567. I have here a small bucket nearly filled with water: to the
handle a piece of string is attached. If I whirl the bucket round in
a vertical plane sufficiently fast, you see no water escapes, although
the bucket is turned upside down once in every revolution. This is
because the water has not _time_ to fall out during such a brief
interval. A body would not fall half an inch from rest in the twentieth
of a second.
568. The action of circular motion upon liquids is illustrated by the
experiment which is represented in Fig. 76.
[Illustration: FIG. 76.]
A glass beaker about half full of water is mounted so that it can
be spun round rapidly. The motion is given by means of a large
wheel turned by a handle, as shown in the figure. When the rotation
commences, the water is seen to rise up against the glass sides and
form a hollow in the centre.
569. In order to demonstrate this clearly, I turn upon the vessel a
beam from the lime-light. I have previously dissolved a little quinine
in the water. The light from the lamp is transmitted through a piece of
dense blue glass. When the light thus coloured falls on the water, the
presence of the quinine makes the entire liquid glow with a bluish hue.
This remarkable property of quinine, which is known as fluorescence,
enables you to see distinctly the hollow form caused by the rotation.
570. You observe that as the speed becomes greater the depth of the
hollow increases, and that if I turn the wheel sufficiently fast the
water is actually driven out of the glass. The shape of the curve which
the water assumes is that which would be produced by the revolution of
a _parabola_ about its axis.
571. The explanation is simple. As soon as the glass begins to revolve,
the friction of its sides speedily imparts a revolving motion to the
water; but in this case there is nothing to keep the particles near the
centre like the string in the revolving weight, so the liquid rises at
the sides of the glass.
572. But you may ask why _all_ the particles of the water should not
go to the circumference, and thus line the inside of the glass with a
hollow cylinder of water instead of the parabola. Such an arrangement
could not exist in a liquid acted on by gravity. The lower parts of the
cylinder must bear the pressure of the water above, and therefore have
more tendency to flatten out than the upper portions. This tendency
could not be overcome by any consequences of the movement, for such
must be alike on all parts at the same distance from the axis.
573. A very beautiful experiment was devised by Plateau for the purpose
of studying the revolution of a liquid removed from the action of
gravity.
The apparatus employed is represented in Fig. 77. A glass vessel 9"
cube is filled with a mixture of alcohol and water. The relative
quantities ought to be so proportioned that the fluid has the same
specific gravity as olive oil, which is heavier than alcohol and
lighter than water. In practice, however, it is found so difficult
to adjust the composition exactly that the best plan is to make two
alcoholic mixtures so that olive oil will just float on one of them,
and just sink in the other. The lower half of the glass is to be filled
with the denser mixture, and the upper half with the lighter. If, then,
the oil be carefully introduced with a funnel it will form a beautiful
sphere in the middle of the vessel, as shown in the figure. We thus see
that a liquid mass freed from the action of terrestrial gravity, forms
a sphere by the mutual attraction of its particles.
[Illustration: FIG. 77.]
Through the liquid a vertical spindle passes. On this there is a
small disk at the middle of its length, about which the sphere of oil
arranges itself symmetrically. To the end of the spindle a handle is
attached. When the handle is turned round slowly, the friction of the
disk and spindle communicates a motion of rotation to the sphere of
oil. We have thus a liquid spheroidal mass endowed with a movement of
rotation; and we can study the effect of the motion upon its form.
We first see the sphere flatten down at its poles, and bulge at its
equator. In order to show the phenomenon to those who may not be near
to the table, the sphere can be projected on the screen by the help of
the lime-light lamp and a lens. It first appears as a yellow circle,
and then, as the rotation begins, the circle gradually transforms into
an ellipse. But a very remarkable modification takes place when the
handle is turned somewhat rapidly. The ellipsoid gradually flattens
down until, when a certain velocity has been attained, the surface
actually becomes indented at the poles, and flies from the axis
altogether. Ultimately the liquid assumes the form of a beautiful ring,
and the appearance on the screen is shown in Fig. 78.
[Illustration: FIG. 78.]
574. The explanation of the development of the ring involves some
additional principles: as the sphere of oil spins round in the liquid,
its surface is retarded by friction; so that when the velocity attains
a certain amount, the internal portions of the sphere, which are in the
neighbourhood of the spindle, are driven from the centre into the outer
portions, but the full account of the phenomenon cannot be given here.
575. The earth was, we believe, originally in a fluid condition. It had
then, as it has now, a diurnal rotation, and one of the consequences of
this rotation has been to cause the form to be slightly protuberant at
the equator, just as we have seen the sphere of oil to bulge out under
similar conditions.
576. Bodies lying on the earth are whirled around in a great circle
every day. Hence, if there were not some force drawing them to the
centre, they would fly off at a tangent. A part of the earth’s
attraction goes for this purpose, and the remainder, which is the
apparent weight, is thus diminished by a quantity increasing from the
pole to the equator (Art. 86).