shew you, that the reason why it is hottest when we are farthest from
the sun is, that in winter when we are nearest to him the days are
shorter, his rays sail very obliquely on us, and are more dispersed than
they are in summer, when he not only remains longer above the horizon,
but being higher, his rays fall more direct on us, by which means the
earth becomes so much heated that it has not time in the short nights to
get cold again.—When the earth is nearest the sun it is summer in the
southern hemisphere, therefore it is reasonable to suppose that the heat
there must far exceed ours in the same latitude; but to counteract this
their summer is shorter by eight days than ours: and it is well known
that it is much colder near the poles in the southern than in the
northern hemisphere: but this is accounted for from there being more
land to retain the heat in the latter than in the former.
PUPIL. My doubts on this head being now removed, I must beg you to give
me such other information as you may think proper.
TUTOR. As there are different degrees of heat and cold, the earth has
been divided into five zones, namely, one torrid, two temperate, and two
frigid zones.
PUPIL. How are they distinguished?
TUTOR. The torrid zone is all that space surrounding the globe contained
between the tropics, having the equator running through the middle of
it. It is so called on account of its excessive heat, for, twice every
year the sun is vertical to the inhabitants, that is, he shines directly
on their heads, and casts no shadow, but under their feet, at noon.
PUPIL. We find it sometimes extremely hot here in our summer; surely, in
the torrid zone it must be almost insupportable?
TUTOR. They are inured to it from their infancy.—But we are departing
from our subject.—The temperate zones are comprehended between the
tropics and polar circles, that between the tropic of Cancer and the
arctic circle is called the north temperate zone, and that between the
tropic of Capricorn and the antarctic circle the south temperate zone.
PUPIL. I suppose they are called temperate because the heat is not so
intense as in the torrid zone?
TUTOR. True. Neither is the cold so severe as in the frigid zones, which
are those regions comprized within the polar circles, and are
denominated north and south, as they are contiguous to the north or
south poles.
PUPIL. Why are they called frigid?
TUTOR. They are called frigid or frozen zones, because near the poles
there are perpetual fields of ice, the heat of the sun, even in summer,
being insufficient to dissolve it.—Now try if you can tell me the
breadth of each zone in degrees.
PUPIL. The torrid zone being twenty-three degrees and a half on each
side the equator must be forty-seven degrees, which must also be the
breadth of the frigid zones, as the polar circles are distant
twenty-three degrees and a half from the poles, which are their centers.
And, as from the equator to either pole is ninety degrees, from the
equator to the tropics twenty-three and a half, and from the polar
circle to the pole twenty-three and a half, if the sum of these, that
is, forty-seven, be taken from ninety, the remainder, forty-three, will
be the breadth of each of the temperate zones.
TUTOR. Very well.
PUPIL. From what you have told me I have no doubt but that the earth is
globular, but I have no proof of it: I must therefore beg your
assistance.
TUTOR. That it cannot be an extended plane, as some have imagined, is
very evident; for, if it were, the angle made with that plane and the
north pole star would be always equal, for reasons I have before given
you: neither can it be cylindrical, that is like a garden roller, as
others have supposed.—If a person travel northward the pole star becomes
more elevated, and if he could penetrate to the north pole of the earth
the star would be in the zenith, or directly over his head: on the
contrary, if he travel southward, it is more and more depressed till he
arrives at the equator, where the star is in the horizon; as he proceeds
it disappears, and other stars rise to his view, invisible to us. Here
then you see it must be circular northward and southward.
PUPIL. I am convinced it must be so.
TUTOR. And it is as certain that it is so east and west: for, navigators
have often sailed round it steering the same course: that is, if they
sail an easterly or westerly course at setting off, by continuing the
same course they will return to the port whence they departed. This you
know they could not do if it were not round, any more than an insect
could, by crossing a round table, arrive at the place it set out from;
but, by going round the edge it would be still going forward and come
again to the point it had left.
PUPIL. It is very evident.
TUTOR. Again. In every direction, if a ship be seen at a distance, the
first things observed are the top-mast and rigging, whilst the hull or
body of the ship is hidden behind the convexity, that is roundness of
the water, just as you would see a man coming over a hill, you would
first see his head, he would be rising more and more to your view till
he arrived at the top, where he would be full in sight.
PUPIL. I am at a loss to account for the convexity of the water. How can
its surface be round?
TUTOR. Have you never observed the drops of water falling from the eaves
of a house?
PUPIL. Often, Sir.
TUTOR. Of what shape were they?
PUPIL. Globular.—But what is the cause of their being so?
TUTOR. Attraction.—For as every particle of water which composes the
drop tends to the same center, every part of the surface must be
equidistant from the center, it must therefore be spherical. In like
manner if you separate quicksilver, each portion will form itself into a
globe.
PUPIL. All this is very clear. And, for the same reason, the water in
the ocean must be convex; for, I remember you told me that it gravitated
towards the center of the earth.
TUTOR. Once more.—I think you must have seen an eclipse of the moon.
PUPIL. I have, Sir.
TUTOR. Of what figure was the darkened part?
PUPIL. Circular.
TUTOR. Take this ball, and hold it before the candle between your finger
and thumb, so that the shadow may be thrown on the wall, and in all
positions you will find it circular.
PUPIL. It is so.
TUTOR. Apply this crown piece in the same manner, with the flat side to
the candle.
PUPIL. It is a circle.
TUTOR. Turn it a little obliquely.
PUPIL. It is now an ellipsis.
TUTOR. Now turn the edge to the candle.
PUPIL. The shadow is a strait line.
TUTOR. You now see that no other body than that of a globe can in all
positions cast a circular shadow.
PUPIL. I do, Sir.
TUTOR. The darkness on the disc of the moon at the time of an eclipse is
the shadow of the earth, which in all situations is circular; the earth,
therefore, which casts the shadow, must be a globe.
PUPIL. It must be so.—But——
TUTOR. The earth is mountainous.—It is so: but remember that the highest
mountain bears no greater proportion to the bulk of the earth than the
small irregularities on the peel of an orange bears to that fruit: that
objection therefore is soon removed. And yet it is not a true sphere.
PUPIL. What then?
TUTOR. A spheroid, that is, it is a little flattened at the poles, and
is in shape not unlike an orange or a turnip. This you will not be
surprized at when I tell you that the equatorial parts are about four
thousand miles from the center of motion.
PUPIL. I suppose then you infer that as the centrifugal force is greater
the farther it is removed from the center, that the parts near the poles
have a tendency to fly off towards the equator.
TUTOR. I do. And as we have finished this part of our subject, I shall
take leave of you.
------------------------------------------------------------------------
DIALOGUE XI.
TUTOR.
I now propose giving you a description of the moon, and I doubt not it
will afford you some degree of pleasure.
PUPIL. Indeed it will, as I know little more than that she is a
secondary planet or satellite, revolving round the earth, and with it
round the sun.
TUTOR. You know her mean distance from the earth.
PUPIL. I did not recollect that: 240 thousand miles.
TUTOR. Right. Her diameter is about 2161 miles, and her bulk about a
fiftieth part of the earth’s. Her axis is almost perpendicular to the
plane of the ecliptic, consequently she can have no diversity of
seasons.
PUPIL. What is her period?
TUTOR. The time she takes to revolve from one point of the heavens to
the same again is called her _siderial_ or _periodical revolution_, and
is performed in 27 days, 7 hours, 43 minutes; but _synodical
revolution_, or the time taken up to revolve from the sun to the same
apparent situation with respect to the sun again, or from change to
change, is 29 days, 12 hours, and 44 minutes.
PUPIL. I do not clearly comprehend it.
TUTOR. If the earth had no annual motion, the period of the moon would
be uniformly 27 days, 7 hours, 43 minutes; but you are to consider that
whilst the moon is revolving round the earth, the earth is advancing in
its orbit, and of course she must be so much longer in completing her
synodical revolution as the difference of time between that and her
siderial revolution. This I will make clear to you in a few
minutes.—What is the situation of the hour-hand and minute-hand of a
watch at twelve o’clock?
PUPIL. They will be in conjunction.
TUTOR. And will they be in conjunction at one?
PUPIL. No, Sir.
TUTOR. Yet the minute-hand has made a complete revolution: but before
they can be in conjunction again the minute-hand must move forward till
it overtakes the hour-hand.
PUPIL. I now understand it, and must beg you to explain to me the
different phases of the moon.
TUTOR. Take this ivory ball, and suspend it by the string with your hand
between your eye and the candle. Let the candle represent the sun, the
ball the moon, and your head the earth. In this situation, as the candle
enlightens only one half of the ball, the part turned from you will be
enlightened, and the part turned to you will be dark. This will be a
representation of the moon at change, and as no part of her enlightened
hemisphere is turned to the earth, she can reflect no light upon it, and
consequently is invisible to us. She now rises and sets nearly with the
sun.—Turn yourself a little to the left, and you will observe a streak
of light like what is called the new moon.
PUPIL. I see it clearly.
TUTOR. Move round one quarter.
PUPIL. One half of the side next me is now enlightened.
TUTOR. You may conceive it to be the moon at first quarter.—Go on, and
you will see the light increase till the ball is opposite to the candle,
when the side next you will be wholly illumined, and will give you a
just idea of the moon at full, which now rises about the time of
sun-setting, being opposite to the sun: and, the farther she advances in
her orbit the later she rises.
PUPIL. It is plain it must be so. She rises with the sun at change,
being then in conjunction: and as she revolves in her orbit the same way
as the earth does on its axis, the earth will have farther to revolve
each day before it can see the moon. At the full she is in opposition,
and of course rises when the sun sets: and so continues to rise later
and later, till the change again.
TUTOR. You imagine that the moon rises exactly with the sun when she is
at change; and when he sets, at full. I will presently convince you of
your mistake; and would have you now proceed with your ball. Place it
again opposite to the candle, and as you turn round you will find the
light gradually decrease as it before increased, that the side that was
before enlightened is now dark, and the dark side light. When you have
gone three quarters round, one half of the side next you will be
enlightened, and will resemble the moon at last quarter. As you go on
the darkened part will increase, till you arrive at the place you set
off from, where the light is quite obscured.
PUPIL. I have now completed the circuit, and am much delighted with it,
as by this simple contrivance I can perceive the various changes of the
moon, and that the western side is enlightened from the change to the
full, and the eastern side from the full to the change.
TUTOR. I find then it has fully answered the purpose intended.
PUPIL. Indeed it has. But if you will give me leave I will use the ball
again.
TUTOR. By all means.
PUPIL. I perceive, as I move round, that the same side of the ball is
turned towards me whilst every part is turned to the candle. Is it so
with the moon?
TUTOR. It is: and as every part of the moon is turned to the sun, she
makes one revolution on her axis whilst she makes one in her orbit.
PUPIL. This is very singular. If the same side of the moon be always
turned to the earth, the opposite side of course can never see it.
TUTOR. And they must likewise be deprived of the earth as a moon.
PUPIL. True. But how is it known that the same side of the moon is
always opposed to the earth?
TUTOR. The moon, like our earth, consists of mountains and valleys,
which, when seen through a good telescope, are very beautiful. The
mountainous parts appear as lucid spots and bright streaks of light: and
as the same spots, &c. are constantly turned to the earth, she must keep
the same side to the earth.
PUPIL. It is very clear. Are there no seas?
TUTOR. It was formerly imagined that the dark parts were seas, but later
observations prove that they are hollow places or caverns, which do not
reflect the light of the sun. Besides, if there were seas there would
consequently be exhalations, and if exhalations, clouds and vapours, and
an atmosphere to support them. That there are no clouds is evident,
because when our atmosphere is clear, and the moon above our horizon in
the night-time, all her parts appear constantly with the same clear,
serene, and calm aspect.
PUPIL. Has the moon then no atmosphere?
TUTOR. If she has it is imperceptible to us: for, when she approaches
any star, we cannot discover with our best telescopes any change of
colour or diminution of lustre in the star till the instant it is lost
behind her: whence it is clear, that she can have no such gross medium
as our atmosphere to surround her.
PUPIL. May we not then doubt whether she be inhabited or not, as without
air we cannot breathe?
TUTOR. The same Almighty Being who created us and gave us air to
breathe, may have provided a different way for their existence. It does
not hold good that, because we could not live there, she is not
inhabited. Fish will live a considerable time in water under an
exhausted receiver: and, I have heard of a toad being found in a block
of marble. Your doubt therefore, I think, ought not to be admitted.
PUPIL. I am satisfied. And must now beg to be informed how I may observe
the moon’s motion.
TUTOR. Her real motion round the earth, may be easily known by remarking
when she is near any particular star. Thus, suppose you see her west,
that is to the right of it, she will be approaching, then in conjunction
with, and afterwards pass it towards the east. Her apparent motion is
that of rising and setting, which is occasioned by the rotation of the
earth on its axis.
PUPIL. I remember not long since, when you shewed me Jupiter, that the
moon was west of him: the next evening I saw her almost appear to touch
him, and soon after at a great distance from him easterly. I now see
that her real motion is from west by south to east, and her apparent
motion from east by south to west.
TUTOR. If you have no objection, I will now explain the cause of
eclipses.
PUPIL. So far from it, that it will give me the greatest pleasure.
TUTOR. Take your ivory ball, suspend it as before, in a right line
between your eye and the candle.—Can you see the candle?
PUPIL. No, Sir.
TUTOR. For what reason.
PUPIL. Because the ball prevents the light coming to me.
TUTOR. This then represents an eclipse of the sun, which can never
happen but when the moon is between the sun and the earth, which must be
at the change: for, as light passes in a right line, the sun is hidden
to that part of the earth which is under the moon, and therefore he must
be eclipsed. If the whole of the sun be obscured by the body of the
moon, the eclipse is total: if only a part be darkened, it is a partial
eclipse; and so many twelfth parts of the sun’s diameter, as the moon
covers, so many digits are said to be eclipsed.
PUPIL. May not the word digit be applied to the moon as well as the sun?
TUTOR. It may: for it means a twelfth part of the diameter of either the
sun, or the moon.
PUPIL. As you have now shewn me the cause of an eclipse of the sun, I am
anxious to have that of the moon explained.
TUTOR. We must again have recourse to your little ball.—Turn yourself
round till it is opposite to the candle in a line with your head, and
you will see that no light can be thrown on it from the candle, because
your head is between them. In like manner the rays of the sun are
prevented falling on the moon, by the interposition of the earth: she
must therefore be eclipsed.
PUPIL. I see it clearly. And as an eclipse of the sun happens when the
moon is at change, that of the moon must be when she is at full; for, it
is then only the earth’s shadow can fall on the moon, the earth being at
no other time between the sun and her.
TUTOR. The diameter of the shadow is about three times that of the moon,
and consequently the moon must be totally eclipsed whilst she continues
in it. On the contrary, the shadow of the moon at an eclipse of the sun,
covers so small a part of the earth’s surface, that the sun is totally
or centrally eclipsed to but a small part of it; and its duration is
very short. But a faint or partial shadow surrounds this darkened shade,
in which the sun is more or less eclipsed, as the place is nearer to or
farther from its center; this partial shadow is called the _penumbra_. I
have prepared for you a little drawing, representing an eclipse both of
the sun and moon, which I think will enable you better to understand
what I have been explaining. (Plate IV. Fig. 1 and 2.) In the former,
_p. p._ is the penumbra.
[Illustration: _Plate IV._
_T. Conder Sculp^t._]
PUPIL. In what does a central differ from a total eclipse?
TUTOR. An eclipse of the sun may be central, and not total; for, those
who are under the point of the dark shadow, will see the edge of the sun
like a fine luminous ring, all around the dark body of the moon when the
sun is eclipsed at the moon’s greatest distance from the earth; but when
she is nearest the earth at an eclipse of the sun, the eclipse is total.
When the penumbra first touches the earth, the general eclipse begins;
when it leaves the earth, the general eclipse ends. An eclipse of the
moon always begins on the moon’s eastern side, and goes off on her
western side; but an eclipse of the sun begins on the sun’s western
side, and goes off on his eastern side. When the moon is eclipsed in
either of her nodes, the eclipse is both central and total.
PUPIL. Pray, what is the reason we have not an eclipse at every full and
change of the moon?
TUTOR. For the same reason that Mercury and Venus are not seen to pass
over she sun’s disc at every inferior conjunction.
PUPIL. Is the orbit of the moon then inclined to the plane of the
ecliptic?
TUTOR. It is: and no eclipse of the sun can happen but when the moon is
within 17 degrees of either of her nodes: neither can there be one of
the moon, unless she be within 12 degrees. At all other new moons she
passeth either above or below the sun, as seen from the earth: and at
all other full moons above or below the earth’s shadow, according as she
is north or south of the ecliptic. You now see that the moon must
sometimes rise before and sometimes after the sun at change, and before
or after he sets at full.
PUPIL. I do, Sir, and am much obliged to you for this pleasing account
of the moon, and of eclipses: and if you have any thing farther to
observe, it will afford me additional pleasure.
TUTOR. You may, at some time or other, have an opportunity of seeing a
total eclipse of the moon; it will therefore be necessary to prepare you
for a phænomenon which otherwise you might be much surprized at, and
that is, that after the moon is immersed in the earth’s shadow, she is
still visible.
PUPIL. This is a phænomenon that I am not able to account for; for, the
moon being an opaque body, she cannot shine by her own light[16], and
the rays of the sun are prevented falling on her by the interposition of
the earth, she cannot therefore shine by reflection.
[Footnote 16: Dr. Herschell supposes the moon and the rest of the
planets may have some inherent light: the side of the planet Venus,
turned from the sun, having been seen, as we see the moon soon after
the change.]
TUTOR. It is by reflection that we see her; for the rays of the sun
which fall upon our atmosphere are refracted or bent into the earth’s
shadow, and so falling upon the moon are reflected back to us. If we had
no atmosphere, she would be totally dark, and of course invisible to us.
PUPIL. What is her appearance?
TUTOR. It is that of a dusky colour, somewhat like tarnished copper.—I
have one thing more to remark before we quit this subject, which is,
that the moon’s nodes have a retrograde or backward motion, in a
direction contrary to the earth’s annual motion, and go through all the
signs and degrees of the ecliptic in little less than nineteen years,
when there will be a regular period of eclipses, or return of the same
eclipses for many ages.
PUPIL. Pray, Sir, what do you propose for our next subject?
TUTOR. The ebbing and flowing of the sea, or cause of the tides.
------------------------------------------------------------------------
DIALOGUE XII.
TUTOR.
In order to explain the cause of the tides, I have since I saw you last
prepared a little drawing for you, (Plate IV. fig. 3.) where S
represents the sun, M the moon at change, E the center of the earth, and
A B C D its surface, covered with water. It is obvious, from the
principles of gravitation, that if the earth were at rest the water in
the ocean would be truly spherical, if its figure were not altered by
the action of some other power. But, daily experience proves that it is
continually agitated.
PUPIL. What is the cause of this agitation?
TUTOR. The attraction of the sun and moon, particularly the latter: for,
as she is so much nearer the earth than the sun, she attracts with a
much greater force than he does, and consequently raises the water much
higher, which, being a fluid, loses as it were its gravitating power,
and yields to their superior force.
PUPIL. What proportion does the attractive power of the sun bear to that
of the moon?
TUTOR. As three to ten. So when the moon is at change, the sun and moon
being in conjunction, or on the same side of the earth, the action of
both bodies is on the surface of the water, the moon raising it ten
parts,[17] and the sun three, the sum of which is thirteen parts,
represented by B _b_. Now it is evident, that if thirteen parts be added
by the attractive power of those bodies, the same number of parts must
be drawn off from some other part, as A _a_, C _c_. It will now be
high-water under the moon at _b_, and its opposite side _d_, and
low-water at _a_ and _c_.
[Footnote 17: By part here I do not mean any specific measure.]
PUPIL. That the attraction of the sun and moon must occasion a swelling
of the waters on the side next them, I can readily conceive, and that
this swell must cause a falling off at the sides: but that the tide
should rise as high on the side opposite to the sun and moon, in a
direction contrary to their attraction, is what I am not able to account
for.
TUTOR. This difficulty will be removed when you consider that all bodies
moving in circles have a constant tendency to fly off from their
centers. Now, as the earth and moon move round their center of gravity,
that part of the earth which is at any time opposite to the moon will
have a greater centrifugal force than the side next her, and at the
earth’s center the centrifugal force exactly balances the attractive
force: therefore, as much water is thrown off by the centrifugal force
on the side opposite to the moon, as is raised on the side next her by
her attraction. Hence, it is plain, that at D, fig. 3, the centrifugal
force must be greater than at the center E, and at E than B, because the
part D is farther from the center of motion than the part B. On the
contrary, the part B being nearer the moon than the center E, the
attracting power must there be strongest, and weakest at D. And, as the
two opposing powers balance each other at the earth’s center, the tides
will rise as high on that side from the moon, by the excess of the
centrifugal force, as they rise on the side next her by the excess of
her attraction.
PUPIL. In this explanation you have mentioned nothing of the sun.