that which respects land and water is called the _sensible horizon_. The
former divides the heavens into two equal parts, and is 90 degrees
distant from a point directly over our heads, called the _zenith_, and
the opposite point of the heavens directly under our feet, called the
_nadir_.—But I must resume the subject of the atmosphere.
PUPIL. Had I not thought you had finished your description of the
atmosphere, I should not have presumed to interrupt you.
TUTOR. What I have told you respecting the horizon is necessary for you
to be acquainted with; therefore, the suspension is immaterial.—You
must, I make no doubt, have observed the sun and moon at rising and
setting to appear larger than when higher above the horizon.
PUPIL. I have, frequently, Sir.
TUTOR. And cannot you tell the reason of it?
PUPIL. No, Sir.
TUTOR. The reason is this: In viewing them, when near the horizon, you
see them through a thicker medium than when they are higher, that is,
you see them through a greater quantity of the atmosphere; and you not
only see them larger, but really above the horizon whilst they are
actually below it.
PUPIL. How do you account for this, Sir?
TUTOR. Light, like material bodies, if it meet with no obstruction, will
move in right lines; now, the rays of the sun in coming to the earth
must pass through a great quantity of the atmosphere, which being a
fluid, refracts or bends the rays of light, by which refraction it is
that we are favoured with the sight of the sun 3-1/4 minutes every
morning before he rises above the horizon, and every evening after he
sinks below it, which in one year amounts to more than 40 hours. This
refraction is greatest near the horizon, and ends in the zenith.
PUPIL. Pray, Sir, can you make this clearer by an experiment?
TUTOR. I have just thought of one. Take a bason filled with water, and a
strait stick or piece of wire; put it perpendicularly into the water,
that is, that it lean neither way, and there will be no refraction;
incline it a little towards the edge of the bason and it will appear a
little bent at the surface of the water; incline it still more, and the
refraction will be greater.
PUPIL. I have often seen this appearance when I have put my stick into
water, but did not before know the cause.
TUTOR. You may try one more experiment. Pour the water out of the bason,
and set the bason on the floor; put a guinea into it, and let it
represent the sun.—Why do you smile?
PUPIL. Because I have not the sun’s representative to try the experiment
with.
TUTOR. Well, well, put a shilling into the bason and call it the moon,
and it will answer the same purpose:—Walk backward till you just lose
sight of it, then the right line from your eye continued over the edge
of the bason must pass beyond the money at the bottom of it.
PUPIL. That is evident.
TUTOR. Keep your position, and desire some friend to pour the water
gently into the bason so as not to remove the money, and you will
clearly distinguish it. Now, if you call the edge of the bason the
horizon, the water the atmosphere, and the shilling the moon, is it not
clear that you will see it above the horizon, when it is really below
it?
PUPIL. I think so, Sir.
TUTOR. Well, try the experiment, and let me know the result when I next
see you.
------------------------------------------------------------------------
DIALOGUE IX.
TUTOR.
I presume, Sir, you have made the experiment I recommended to you.
PUPIL. I have, Sir; and am so well convinced of what you told me, that
nothing farther need be said on the subject.
TUTOR. As that is the case, I shall proceed.—I dare say you do not
forget what the plane of the ecliptic is.
PUPIL. I do not, Sir; but have a perfect recollection of it.
TUTOR. Now, remember, that the axis of the earth is not upright or
perpendicular to the plane of the ecliptic, but inclines to, or leans
towards it, 23-1/2 degrees, and makes an angle with it of 66-1/2
degrees.
PUPIL. An angle signifies a corner; but that cannot be the meaning here.
TUTOR. That is what is generally understood by an angle: but, in
geometry, it means the meeting of any two lines which incline to one
another, in a certain point. Now, if you conceive the axis of the earth
to be one line, and the plane of the ecliptic the other, the point where
they meet or cross each other will form an angle.
PUPIL. I think I understand it; but how can it contain 23-1/2 or 66-1/2
degrees?
TUTOR. You know what a degree is.
PUPIL. If I remember right it is the 360th part of a circle.
TUTOR. It is so: and the measure of an angle is an arc or part of the
circumference of a circle, whose angular point is the center: and so
many 360th parts as any arc contains, so many degrees the measure of the
angle is said to be; thus, Z C P (Plate III. fig. 1.) makes an angle of
23-1/2 degrees, because the arc Z P contains 23-1/2 360th parts of the
whole circle. Then if A B represent the plane of the ecliptic, and N C S
the axis of the earth, as D N contains the same number of degrees as Z
P, will not its inclination from a perpendicular be 23-1/2 degrees?
[Illustration: _Plate III._
_T. Conder Sculp^t._]
PUPIL. Nothing can be plainer.
TUTOR. For the same reason, as P B contains 66-1/2 parts of the whole
circle, the axis of the earth makes an angle of 66-1/2 degrees with the
plane of the ecliptic. And, if you add 23-1/2 to 66-1/2 the sum will be
90, which is the measure Z B, or the fourth part of the circle, and
makes what is called a right angle, at the point or center C.
PUPIL. It is very clear:—but what do the other letters refer to?
TUTOR. The extremities of the earth’s axis are called the poles, N the
north, and S the south pole, and P the north-pole star, to which, and to
the opposite part of the heavens, the axis always points. These
extremities in the heavens appear motionless, whilst all other parts
seem in a continual state of revolution: the circle of motion appears to
increase with the distance from the apparently motionless points to that
circle in the heavens which is at an equal distance between them, called
the equinoctial, represented by the letters Æ Q; and is the same I
promised some time ago to explain to you.
PUPIL. I recollect it: and as the line A B represents the plane of the
ecliptic, I suppose the line Æ Q is the plane of the equinoctial, which
I see crosses it as you then told me.
TUTOR. You are right: and it makes an angle with it of 23-1/2 degrees.
It is called the equinoctial, because when the sun appears there, that
is, in Aries or Libra, the days and nights are equal in all parts of the
world, which I shall shew you in due time; and shall now explain to you
what I have just mentioned, that the axis of the earth always points to
the same parts of the heavens. I am apprehensive you will think it
strange that this should be the case, and the axis keep parallel to
itself.
PUPIL. What am I to understand by the axis being parallel to itself?
TUTOR. Two lines are said to be parallel when they do not incline to but
keep at equal distances from each other; so that if they were infinitely
continued, they would never meet. Now, if you can conceive a line drawn
parallel to the earth’s axis in any part of its orbit, it will be
parallel to it in every other part of it. A little drawing I have by me,
(Plate III. fig 2.) where the earth is represented in four different
parts of its orbit, I think will make this plain to you.
PUPIL. I comprehend your meaning clearly. But, as the orbit of the earth
is 190 millions of miles in diameter, I have not the least conception
how it can incline to the same points. Had you not told me to the
contrary, I should have thought it must move round them in every
revolution of the earth about the sun.
TUTOR. That such a motion would be perceptible is evident, if the fixed
stars were near the earth; but, compared with their distance, 190
millions of miles is but a mere point: therefore, the axis always
inclines to the same points of the heavens.
PUPIL. This is a greater proof of the inconceivable distance of the
stars than what you mentioned before, and I thought that very
astonishing:
Wonders on wonders constantly arise,
Whene’er we view the earth, or sea, or skies.
TUTOR. It is very true. And the more we search, the more we have cause
to admire the works of the Almighty.
PUPIL. Pray, Sir, what is the next thing you propose?
TUTOR. To make you acquainted with the other circles you see in the
figure (Plate III. fig. 1.) as it is very necessary you should know
them.
PUPIL. Will you be kind enough to tell me their names, Sir, and I will
endeavour to remember them?
TUTOR. That line which divides the globe into two equal parts, called
the northern and southern hemispheres, which answers to the equinoctial
in the heavens, and is equally distant from the two poles, is called the
_equator_; the other which crosses it, as I before told you, is the
_ecliptic_; the smaller circle, north of the equator, is the _tropic of
Cancer_; that south of it, the _tropic of Capricorn_; the circles next
the poles are called the _polar circles_; or that next the north pole,
the _arctic circle_, and that next the south pole, the _antarctic
circle_; each of which is 23-1/2 degrees distant from its respective
pole, as are the tropics from the equator.
PUPIL. You have not mentioned the lines which cross the other circles,
and terminate in the poles; what are they called?
TUTOR. They are called _meridians_, because when any of them, as the
earth revolves on its axis, is opposite to the sun, it is mid-day or
noon along that line. Twenty-four of these lines are usually drawn on
the globe to correspond with the twenty-four hours of the day; but you
are not to suppose there are no more than twenty-four; for every place
that lies ever so little east or west of another place has a different
meridian.—To make this clearer to you, we will suppose the upper 12
(Plate III. fig. 1.) to be opposite the sun, it will of course be noon
along that line; the next meridian marked 1, being 15 degrees east, will
have passed the meridian 1 hour, consequently it will there be one in
the afternoon, and so on, according to the order of the figures, till
you come to the lower 12, which being the part of the earth turned
directly from the sun, it will be midnight on that meridian; on the next
meridian, as you proceed round, it will be one in the morning, the next
two, and so on till you arrive at the upper twelve, where you set off.
So you see there must be a continual succession of day and night. This
difference of time between places lying under different meridians is
what is called longitude.
PUPIL. I think I have heard of a Mr. Harrison, who made a time-keeper
for determining the longitude. Shall I trespass at all if I beg a little
farther information on this subject?
TUTOR. It is my wish at all times to satisfy your curiosity, when I can
do it with propriety. I shall therefore comply with your request.—Mr.
Harrison’s time-keeper, and those made since by other artists, are so
constructed, that the heat and cold of different climates will not
affect them; for, all metals are more or less expanded by heat, and
contracted by cold; for which reason it is, that a clock or watch made
in the usual way will not keep equal time. Now, all that is required of
these time-keepers to ascertain the longitude is this: Suppose a captain
of a vessel sailing from London to the West Indies, we will say
Kingston, in Jamaica. On his passage thither he makes an observation,
and finds the sun on the meridian, or that it is twelve o’clock in that
situation, when by his time-keeper it is two in the afternoon in London,
whence he concludes he is 30 degrees west of London.
PUPIL. I must beg you to explain this to me, as I do not understand why
two hours of time should be equal to 30 degrees of longitude.
TUTOR. You must consider, that as the earth makes a complete revolution
on its axis in 24 hours, it must pass over 360 degrees in that time:
now, if you divide 360 by 24, the quotient 15, will be the number of
degrees passed over in one hour; 30 degrees will be equal to two hours,
&c. The difference of time between London and his situation is two
hours, consequently the difference of longitude must be 30 degrees: and,
it must be west, because the sun had passed the meridian of London; for,
as the earth revolves from west by south to east, one place which lies
east of another must come first to the meridian or opposite to the sun.
Therefore, when longitude is reckoned from London, if the place lie east
of that meridian the time will be before; if west, after London.
PUPIL. I see it clearly; and as 60 minutes make an hour, if I divide it
by 15, the quotient 4 will be the minutes answering to one degree.
TUTOR. You are right: and for the same reason, 4 seconds of time are
equal to one minute of longitude, which you know is the 60th part of a
degree.—Our captain when arrived at Kingston, finds the difference of
time between it and London 5 ho. 6 min. 32 sec. Can you tell me the
longitude of Kingston?
PUPIL. If I bring the hours and minutes to minutes, and divide by 4, the
quotient I think will be degrees, will it not?
TUTOR. It will: and the seconds of time divided by 4, will be minutes of
longitude. Now try if you can do it.
PUPIL. Five hours 6 minutes, multiplied by 60 will be 306 minutes, this
divided by 4, will give 76 degrees and 2 over, which 2 is half a degree,
or 30 minutes: and 32 seconds of time divided by 4, will be 8 minutes of
longitude, the sum of which is 76 degrees 38 minutes for the longitude
of Kingston.
TUTOR. Very well.—I have just now thought of another method of reducing
time to longitude, and longitude to time, which you may probably find
easier. However, when you are in possession of both, you may use which
you please.
PUPIL. That which is easiest must, I think, be best.
TUTOR. I will give it you, and let me have your opinion of it.
To reduce time to longitude.
Multiply the hours, minutes, and seconds of time by 15, or
rather by the factors as they are called, namely 3 and 5,
carrying one for every 60 in the minutes and seconds, and
setting down the remainder, thus:
ho. min. sec.
5 6 32 difference of
3 time.
────────────────
15 19 36
5
────────────────
Degrees 76 38 0 longitude.
════════════════
Divide the degrees and minutes of longitude by 5 and 3 and the
quotient will be the difference of time.
PUPIL. I give this the preference.
TUTOR. As longitude is seldom mentioned without being accompanied with
latitude, that you may not be ignorant of its meaning when you meet with
it, I shall just tell you that it is the distance of any place from the
equator, reckoned in degrees and minutes on the meridian, and is either
north or south as the place lies north or south of the equator. The
latitude of any place is equal to the elevation of the pole above the
horizon. The latitude of the heavenly bodies is reckoned from the
ecliptic, and terminates in the arctic and antarctic circles: and their
longitude begins at the point Aries.
PUPIL. What is the measure of a degree?
TUTOR. A degree of latitude is 60 geographical, or 69-1/2 English miles:
and a degree of longitude on the equator is equal to it, because the
equator as well as the meridians divides the globe into two equal parts.
But a degree of longitude decreases as you approach the poles: for at
the poles the meridians meet in a point, consequently a degree there can
have no dimension. To-morrow I will shew you the cause of the seasons.
------------------------------------------------------------------------
DIALOGUE X.
PUPIL.
I think, Sir, when you left me last night you told me our next business
would be to explain the nature of the seasons?
TUTOR. I did so, and am persuaded you will find no great difficulty in
comprehending it.—Cast your eye on the little drawing I gave you, (Plate
III. fig. 2.) where the earth is represented as situated at the four
quarters of the year, namely, Spring, Summer, Autumn, and Winter.—But
before we proceed to an explanation it will be necessary to remark,
that, in the little scheme the eye is supposed to be elevated above the
plane of the earth’s orbit, and that we see it very obliquely. The orbit
by this means appears very elliptical; and, the enlightened hemisphere,
or that half of the earth which is turned to the sun in the spring, and
the darkened hemisphere, or that turned from him in the autumn, are
there represented.
PUPIL. This I understand.
TUTOR. Well then, we will begin with the spring.—In this situation of
the earth the equator is exactly opposed to the sun: and, as he always
enlightens a hemisphere, or half of its surface, his rays will reach to
both the poles: whence, from the diurnal revolution of the earth, the
day and night are equal all over the globe.
PUPIL. This I remember you told me happened when the sun was in Aries
and Libra. The sun is now entering Aries: and, as we are in the rays of
the sun one half of the diurnal revolution, and in the shadow of the
earth, or dark, the other half, the day and night must be equal.
TUTOR. Certainly. And as the sun enters Aries in the equinoctial, it is
then called the _Vernal_, that is, _Spring Equinox_. When the sun enters
the opposite sign Libra, the same effects are produced, and it is then
called the _Autumnal Equinox_.
PUPIL. You have passed on from Spring to Autumn.
TUTOR. I have so.—We will now return, and trace the earth in its orbit
from spring to summer.—You have already seen that the north and south
poles are both enlightened, and that the day and night are equal at the
equinoxes. If the axis of the earth were perpendicular to the plane of
the earth’s orbit, this would constantly be the case, and we should have
no diversity of seasons: for, the sun being over the equator, the poles
must be perpetually enlightened, and of course we should have equal day
and night at all times of the year.
PUPIL. That is plain. I suppose then that it is to the inclination of
the earth’s axis we are indebted for the increase and decrease of days.
TUTOR. It is occasioned by the inclination of the earth’s axis and its
preserving its parallelism, which I explained to you last evening.—As
the sun is now in the first point of Aries, the earth you know must be
in the beginning of Libra, it being the opposite sign.—Now fix your
attention on the scheme, and imagine the earth to be advancing in its
orbit through Libra, Scorpio, and Sagittarius: and at the first degree
of Capricorn give me your opinion of the earth’s position.
PUPIL. The north pole is turned to the sun, the south pole from him, and
the tropic of Cancer is opposite to him.
TUTOR. How many degrees are the tropics from the equator, or, in other
words, what is the inclination of the earth’s axis?
PUPIL. Twenty-three degrees and a half.
TUTOR. And so far are the rays of the sun cast beyond the north pole,
and fall short of the south pole: so that the whole of the arctic circle
is enlightened, and the antarctic circle involved in darkness.
PUPIL. What conclusion am I to draw from this?
TUTOR. That in the northern half of the globe it is the longest day, or
summer, and in the southern half the shortest, or winter, whilst under
the equator the days and nights are equal.
PUPIL. I used to think that when it was winter or summer here it was so
in every part of the world.
TUTOR. You now find your mistake. For as the earth is making its
progress from Libra, the north pole is approaching the sun, and the
south pole receding from him: consequently the length of the day is
increasing in the northern hemisphere and decreasing in the
southern.—The sun has now been three months above the horizon of the
north pole, and the same time below that of the south pole, and in three
months more, when the earth arrives at Aries, the scene will be
reversed: the sun will be over the equator, both poles will be again
enlightened, and the day and night will be equal in every part of the
globe. The sun will now be rising to the south and setting to the north
pole. This is our Autumn.
PUPIL. And as the earth is advancing towards winter, the south pole will
be turning to the sun, and the north pole from him, whence I conclude
that when the earth is in Cancer it must be summer, south of the
equator, when it is our winter.
TUTOR. Most assuredly. For you see that the sun is over the tropic of
Capricorn, which you know is as much south of the equator as the tropic
of Cancer is north of it, where the sun was in our summer. The antarctic
circle is now enlightened, and the arctic obscured in shade; but, under
the equator there is neither increase nor decrease, the days and nights
being each twelve hours.
PUPIL. It is now our winter, the sun has been three months above the
horizon of the south pole, and will continue so till the vernal equinox,
when he will again rise to the north pole, and so on in regular
succession.
TUTOR. It must be plain then to you that there can be but one day and
one night at each of the poles, reckoning the time the sun is above or
below their respective horizons; under the arctic and antarctic circles,
the longest day is twenty-four hours, and in the shortest the sun is
just visible in the horizon at noon. The longest day decreases in length
the nearer we approach the equator, where I before observed there is no
variation, because the circle bounding light and darkness, in every
position of the earth, divides the equator into two equal parts; and, it
must be observed, that the longest day and longest night are equal to
each other in every part of the globe.
PUPIL. If the longest day under the arctic circle be just twenty-four
hours, the sun must rise in the north.
TUTOR. He does so, makes a complete circle and sets in the [15]north
again. From the arctic circle to the equator, he rises north of the east
and sets north of the west: at the equator he rises due east and sets
due west, thence southward to the antarctic circle, he rises south of
the east, and sets south of the west: and under the antarctic circle, as
I observed just now, he is visible in the horizon in the south at noon.
[Footnote 15: Here it must be observed that there will be a little
variation from sun-rising to sun-setting, as the earth is advancing
in its orbit.]
PUPIL. We usually say, the sun rises in the east and sets in the west.
TUTOR. At the equinoxes it must be so in all parts of the globe, the
poles excepted: in every other situation, except under the equator,
there is a continual change. What I have now told you, respecting the
northern hemisphere, will be reversed at our shortest day: that is, in
the northern hemisphere the sun will rise south of the east and set
south of the west; and, in the southern hemisphere the contrary, the sun
will be in the horizon, at noon, under the arctic circle, and the day
will be twenty-four hours under the antarctic circle.
PUPIL. Pray Sir, are the regions within the polar circles inhabited? If
they are, their situation, in winter, must, I think, be dreadful.
TUTOR. It is foreign to my present purpose to speak of the inhabitants
of the earth, as that more properly belongs to Geography. Thus much
however I shall tell you, that, although it must be very cold and
dreary, they are not so long deprived of light as you may imagine; for,
even under the poles, when the sun is hidden from them, they are but a
short time in total darkness, for, you must recollect, that the twilight
continues till the sun is eighteen degrees below the horizon; and the
sun’s greatest depression, you know, can be but twenty three degrees and
a half, equal to the inclination of the earth’s axis. Besides this, the
moon is above the horizon of the poles a fortnight together; being half
her period north, and the other half south, of the equator; and, as the
moon at full is in the sign opposite to the sun, the tropical full moons
must be twenty-four hours above the horizon at the polar circles.
PUPIL. This description is very pleasing, as I had no idea of their
being favoured with so much light in the absence of the sun: and, I
find, as the sun is longer above the horizon in summer than in winter,
the moon, on the contrary, continues longer with us in winter, when we
most need her assistance, than she does in summer.