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.]