air in which it vibrates, and by the friction of the part by which it is
suspended: were it possible to remove these obstacles, the motion of a
pendulum would be perpetual, and its vibrations perfectly regular; each
being of equal distance, and performed in equal times.
_Emily._ That is the natural result of the uniformity of the power which
produces these vibrations, for the force of gravity being always the
same, the velocity of the pendulum must consequently be uniform.
_Caroline._ No, Emily, you are mistaken; the force is not every where
the same, and therefore the effect will not be so either. I have
discovered it, Mrs. B.; since the force of gravity is less at the
equator than at the poles, the vibrations of the pendulum will be slower
at the former place than at the latter.
_Mrs. B._ You are perfectly right, Caroline; it was by this means that
the difference of gravity was discovered, and the true figure of the
earth ascertained.
_Emily._ But how do they contrive to regulate their time in the
equatorial and polar regions? for, since in our part of the earth the
pendulum of a clock vibrates exactly once in a second, if it vibrates
faster at the poles, and slower at the equator, the inhabitants must
regulate their clocks in a manner different from us.
_Mrs. B._ The only alteration required is to lengthen the pendulum in
one case, and to shorten it in the other; for the velocity of the
vibrations of a pendulum depends on its length; and when it is said that
a pendulum vibrates quicker at the pole than at the equator, it is
supposed to be of the same length. A pendulum which vibrates seconds in
this latitude is about 39-1/7 inches long. In order to vibrate at the
equator in the same space of time, it must be somewhat shorter; and at
the poles, it must be proportionally lengthened.
The vibrations of a pendulum, resemble the descent of a body on an
inclined plane, and are produced by the same cause; now you must
recollect, that the greater the perpendicular height of such a plane, in
proportion to its length, the more rapid will be the descent of the
body; a short pendulum ascends to a greater height than a larger one, in
vibrating a given distance, and of course its descent must be more
rapid.
I shall now, I think, be able to explain to you the cause of the
variation of the seasons, and the difference in the length of the days
and nights in those seasons; both effects resulting from the same cause.
In moving round the sun, the axis of the earth is not perpendicular to
the plane of its orbit. Supposing this round table to represent the
plane of the earth's orbit, and this little globe, the earth; through
this I have passed a wire, representing its axis and poles. In moving
round the table, I do not hold the wire perpendicular to it, but
obliquely.
_Emily._ Yes, I understand, the earth does not go round the sun in an
upright position, its axis is slanting or oblique; and, it of course,
forms an angle with a line drawn perpendicular to the plane of the
earth's orbit.
_Mrs. B._ All the lines, which you learnt in your last lesson, are
delineated on this little globe; you must consider the ecliptic as
representing the plane of the earth's orbit; and the equator, which
crosses the ecliptic in two places, then shows the degree of obliquity
of the axis of the earth; which amounts to 23-1/2 degrees, very nearly.
The points in which the ecliptic intersects the equator, are called the
equinoctial points.
But I believe I shall render the effects of the obliquity of the earth's
axis clearer to you, by the revolution of the little globe round a
candle, which shall represent the sun. (Plate IX. fig. 2.)
As I now hold it, at A, you see it in the situation in which it is in
the midst of summer, or what is called the summer solstice, which is on
the 21st of June.
_Emily._ You hold the wire awry, I suppose, in order to show that the
axis of the earth is not upright?
_Mrs. B._ Yes; in summer, the north pole is inclined towards the sun. In
this season, therefore, the northern hemisphere enjoys much more of his
rays than the southern. The sun, you see, now shines over the whole of
the north frigid zone, and notwithstanding the earth's diurnal
revolution, which I imitate by twirling the ball on the wire, it will
continue to shine upon it as long as it remains in this situation,
whilst the south frigid zone is at the same time completely in darkness.
_Caroline._ That is very strange; I never before heard that there was
constant day or night in any part of the world! How much happier the
inhabitants of the north frigid zone must be than those of the southern;
the first enjoy uninterrupted day, while the last are involved in
perpetual darkness.
_Mrs. B._ You judge with too much precipitation; examine a little
further, and you will find, that the two frigid zones share an equal
fate.
We shall now make the earth set off from its position in the summer
solstice, and carry it round the sun; observe that the pole is always
inclined in the same direction, and points to the same spot in the
heavens. There is a fixed star situated near that spot, which is hence
called the north polar star. Now let us stop the earth at B, and examine
it in its present situation; it has gone through one quarter of its
orbit, and is arrived at that point at which the ecliptic cuts, or
crosses, the equator, and which is called the autumnal equinox.
_Emily._ The sun now shines from one pole to the other, just as it would
constantly do, if the axis of the earth were perpendicular to its orbit.
_Mrs. B._ Because the inclination of the axis is now neither towards the
sun, nor in the contrary direction; at this period of the year, the days
and nights are equal in every part of the earth. But the next step she
takes in her orbit, you see, involves the north pole in darkness, whilst
it illumines that of the south; this change was gradually preparing as I
moved the earth from summer to autumn; the arctic circle, which was at
first entirely illumined, began to have short nights, which increased as
the earth approached the autumnal equinox; and the instant it passed
that point, the long night of the north pole commences, and the south
pole begins to enjoy the light of the sun. We shall now make the earth
proceed in its orbit, and you may observe that as it advances, the days
shorten and the nights lengthen, throughout the northern hemisphere,
until it arrives at the winter solstice, on the 21st of December, when
the north frigid zone is entirely in darkness, and the southern has
uninterrupted daylight.
[Illustration: PLATE X.]
_Caroline._ Then, after all, the sun which I thought so partial, confers
his favours equally on all.
_Mrs. B._ Not so either: the inhabitants of the torrid zone have much
more heat than we have, as the sun's rays fall perpendicularly twice in
the course of a year, on every place within the tropics, while they
shine more or less obliquely on the rest of the world, and almost
horizontally at the poles; for during their long day of six months, the
sun moves round their horizon without either rising or setting; the only
observable difference, is that it is more elevated by a few degrees at
mid-day, than at midnight.
_Emily._ To a person placed in the temperate zone, in the situation in
which we are in England, the sun will shine neither so obliquely as it
does on the poles, nor vertically as at the equator; but its rays will
fall upon him more obliquely in autumn, and winter, than in summer.
_Caroline._ And therefore, the inhabitants of the temperate zones, will
not have merely one day, and one night, in the year, as happens at the
poles, nor will they have equal days, and equal nights, as at the
equator; but their days and nights will vary in length, at different
times of the year, according as their respective poles incline towards,
or from the sun, and the difference will be greater in proportion to
their distance from the equator.
_Mrs. B._ We shall now follow the earth through the other half of her
orbit, and you will observe, that now exactly the same changes take
place in the southern hemisphere, as those we have just remarked in the
northern. Day commences at the south pole, when night sets in at the
north pole; and in every other part of the southern hemisphere the days
are longer than the nights, while, on the contrary, our nights are
longer than our days. When the earth arrives at the vernal equinox, D,
where the ecliptic again cuts the equator, on the 21st of March, she is
situated, with respect to the sun, exactly in the same position, as in
the autumnal equinox; and the only difference with respect to the
earth, is, that it is now autumn in the southern hemisphere, whilst it
is spring with us.
_Caroline._ Then the days and nights are again every where equal.
_Mrs. B._ Yes, for the half of the globe which is enlightened, extends
exactly from one pole to the other, the sun has just risen to the north
pole, and is just setting to the south pole; but in every other part of
the globe, the day and night is of twelve hours length; hence the word
equinox, which is derived from the Latin, meaning equal night.
As our summer advances, the days lengthen in the northern hemisphere,
and shorten in the southern, till the earth reaches the summer solstice,
when the north frigid zone is entirely illumined, and the southern is in
complete darkness; and we have now brought the earth again to the spot
from whence we first accompanied her.
_Emily._ This is indeed a most satisfactory explanation of the cause of
the different lengths of our days and nights, and of the variation of
the seasons; and the more I learn, the more I admire the simplicity of
means by which such wonderful effects are produced.
_Mrs. B._ I know not which is most worthy of our admiration, the causes,
or the effects of the earth's revolution round the sun. The mind can
find no object of contemplation more sublime, than the course of this
magnificent globe, impelled by the combined powers of projection and
attraction, to roll in one invariable course, around the source of light
and heat: and what can be more delightful than the beneficent effects of
this vivifying power on its attendant planet. It is at once the grand
principle which animates and fecundates nature.
_Emily._ There is one circumstance in which this little ivory globe
appears to me to differ from the earth; it is not quite dark on that
side of it which is turned from the candle, as is the case with the
earth when neither moon nor stars are visible.
_Mrs. B._ This is owing to the light of the candle, being reflected by
the walls of the room, on every part of the globe, consequently that
side of the globe, on which the candle does not directly shine, is not
in total darkness. Now the skies have no walls to reflect the sun's
light on that side of our earth which is in darkness.
_Caroline._ I beg your pardon, Mrs. B., I think that the moon, and
stars, answer the purpose of walls in reflecting the sun's light to us
in the night.
_Mrs. B._ Very well, Caroline; that is to say, the moon and planets;
for the fixed stars, you know, shine by their own light.
_Emily._ You say, that the superior heat of the equatorial parts of the
earth, arises from the rays falling perpendicularly on those regions,
whilst they fall obliquely on these more northern regions; now I do not
understand why perpendicular rays should afford more heat than oblique
rays.
_Caroline._ You need only hold your hand perpendicularly over the
candle, and then hold it sideways obliquely, to be sensible of the
difference.
_Emily._ I do not doubt the fact, but I wish to have it explained.
_Mrs. B._ You are quite right; if Caroline had not been satisfied with
ascertaining the fact, without understanding it, she would not have
brought forward the candle as an illustration; the reason why you feel
so much more heat if you hold your hand perpendicularly over the candle,
than if you hold it sideways, is because a stream of heated vapour
constantly ascends from the candle, or any other burning body, which
being lighter than the air of the room, does not spread laterally but
rises perpendicularly, and this led you to suppose that the rays were
hotter in the latter direction. Had you reflected, you would have
discovered that rays issuing from the candle sideways, are no less
perpendicular to your hand when held opposite to them, than the rays
which ascend when your hand is held over them.
The reason why the sun's rays afford less heat when in an oblique
direction, than when perpendicular, is because fewer of them fall upon
an equal portion of the earth; this will be understood better by
referring to plate 10. fig. 1, which represents two equal portions of
the sun's rays, shining upon different parts of the earth. Here it is
evident, that the same quantity of rays fall on the space A B, as fall
on the space B C; and as A B is less than B C, the heat and light will
be much stronger in the former than in the latter; A B, you see,
represents the equatorial regions, where the sun shines perpendicularly;
and B C, the temperate and frozen climates, where his rays fall more
obliquely.
_Emily._ This accounts not only for the greater heat of the equatorial
regions, but for the greater heat of our summers, as the sun shines less
obliquely in summer than in winter.
_Mrs. B._ This you will see exemplified in figure 2, in which the earth
is represented, as it is situated on the 21st of June, and England
receives less oblique, and consequently a greater number of rays, than
at any other season; and figure 3, shows the situation of England on the
21st of December, when the rays of the sun fall most obliquely upon her.
But there is also another reason why oblique rays give less heat, than
perpendicular rays; which is, that they have a greater portion of the
atmosphere to traverse; and though it is true, that the atmosphere is
itself a transparent body, freely admitting the passage of the sun's
rays, yet it is always loaded more or less with dense and foggy vapour,
which the rays of the sun cannot easily penetrate; therefore, the
greater the quantity of atmosphere the sun's rays have to pass through
in their way to the earth, the less heat they will retain when they
reach it. This will be better understood, by referring to fig. 4. The
dotted line round the earth, describes the extent of the atmosphere, and
the lines which proceed from the sun to the earth, the passage of two
equal portions of the sun's rays, to the equatorial and polar regions;
the latter you see, from its greater obliquity, passes through a greater
extent of atmosphere.
_Caroline._ And this, no doubt, is the reason why the sun, in the
morning and in the evening, gives so much less heat, than at mid-day.
_Mrs. B._ The diminution of heat, morning and evening, is certainly
owing to the greater obliquity of the sun's rays; and they are also
affected by the other, both the cause, which I have just explained to
you; the difficulty of passing through a foggy atmosphere is perhaps
more particularly applicable to them, as mist and vapours are prevalent
about the time of sunrise and sunset. But the diminished obliquity of
the sun's rays, is not the sole cause of the heat of summer; the length
of the days greatly conduces to it; for the longer the sun is above the
horizon, the more heat he will communicate to the earth.
_Caroline._ Both the longest days, and the most perpendicular rays, are
on the 21st of June; and yet the greatest heat prevails in July and
August.
_Mrs. B._ Those parts of the earth which are once heated, retain the
heat for some length of time, and the additional heat they receive,
occasions an elevation of temperature, although the days begin to
shorten, and the sun's rays to fall more obliquely. For the same reason,
we have generally more heat at three o'clock in the afternoon, than at
twelve, when the sun is on the meridian.
_Emily._ And pray, have the other planets the same vicissitudes of
seasons, as the earth?
_Mrs. B._ Some of them more, some less, according as their axes deviate
more or less from the perpendicular, to the plane of their orbits. The
axis of Jupiter, is nearly perpendicular to the plane of his orbit; the
axes of Mars, and of Saturn, are each, inclined at angles of about sixty
degrees; whilst the axis of Venus is believed to be elevated only
fifteen or twenty degrees above her orbit; the vicissitudes of her
seasons must therefore be considerably greater than ours. For further
particulars respecting the planets, I shall refer you to Bonnycastle's
Introduction to Astronomy.
I have but one more observation to make to you, relative to the earth's
motion; which is, that although we have but 365 days and nights in the
year, she performs 366 complete revolutions on her axis, during that
time.
_Caroline._ How is that possible? for every complete revolution must
bring the same place back to the sun. It is now just twelve o'clock, the
sun is, therefore, on our meridian; in twenty-four hours will it not
have returned to our meridian again, and will not the earth have made a
complete rotation on its axis?
_Mrs. B._ If the earth had no progressive motion in its orbit whilst it
revolves on its axis, this would be the case; but as it advances almost
a degree westward in its orbit, in the same time that it completes a
revolution eastward on its axis, it must revolve nearly one degree more
in order to bring the same meridian back to the sun.
_Caroline._ Oh, yes! it will require as much more of a second revolution
to bring the same meridian back to the sun, as is equal to the space the
earth has advanced in her orbit; that is, nearly a degree; this
difference is, however, very little.
_Mrs. B._ These small daily portions of rotation, are each equal to the
three hundred and sixty-fifth part of a circle, which at the end of the
year amounts to one complete rotation.
_Emily._ That is extremely curious. If the earth then, had no other than
its diurnal motion, we should have 366 days in the year.
_Mrs. B._ We should have 366 days in the same period of time that we now
have 365; but if we did not revolve round the sun, we should have no
natural means of computing years.
You will be surprised to hear, that if time is calculated by the stars
instead of the sun, the irregularity which we have just noticed does not
occur, and that one complete rotation of the earth on its axis, brings
the same meridian back to any fixed star.
_Emily._ That seems quite unaccountable; for the earth advances in her
orbit with regard to the fixed stars, the same as with regard to the
sun.
_Mrs. B._ True, but then the distance of the fixed stars is so immense,
that our solar system is in comparison to it but a spot, and the whole
extent of the earth's orbit but a point; therefore, whether the earth
remain stationary, or whether it revolved in its orbit during its
rotation on its axis, no sensible difference would be produced with
regard to the fixed stars. One complete revolution brings the same
meridian back to the same fixed star; hence the fixed stars appear to go
round the earth in a shorter time than the sun by three minutes
fifty-six seconds of time.
_Caroline._ These three minutes fifty-six seconds is the time which the
earth takes to perform the additional three hundred and sixty-fifth part
of the circle, in order to bring the same meridian back to the sun.
_Mrs. B._ Precisely. Hence the stars gain every day three minutes
fifty-six seconds on the sun, which makes them rise that portion of time
earlier every day.
When time is calculated by the stars it is called sidereal time; when by
the sun, solar, or apparent time.
_Caroline._ Then a sidereal day is three minutes fifty-six seconds
shorter, than a solar day of twenty-four hours.
_Mrs. B._ I must also explain to you what is meant by a sidereal year.
The common year, called the solar or tropical year, containing 365 days,
five hours, forty-eight minutes and fifty-two seconds, is measured from
the time the sun sets out from one of the equinoxes, or solstices, till
it returns to the same again; but this year is completed, before the
earth has finished one entire revolution in its orbit.
_Emily._ I thought that the earth performed one complete revolution in
its orbit, every year; what is the reason of this variation?
_Mrs. B._ It is owing to the spheroidal figure of the earth. The
elevation about the equator produces much the same effect as if a
similar mass of matter, collected in the form of a moon, revolved round
the equator. When this moon acted on the earth, in conjunction with, or
in opposition to the sun, variations in the earth's motion would be
occasioned, and these variations produce what is called the precession
of the equinoxes.
[Illustration: PLATE XI.]
_Emily._ What does that mean? I thought the equinoctial points, were
fixed points in the heavens, in which the equator cuts the ecliptic.
_Mrs. B._ These points are not quite fixed, but have an apparently
retrograde motion, among the signs of the zodiac; that is to say,
instead of being at every revolution in the same place, they move
backwards. Thus if the vernal equinox is at A, (fig. 1. plate XI.) the
autumnal one, will be at B, instead of C, and the following vernal
equinox, at D, instead of at A, as would be the case if the equinoxes
were stationary, at opposite points of the earth's orbit.
_Caroline._ So that when the earth moves from one equinox to the other,
though it takes half a year to perform the journey, it has not travelled
through half its orbit.
_Mrs. B._ And, consequently, when it returns again to the first equinox,
it has not completed the whole of its orbit. In order to ascertain when
the earth has performed an entire revolution in its orbit, we must
observe when the sun returns in conjunction with any fixed star; and
this is called a sidereal year. Supposing a fixed star situated at E,
(fig. 1. plate XI.) the sun would not appear in conjunction with it,
till the earth had returned to A, when it would have completed its
orbit.
_Emily._ And how much longer is the sidereal, than the solar year?
_Mrs. B._ Only twenty minutes; so that the variation of the equinoctial
points is very inconsiderable. I have given them a greater extent in the
figure, in order to render them sensible.
In regard to time, I must further add, that the earth's diurnal motion
on an inclined axis, together with its annual revolution in an elliptic
orbit, occasions so much complication in its motion, as to produce many
irregularities; therefore the true time cannot be measured by the
apparent place of the sun. A perfectly correct clock, would in some
parts of the year be before the sun, and in other parts after it. There
are but four periods in which the sun and a perfect clock would agree,
which is the 15th of April, the 16th of June, the 23d of August, and the
24th of December.
_Emily._ And is there any considerable difference between solar time,
and true time?
_Mrs. B._ The greatest difference amounts to between fifteen and sixteen
minutes. Tables of equation are constructed for the purpose of pointing
out, and correcting these differences between solar time and equal or
mean time, which is the denomination given by astronomers, to true time.
Questions
1. (Pg. 92) What does the line A B, (fig. 2 plate 8.) represent, and
what are its extremities called?
2. (Pg. 92) What is meant by the equator, and how is it situated?
3. (Pg. 92) There are two hemispheres; how are they named and
distinguished?
4. (Pg. 92) What are the circles near the poles called?
5. (Pg. 92) What do the lines I K, and L M, represent?
6. (Pg. 92) What circle is in part represented by the line L K?
7. (Pg. 92) Against what mistake must you guard respecting this line?
8. (Pg. 92) What is meant by a plane, and how could one be represented?
9. (Pg. 93) Describe what is intended by the plane of the earth's orbit.
10. (Pg. 93) Extending this plane to the fixed stars, what circle would
it form, and among what particular stars would it be found?
11. (Pg. 93) What is fig. 1. plate 9, designed to represent?
12. (Pg. 93) The ecliptic does not properly belong to the earth, for
what purpose then is it described on the terrestrial globe?
13. (Pg. 93) What does the obliquity of the ecliptic to the equator
serve to show?
14. (Pg. 93) Within what limits do you find the torrid zone?
15. (Pg. 93) What two zones are there between the torrid, and the two
frigid zones?
16. (Pg. 93) Where are the frigid zones situated?