_Amplitude_ is 24 degrees Northerly.
_Oblique Ascension_, 20.
_Oblique Descension_, 58.
_Ascensional Difference_, 19.
_Semi-diurnal Arch_, 109.
His continuance above the horizon, 14½ hours.
Sun rises at three quarters past four.
Sun sets a quarter past seven.
These things for the Sun vary every day; but for a Fixed Star the day
of the month need not be given, for they are the same all the year
round.
In the latitude of 51½ North, _Syrus_’s
_Amplitude_ is about 28 degrees Southerly.
_Oblique Ascension_, 121.
_Oblique Descension_, 75.
_Ascensional Difference_, 23.
_Semi-diurnal Arch_, 67.
Continuance above the horizon, 9 hours.
PROB. XXXVIII. _The Latitude and the Day of
the Month being given; to find the Hour when any
known Star will be upon the meridian, and also the
time of its rising and setting._
Having rectified the globe for the latitude of the Sun’s place, bring
the given Star to the meridian, and also to the East or West side
of the horizon, and the index will shew accordingly when the Star
_culminates_, or the time of the _rising_ or _setting_.
Thus at _London_, on the 21st of _January_, _Syrius_ will be upon the
meridian, at a quarter past ten in the evening; rises at 5¼ hours, and
sets at three quarters past two in the morning.
By the converse of this problem, knowing the time when any Star is upon
the meridian, you may easily find the Sun’s place. Thus, bring the
given Star to the meridian, and set the index to the given hour; then
turn the globe ’till the index points to 12 at noon, and the meridian
will cut the Sun’s place in the ecliptic. Thus when _Syrius_ comes to
the meridian at 10½ hours after noon, the Sun’s place will be ≈ ¼ deg.
PROB. XXXIX. _To find at what time of the Year
a given Star will be upon the Meridian, at a given
Hour of the Night._
Bring the Star to the meridian, and set the index to the given hour,
then turn he globe ’till the index points to 12 at noon, and the
meridian will cut the ecliptic in the Sun’s place; whence the day of
the month may be easily found in the kalendar upon the horizon.
PROB. XL. _The Day of the Month, and the
Azimuth of any known Star being given; to find the
Hour of the Night._
Having rectified the globe for the latitude and the Sun’s place, if
the given Star be due North or South, bring it to the meridian, and
the index will show the hour of the night. If the Star be in any other
direction, fix the quadrant of altitude in the zenith, and set it to
the Star’s azimuth in the horizon; then turn the globe about until the
quadrant cuts the center of the Star, and the index will shew the hour
of the night.
The bearing of any point in the heavens may be found by the following
methods.
Having a meridian line drawn in two windows, that are opposite to
one another, you may cross it at right angles with another line
representing the East and West; from the point of the intersection
describe a circle, and divide each quadrant into 90 degrees; then get
a smooth board, of about 2 feet long, and ¾ foot broad (more or less,
as you judge convenient) and on the back part of it fix another small
board crossways, so that it may serve as a foot to support the biggest
board upright, when it is set upon a level, or an horizontal plane. The
board being thus prepared, set the lower edge of the smooth, or fore
side of it, close to the center of the circle, then turn it about to
the meridian, or to any azimuth point required (keeping the edge of it
always close to the center) and casting your eye along the flat side of
it, you will easily perceive what Stars are upon the meridian, or any
other bearing that the board is set to.
PROB. XLI. _Two known Stars having the same Azimuth, or
the same Height, being given; to find the Hour of
the Night._
Rectify the globe for the latitude, the zenith, and the Sun’s place.
1. When the two Stars are in the same azimuth, turn the globe, and also
the quadrant about, until both Stars coincide with the edge thereof;
then will the index shew the hour of the night; and where the quadrant
cuts the horizon, is the common azimuth of both Stars.
2. If the two Stars are of the same altitude, move the globe so that
the same degree on the quadrant will cut both Stars, then the index
will shew the hour.
This problem is useful when the quantity of the azimuth of the two
Stars in the first case, or of their altitude in the latter case, is
not known.
_If two Stars were given, one on the meridian, and the
other in the East or West part of the horizon; to
find the Latitude._
Bring that Star which was observed on the meridian, to the meridian of
the globe, and keep the globe from turning round its axis; then slide
the meridian up or down in the notches, ’till the other Star is brought
to the East or West part of the horizon, and that elevation of the Pole
will be the _Latitude_ sought.
PROB. XLII. _The Latitude, Day of the Month,
and the Altitude of any known Star being given; to
find the Hour of the Night._
Rectify the globe for the latitude, zenith, and Sun’s place: Turn the
globe, and the quadrant of altitude, backward or forward, ’till the
center of that Star meets the quadrant in the degree of altitude given;
then the index will point the true hour of the night; and also where
the quadrant cuts the horizon, will be the azimuth of the Star at that
time.
_If the Latitude, the Sun’s Altitude, and his
Declination (instead of his Place in the Ecliptic)
are given; to find the Hour of the Day and Azimuth._
Rectify the globe for the latitude and zenith, and having brought
the _equinoctial colure_ to the meridian, set the index to 12 at
noon; which being done, turn the globe and the quadrant, until the
given declination in the equinoctial colure, cuts the altitude on the
quadrant; then the index will shew the _Hour_ of the day, and the
quadrant cut the _Azimuth_ in the horizon.
_If the Altitude of two Stars on the same Azimuth were
given; to find the Latitude of the Place._
Set the quadrant over both Stars at the observed degrees of altitude,
and keep it fast upon the globe with your fingers; then slide the
meridian up or down in the notches, ’till the quadrant cuts the given
azimuth in the horizon; that elevation of the Pole will be the latitude
required.
PROB. XLIII. _Having the Latitude of the
place, to find the degree of the Ecliptic, which
rises or sets with a given Star; and from thence
to determine the time of its_ Cosmical _and_
Achronical _rising and setting._
Having rectified the globe for the latitude, bring the given Star to
the Eastern side of the horizon, and mark what degree of the ecliptic
rises with it: Look for that degree in the wooden horizon, and right
against it, in the kalendar, you will find the month and day when the
Star _rises Cosmically_. If you bring the Star to the Western side of
the horizon, that degree of the ecliptic which rises at that time,
will give the day of the month when the said Star _sets Cosmically_.
So likewise against the degree which sets with the Star, you will find
the day of the month of the _Achronical setting_; and if you bring it
to the Eastern part of the horizon, that degree which sets at that time
will be the Sun’s place when the Star _rises Achronically_.
Thus, in the latitude of _London_, _Syrius_, or the _Dog-Star_, rises
_Cosmically_ the 10th of _August_, and sets _Cosmically_ the 10th of
_October_. _Aldebaran_, or the _Bull’s Eye_, rises _Achronically_ on
the 22d of _May_, and sets _Achronically_ on the 19th of _December_.
PROB. XLIV. _Having the Latitude of the place,
to find the time when a Star rises and sets_
Heliacally.
Having rectified the globe for the latitude, bring the Star to the
Eastern side of the horizon, and turn the quadrant round to the Western
side, ’till it cuts the ecliptic in 12 degrees of altitude above the
horizon, if the Star be of the first magnitude; then that point of the
ecliptic which is cut by the quadrant, is 12 degrees high above the
Western part of the horizon, when the Star rises; but at the same time
the opposite point in the ecliptic is 12 degrees below the Eastern
part of the horizon, which is the depression of a Star of the _first
magnitude_, when she _rises Heliacally_; or has got so far from the
Sun’s beams, that she may be seen in the morning before Sun-rising.
Wherefore look for the said point of the ecliptic on the horizon, and
right against it will be the day of the month when the Star _rises
Heliacally_. To find the _Heliacal setting_, bring the Star to the West
side of the horizon, and turn the quadrant about to the Eastern side,
’till the 12th degree of it above the horizon, cuts the ecliptic; then
that degree of the ecliptic which is opposite to this point, is the
Sun’s place when the Star _sets Heliacally_.
Thus you will find that _Arcturus_ rises Heliacally the 28th of
_September_, and sets Heliacally _December_ the 2d.
PROB. XLV. _To find the place of any Planet
upon the globe; and so by that means, to find its
place in the Heavens: Also to find at what Hour any
Planet will rise or set, or be on the meridian at
any one Day in the Year._
You must first seek in an Ephemeris (_White_’s Ephemeris will do
well enough) for the place of the Planet proposed on that day; then
mark that point of the ecliptic, either with chalk, or by sticking
on a little black patch; and then for that night you may perform any
problem, as before, by a Fixed Star.
Let it be required to find the situation of _Jupiter_ among the Fixed
Stars in the heavens, and also what time he rises and sets, and comes
to the meridian on the 19th of _May_, 1757, N. S. at _London_.
Looking for the 19th of _May_, 1757, in _White_’s Ephemeris, I find
that _Jupiter_’s place at that time is in about 12 degrees of ♏;
latitude about 1¼ degree North. Then looking for that point upon the
Celestial globe, I find that ♃ is then nearly in conjunction with the
bright Star in the Southern Balance, and about 1 degree North of it.
To find when he rises and sets, and comes to the meridian: Having put
a little black patch on the place of _Jupiter_, elevate the globe
according to the latitude, and having brought the Sun’s place to
the meridian, set the hour index to 12 at noon; then turn the mark
which was made for _Jupiter_, to the Eastern part of the horizon,
I find ♃ will rise somewhat more than half an hour after three in
the afternoon; and turning the globe about, I find it comes to the
meridian a little before eleven at night; and sets almost a quarter
past six next morning.
This example being understood, it will be easy to find when either of
the other two superior Planets, _viz. Mars_ and _Saturn_, rise, set,
and come to the meridian.
I shall conclude this subject about the Globes with the following
problems.
PROB. XLVI. _To find all that space upon the
Earth, where an Eclipse of one of the Satellites
of_ Jupiter _will be visible._
Having found that place upon the Earth, in which the Sun is vertical at
the time of the eclipse, by _Prob. 13_, elevate the globe according to
the latitude of the said place; then bring the place to the meridian,
and set the hour index to 12 at noon. If _Jupiter_ be in consequence of
the Sun, draw a line with black lead, or the like, along the Eastern
side of the horizon, which line, will pass over all those places where
the Sun is setting at that time; then count the difference betwixt the
right ascension of the Sun, and that of _Jupiter_, and turn the globe
Westward, ’till the hour index points to this difference; then keep the
globe from turning round its axis, and elevate the meridian, according
to the declination of _Jupiter_. The globe being in this position, draw
a line along the Eastern side of the horizon; then the space between
this line, and the line before drawn, will comprehend all those places
of the Earth where _Jupiter_ will be visible, from the setting of the
Sun, to the setting of _Jupiter_.
But if _Jupiter_ be in antecedence of the Sun (_i. e._ rises before
him) having brought the place where the Sun is vertical, to the zenith,
and put the hour index to 12 at noon, draw a line on the Western side
of the horizon; then elevate the globe according to the declination of
_Jupiter_, and turn it about Eastward, until the index points to so
many hours distant from noon, as is the difference of right ascension
of the Sun and _Jupiter_. The globe being in this position, draw a line
along the Western side of the horizon; then the space contained between
this line, and the other last drawn, will comprehend all those places
upon the Earth where the Eclipse is visible, between the rising of the
Sun, and that of _Jupiter_.
[Illustration]
_The_ DESCRIPTION _of the Great_ ORRERY,
_lately made by Mr._ THOMAS WRIGHT,
Mathematical Instrument-Maker to his late
MAJESTY, and now by BENJAMIN
COLE, _his Successor_.
The ORRERY is an Astronomical Machine, made to represent the motions of
the Planets. These machines are made of various sizes, some having more
Planets than others; but I shall here confine myself to the description
of that above-mentioned.
In the Introduction we gave a short account of the _Order_, _Periods_,
_Distances_, and _Magnitudes_ of the _Primary Planets_; and of the
_Distances_ and _Periodical Resolutions_ of the _Secondary Planets_
round their respective Primaries. We shall here explain their
_Stations_, _Regradations_, _Eclipses_, _Phases_, _&c._ but first let
us take a general view of the _Orrery_.
[Sidenote: The Description of the _Orrery_.]
[Sidenote: Vide _Frontispiece_.]
The frame which contains the wheel-work, _&c._ that regulates the whole
_Machine_, is made of fine ebony, and is near four feet in diameter;
the outside thereof is adorned with twelve pilasters, curiously wrought
and gilt: Between these pilasters the twelve Signs of the _Zodiac_ are
neatly painted, with gilded frames. Above the frame is a broad ring,
supported with twelve pillars: This ring represents the _Plane_ of the
_Ecliptic_, upon which there are two scales of degrees, and between
those the names and characters of the twelve Signs. Near the outside is
a scale of months and days, exactly corresponding to the Sun’s place at
noon, each day throughout the year.
Above the ecliptic stands some of the principal circles of the sphere,
according to their respective situations in the heavens, _viz._ N°
10, are the two _Colures_, divided into degrees, and half degrees;
N° 11, is one half of the Equinoctial Circle, making an angle with
the ecliptic of 23½ degrees. The _Tropic of Cancer_, and the _Arctic
Circle_, are each fixed parallel, and at their proper distance from
the equinoctial. On the Northern half of the ecliptic is a brass
semicircle, moveable upon two points fixed in ♈ and ♎: This semicircle
serves as a moveable horizon, to be put to any degree of latitude upon
the North part of the meridian. The whole machine is also so contrived,
as to be set to any latitude, without in the least affecting any of
the inside motions: For this purpose there are two strong hinges (N°
13,) fixed to the bottom frame, upon which the instrument moves, and a
strong brass arch, having holes at every degree, thro’ which a strong
pin is to be put, according to the elevation. This arch and the two
hinges, support the whole machine, when it is lifted up according to
any latitude; and the arch at other times lies conveniently under the
bottom frame.
When the machine is set to any latitude (which is easily done by two
men, each taking hold of two handles, conveniently fixed for that
purpose) set the moveable horizon to the same degree upon the meridian,
and you may form an idea of the respective altitude, or depressions of
the Planets, above or below the horizon, according to their respective
positions, with regard to the meridian.
Within the ecliptic, and nearly in the same place thereof, stands the
Sun, and all the Planets, both Primary and Secondary. The Sun (Nº
1.) stands in the middle of the whole system, upon a wire, making an
angle with the plane of the ecliptic, of about 82 degrees; which is
the inclination of the Sun’s axis, to the axis of the ecliptic. Next
to the Sun is a Small ball (Nº 2.) representing _Mercury_: Next to
_Mercury_ is _Venus_ (Nº 3.) represented by a larger ball (and both
these stand upon wires,) so that the balls themselves may be more
visibly perceived by the eye. The Earth is represented (Nº 4.) by an
ivory ball, having some of the principal meridians and parallels, and a
little sketch of a map described upon it. The wire which supports the
Earth, makes an angle with the plane of the ecliptic 66½ degrees, which
is the inclination of the Earth’s axis to that of the ecliptic. Near
the bottom of the Earth’s axis is a Dial Plate (Nº 9.) having an index
pointing to the hours of the day, as the Earth turns round its axis.
Round the Earth is a ring, supported by two small pillars, which ring
represents the Orbit of the Moon, and the division upon it answers to
the Moon’s latitude; the motion of this ring represents the motion of
the Moon’s Orbit, according to that of the Nodes. Within this ring
is the Moon (Nº 5.) having a black cap or case, which by its motion,
represents the _Phases_ of the Moon according to her age. Without the
Orbits of the Earth and Moon is _Mars_ (Nº 6.) The next in order to
_Mars_ is _Jupiter_, and his four Moons (Nº 7); each of these moons is
supported by a crooked wire fixed in a socket, which turns about the
pillar that supports _Jupiter_. These satellites may be turned by the
hand to any position; and yet when the machine is put in motion, they
will all move in their proper times. The outermost of all is _Saturn_,
and his five Moons (Nº 8.) These moons are supported and contrived
after the same manner with those of _Jupiter_. The whole machine is put
into motion by turning a small winch (like the key of a clock, Nº 14.)
and all the inside work is so truly wrought, that it requires but very
small strength to put the whole motion.
Above the handle there is a cylindrical pin, which may be drawn a
little out, or pushed in, at pleasure: when it is pushed in, all the
Planets, both primary and Secondary, will move according to their
respective periods, by turning the handle: When it is drawn out, the
motions of the Satellites of _Jupiter_ and _Saturn_ will be stopped,
while all the rest move without interruption. This is a very good
contrivance to preserve the instrument from being clogged by the
swift motions of the wheels belonging to the Satellites of _Jupiter_
and _Saturn_, when the motions of the rest of the Planets are only
considered.
There is also a brass lamp having two convex glasses, to be put in the
room of the Sun; and also a smaller Earth and Moon, made somewhat in
proportion to their distance from each other, which may be put on at
pleasure.
The lamp turns round in the same time with the Earth, and by means of
the glasses cast a strong light upon her; and when the smaller Earth
and Moon are placed on, it will be easy to shew when either of them may
be eclipsed.
Having thus given a brief description of the outward part of this
machine, I shall next give an account of the phænomena explained by it,
when it is put into motion.
_Of the Motions of the Planets in general._
Having put on the handle, push in the pin which is just above it, and
place a small black patch (or bit of wafer) upon the middle of the Sun
(for instance) right against the first degree of ♈; you may also place
patches upon _Venus_, _Mars_, and _Jupiter_, right against some noted
point in the ecliptic. If you lay a thread from the Sun to the first
degree of ♈, you may set a mark where it intersects the orbit of each
Planet, and that will be a help to note the time of their revolutions.
One entire turn of the handle answers to the diurnal motion of the
Earth round her axis, as may be seen by the motion of the hour index,
which is placed at the foot of the wire on which the terella is fixed.
When the index has moved the space of ten hours, you may observe that
_Jupiter_ has made one revolution compleat round its axis; the handle
being turned until the hour index has passed over 24 days, 8 hours,
will bring the patch upon _Venus_ to its former situation with respect
to the ecliptic, which shews that ♀ has made one entire revolution
round her axis. _Mars_ makes one compleat revolution round its axis
in 24 hours and about 40 minutes. When the handle is turned 25½ times
round, the spot upon the Sun will point to the same degree of the
ecliptic, as it did when the instrument was first put into motion. By
observing the motions of the spots upon the surface of the Sun, and
of the Planets in the heavens, their diurnal motion was discovered;
after the same manner as we do here observe the motions of their
representatives, by that of the marks placed upon them.
If while you turn the handle you observe the Planets, you will see
them perform their motions in the same relative times as they really
do in the heavens, each making its period in the times mentioned in
the Tables, _Page_, 28, 27¼ turns of the handle will bring the Moon
round the Earth, which is called a _Periodic_ Month; and all the while
she keeps the same face towards the Earth; for the Moon’s annual and
diurnal motion are performed both in the same time nearly, so that we
always see the same face or side of the Moon.
If before the instrument is put into motion, the satellites of
_Jupiter_ and _Saturn_ be brought into the same right line from their
respective primaries, you will see them, as you turn the handle,
immediately dispersed from one another, according to their different
celerities. Thus one turn of the handle will bring the first of
_Jupiter_’s Moons about ⁴/₇ part round _Jupiter_, while the second has
described but ²/₇ part, the third but above ¹/₇, and the fourth not
quite ¹/₁₆ part, each of its respective orbits. If you turn the handle
until the hour index has moved 18½ hours more, the first satellite will
then be brought into its former position, and so has made one entire
revolution; the second at the same time will be almost diametrically
opposite to the first, and so has made a little more than half of
one revolution; the others will be in different aspects, according
to the length of their periods, as will be plainly exhibited by the
instrument. The same observations may be made with respect to the
satellites of _Saturn_.
The machine is so contrived, that the handle may be turned either way;
and, if before you put it into motion, you observe the aspect (or
situation with respect to each other) of the Planets, and then turn the
handle round any number of times; the same number of revolutions being
made backwards, will bring all the Planets to their former situations.
I shall next proceed to particulars.
_Of the Stations and Retrogradations of the Planets._
[Sidenote: _Retrograde Motion of the Planets._]
The primary Planets, as they all turn round the Sun, at different
distances, and in different times, appear to us from the Earth to have
different motions; as sometimes they appear to move from West to East,
according to the order of the signs, which is called their _Direct
Motion_; then by degrees they slacken their pace, until at last they
lose all their motion, and become _Stationary_, or not to move at all;
that is, they appear in the same place with respect to the fixed Stars
for some time together; after which they again begin to move, but with
a contrary direction, as from East to West, which is called their
_Retrograde Motion_; then again they become stationary, and afterwards
reassume their direct motion. The reason of all these appearances is
very evidently shewn by the _Orrery_.
_Of the Stations_, &c. _of the Inferior Planets._
We shall instance in the Planet _Mercury_, because his motion round the
Sun differs more from the Earth’s than that of _Venus_ does.
When _Mercury_ is in his superior conjunction (or when he is in a
direct line from the Earth beyond the Sun) fasten a string about the
axis of the Earth, and extend it over _Mercury_ to the ecliptic; then
turning the handle, keep the thread all the while extended over ☿,
and you will find it move with a direct motion in the ecliptic, but
continually slower, until _Mercury_ has the greatest elongation from
the Earth. Near this position, the thread for some time will lay over
_Mercury_ without being moved in the ecliptic, tho’ the Earth and
_Mercury_ both continue their progressive motion in their respective
orbits. When _Mercury_ has got a little past this place, you will find
the thread must be moved backward in the ecliptic, beginning first
with a slow motion, and then faster by degrees, until _Mercury_ is in
his inferior conjunction, or directly between the Earth and the Sun.
Next this position of ☿, his retrograde motion will be the swiftest;
but he still moves the same way, tho’ continually slower, ’till he has
again come to his greatest elongation, where he will appear the second
time to be stationary; after which he begins to move forward, and that
faster by degrees, until he is come to the same position with respect
to the Earth, that he was in at first. The same observations may be
made relating to the motions of _Venus_. In like manner the different
motions observed in the superior Planets may be also explained by the
_Orrery_. If you extend the thread over _Jupiter_, and proceed after
the same manner as before we did in regard to _Mercury_, you will
find that from the time _Jupiter_ is in conjunction with the Sun, his
motion is direct, but continually slower, until the Earth is nearly in
a quadrate aspect with _Jupiter_, near which position _Jupiter_ seems
to be stationary: After which he begins to move, and continually mends
his pace, until he comes in opposition to the Sun, at which time his
retrograde motion is swiftest. He still seems to go backward, but with
a slower pace, ’till the Earth and he are again in a quadrate aspect,
where _Jupiter_ seems to have lost all his motion; after which he again
resumes his direct motion, and so proceeds faster by degrees, ’till the
Earth and he are again in opposition to each another.
[Sidenote: _Plate 3_. _Fig. 1_.]
These different motions observed in the Planets, are easily
illustrated, as followeth: The lesser circle round the Sun is the
orbit of _Mercury_, in which he performs his revolution round the
Sun, in about three months, or while the Earth is going thro’ ¼ part
of her orbit, or from A to N. The numbers 1, 2, 3, _&c._ in the orbit
of _Mercury_, show the spaces he describes in a week nearly, and the
distance AB, BC, DC, _&c._ in the Earth’s orbit, do likewise show her
motion in the same time. The letters A, B, C, _&c._ in the great orb,
are the motions of _Mercury_ in the Heavens, as they appear from the
Earth. Now if the Earth be supposed in A, and _Mercury_ in 12, near his
superior conjunction with the Sun; a spectator on the Earth will see ☿,
as if he were in the point of the Heavens A, and while ☿ is moving from
12 to 1, and from 1 to 2, _&c._ the Earth in the same time also moves
from A to B, and from B to C, _&c._ All which time ☿ appears in the
Heavens to move in a direct motion from A to B, and from B to C, _&c._
but gradually slower, until he arrives near the point G; near this
place he appears stationary, or to stand still; and afterwards (tho’ he
still continues to move uniformly in his own orbit, with a progressive
motion) yet in the sphere of the fixed Stars he will appear to be
retrograde, or to go backwards, as from G to H, from H to I, _&c._
until he has arrived near the point L, where again he will appear to be
stationary; and afterwards to move in a direct motion from L to M, and
from M to N, _&c._
What has been here shewed concerning the motions of _Mercury_, is
also to be understood of the motions of _Venus_; but the conjunctions
of _Venus_ with the Sun do not happen so often as in _Mercury_; for
_Venus_ moving in a larger orbit, and much slower than _Mercury_, does
not so often overtake the Earth. But the retrogradations are much
greater in _Venus_ than they are in _Mercury_, for the same reasons.
[Sidenote: _Fig. 2._]
The innermost circle represents the Earth’s orbit, divided into 12
parts, answering to her monthly motion; the greatest circle is in the
orbit of _Jupiter_, which he describes in about 12 years; and therefore
the ¹/₁₂ thereof, from A to N, defines his motion, in one of our years
nearly; and the intermediate divisions, A, B, C, _&c._ his monthly
motion. Let us suppose the Earth to be in the point of her orbit 12,
and _Jupiter_ in A, in his conjunction with the Sun; it is evident
that from the Earth _Jupiter_ will be seen in the great orb, or in the
point of the Heavens A, and while the Earth is moving from 12 to 1, 2,
_&c._ ♃ also moves from A to B, _&c._ all which time he appears in the
Heavens to move with a direct motion from A to B, C, _&c._, until he
comes in opposition to the Earth near the point of the Heavens E, where
he appears to be stationary; after which ♃ again begins to move (tho’
at first with a slow pace) from E through F, H, I to K, where again he
appears to stand still, but afterwards he reassumes his direct motion
from I thro’ K, to M, _&c._
From the construction of the preceding figure it appears, that when
the superior Planets are in conjunction with the Sun, their direct
motion is much quicker than at other times; and that because they
really move from West to East, while the Earth in the opposite part
of the Heavens is carried the same way, and round the same center.
This motion afterwards continually slackens until the Planet comes
almost in opposition to the Sun, when the line joining the Earth and
Planet, will continue for some time nearly parallel to itself, and so
the Planet seems from the Earth to stand still; after which, it begins
to move with a slow motion backward, until it comes into a quartile
aspect with the Sun, when again it will appear to be stationary, for
the above reasons; after that it will resume its direct motion, until
it comes into a conjunction with the Sun, then it will proceed as above
explained. Hence it also appears, that the retrogradations of the
superior Planets are much slower than their direct motions, and their
continuance much shorter; for the Planet, from its last quarter, until
it comes in opposition to the Sun, appears to move the same way with
the Earth, by whom it is then overtaken: After which it begins to go
backwards, but with a slow motion, because the Earth being in the same
part of the Heavens, and moving the same way that the Planet really
does, the apparent motion of the Planet backwards, must thereby be
lessened.
What has been here said concerning the motions of _Jupiter_, is also
to be understood of _Mars_ and _Saturn_. But the retrogradations
of _Saturn_ do oftener happen than those of _Jupiter_, because the
Earth oftener overtakes _Saturn_; and for the same reason, the
regressions of _Jupiter_ do oftener happen than those of _Mars_. But
the retrogradations of _Mars_ are much greater than those of _Jupiter_,
whose are also much greater than those of _Saturn_.
In either of the satellites of _Jupiter_ or _Saturn_, these different
appearances in the neighbouring Worlds are much oftener seen than they
are by us in the primary Planets.
We never observe these different motions in the Moon, because she turns
round the Earth as her center; neither do we observe them in the Sun,
because he is the center of the Earth’s motion; whence the apparent
motion of the Sun always appears the same way round the Earth.
_Of the Annual and Diurnal Motion of the Earth, and of
the increase and decrease of Days and Nights._
The Earth in her annual motion round the Sun, has her axis always in
the same direction, or parallel to itself; that is, if a line be drawn
parallel to the axis, while the Earth is in any point of her orbit, the
axis in all other positions of the Earth will be parallel to the said
line. This parallelism of the axis, and the simple motion of the Earth
in the ecliptic, solves all the phænomena of different seasons. These
things are very well illustrated by the _Orrery_.
[Illustration: Plate 3.]
If you put on the lamp in the place of the Sun, you will see how one
half of our globe is always illuminated by the Sun, while the other
hemisphere remains in darkness; how Day and Night are formed by the
revolution of the Earth round her axis; for as she turns from West to
East, the Sun appears to move from East to West. And while the Earth
turns in her orbit, you may observe that her axis always points the
same way, and the several seasons of the year continually change.
To make these things plainer, we will take a view of the Earth in
different parts of her orbit.
When the Earth is in the first point of _Libra_ (which is found by
extending a thread from the Sun, and over the Earth, to the ecliptic)
we have the _Vernal Equinox_, and the Sun at that time appears in the
first point of ♈. In this position of the Earth, two Poles of the world
are in the line separating light and darkness; and as the Earth turns
round her axis, just one half of the equator, and all its parallels,
will be in the light, and the other half in the dark; and therefore the
days and nights must be every where equal.
As the Earth moves along in her orbit, you will perceive the North
Pole advances by degrees into the illuminated hemisphere, and at the
same time the South Pole recedes into darkness; and in all places to
the Northward of the equator, the days continually lengthen, while the
contrary happens in the Southern parts, until at length the Earth is
arrived in _Capricorn_. In this position of the Earth all the space
included within the arctic circle falls wholly within the light, and
all the opposite part lying within the antarctic circle, is quite
involved in darkness. In all places between the equator and the arctic
circle, the days are now at the longest, and are gradually longer, as
the place are more remote from the equator. In the Southern hemisphere
there is a contrary effect. All the while the Earth is travelling from
_Capricorn_ towards _Aries_, the North Pole gradually recedes from the
light, and the South Pole approaches nearer to it; the days in the
Northern hemisphere gradually decrease, and in the Southern hemisphere
they increase in the same proportion, until the Earth be arrived in
♈; then the two Poles of the world lie exactly in the line separating
light and darkness, and the days are equal to the nights in all places
of the world. As the Earth advances towards _Cancer_, the North Pole
gradually recedes from the light, while the Southern one advances into
it, at the same rate. In the Northern hemisphere the days decrease,
and in the Southern one they gradually lengthen, until the Earth being
arrived in _Cancer_, the North frigid Zone is all involved in darkness,
and the South frigid Zone falls intirely within the light; the days
every where in the Northern hemisphere are now at the shortest, and to
the Southward they are at the longest. As the Earth moves from hence
towards _Libra_, the North Pole gradually approaches the light, and
the other recedes from it; and in all places to the Northward of the
equator, the days now lengthen, while in the opposite hemisphere they
gradually shorten, until the Earth has gotten into ♎; in which position
the days and nights will again be of equal length in all parts of the
world.
You might have observed that in all positions of the Earth, one half
of the equator was in the light, and the other half in darkness;
whence under the equator, the days and nights are always of the same
length: And all the while the Earth was going from ♎ towards ♈, the
North Pole was constantly illuminated, and the South Pole all the
while in darkness; and for the other half year, the contrary. Sometimes
there is a semicircle exactly facing the Sun, fixed over the middle of
the Earth, which may be called the horizon of the disk: This will do
instead of the lamp, if that half of the Earth which is next the Sun be
considered, as being the illuminated hemisphere, and the other half, to
be that which lies in darkness.
[Sidenote: _Plate 4._]
The great circle ♈, ♉, ♊ &_c._ represent the Earth’s annual orbit; and
the four lesser circles ESQC, the ecliptic, upon the surface of the
Earth, coinciding with the great ecliptic in the Heavens. These four
lesser figures represent the Earth in the four cardinal points of the
ecliptic, P being the North Pole of the equator, and _p_ the North Pole
of the ecliptic; SPC, the solstitial colure which is always parallel to
the great solstitial colure ♋ ☉ ♑ in the Heavens; EPQ the equinoctial
colure. The other circles passing thro’ P, are meridians at two hours
distance from one another; the semicircle EÆQ is the Northern half of
the equator; the parallel circle touching the ecliptic in S, is the
tropic of _Cancer_; the dotted circle, the parallel of _London_, and
the small circle, touching the Pole of the ecliptic, is the _Arctic
Circle_. The shaded part, which is always opposite to the Sun, is the
obscure hemisphere, or that which lies in darkness; and that which is
next the Sun, is the illuminated hemisphere.
If we suppose the Earth in ♎, she will then see the Sun in ♈ (which
makes our vernal equinox) and in this position the circle bounding
light and darkness, which here is SC, passes thro’ the Poles of the
World, and bisects all the parallels of the equator; and therefore the
diurnal and nocturnal arches, or the length of the days and nights, are
equal in all places of the world.
But while the Earth in her annual course, moves through ♏, ♐, to ♑, the
line SC, keeping still parallel to itself, or to the place where it was
at first, the Pole P will, by this motion, gradually advance into the
illuminated hemisphere; and also the diurnal arches of the parallels
gradually increase, and consequently the nocturnal ones decrease in
the same proportion, until the Earth has arrived into ♑; in which
position the Pole P, and all the space within the arctic circle, fall
wholly within the illuminated hemisphere, and the diurnal arches of all
the parallels that are without this circle, will exceed the nocturnal
arches more or less, as the places are nearer to, or farther off from
it, until the distance from the Pole is as far as the equator, where
both these arches are always equal.
Again, while the Earth is moving from ♑ through ♒, ♓, to ♈, the Pole P
begins to incline to the line, distinguishing light and darkness, in
the same proportion that before it receded from it; and consequently
the diurnal arches gradually lessen, until the Earth has arrived into
♈ where the Pole P will again fall on the horizon, and so cause the
days and nights to be every where equal. But when the Earth has passed
♈, while she is going thro’ ♉, and ♊, _&c._ the Pole P will begin to
fall in the obscure hemisphere, and so recede gradually from the light,
until the Earth is arrived in ♋; in which position not only the Pole,
but all the space within the arctic circle, are involved in darkness,
and the diurnal arches of all the parallels, without the arctic circle,
are equal to the nocturnal arches of the same parallels, when the
Earth was in the opposite point ♑; and it is evident that the days are
now at the shortest, and the nights the longest. But when the Earth
has past this point, while she is going through ♌ and ♏, the Pole P
will again gradually approach the light, and so the diurnal arches of
the parallels gradually lengthen, until the Earth is arrived in ♎; at
which time the days and nights will again be equal in all places of the
World, and the Pole itself just see the Sun.
[Illustration: Plate 4.]
Here we only considered the phænomena belonging to the Northern
parallels; but if the Pole P be made the South Pole, then all the
parallels of latitude will be parallels of South latitude, and the
days, every where, in any position of the Earth, will be equal to the
nights of those who lived in the opposite hemisphere, under the same
parallels.
_Of the Phases of the Moon, and of her Motion
in her Orbit._
[Sidenote: _Nodes._]
[Sidenote: _Dragon’s Head._]
[Sidenote: _Dragon’s Tail._]
[Sidenote: _Retrograde Motion of the Nodes._]
The orbit of the Moon makes an angle with the plane of the ecliptic, of
above 5¼ degrees, and cuts it into two points, diametrically opposite
(after the same manner as the equator and the ecliptic cut each other
upon the globe, in ♈ and ♎) which points are called the _Nodes_; and
a right line joining these points, and passing through the center of
the Earth, is called the _Line of the Nodes_. That node where the
Moon begins to ascend Northward above the plane of the ecliptic, is
called the _Ascending Node_, and the _Head of the Dragon_, and is thus
commonly marked [Symbol]. The other node from whence the Moon, descends
to the Southward of the ecliptic, is called the _Descending Node_, and
the _Dragon’s Tail_, and is thus marked [Symbol]. The line of nodes
continually shifts itself from East to West, contrary to the order of
the signs; and with this _retrograde_ motion, makes one revolution
round the Earth, in the space of about 19 years.
[Sidenote: _Periodical Month._]
[Sidenote: _Synodical Month._]
The Moon describes its orbit round the Earth in the Space of 27 days
and 7 hours, which space of time is called a _Periodical Month_; yet
from one conjunction to the next, the Moon spends 29 days and a half,
which is called a _Synodical Month_; because while the Moon in her
proper _Orbit_ finishes her course, the Earth advances near a whole
sign in the ecliptic; which space the Moon has still to describe,
before she will be seen in conjunction with the Sun.
When the Moon is in conjunction with the Sun, note her place in the
ecliptic; then turning the handle, you will find that 27 days and 7
hours will bring the Moon to the same place; and after you have made
2¼ revolutions more, the Moon will be exactly betwixt the Sun and the
Earth.
[Sidenote: _Phases of the Moon._]
The Moon all the while keeps in her orbit, and so the wire that
Supports her continually rises or falls in a socket, as she changes her
latitude; the black cap shifts itself, and so shews the phases of the
Moon, according to her age, or how much of her enlightened part is seen
from the Earth. In one synodical month, the line of the nodes moves
about 1½ degree from West to East, and so makes one entire revolution
in 19 years.
Let AB be an arch of the Earth’s orbit, and when the Earth is in
T, let the Moon be in N, in conjunction with the Sun in S, while
the Moon is describing her orbit NAFD, the Earth will describe the
arch of her orbit T _t_; and when the Earth has got into the point
_t_, the Moon will be in the point of her orbit _n_, having made
one compleat revolution round the Earth. But the Moon, before she
comes in conjunction with the Sun, must again describe the arch _n
o_; which arch is similar to T _t_, because the lines FN, _f n_, are
parallel; and because, while the Moon describes the arch _n o_, the
Earth advances forward in the ecliptic; the arch described by the
Moon, after she has finished her periodical month, before she makes a
synodical month, must be somewhat greater than _n o_. To determine the
mean length of a synodical month, find the diurnal motion of the Moon
(or the space she describes round the Earth in one day) and likewise
the diurnal motion of the Earth; then the difference betwixt the two
motions, is the apparent motion of the Moon round the Earth in one day;
then it will be, as this differential arch is to a whole circle; so is
one day to that space of time wherein the Moon appears to describe a
compleat circle round the Earth, which is about 29½ days. But this is
not always a true _Lunation_, for the motion of the Moon is sometimes
faster, and sometimes slower, according to the position of the Earth in
her orbit.
In one synodical month the Moon has all manner of aspects with the
Sun and Earth, and because she is opaque, that face of hers will only
appear bright which is towards the Sun, while the opposite remains in
darkness. But the inhabitants of the Earth can only see that face of
the Moon which is turned towards the Earth; and therefore, according to
the various positions of the Moon, in respect of the Sun and Earth, we
observe different portions of her illuminated face, and so a continual
change in her[7]_Phases_.
Let S be the Sun, RTV an arch of the Earth’s orbit, T the Earth, and
the circle ABCD, _&c._ the Moon’s orbit, in which she turns round the
Earth in the space of a month; and let A, B, C, _&c._ be the centers of
the Moon in different parts of her orbit.
Now if with the lines S A, S B, _&c._ we join the centers of the Sun
and Moon, and at right angles to these draw the lines H O; the said
lines H O will be the circles that separate the illuminated part of the
Moon from the dark and obscure. Again, if we conceive another line I
L to be drawn at right angles to the lines TA, TB, _&c._ passing from
the center of the Earth to the Moon, the said line I L will divide the
visible hemisphere of the Moon, or that which is turned towards us,
from the invisible, or that which is turned from us; and this circle
may be called the _Circle of Vision_.
[Sidenote: _Full Moon._]
[Sidenote: _Half Moon._]
[Sidenote: _New Moon._]
Now it is manifest, that whenever the Moon is in the position A, or in
that point of her orbit which is opposite to the Sun, the circle of
vision, and the circle bounding light and darkness, do coincide, and
all the illuminated face of the Moon is turned towards the Earth, and
is visible to us; and in this position the _Moon_ is said to be _full_.
But when the Moon arrives to B, all her illuminated face is then not
towards the Earth, there being a part of it, HBI, not to be seen by
us; and then her visible face is deficient from a circle, and appears
of a gibbous form, as in B. _Fig. 3_. Again when she arrives to C, the
two forementioned circles cut each other at right angles, and then we
observe a _half Moon_, as in C, _Fig. 3_. And again the illuminated
face of the Moon is more and more turned from the Earth, until she
comes to the Point E, where the circle of vision, and that bounding
light and darkness, do again coincide. Here the Moon disappears, the
illuminated part being wholly turned from the Earth; and she is now
said to be in _Conjunction_ with the _Sun_, because she is in the
same direction from the Earth that the Sun is in, which position we
call a _New Moon_. When the Moon is arrived to F, she again assumes
a horned figure, but her horns (which before the change were turned
Westward) have now changed their position, and look Eastward. When she
has arrived to a quadrate aspect at G, she will appear bissected, like
a half Moon, afterwards she will still grow bigger, until at last she
comes to A, where again she will appear in her full splendor.
The same appearances which we observe in the Moon are likewise observed
by the _Lunarians_ in the Earth, our Earth seeing a Moon to them, as
their Moon is to us; and we are observed by them to be carried round
in the space of time that they are really carried round the Earth. But
the same phases of the Earth and Moon happen when they are in contrary
position; for when the Moon is in conjunction to us, the Earth is then
in opposition to the Moon, and the _Lunarians_ have then a full Earth,
as we in a similar position have a full Moon. When the Moon comes in
opposition to the Sun, the Earth, seen from the Moon, will appear in
conjunction with her, and in that position the Earth will disappear;
afterwards she will assume a horned figure, and so shew the same phases
to the inhabitants of the Moon as she does to us.
_Of the Eclipses of the Sun and Moon._
[Sidenote: _Eclipse._]
An _Eclipse_ is that deprivation of light in a Planet, when another is
interposed betwixt it and the Sun. Thus, an eclipse of the Sun is made
by the interposition of the Moon at her conjunction, and an eclipse
of the Moon is occasioned by the shadow of the Earth falling upon the
Moon, when she is in opposition to the Sun.
[Sidenote: _Fig. 4_.]
[Sidenote: _Lunar Eclipse._]
Let S be the Sun, T the Earth, and ABC its shadow; now if the Moon,
when she is in opposition to the Sun, should come into the conical
space ABC, she will then be deprived of the solar light, and so undergo
an eclipse.
[Sidenote: _Solar Eclipse._]
[Sidenote: _Fig. 5._]
In the same manner, when the shadow of the Moon falls upon the Earth
(which can never happen but when the Moon is in conjunction with
the Sun) that part upon which the shadow falls will be involved in
darkness, and the Sun eclipsed. But because the Moon is much less than
the Earth, the shadow of the ☽ cannot cover the whole Earth, but only a
part of it. Let S be the Sun, T the Earth, ABC the Moon’s orbit, and L
the Moon in conjunction with the Sun: Here the shadow of the Moon falls
only upon the part DE of the Earth’s surface, and there only the Sun
is intirely hid: but there are other parts EF, DG, on each side of the
shadow, where the inhabitants are deprived of part of the Solar rays,
and that more or less, according to their distance from the shadow.
Those who live at H and I will see half of the Sun eclipsed, but in the
spaces FM, GN, all the Sun’s body will be visible, without any eclipse.
From the preceding figure it appears, that an eclipse of the Sun does
not reach a great way upon the superficies of the Earth; but the whole
body of the Moon may sometimes be involved in the Earth’s shadow.
[Sidenote: _Fig. 6._]
Although the Moon seen from the Earth, and the Earth seen from the
Moon, are each alternately, once a month, in conjunction with the Sun;
yet, by reason of the inclination of the Moon’s orbit to the ecliptic,
the Sun is not eclipsed every new Moon, nor the Moon at every full.
Let T be the Earth, DTE an arch of the ecliptic, ALBF, the Moon’s
orbit, having the Earth T, in its center; and let AGBG be another
circle coinciding with the ecliptic, and A, B, the nodes, or the two
points where the Moon’s orbit and the ecliptic cut each other. A the
ascending node, and B the descending node. The angle GAL equal to GBL
is the inclination of the Moon’s orbit to the ecliptic, being about
5¼ degrees. Now a spectator from the Earth at T, will observe the Sun
to move in the circle AGBC, and the Moon in her orbit ALBF; whence it
is evident, that the Sun and Moon can never be seen in a direct line,
from the center of the Earth, but when the Moon is in one of the nodes
A or B; and then only will the Sun appear centrally eclipsed. But if
the conjunction of the Moon happens when she is any where within the
distance A _c_ of the nodes, either North or South, the Sun will then
be eclipsed, more or less, according to the distance from the node A,
or B. If the conjunction happens when the Moon is in _b_, the Sun will
be then one half eclipsed; and if it happens when she is in _c_, the
Moon’s limb will just touch the Sun’s disk, without hiding any part of
it.
The shadow of the Earth at the place where the Moon’s orbit intersects
it, is three times as large as the Moon’s diameter, as in _Fig. 4._ and
therefore it often happens that eclipses of the Moon are total, when
they are not central: And for the same reason the Moon may sometimes be
totally eclipsed for three hours together; whereas total eclipses of
the Sun can scarcely ever exceed four minutes.
The eclipses of the Sun and Moon are very well explained by the
_Orrery_: Thus having put the lamp in the place of the Sun, and the
little Earth and the little Moon in their proper places, instead of the
larger ones, let the room wherein the instrument stands be darkened;
then turning the handle about, you will see when the conjunction of the
Moon happens. When she is in or near one of the nodes, her shadow will
fall upon the Earth, and so deprive that part upon which it falls of
the light of the Sun: If the conjunction happens when the Moon is not
near one of the nodes, the light of the lamp will fall upon the Earth,
either above or below the Moon, according to her latitude at that time.
In like manner, when the full Moon happens near one of the nodes,
the shadow of the Earth will fall upon the Moon; and if the Moon’s
latitude be but small, her whole face will be involved in darkness. At
other times, when the full Moon happens when she is not near one of
her nodes, the shadow of the Earth will pass either above or below the
Moon, and so by that means the Moon will escape being eclipsed.
_Of the Eclipses of the_ Satellites _of_ Jupiter.
The apparent diameters of the inferior Planets are so small, that when
they pass betwixt us and the Sun, they only appear like small spots
upon the Sun’s surface, without depriving us of any sensible quantity
of his light. The shadow of the Earth likewise terminates before it
reaches any of the superior Planets, so that they are never eclipsed by
us; and the Earth when she is in conjunction with the Sun, only appears
like a black spot upon his surface.
But _Jupiter_ and his Moons mutually eclipse each other, as our Earth
and Moon do; as also doth _Saturn_ and his Moons. The satellites of
_Jupiter_ become twice hid from us, in one circulation round ♃; _viz._
once behind the body of _Jupiter_, _i. e._ when they are in the right
line joining the centers of the Earth and ♃; and again they become
invisible when they enter the shadow of _Jupiter_, which happens when
they are at their Full, as seen from ♃, at which times they also suffer
eclipses; which eclipses happen to them after the same manner as they
do to our Moon, by the interposition of the Earth betwixt her and the
Sun.
[Sidenote: _Fig. 7._]
Let S be the Sun, ABT the Earth’s orbit; and C ♃ D, an arch of
_Jupiter_’s orbit, in which let _Jupiter_ be in the point ♃; and let
CFDH be the orbit of one of _Jupiter_’s satellites, which we will here
suppose to be the farthest from him. These satellites, while they move
thro’ the inferior parts of their orbs, _viz._ from D thro’ H, I, to
C, seem from the Earth and the Sun to have a retrograde motion; but
when they are in the superior part of their orbit, they are then seen
to move from West to East, according to their true motion. Now while
they describe the superior part of their orbits, they will be twice hid
from the Earth, once in the shadow of ♃, and once behind his body. If
_Jupiter_ be more Westerly than the Sun, that is, when the Earth is in
A, they will be first hid in the shadow F, and afterwards behind the
body of ♃ in G: But when the Earth is in B, then they are first hid
behind ♃’s body in E, and afterwards fall into the shadow F. While the
satellites describe the inferior parts of their orbit, they only once
disappear, which may be either in I or H, according to the position of
the Earth, in which places they cannot be distinguished from the body
of _Jupiter_.
[Illustration: Plate 5
_Fig. I_
_Fig. II_
_Fig. III_
_Fig. IV_
_Fig. V_
_Fig. VI_
_Fig. VII_]
When the satellites seen from ♃ are in conjunction with the Sun, their
shadows will then fall upon ♃, and some part of his body be involved in
darkness, to which part the Sun will be totally eclipsed.
By observing the eclipses of _Jupiter_’s satellites, it was first
discovered that light is not propogated instantaneously, though it
moves with an incredible swiftness: For if light came to us in an
instant, an observer in T will see an eclipse of one of the satellites,
at the same time that another in K would. But it has been found by
observations, that when the Earth is in K, at her nearest distance from
_Jupiter_, these eclipses happen much sooner than when she is in T.
Now having the difference of time betwixt these appearances in K and
T, we may find the length of time the light takes in passing from K to
T, which space is equal to the diameter of the Earth’s annual orb. By
these kinds of observations it has been found, that light reaches from
the Sun to us in the space of eleven minutes of time, which is at least
at the rate of 100,000 miles in a second.
_FINIS._
[Illustration]
AN INDEX OF THE ASTRONOMICAL TERMS Made Use of in this BOOK.
_Acronical_ Rising and Setting of the Stars Page 96
_Almacanthers_ 63
_Altitudes_ ib.
——— _Meridian Altitude_ 63
_Amplitude_ 62
_Amphiscians_ 91
_Annual Motion_ 7
_Antœci_ 92
_Antarctic Circle_ 53
——— _Pole_ ib.
_Antipodes_ 93
_Arctic Circle_ 52
_Arctic Pole_ 53
_Ascension_ 68
——— _Right_ ib.
——— _Oblique_ 69
_Ascensional Difference_ ib.
_Ascians_ 91
——— _Heteroscians_ ib.
_Asterisms_ 36
_Atmosphere_ 81
_Axis_ 43
——— _of the World_ 49
_Azimuth_ 61
Babylonish _Hours_ 71
_Bissextile_ 78
_Circle_ 42
——— Great _Circles_ ib.
——— Parallel, _or_ lesser _Circles_ 43
——— Secondary _Circles_ ib.
_Circles of the Sphere_ 47
_Climates_ 93
_Colures_ 53
——— _Equinoctial Colure_ ib.
——— _Solstitial Colure_ 54
_Comets_ 29
_Conjunction_ 11, 207
_Constellations_ 36
_Cosmical_ rising and setting of the Stars 96
_Crepusculum_ 83
_Day_, Natural _and_ Artificial 69
_Declination_ 52
_Diurnal Motion_ 7
_Diurnal Arch_ 68
_Eclipses_ 208
——— _Solar_ ib.
——— _Lunar_ ib.
_Eclipses of_ Jupiter’s _Satellites_ 212
_Ecliptic_ 53
_Egyptian Year_ 75
_Elongation_ 18
_Equator, or Equinoctial_ 48
_Equinoctial Points_ 53
——— _Precession of_ 55
——— _Vernal and Autumnal_ 70
_Excentricity_ 4
_Galaxy, or Milky Way_ 38
_Geocentric Place_ 19
_Globe_ 42
——— _Terrestrial_ 43
——— _Celestial_ 44
Gregorian _Account_ 80
_Heliacal_ rising and setting of the Stars 96
_Heliocentric Place_ 19
_Hemisphere_ 42
——— _Northern and Southern_ 49
_Heteroscians_ 91
_Horizon_ 58
——— _Sensible_ ib.
——— _Rational_ 59
_Hour Circles_ 50