abundance in the autumn, or in green-houses at almost any time of the
year. To mount these webs so that the beads may be seen, take a small
flat ring of any material, or a piece of card-board with a hole cut out
with a gun-wad cutter, or otherwise. Smear the face of the ring, or the
card, with a very little strong gum. Choose a freshly-made web, and then
pass the ring, or the card, across the web so that some of the spiral
web (not the central part of the web) remains stretched across the hole.
This must be done without touching or damaging the pieces that are
stretched across, except at their ends. The beads are too small to be
seen with the naked eye. A strong magnifying-glass, or a low power
microscope, will show the beads and their marvellous regularity. The
beads on the webs of very young spiders are not so regular as those on
spiders that are fully grown. Those beautiful beads, easily visible to
the naked eye, on spider lines in the early morning of an autumn day,
are not made by the spider, but are simply dew. They very perfectly show
the spherical form of small water-drops.


_Photographs of Water-jets._

These are easily taken by the method described by Mr. Chichester Bell.
The flash of light is produced by a short spark from a few Leyden-jars.
The fountain, or jet, should be five or six feet away from the spark,
and the photographic plate should be held as close to the stream of
water as is possible without touching. The shadow is then so definite
that the photograph, when taken, may be examined with a powerful lens,
and will still appear sharp. Any rapid dry plate will do. The room, of
course, must be quite dark when the plate is placed in position, and the
spark then made. The regular breaking up of the jet may be effected by
sound produced in almost any way. The straight jet, of which Fig. 41 is
a representation, magnified about three and a quarter times, was
regularly broken up by simply whistling to it with a key. The fountains
were broken up regularly by fastening the nozzle to one end of a long
piece of wood clamped at the end to the stand of a tuning-fork, which
was kept sounding by electrical means. An ordinary tuning-fork, made to
rest when sounding against the wooden support of the nozzle, will
answer quite as well, but is not quite so convenient. The jet will break
up best to certain notes, but it may be tuned to a great extent by
altering the size of the orifice or the pressure of the water, or both.


_Fountain and Sealing-wax._

It is almost impossible to fail over this very striking yet simple
experiment. A fountain of almost any size, at any rate between
one-fiftieth and a quarter of an inch in the smooth part, and up to
eight feet high, will cease to scatter when the sealing-wax is rubbed
with flannel and held a few feet away. A suitable size of fountain is
one about four feet high, coming from an orifice anywhere near
one-sixteenth of an inch in diameter. The nozzle should be inclined so
that the water falls slightly on one side. The sealing-wax may be
electrified by being rubbed on the coat-sleeve, or on a piece of fur or
flannel which is _dry_. It will then make little pieces of paper or cork
dance, but it will still act on the fountain when it has ceased to
produce any visible effect on pieces of paper, or even on a delicate
gold-leaf electroscope.


_Bouncing Water-jets._

This beautiful experiment of Lord Rayleigh's requires a little
management to make it work in a satisfactory manner. Take a piece of
quill-glass tube and draw it out to a very slight extent (see a former
note), so as to make a neck about one-eighth of an inch in diameter at
the narrowest part. Break the tube just at this place, after first
nicking it there with a file. Connect each of these tubes by means of an
india-rubber pipe, or otherwise, with a supply of water in a bottle, and
pinch the tubes with a screw-clip until two equal jets of water are
formed. So hold the nozzles that these meet in their smooth portions at
every small angle. They will then for a short time bounce away from one
another without mixing. If the air is very dusty, if the water is not
clean, or if air-bubbles are carried along in the pipes, the two jets
will at once join together. In the arrangement that I used in the
lantern, the two nozzles were nearly horizontal, one was about half an
inch above the other, and they were very slightly converging. They were
fastened in their position by melting upon them a little sealing-wax.
India-rubber pipes connected them with two bottles about six inches
above them, and screw-clips were used to regulate the supply. One of the
bottles was made to stand on three pieces of sealing-wax to electrically
insulate it, and the corresponding nozzle was only held by its
sealing-wax fastening. The water in the bottles had been filtered, and
one was coloured blue. If these precautions are taken, the jets will
remain distinct quite long enough, but are instantly caused to recombine
by a piece of electrified sealing-wax six or eight feet away. They may
be separated again by touching the water issuing near one nozzle with
the finger, which deflects it; on quietly removing the finger the jet
takes up its old position and bounces off the other as before. They can
thus be separated and made to combine ten or a dozen times in a minute.


_Fountain and Intermittent Light._

This can be successfully shown to a large number of people at once only
by using an electric arc, but there is no occasion to produce this light
if not more than one person at a time wishes to see the evolution of the
drops. It is then merely necessary to make the fountain play in front of
a bright background such as the sky, to break it up with a tuning-fork
or other musical sound as described, and then to look at it through a
card disc equally divided near the edge into spaces about two or three
inches wide, with a hole about one-eighth of an inch in diameter between
each pair of spaces. A disc of card five inches in diameter, with six
equidistant holes half an inch from the edge, answers well. The disc
must be made to spin by any means very regularly at such a speed that
the tuning-fork, or stretched string if this be used, when looked at
through the holes, appears quiet, or nearly quiet, when made to vibrate.
The separate drops will then be seen, and everything described in the
preceding pages, and a great deal more, will be evident. This is one of
the most fascinating experiments, and it is well worth while to make an
effort to succeed. The little motor that I used is one of Cuttriss and
Co.'s P. 1. motors, which are very convenient for experiments of this
kind. It was driven by four Grove's cells. These make it rotate too
fast, but the speed can be reduced by moving the brushes slightly
towards the position used for reversing the motor, until the speed is
almost exactly right. It is best to arrange that it goes only just too
fast, then the speed can be perfectly regulated by a very light pressure
of the finger on the end of the axle.


_Mr. Chichester Bell's Singing Water-jet._

For these experiments a very fine hole about one seventy-fifth of an
inch in diameter is most suitable. To obtain this, Mr. Bell holds the
end of a quill-glass tube in a blow-pipe flame, and constantly turns it
round and round until the end is almost entirely closed up. He then
suddenly and forcibly blows into the pipe. Out of several nozzles made
in this way, some are sure to do well. Lord Rayleigh makes nozzles
generally by cementing to the end of a glass (or metal) pipe a piece of
thin sheet metal in which a hole of the required size has been made. The
water pressure should be produced by a head of about fifteen feet. The
water must be quite free from dust and from air-bubbles. This may be
effected by making it pass through a piece of tube stuffed full of
flannel, or cotton-wool, or something of the kind to act as a filter.
There should be a yard or so of good black india-rubber tube, about
one-eighth of an inch in diameter inside, between the filter and the
nozzle. It is best not to take the water direct from the water-main, but
from a cistern about fifteen feet above the nozzle. If no cistern is
available, a pail of water taken up-stairs, with a pipe coming down, is
an excellent substitute, and this has the further advantage that the
head of water can be easily changed so as to arrive at the best result.

The rest of the apparatus is very simple. It is merely necessary to
stretch and tie over the end of a tube about half an inch in diameter a
piece of thin india-rubber sheet, cut from an air-ball that has not been
blown out. The tube, which may be of metal or of glass, may either be
fastened to a heavy foot, in which case a side tube must be joined to
it, as in Fig. 47, or it may be open at both ends and be held in a
clamp. It is well to put a cone of card-board on the open end (Fig. 48),
if the sound is to be heard by many at a time. If the experimenter alone
wishes to hear as well as possible when faint sounds are produced, he
should carry a piece of smooth india-rubber tube about half an inch in
diameter from the open end to his ear. This, however, would nearly
deafen him with such loud noises as the tick of a watch.


_Bubbles and Ether._

Experiments with ether must be performed with great care, because, like
the bisulphide of carbon, it is dangerously inflammable. The bottle of
ether must never be brought near a light. If a large quantity is
spilled, the heavy vapour is apt to run along the floor and ignite at a
fire, even on the other side of a room. Any vessel may be filled with
the vapour of ether by merely pouring the liquid upon a piece of
blotting-paper reaching up to the level of the edge. Very little is
required, say half a wine-glassful, for a basin that would hold a gallon
or more. In a draughty place the vapour will be lost in a short time.
Bubbles can be set to float upon the vapour without any difficulty. They
may be removed in five or ten seconds by means of one of the small light
rings with a handle, provided that the ring is wetted with the soap
solution and has _no_ film stretched across it. If taken to a light at a
safe distance the bubble will immediately burst into a blaze. If a
neighbouring light is not close down to the table, but well up above the
jar on a stand, it may be near with but little risk. To show the burning
vapour, the same wide tube that was used to blow out the candle will
answer well. The pear shape of the bubble, owing to its increased weight
after being held in the vapour for ten or fifteen seconds, is evident
enough on its removal, but the falling stream of heavy vapour, which
comes out again afterwards, can only be shown if its shadow is cast upon
a screen by means of a bright light.


_Experiment with Internal Bubbles._

For these experiments, next to a good solution, the pipe is of the
greatest importance. A "churchwarden" is no use. A glass pipe 5/16 inch
in diameter at the mouth is best. If this is merely a tube bent near the
end through a right angle, moisture condensed in the tube will in time
run down and destroy the bubble occasionally, which is very annoying in
a difficult experiment. I have made for myself the pipe of which Fig. 67
is a full size representation, and I do not think that it is possible to
improve upon this. Those who are not glass-blowers will be able, with
the help of cork, to make a pipe with a trap as shown in Fig. 68, which
is as good, except in appearance and handiness.

In knocking bubbles together to show that they do not touch, care must
be taken to avoid letting either bubble meet any projection in the
other, such as the wire ring, or a heavy drop of liquid. Either will
instantly destroy the two bubbles. There is also a limit to the violence
which may be used, which experience will soon indicate.

In pushing a bubble through a ring smaller than itself, by means of a
flat film on another ring, it is important that the bubble should not be
too large; but a larger bubble can be pushed through than would be
expected. It is not so easy to push it up as down because of the heavy
drop of liquid, which it is difficult to completely drain away.

[Illustration: Fig. 67. Length of Stem 9 Inches]

[Illustration: Fig. 68. Length of Stem 9 Inches]

To blow one bubble inside another, the first, as large as an average
orange, should be blown on the lower side of a horizontal ring. A light
wire ring should then be hung on to this bubble to slightly pull it out
of shape. For this purpose thin aluminium rings are hardly heavy enough,
and so either a heavier metal should be used, or a small weight should
be fastened to the handle of the ring. The ring should be so heavy that
the sides of the bubble make an angle of thirty or forty degrees with
the vertical, where they meet the ring as indicated in Fig. 56. The
wetted end of the pipe is now to be inserted through the top of the
bubble, until it has penetrated a clear half inch or so. A new bubble
can now be blown any size almost that may be desired. To remove the pipe
a slow motion will be fatal, because it will raise the inner bubble
until it and the outer one both meet the pipe at the same place. This
will bring them into true contact. On the other hand, a violent jerk
will almost certainly produce too great a disturbance. A rather rapid
motion, or a slight jerk, is all that is required. It is advisable
before passing the pipe up through the lower ring, so as to touch the
inner bubble, and so drain away the heavy drop, to steady this with the
other hand. The superfluous liquid can then be drained from both bubbles
simultaneously. Care must be taken after this that the inner bubble is
not allowed to come against either wire ring, nor must the pipe be
passed through the side where the two bubbles are very close together.
To peel off the lower ring it should be pulled down a very little way
and then inclined to one side. The peeling will then start more readily,
but as soon as it has begun the ring should be raised so as not to make
the peeling too rapid, otherwise the final jerk, when it leaves the
lower ring, will be too much for the bubbles to withstand.

Bubbles coloured with fluorescine, or uranine, do not show their
brilliant fluorescence unless sunlight or electric light is concentrated
upon them with a lens or mirror. The quantity of dye required is so
small that it may be difficult to take little enough. As much as can be
picked up on the last eighth of an inch of a pointed pen-knife will be,
roughly speaking, enough for a wine-glassful of the soap solution. If
the quantity is increased beyond something like the proportion stated,
the fluorescence becomes less and very soon disappears. The best
quantity can be found in a few minutes by trial.

To blow bubbles containing either coal-gas or air, or a mixture of the
two, the most convenient plan is to have a small T-shaped glass tube
which can be joined by one arm of the T to the blow-pipe by means of a
short piece of india-rubber tube, and be connected by its vertical limb
with a sufficient length of india-rubber pipe, one-eighth of an inch in
diameter inside, to reach to the floor, after which it may be connected
by any kind of pipe with the gas supply. The gas can be stopped either
by pinching the india-rubber tube with the left hand, if that is at
liberty, or by treading on it if both hands are occupied. Meanwhile air
can be blown in by the other arm of the T, and the end closed by the
tongue when gas alone is required. This end of the tube should be
slightly spread out when hot by rapidly pushing into it the _cold_ tang
of a file, and twisting it at the same time, so that it may be lightly
held by the teeth without fear of slipping.

If a light T-piece or so great a length of small india-rubber tube
cannot be obtained, then the mouth must be removed from the pipe and the
india-rubber tube slipped in when air is to be changed for gas. This
makes the manipulation more difficult, but all the experiments, except
the one with three bubbles, can be so carried out.

The pipe must in every case be made to enter the highest point of a
bubble in order to start an internal one. If it is pushed horizontally
through the side, the inner bubble is sure to break. If the inner bubble
is being blown with gas, it will soon tend to rise. The pipe must then
be turned over in such a manner that the inner bubble does not creep
along it, and so meet the outer one where penetrated by the pipe. A few
trials will show what is meant. The inner bubble may then be allowed to
rest against the top of the outer one while being enlarged. When it is
desired after withdrawing the pipe to blow more air or gas into either
the inner or the outer bubble, it is not safe after inserting the pipe
again to begin to blow at once; the film which is now stretched across
the mouth of the pipe will probably become a third bubble, and this,
under the circumstances, is almost certain to cause a failure. An
instantaneous withdrawal of the air destroys this film by drawing it
into the pipe. Air or gas may then be blown without danger.

If the same experiment is performed upon a light ring with cotton and
paper attached, the left hand will be occupied in holding this ring, and
then the gas must be controlled by the foot, or by a friend. The light
ring should be quite two inches in diameter. If, when the inner bubble
has begun to carry away the ring, &c., the paper is caught hold of, it
is possible, by a judicious pull, to cause the two bubbles to leave the
ring and so escape into the air one inside the other. For this purpose
the smallest ring that will carry the paper should be used. With larger
rings the same effect may be produced by inclining the ring, and so
allowing the outer bubble to peel off, or by placing the mouth of the
pipe against the ring and blowing a third bubble in real contact with
the ring and the outer bubble. This will assist the peeling process.

To blow three bubbles, one inside the other two, is more difficult. The
following plan I have found to be fairly certain. First blow above the
ring a bubble the size of a large orange. Then take a small ring about
an inch in diameter, with a straight wire coming down from one side to
act as a handle, and after wetting it with the solution, pass it
carefully up through the fixed ring so that the small ring is held well
inside the bubble. Now pass the pipe, freshly dipped in the solution,
into the outer or No. 1 bubble until it is quite close to the small
ring, and begin to blow the No. 2 bubble. This must be started with the
pipe almost in contact with the inner ring, as the film on this ring
would destroy a bubble that had attained any size. Withdraw the pipe,
dip it into the liquid, and insert it into the inner bubble, taking care
to keep these two bubbles from meeting anywhere. Now blow a large
gas-bubble, which may rest against the top of No. 2 while it is growing.
No. 2 may now rest against the top of No. 1 without danger. Remove pipe
from No. 3 by gently lowering it, and let some gas into No. 2 to make it
lighter, and at the same time diminish the pressure between Nos. 2 and
3. Presently the small ring can be peeled off No. 2 and removed
altogether. But if there is a difficulty in accomplishing this, withdraw
the pipe from No. 2 and blow air into No. 1 to enlarge it, which will
make the process easier. Then remove the pipe from No. 1. The three
bubbles are now resting one inside the other. By blowing a fourth
bubble, as described above, against the fixed ring, No. 1 bubble will
peel off, and the three will float away. No. 1 can, while peeling, be
transferred to a light wire ring from which paper, &c. are suspended.
This description sounds complicated, but after a little practice the
process can be carried out almost with certainty in far less time than
it takes to describe it; in fact, so quickly can it be done, and so
simple does it appear, that no one would suppose that so many details
had to be attended to.


_Bubbles and Electricity._

These experiments are on the whole the most difficult to perform
successfully. The following details should be sufficient to prevent
failure. Two rings are formed at the end of a pair of wires about six
inches long in the straight part. About one inch at the opposite end
from the ring is turned down at a right angle. These turned-down ends
rest in two holes drilled vertically in a non-conductor such as ebonite,
about two or three inches apart. Then if all is right the two rings are
horizontal and at the same level, and they may be moved towards or away
from one another. Separate them a few inches, and blow a bubble above or
below each, making them nearly the same size. Then bring the two rings
nearer together until the bubbles just, and only just, rest against one
another. Though they may be hammered together without joining, they will
not remain long resting in this position, as the convex surfaces can
readily squeeze out the air. The ebonite should not be perfectly warm
and dry, for it is then sure to be electrified, and this will give
trouble. It must not be wet, because then it will conduct, and the
sealing-wax will produce no result. If it has been used as the support
for the rings for some of the previous experiments, it will have been
sufficiently splashed by the bursting of bubbles to be in the best
condition. It must, however, be well wiped occasionally.

A stick of sealing-wax should be held in readiness under the arm, in a
fold or two of _dry_ flannel or fur. If the wax is very strongly
electrified, it is apt to be far too powerful, and to cause the bubbles,
when it is presented to them, to destroy each other. A feeble
electrification is sufficient; then the instant it is exposed the
bubbles coalesce. The wax may be brought so near one bubble in which
another one is resting, that it pulls them to one side, but the inner
one is screened from electrical action by the outer one. It is important
not to bring the wax very near, as in that case the bubble will be
pulled so far as to touch it, and so be broken. The wetting of the wax
will make further electrification very uncertain. In showing the
difference between an inner and an outer bubble, the same remarks with
regard to undue pressure, electrification, or loss of time apply. I have
generally found that it is advisable in this experiment not to drain the
drops from both the bubbles, as their weight seems to steady them; the
external bubble may be drained, and if it is not too large, the process
of electrically joining the outer bubbles, without injury to the inner
one, may be repeated many times. I once caused eight or nine single
bubbles to unite with the outer one of a pair in succession before it
became too unwieldy for more accessions to be possible.

       *       *       *       *       *

It would be going outside my subject to say anything about the
management of lanterns. I may, however, state that while the experiments
with the small bubbles are best projected with a lens upon the screen,
the larger bubbles described in the last lecture can only be projected
by their shadows. For this purpose the condensing lens is removed, and
the bare light alone made use of. An electric arc is far preferable to a
lime-light, both because the shadows are sharper, and because the
colours are so much more brilliant. No oil lamp would answer, even if
the light were sufficient in quantity, because the flame would be far
too large to cast a sharp shadow.

In these hints, which have in themselves required a rather formidable
chapter, I have given all the details, so far as I am able, which a
considerable experience has shown to be necessary for the successful
performance or the experiments in public. The hints will I hope
materially assist those who are not in the habit of carrying out
experiments, but who may wish to perform them for their own
satisfaction. Though people who are not experimentalists may consider
that the hints are overburdened with detail, it is probable that in
repeating the experiments they will find here and there, in spite of all
my care to provide against unforeseen difficulties, that more detail
would have been desirable.

Though it is unusual to conclude such a book as this with the fullest
directions for carrying out the experiments described, I believe that
the innovation in the present instance is good, more especially because
many of the experiments require none of the elaborate apparatus which so
often is necessary.


THE END.

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

[Illustration: Fig. 35

THAUMATROPE for showing the formation and oscillation of drops.]