If you again consider these two cases, you will see that a p

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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. Rucker. 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. Rucker 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.]