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is easily answered ; for these forces are necessarily in the same plane ; but
they do not all pass through the same point, and therefore they are not
in equilibrium. To balance these forces, then, there must be some other
force acting on the ball in the same plane with them, and which does not
pass through p, or the centre of the ball. Now, besides the water which
leaves the ball at p, there is the water which adheres to the ball until
thrown off by centrifugal force ; and to this we must look for the
required force. The effect of a drop adhering to the ball will be very
complex, being due to its weight, centrifugal force, and friction. However,
if we neglect the weight as being very small, and therefore only able to
increase slightly the weight of the ball, and to shift the point at which
it acts a little way from the centre, the forces which the drop will produce
may be stated accurately. For whenever a drop whose weight is w (Ibs.)
comes on to the ball with a velocity v (feet per second), and leaves with a
velocity u, its whole effect, minus that of its weight while it is on the ball,
is equivalent to a force wv/g (Ibs.) acting for one second, in the direction in


which the drop was moving, and at the point at which it comes on to the
ball, and a force wu/g at the point at which it leaves, and in a direction
opposite to, that in which it flies off. The first of these forces will form
part of P f and R; and therefore, besides the forces at the point P, the
effect of any adhering drop will be equivalent to a reaction, such as would
be produced if the force necessary to throw the drop from the ball were
concentrated at the point at which it leaves. If several drops be leaving
the ball at the same time, the several reactions will have a single resultant,
which will not pass through p, or the centre, unless they should be distributed
equally all round the ball, in which case the reactions would simply produce
a couple on the ball, and would not have a single resultant. If the drops
are not leaving equally all round, the resultant will act in a direction
opposite to that in which the greatest number fly off. If, then, more water
is thrown off in one direction than in another, and this direction is the same
as that of the resultant of the three forces P', R, and W, this water will
produce a force such as it has been shown must, exist. First, then, is there
any reason why more water should be thrown off in one direction than in
another ? and, second, in what direction will that be ? The water comes on
to the ball at p, and that which adheres is at first spread out in the form
of a thin film, on which centrifugal force immediately acts to collect it at
the equator. As it collects at the equator, the adhesion becomes less, com-
pared with the mass of water, and the drops separate themselves and fly
off; in this way the water would begin to leave at p, and go on until it
was all thrown off, so that much more water would leave above p than
below. But, besides this, the weight of the water will tend to keep it on
or to throw it off, arid its action to keep it on will be greatest up to the
top, after which the conditions for its leaving become more favourable ; so
that the water may begin to leave at p, or not till it has passed over the
top of the ball; but in either case most of the water will be thrown off
before it gets below the horizontal circle on the opposite side to p. On
examining the ball, it appears that the water which adheres begins to
leave at the top. And by far the greater part of the water flies away from
the jet.

It is the discovery of this fact which has enabled me to explain the
phenomenon; for this water causes a resultant reaction, which is the
additional force necessary to maintain the equilibrium of the ball.

Let this resultant reaction be called Q: it will act towards the jet, and
its effect will be, first, to force the ball into the jet, and so will help to
counteract the obliquity of P ; secondly, it will assist in supporting the ball ;
and, thirdly, since it opposes the rotation, it will balance the tangential
force R, caused by the friction at p; and, provided it have the proper



magnitude, together with the forces P', R, and W, it is all that is requisite
to explain the equilibrium.

It remains to explain the fact, that the ball will fall back again into the
jet after it has been driven out of it. This may be done ; for the force P
which forces the ball out, ceases as soon as contact ceases ; but not so with
Q, which drives the ball back again towards the jet; for there will still be
some water to be thrown off, so that perhaps for half a revolution Q will
continue imdiminished, and so bring the ball back again into the jet.


With respect to the position of the ball when in equilibrium, nothing
very definite can be established, as there are no known laws of adhesion ;
but it may be shown by general reasoning, that there are limits between
which the point p must be, so that there may be equilibrium.

Let the point p be at a fixed height, P equal the full force of the jet
at this height when acting on the bottom of the ball or on a perpen-
dicular plane, and let P' be the force on the ball. Then, if a be the
angle which the normal at p makes with the vertical,

P' = P cos a,

and the horizontal component

p p

P' sin a = 2 sin a cos a = sin 2a ;
Z 2i


P' sin a = ^- , and is a maximum when a = 45,



P' sin a = when a = 0, or a = 90 ;

so that the tendency of the jet to force the ball to one side increases from
nothing to P/2 as p moves from the bottom to a point at which the normal
makes an angle of 45 with the vertical, and then decreases to nothing as p
moves to the middle of the ball.

The force Q may be fairly assumed to increase as the speed of rotation
increases; and this will be as the point of contact moves from the bottom
to the middle of the ball. In the same way the force R, which will neces-
sarily increase as Q increases, will increase as p moves from the bottom to
the middle of the ball ; and its horizontal component will follow nearly the
same law as that of P.


Considering, then, the horizontal forces only, there must be some position
for p in which the horizontal component of Q and R will be equal to that of
P ; and if a horizontal circle be drawn through this point, it will limit the
part of the ball in which p must be for equilibrium to be possible.

For any deviation without this circle the equilibrium will be stable ;
i.e. if the centre of the ball gets so far from the jet that the ball is struck
in some point without this circle, it will come back again. As to the nature
of the equilibrium for any deviation within this circle, I cannot speak
positively; but it is probably nearly neutral all over the enclosed area.
This seems to agree very well with the fact that the ball is in equilibrium
when struck 45 below its horizontal circle, and oscillates about this position.

The following is a description of some experiments. The object was to
ascertain: first, whether or not air is the medium by which the water
acts on the ball ; secondly, how far the horizontal equilibrium of the ball
depends on its rotation ; and, thirdly, what is the exact position of the point
in which the ball must be struck so as to be in equilibrium, and, moreover,
what is the nature of the equilibrium :

The apparatus employed in these experiments consisted of a wheel, three
inches in diameter and half an inch broad at the rim, , jm

made of painted wood, capable of turning very freely
about its axis, and suspended by two wires, with its
axis horizontal, so that it could swing like a pendulum.
A vertical jet of water was so arranged that it could be
made to strike the reel at any point from below, or to
miss it altogether. This was done by bringing the jet
out of a horizontal pipe which would slide backwards
and forwards in the same direction as the wheel could
swing. This pipe was furnished with a cock, so that the
force of the jet might be altered.

In experiment No. 1, the pipe from which the jet issued was pushed
forward so that the jet missed the reel by about an inch, and the jet was
turned on to rise about six feet above the reel ; the pipe was then brought
back until the water passed as near as possible to the reel without touching
it but there was no apparent effect produced on the reel. The tap was
turned so as to increase and then diminish the height to which the jet rose
still, without any effect.

Experiment No. 2 was made with the same apparatus as No. 1. The
reel was then changed for one six inches in diameter, and the same experi-
ment repeated.


The jet was placed so that it missed the reel (when hanging freely) by
about two inches, and the water was turned on to rise about six feet. The
reel was then pushed forward until it touched the jet, and then let go ; it
immediately began to turn about its axis, but left the jet, swinging backwards
and forwards, touching the jet each time, and each time gaining in speed of
rotation. This went on for several oscillations : but as it got to turn faster,
it appeared to stick to the jet for an instant before letting go ; and having
done this once or twice, it stuck to the jet altogether, and remained in
contact with it, spinning rapidly. The experiment was then repeated with
the jet at different distances, and with the larger wheel ; the result was
the same in all cases. I found it possible, however, either to increase or
to diminish the force of the jet enough to prevent the reel from remaining
in contact with it. The limits were about 2 and 8 feet.

In experiment No. 3, the position of the reel when free was carefully
marked, so that the least alteration could be noticed, and the jet was placed
directly under its centre. In this position the jet did not cause the reel to
move to either side in particular, but to oscillate backwards and forwards.
The jet was then pushed slowly forwards, and the motion of the ball watched.
At first it moved away from the jet slightly, and remained away until it
was struck about 60 from its lowest point, after which it gradually came
back to its initial position, which it reached when struck about 65 from
its lowest point.

The forward motion of the jet being continued, the ball began to follow
the jet, the point in which it was struck moving upwards very slowly. When
the reel finally fell from the jet and came back into its initial position, the
jet missed it by about 2^- inches.

During the experiment the force of the jet was altered; but within
moderate limits this did not affect the position of equilibrium.

This clearly shows that the position of equilibrium is about 25 from
the horizontal circle, and for any deviation below this the equilibrium is
much more nearly neutral than for any deviation above it.



[From the Fifth Volume of the Third Series of " Memoirs of the Literary
and Philosophical Society of Manchester." Session 1870-71.]

(Read November 29, 1870.)

ALTHOUGH the tails of comets are usually assumed to be material
appendages, which accompany these bodies in their flight through the
heavens (and the appearance they present certainly warrants such an
assumption), yet this is not the only way in which these tails may be
accounted for. They may be simply an effect produced by the comet on the
material through which it is passing, an effect analogous to that which
we sometimes see produced by a very small insect on the surface of still
water. We see a dark spot, and on looking closer we find a small fly or moth
flapping its wings and creating a disturbance which was visible before the
insect which produced it.

There is nothing else that we can conceive their tails to be ; so that they
must be one or the other of these two things, either

(1) Material appendages of the nucleus, whether the material be limited
to the illuminated tail or surround the comet on all sides or

(2) Matter which exists independently of the comet, and on which the
comet exerts such a physical influence as to render it visible.

Respecting the composition of these bodies Sir John Herschel says :
" There is beyond question some profound secret and mystery of nature
concerned in the phenomenon of their tails. Perhaps it is not too much to
hope that future observation, borrowing every aid from rational speculation,


grounded on the progress of physical science generally (especially those
branches of it which relate to the setherial or imponderable elements), may
ere long enable us to penetrate this mystery, and to declare whether it is
matter in the ordinary acceptation of the term, that is projected from their
heads with such extravagant velocities, and if not impelled, at least directed
in its course by reference to the sun as a point of avoidance. In no respect
is the question as to the materiality of the tail more forcibly pressed on us
for consideration, than in that of the enormous sweep which it makes round
the sun in perihelio, in the manner of a straight and rigid rod, in defiance of
the law of gravitation, nay, even of the received laws of motion, extending
(as we have seen in the comets of 1680 and 1843) from near the sun's surface
to the earth's orbit, yet whirled round unbroken : in the latter case through
an angle of 180 in little more than two hours. It seems utterly incredible
that in such a case it is one and the same material object which is thus
brandished. If there could be conceived such a thing as a negative shadow,
a momentary impression made upon the luminiferous a3ther behind the
comet, this would represent in some degree the conception such a phenomenon
irresistibly calls up. But this is not all. Even such an extraordinary excite-
ment of the aether, conceive it as we will, will afford no account of the
projection of lateral streamers, of the effusion of light from the nucleus of
the comet towards the sun and its subsequent rejection, of the irregular
and capricious mode in which that effusion has been seen to take place,
none of the clear indications of alternate evaporation and condensation
going on in the immense regions of space occupied by the tail and coma
none, in short, of innumerable other facts which link themselves with almost
equally irresistible cogency to our ordinary notions of matter and force."

There can be no doubt that, if these tails are matter moving with the
comet, this matter must be endowed with properties such as we not only have
no experience of, but of which we can form no conception. This would almost
seem a sufficient reason for rejecting the first hypothesis. Moreover, on the
second hypothesis there is no difficulty in the immense velocity with which
these tails are projected from the head, or whirled round, when the comet is
in perihelio ; for, to take the " negative shadow " as an illustration, here we
should have a velocity of projection equal to that of light, and the only effect
of the whirling would be a slight lagging in the extremity of the tail, causing
curvature similar to that which actually exists ; and whatever the action may
be, if its velocity of emission or transmission be sufficiently great, this effect
will be the same. But whether this hypothesis is to be rejected because
it involves assumptions beyond conception, or contrary to experience, must
depend on the answers to the following question : Do we know, or can we
conceive, any physical state, into which any substance which can be conceived
to occupy the space traversed by comets could possibly be brought, so as to
make it present the appearance exhibited by comets ?


I think the answer must be in the affirmative, and that we may leave
out the terms conceive and conceivable. For electricity is a well-known
state, and gases are well-known substances ; and when electricity under
certain conditions, as in Dr Geissler's tubes, is made to traverse exceedingly
rare gas, the appearance produced is similar to that of the cornets' tails ; the
rarer this gas is, the more susceptible is it of such a state ; and, so far as we
know, there is no limit to the extent of gas that may be so illuminated.
Hence we may suppose the exciting cause to be electricity, and the material
on which it acts, and which fills space, to have the same properties as those
possessed by gas. What is more, we can conceive the sun to be in such a
condition, as to produce that influence on this electricity which should cause
the tail to occupy the direction it does ; for such an electrical discharge will
be powerfully repelled by any body charged with similar electricity in its

The electricity would be discharged by the comets on account of some
influence which the sun may have on them, such an influence being well
within the limits of our conception.

The appearances of the comet in detail, such as the emission of jets of
light towards the sun, and the form of the illuminated envelope, are all such
as would necessarily accompany such an electrical discharge.

In fact, if the possibility of such a discharge is admitted, I believe it will
explain all the phenomena of comets. As to the possibility, or even the
probability, of such a discharge, I think it may be established on very good

The tails of comets may or may not be one with their heads ; but
whichever is the case, it is certain that the difference in the appearance of
comets and of planets indicates some essential difference, either in the
materials of which these bodies are respectively composed, or else in the
conditions under which their materials exist. Now, from the motion of
comets, we know that their heads follow the same laws of motion and
gravitation as all other matter ; and therefore we have good evidence, so far
as .it goes, that comets and planets are similarly constituted as regards
materials. And since the appearance of a comet changes very much as it
passes round the sun, any assumptions with regard to the material of comets,
in order to account for their difference from planets, would not account for the
variety of appearance the same comet presents at different times. On the
other hand, the conditions of comets and planets must necessarily be very
different, from the extreme difference in the shapes of the orbits they describe.
Each planet remains nearly at a constant distance from the sun (whatever
that distance may be), so that the heat, or any physical effect the sun may
have upon it, will also be constant; on the comets its action must change


rapidly from time to time, particularly when the comet is in certain parts of
its orbit. Hence we may say that the temperature and general physical
condition of planets is nearly constant, and that of comets, for the most part,
continually varying.

There is, too, a very remarkable connexion between the appearance of the
comet and the rate at which the sun's action on it changes. Herschel says :
" Sometimes they first make their appearance as faint and slow-moving objects,
with little or no tail, but by degrees accelerate, enlarge, and throw out from
them this appendage, which increases in length and brightness till (as always
happens in such cases) they approach the sun and are lost in his beams.
After a time they again emerge on the other side, receding from the sun with
a velocity at first rapid, but gradually decreasing. It is, for the most part,
after thus passing the sun that they shine forth in all their splendour, and
their tails acquire their greatest length and development, thus indicating
plainly the sun's rays as the exciting cause of that extraordinary emanation.
As they continue to recede from the sun, their motion diminishes, and their
tail dies away, or is absorbed into the head, which itself grows continually
feebler, and is at length altogether lost sight of."

Here, although unconsciously, Herschel has connected the increase of
brightness with the increase of speed with which cornets approach the sun,
and the diminution in brightness with the diminution of the velocity with
which they leave the sun. And although from Herschel's remark just quoted,
it might be inferred that proximity to the sun is the cause of the increase of
brightness, this is proved not to be the case ; for (as in the case of Halley's
comet) when near its perihelion the tail sometimes dies away, and the comet
shrinks. In such cases, when the comet is nearest to the sun there is no
development of tail, which shows clearly that it is not the intensity of the
sun's rays, but the change in their intensity, that is the exciting cause of
these extraordinary appearances ; so that there is no reason to suppose that
a planet composed of the same material as a comet, no matter how close to
the sun, would show a vestige of tail or other cometic appearance.

It is, then, to this change in position that we must attribute those
peculiar appearances which belong to comets.

Now is not electricity the very effect which would naturally result from
such a state of change and variation in condition ?

A. de la Rive remarks, " Electricity is one of the most frequent forms
which the forces of nature assume in their transformations." It certainly
often accompanies a change in temperature. There is every indication that
it is so in our atmosphere ; for the times when its intensity is a maximum,
are just after sunrise, and just after sunset, both winter and summer.


For these reasons it seems to me not only possible, but probable, that these
strange visitors to our system are clothed in electrical garments, with which
the regular inhabitants are unacquainted.

The electricity must, after all, depend on the composition of the comet ; for
known substances do not all show the same electrical properties. Hence, by
assuming comets to be composed of various materials, we have a source to
which we can attribute the different appearances presented by the different
individuals. To the same source we may attribute the irregularity in the
direction of their tails, and the lateral streamers they occasionally send out.

Secondly, I think this electrical hypothesis is supported by the, to me,
seeming analogy between comets, the corona, and the aurora an analogy
which suggests that they must all be due to the same cause. They may be
all described as streams of light or streamers, having their starting point more
or less undefined, and traversing spaces of such extent, and with such
velocities, as entirely to preclude the possibility of their being material in any
sense of that word with which we are acquainted.

The aurora has long been considered an electrical phenomenon ; and
recently the same effect has been produced by the discharge of electricity of
very great intensity through a very rare gas, there being no limit to the space
which it will thus traverse. This being so, why should not the tails of comets,
and the corona also, be electrical phenomena ? Their appearance and behaviour
correspond exactly with those of the aurora ; and there is surely nothing very
difficult in imagining the sun, which is the source of so much heat, being also
the source of some electricity. Neither will there appear any thing wonderful
in the electricity of comets, when we consider that of the earth. We must
not look on our inability to explain the cause of such an electrical discharge
as fatal to its existence ; for we cannot any more explain the existence of the
electricity which causes the aurora. If we cannot explain whence these
electricities come, we can at least show that the conditions, which are most
favourable to the development of the aurora, exist in much greater force on
the comets than they do on the earth. The greatest development of the
aurora borealis takes place at the equinoxes. There is a cessation in summer,
and another in winter. Now the equinoxes are the times when the action of
the sun on our northern hemisphere is changing most rapidly. Hence the
condition favourable for the aurora is change in the action of the sun. The
same thing is pointed out by the diurnal variation in the electricity of the

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