ïn TVhich a Comprehensive View of the Solar System is given 5 and tW
Use of the Globes is farther shewn, in thé explanation
of Spherical Triangles.

BLOBS AND MATHEMATICAL INSTRBMEIfT M.VKER TO HIS MAJESTT ; OPTtCIJC«
to ms B. H. TCHE PRINCE OF WALE^, amp;C. 5 AND BROTHER
To THE LATE GEORGE ADAMS.

It is the privilege of real greatness not to
be afraid of diminution by condescending to
the notice of little things ; and I therefore
can boldlj solicit the patronage of your -Ma-
jesty to the humble labours by which I
have endeavoured to improve the instru-
ments of science, and make the globes on
which the earth and sky are delineated less
defective in-their construction, and less dif-
ficult in their use.

Geography is in a peculiar manner the
science of princes. When a private student
revolves the terraqueous globe, he beholds
a succession of countries in which he haç

no more interest than in the imaginary
regions of Jupiter and Saturn. But your
Majesty must contemplate the scientific
pictui-e with other sentiments, and consider,
as oceans and continents are rolling before
you, how large a part of mankind is now
waiting on your determinations, and may
receive benefits or suffer evils, as your in-
fluence is extended or withdrawn.

The provinces which your Majesty's arms
have added to your dominions make no in-
considerable part of the orb allotted to hu-
man beings. Your power is acknowledged
by nations whose names we know not yefc
how to write, and whose boundaries we
cannot yet describe. But your Majesty's
lenity and beneficence give us reason to ex-
pect the time when science shall be advanced
by the diffusion of happiness ; when the
desarts of America shall become pervious
and safe, when those who are now restrained
by fear shall be attracted by reverence, and
multitudes who now range the woods for

prey, and live at the mercy of winds and
seasons, shall, by the paternal care of your
Majesty, enjoy the plenty of cultivated lands,
the pleasures of society, the security of law,
and the light of Revelation.

Deeming it proper to oflfer my reasons for reprinting
this work in its present shape, i beg first to premise, that it
has been my wish in this instance to give it according to
the original text, with the exception of a few notes, that it
may possess the merit of being the genuine production of my
Father, viz. of George Adams, Sen. ; who died in the year
1773. As a tribute due to his memory, it is but justice to
say, that, for its plain unadorned language, perspicuity of defi-
nition, and copiousness of illustration, it has been rarely ex-
celled, I believe never as an Elementary Treatise; in proof of
which, it is only necessary to adduce the fact that even at this mo-
ment the work is sought after with as great avidity as formerly.

My Brother, the late George Adams, (who resigned his
breath in the year 1795), treading in his Father's steps as an
Author, reprinted and published the same work for many
years, together with several of his own ; by which he ac-
quired the deserved approbation of a discriminating Public j
and, such was his worth among a wide and extended'circle
of Friends, and in the scientific virorld, that his demise was
considered a national loss. Having paid the debt of nature,
his stock in trade, together with a valuable library (collected
by my Father and himself during a period of 60 years), the
copyrights of his own works, with those written by my
Father also, were all sold by public auction. Over these and
other events that occurred at this period, I will draw the veil,
since to recapitulate them would neither be interesting nor
useful to the. Public, and would only serve to bring back to

recollcction circumstances that were not only unpleasant, but
prejudicial and injurious to me; suffice it to say, that, from
the respect I owed to the memory of my Brother, though I
possessed at the time they were sold an inherent and exclu-
sive right to all my Father's works, I offered no bar to, or
anywise prevented, the sale of them, rids work was there-
fore disposed of among the rest, and falling into other hands,
ft passed through several editions. While it continued to be
regularly reprinted as each edition was sold, and the Public
and myself * sufTered no disappointment from the want of it, I
was perfectly indifferent as to who or what person was the
Publisher; but when it became neglected, and was omitted to
be published for nearly three years, I felt not only that I was
called upon to publish it, but that to withhold it any longer
from the Public would be to incur censure myself, which I
trust I shall ever, as hitherto, have judgment enough to avoid.
With the utmost deference therefore, 1 submit this work, the
honest labour of my Parent, though long deceased, to a gener-
ous and discerning Public. If it were necessary to advanee
facts to prove the truthof my assertions with respect to my right
to pLiblish it, I have only to state that shortly after the decease
of my SrothcFj 1 wjis put in possession of all niy Father's
manuscripts, which are numerous. They were the genuine
and free gift of my Mother, and were accompanied with the
original copper-plates, both for the work on the Globes, and
that on the Microscopc; the cuts therefore, that have been
affixed to those two works, published by others for the last
2 5 years, will be found to be copies from my plates ; and the
Public will in their judgment decide as to their superiority or
inferiority.

I may at somefutare time lay before the Public the original
octavo work on the Microscope,! published also by my Father,
wilAi the plates, 60 in number, which have for many years

* I myself, because it was particularly adapted to and written for
Adams (Jiobes, which are manufactured by me.

remained dormant in my closet; but for the present I shall
pontenl myself with publishing this work, and hope the price
will be considered very moderate, not wishing so much to
derive emolument from the work, as to give to it the greatest
publicity possible.

I have prepared a Catalog uc of Philosophical Instruments,
of a far more detailed and descriptive kind than is usual, and
comprising more articles than any Other hitherto published,
which I beg leave to offer also to the notice of the Public to-
gether with the work alluded to ; and remain.

The connection of astronomy with geography
is so evident, and both in conjunction are so ne-
cessary to a learned education, that no man will
be thought to have deserved ill of the republic of
letters, who has applied his endeavours to throw
any new light upon such useful sciences. And
as the phoenomena of the earth and heavens can
be adequately illustrated only by the mechanical
contrivance of globes, whatever improvement is
made in these must deserve regard, in proportion
as it facilitates the attainment of astronomical and
geographical knowledge. *

As to maps and all projections of the sphere
in piano, their use is more difficult than those of
the globe, of which indeed they are only so many
pictures ; nor can they be thoroughly understood
without more skill in geometry than is commonly
possessed by beginners, for whose use the fol-
lowing treatise is principally designed ; though it
also contains some observations, which I hope will
not be altogether unacceptable to a more learned
reader.

The globes now offered to the public, are of
a construction new and peculiar ; they are con-
trived to solve the various phoenomena of the
earth and heavens in a more easy and natural
manner than any hitherto published, and are so
suspended that the student may elevate the south
pole; a thing impracticable in the use of common
globes.

That agreement too, which is here pointed
out between the celestial and terrestrial sphere,

the same has been effected under my immediate instructions, and
the globes thus newly mounted according to the Abbé Vinson's plan
are respectfully submitted to the inspection of the public. They
may be seen during the hours of business at my house, and the
public are further informed that the Abbe is engaged in preparing
a treatise thereon.

will be found to open a large field of geographical
and astronomical knowledge; and will afford both
instruction and ainusement to every unprejudiced
inquirer. This correspondence arises from a com-
parison of one globe with the other, or of the dis-
tances of different places on the earth's surface,
with the relative distances of such fixed stars as
answer to them in the heavens.

By these steps of science, the mind of man
may be raised to the contemplation of the divine
wisdom, which has so adjusted the proportion of
days, months, seasons, and years, in the different
parts of the terraqueous globe, as to have distri-
buted with an impartial hand, though after a man-
ner wonderfully various, an equal share of the sun's
light to every nation under heaven.

By these globes, with little or no experience in
astronomy, may be seen how the moon changes
her place every night, by observing her position
with respect to any fixed star, and how she proceeds
regularly from it to the eastward ; as the several
planets also may be observed to do, some more
slowly than others, as their orbits are more or less
remote from the center of the system ; while the

regularity of their motions, strictly conformable
at all times to the laws of their Creator, exhibits
a striking pattern of obedience to every rational
spectator.

But it will be proper in this place to inform the
reader what he is to expect in the globes, and in
the following treatise intended to accompany and
Explain them.

The superior accuracy with which the plates
are drawn and engraved will, it is hoped, appear
to competent judges at the first sight; for the per-
fecting of which no expence of time or labour
hath been spared. The celestial globe is improved
by the addition of several thousand stars more
than have appeared upon any globe hitherto pub-
lished ; all the latest discoveries in geography
and astronomy are in both of them strictly fol-
lowed, and many new lines and circles are in-
scribed, the use of which will be fully explained
hereafter.

In the treatise, we have made choice of that
method of finding the times of equinox, which
13 the most modern and simple; and which per-

haps gives the truest mean length of a tropical
year ; that the young student may with greater
ease and pleasure be made acquainted with the first
principles, and from them be carried on to the more
abstruse parts of astronomy.

To render this book as extensively useful as
possible, I have endeavoured, with all the clear-
ness I am master of, to express both my own and
the sentiments of other authors on the same sub-
ject ; and I think it my duty to acknowledge the
assistance I have received in the course of this
work, as well from books, as from some worthy
fnends ; as I would not willingly incur the imputa-
tion either of plagiarism or ingratitude. If there
should appear to be any defects, to which every
human work is liable, the reader, I hopç, will
make some favourable allowance for the undertaker
of a task so complicated and laborious, and correct
my errors for himself as well as he is able,

N. B. When the reader is hereafter directed to
apply a card, or the edge of a card, to any part of
the globe, it is to be understood that he should cut
a card of any kind, exactly in the size and shape of
A B Ç D, fig. 4, for the globes of eighteen Inches

diameter; and of the size and shape of EFGIJ/
for thdse of twelve inches diameter; then, if the
arch B C, or F G, are applied to the surface of
their respective globes^ the lines A B, or CD,
E F, and G H, will become radii from the center
of the globe. It is frequently required to know
what point upon tli6 strong brsss mcriditin, or
broad paper circle, exactly answers to a given point
upon the globe, and as this cannot be well known
by inspection, on account of the necessary distance
of these two circles from the surface, if the corner
B or F be applied to the given point upon the
globe, the edge of the card will exactly mark the
degree or part of the degree required.

For elevating the pole exactly, the card is to be
]aid upon the broad paper circle, and its edge ap^
plied to the strong brass meridian, by which means
the degree, and parts of a degree, may be ascer-
tained with sufficient acctiracV.

Proe. III. To find all those places which have the same lati-
tude with any given place................i .... 49

VIII. To find what places have mid-day, or the sun
upon their raeridvan, at any given hour of the

X. At any given lime ojf the day at the place where
you are to find the hour at any other place pro-
posed....................................ifejd,

XI. The latitude and longitude of any place beiiOg
known, to find that place upon the globe; or if
it be not inserted, to find its place, and fix the

XIV.nbsp;To represent the apparent diurnal motion of the
sun, moon, and stars, on the celestial globe ..... 81

Their time of rising, oblique ascension, right ascension, de-
clination, oblique descension, ascensional difference, amp;c.
from Al t. 1()7 to 20()
yarallt'ls of altitude, what..............................8%

PROB XVi To find the.azimu!h of the sun or any star .... 8lt;)
To find the angle of position and bearing of one place from

Prob. XVII. To rectify the terrestrial glnbe that the en-
lightened half may be apparpt for any time

XXVII. To find all those places on the globe over
whose zenith the sun will pass on any given

XXVIH. To find the sun's declination, and thence the
parallel of latitude corresponding therewith,

XXIX. To find those two days on which the sun
will be vertical to any place between the
topics.................................108

XXX. The day and hour at any place being given,
to find where the sun is vertical at that

Piiob. XXXI. The time of the day being given, to find all
those places vvhere'the snn is then rising and
setting on the meridian, whe:e he is vertical,
also, niidiiight, twilight, dai knight, amp;c. at the

XXXII. To find the tin^e of the sun's rising and
setting, length of day and night, amp;c, in any
place between the polar circles; and also to
find the climate........................110

XXXIII.nbsp;To find those places within the polar circles
on which the sun begins to shine, the time he
shines, when he begins to disappear, length
of his absence, and the first and last day of

XXXVI. To tind the latitude of a place in which its
longest day may be of any given length be-
tween twelve and twenty-four hours ........ ibid.

XXXVII. To find the distance between any two places. . ibid.
XXXVIII. To find all those places which are at the same

• XXXIX. To shew at one view upon the terrestrial globe
for any place the sun's meridian altitude, his
amplitude, or point of the compass on which
he rises and sets everv day in the year......ibid.

XL. To shew at one view upon the terrestrial
globe the length of the days and nights
at any particular place for all times of the

XLIII. To find on what day of the j-ear any .star
passes the meridian at any proposed hour of

To iind the time of the sun's entry into the lirst point of
Libra or Aries, and thence that point in the equator to

Precepts for the use of the tables of retrocession and au-
tumnal equinoxes..............i...................

To reduce hours, minutes, and seconds of time, into de-
grees, minutes, and seconds of the equator ............

the time of an equinox, as well as that point .
upon the equator to which the sun is vertical

Of the natural agreement between the celestial and ter-
restrial spheres ; or, how to gain a perfect idea of the
situation and distance of all places upon the earth by

PiioB. XLVI. To find the solar correspondence to a fixed
point upon the earth, when the sun is seen
by an observer situated upon any other point

Prob. XLVIII. To find the time of the right ascension of
any star upon any particular meridian on any

XLIX. To rectify the celestial globe for any time
in the evening of any day in the year by
the knowledge of the time when the first
point of Aries shall pass the meridian

A general description of the passage of the star y in the
bead of the constellation Draco, over the parallel of
I/ondon.......................................... l63

PUOB. LI. Tö find a signal or warning-star that shall be
upon or near the meridian of ap observer at the
time any known star is perpendicular to any

LVII. To observe the sun's altitude by the terreslrial
glob«, when he shines bright, or when he can

JLVIII. To place ihe tenestrial globe in the sun's rajs
that it may represent the natural position of
tlie earth, either 'oy a meridian-line, or with.

LXI. To shew that in some places of the earth's
surface the sun will 'oe twice on the same
azimuth in the morning, and twice on the same

i;XII. To observe the hour of the day in thé most
natural manner when the terrestrial globe i«

LXV. To find what azimuth the paoon is upon at any
place, when it is flood or liigh water; and
thence the high tide foy any day 0(f the nwon's

The use of the globes in the solution of right-angled spheri-
cal triangles ......................................203

Prob. LXXVII. Given, the sun's place, the inclitiation of
the ecliptic and equator : to find the sun's
right ascension, distance from the nortj»^
pole, and the angle which the meridian,,
passing through the sun at that place, makes
wi h the ecliptic......................ibid.

LXXVIII. Given, the sun's place, declination, and
latitude: to find his iigt;ing and setting;
the length of the day and night; the am-
plitude of the rising-suH from the east, and
of the setiing-sun from the west; and
that of the path of the vertex in the edge

LXXIX. Given, the latitude and declination; to
find the sun's distance from tlie vertex
at the hour of six, and his ampliii,jde at

LXXX. To find the sun's distance from the ver-
■ tex when due east atgt;d west, and the hour
from noon when in either of these points .. 221
LXXXl. Given, the hour from noon, and the sun's
distance from the pole : to find bis distance

the latitude and sun's lt;3\s1anee from the
vertex by observation : to find the time of
the day, and the azimuth upon wliich the

Prob.LXXXIII. Given, the latitude, sun's place, and right
ascension : to find what point of the eclip-
tic culminates, its highest point, amp;c.
The distance of the nonagesimal from the
vertex, and the angle made by the vertical
circle passing through the sun at that time

LXXXIV. Given, the latitude, right ascension, and
declination of any point of the ecliptic,
or of a fixed star : to find its rising or
setting amplitude, its ascensional .difference,

LXXXV. Given, the latitude, the points of the
ecliptic with which a star rises or sets,
and the altitude of the nonagesimal when
those points are upon the horizon : to find
in what points of the ecliptic the sun must
be to make the star .vhen rising or setting
appear just free from the solar rays; and
thence the times of its heliacal rising and

LXXXVI. Given, the latitude, and ancient longitude,
of a fixed siar : to find its right ascension,

most noble and exalted branch of human literature,
regards the various phoEnoniena of those heavenly
bodieF, wiiich the invention of carious instruments
hath brouglit within our observation, from the sur-
face of the terrestrial globe.

It discovers to us their situation, magnitudes, dis-
tances, and motions ; and enables us to determine
with precision the length of years, months, and
days, and to account for the vicissitudes of the sea-
sons ; and, in a word, explains whatever falls within .
oiir consideration, as thé» proper subject of this useful
and interesting study.

1. Consists of the sun, (from which it receives its
denomination,) six primary, ten secondary planets,
and the comets. These, with that collection of in-
numerable spherical bodies which compose the uni-
verse, are called the system of the world ; all which
appear to the inhabitants of the earth, as if they were
within one and the same concave sphere.

1. The Copernican, or solar system, supposes the
sun in the centre, having a motion round its axis,
which is completed in about 254- days. This motion
was discovered by the revolution of those spots
which are frequently seen in its disc, and are sup-
posed to adhere to its surface ; and its axis is inclined
to the plane of the ecliptic in an angle of about 874-
degrees.

3. The six primary planets move round the sun in
their respective elliptical orbits, from west to east, at
different distances, and in various periodical times.
Their names and characters, in the order in which
they revolve about the sun, are expressed in fig. 2,
and are as follow :

'4. The planets are distinguished from the fixed
stars, by their motion, and the steadiness of their
light. The apparent diameter of the fixed stars is so
small, by reason of their immense distance, that every
small at^m floating^in our atmosphere intercepts
hnbsp;light, and causes then^to twinkle. But that of

, the planets being greater, as they are nearer to us,
they shine with a steady light.

1nbsp; Uranus, or the Georgian planet was discovered by Dr. Her-
schel in the year 1781. It had been seen by Flamsteed and other
astronomers, but not distinguished from the fixed stars. It revolves
round the sun in 81 years and 29 days. Its synodical revolution
is 370 days. Its motion begins to be retrograde when, previous to
the opposition,^ the planet is about 105° from the sun; its retro-
grade motion continues about 142 days, it is apparently stationary
ten days, and its arc of retrogradation is about 4'.

with respect to each other, but the planets change
theirs from one part of the heavens to another.

6.nbsp;Some of the primary planets are attended with
smaller, called secondary planets, moons, or satellites.
Our earth is attended by the moon ; Jupiter by four,
and Saturn by five satellites; the nine last are not
visible without the assistance of a telescope.

7.nbsp;The observation of comets, seen sometimes
within the limits of the solar system, hath been
hitherto so imperfect, that we shall only take notice
for the present, that they are supposed to move
round the sun, in very eccentric orbits, and appear
to us only when they are in that part of their orbit
nearest the sun : they move in various directions and
inclinations ; the lower part of one of these orbits is
represented in fig. 2.

As the sun ha« a number of planets and comets
moving round him, so every fixed star is supposed to
be a sun, and to have a system of its own.

8.nbsp;The path described by a planet in its motion
round the sun is called its orbit. In fig. 3, their
several orbits are represented by concentric circles:
the paths which they describe are elliptical, and the
sun is in one of the foci. In fig. 3, A T P V is an
ellipse, AP its transverse, VT its conjugate diame-
ter, S and N are its two foci, C is the centre of the
ellipse ; the distance between C S or c N is called
the eccentricity.

9.nbsp;The orbit of every planet is in a plane passing
through the sun, which planes are inclined to one
another: thus in fig. 4, let A B C D represent the
earth's orbit, or plane of the ecliptic; this is taken

for a standard, from which the inclination of each
orbit of the planets, as E D F B, is measured. The
mchnation of the orbit of Mercury is 7°, that of Ve-
nus 3='24', ofMarslquot;.5r, of Jupiter 10' of Sa-
turn 2° 30'.*

10. To a spectator from the s;..n, the planes of the
orbit of each planet produced to the fixed stars would
mark, in the celestial sphere, their several inclir.ecl
heliocentric orbits ; their passage through these is
their heliocentric motion. These extended planes,
to a spectator on the earth, mark' out in tiie starrv
sphere their geocentric orbits ; and their apparent
motion through these, is called tl.eir geocentric
motion.

IJ. The latitude of a planet seen from the earth,
is called its geocentric, if seen from the sun, its he-
liocentric, latitude.

12.nbsp;Are two points iil which it intersects the plane
of the ecliptic. In fig. 4, ABCD is the plane of the
ecliptic; EBFD is the orbit of a planet, in which
the points B and D arc the two nodes. B the ascend-
ing, D the descending node; the point E is called
its greatest northern, and F its greatest southern
limit.

13.nbsp;The line of the nodes is a line BD drawn
through the sun from one node to the other.

A planet, seen from the earth, never appears in
the ecliptic, but when it is in one of its nodes: in
all other parts of its orbit it has geocentric latitude.

ferior, because their orbits are included withiu that
of tiie earth ; see (ig. 2.

15.nbsp;Moves round the sun in 87 d. 23 h. l6 m.
which is called his periodical time. If we call the
mean distance of the earth from the sim lOOO, the
i«ean distance of mercury is 38/, his eccentricity 80.
No spots have yet been observed in Mercury ; there-
fore it is not certainly known wliether he turns about
his axis or not; but it is inost probable that he
does.¹

16.nbsp;Performs her revolution round the sun in
224 d. l6 h. 4g m. which is called her periodical
time ; her mean distance is 724, and her eccentricity
5 ; her motion about her axis is perfonned in 24 d.-f
8 h. according to Bianchini; and the inclination of
her axis to the plane of the ecliptic, is 15 deg.:]:

17.nbsp;The greatest distance of the earth, or of any
planet from the sun, is called its aphelion or higher
apsis; its least distance is called the perihelion, or

1nbsp; The orbit of Mercury being elliptical and more,eccentric than
any of the other planets, itamp; distance from the sun is very varia-
ble, its greatest distance being 46,665, its least 30,754. Its
orbit revolves in its own plane with a very slow motion, the point
nearest the sun called the PeriheHon moving 1° 57' 20quot; accord-
ing to the order of the signs, in a century. The nodes, or points
of its intersection with the ecliptic, move westward or contrary to
the order of the signs 43quot; in a year. Mercury is estimated to be
a little more than one third as large as the earth.

f The magnitude and diurnal rotation of Venus are supposed to
differ but little from those of the Earth.

t The line of the apsides of this planet, or greater axis of the
ellipse, has a slow motion eastward of 2° 44'46quot; in a century,
-and itü nodes move in a contrary direction 31quot; annually.

lower apsis. Thus in fig. 3, A is the place of ihe
aphelion, P that of the perihelion. The axis P A of
any planet's ellipsis is called the line of the apsides ;
the extreme points of its shortest diameter t v, are
the places of its mean distance from the sun ; and
S T, or s v, the line of its mean distance.

18.nbsp;A planet is said to be in conjunction with the
sun, when its apparent place, seen from the earth, is
in or near the sun's place ; it is said to be in oppo-
sition, when the earth is between the sun and
planet.

19.nbsp;Is its apparent distance from the sun, as seen
from the earth. A planet has no elongation when in
conjunction with the sun ; in opposition, it has 180
deg. In fig. 5, t T t represents a part of the earth's
orbit; T the earth, S the sun ; A C E an arch of the
starry sphere, and d the place of Venus in her orbit.
a spectator upon the earth at T would refer the
sun's place to those fixed stars at C, and that of
Venus to those at D ; in this case the angle C T D
is the apparent distance between the sun and Venus,
and is called the angle of elongation.

20.nbsp;An inferior planet may be in conjunction with
the sun in two situations ; first, when it is between
the earth and the sun, called the inferior conjunc-
tion ; second, when the sun is between the earth
and planet, called its superior conjunction; but it
can never be in opposition tp the sun.

21.nbsp;The greatest elongation of an inferior planet
is when a line T E, drawn from the earth at T,
through the planet at e, is a tangent to the orbit of
the planets

gt; 22. As an inferior planet moves from its greatest
elongation at a, fig. through c, its superior con-
junction, to e, its greatest elongation on the other
side of the sun, its geocentric motion is direct.

23.nbsp;When the earth is at T, Venus at a, a specta-
tor at T sees the planet at a, in the line T a A among
the fixed stars at A : when the planet is come to b,
it appears m the line T b B, or amongst the stars at
b; at c, it IS in its superior conjunction, and seen
among ttie stars at C; at d, it appears among the
stars at D ; and when it arrives at e, it appears among
those at E. In this motion, Venus appears to de-
scribe the arc A B C D E, in the concave sphere of
the heavens: and as these letters are in the same
direction with a b c d e, which express the planet's
motion round the sun, its apparent motion seen from
the earth is therefore direct, from west to east, or
according to the order of the signs.

24.nbsp;An inferior planet passing from e, its greatest
elongation, through f, its inferior conjunction, to a,
its greatest elongation on the other side of the sun,
its geocentric motion is retrograde.

As Venus is moving from e to n, she appears In
the line T n d D, and is seen among the stars at d ;
when she comes to f, her inferior conjunction, sh^
appears amongst the stars at C ; at m, she is seen in
the concave sphere at B ; and when she is at a, in
her own orbit, she appears at A, in the heavens.
Hence, as the planet passed through e n f m a, in its
natural motion, its apparent motion was backwards,
through E D C B A, or contrary to the order of the.
signs.

25.nbsp;When the inferior planets are at their greatest
elongation, they appear stationary, or continue iu

the same place for some time, before their motion
changes from direct to retrograde, or from retrograde
to direct again.

26 In order to have a clear idea of the apparent
motion of a planet, conceive the lines T a A, T b B,
amp;c. to move with the earth ; so that the points
enfma, whilst the earth performs its revolution,
may run through the orbit of the planet.

27.nbsp;The inclination of the orbits of the planets to
the plane of the ecliptic is the cause why they do
not seem to move in the ecliptic line, but are some-
tihies above, and at others below it. In fig. 6, let
N V N Q be a circle in the plane of T t the ecliptic,
and NAN, the planet's inclined orbit, S the sun,
the earth at T, and the planet at A; if.the short line
V A be imagined perpendicular to the pkuie of the
ecliptic, and to pass through the planet at A, the
angle VTA, is the latitude of the planet, which is
called the geocentric latitude, to distinguish it from
the heliocentric latitude, as seen from the sun, which
is represented by the angle ASV.

28.nbsp;When a planet is in the node at N, it appears
in the ecliptic line; as it recedes from thence its
latitude increases; and this is different, according to
the situation of the earth ; so that the latitude is
greater when the earth is at T, and the planet at A,
than when the earth is at t, and the planet at V.

2p, A planet is said to be in quadrature when it is
90 deg, distant from the sun ; the inferior planets
cannot b^ in quadrature, as their greatest elongaticjn
can never be a right angle; therefore they never ap-
pear far from the sun ; for Venus and Mercury aro

only seen in an evening towards the west, soon after
sun-set, or a little before the sun rises in the morn-
ing, The greatest elongation of Mercury is 33 deg.
and of Venus 48 deg¹

30.nbsp;As Venus moves from her superior to her in-
ferior conjunction, she sets after the sun, and is called
the evening-star; and as she is moving from her in-
ferior to her superior conjunction, she rises before the
sun, and is called the morning-star.

31.nbsp;The sun, being larger than any planet, en-
lightens a little more than an hemisphere ; and as we
can only see half a planet at once, that hemisphere
which we see is called the disc of the planet. Th^
inferior planets are not visible to us, when in their
inferior conjunction, but their whole disc is illumi-
nated in their superior conjunction : and when they
are in one of their nodes, they appear on the disc of
the sun like a black spot; and this is called a transit
of the planet across the disc of the sun. As the en-
lightened hemispheres of the inferior planets are
sometimes more, at others less turned towards the
earth, they appear through .1 telescope to have all
the phases of the moon.

32.nbsp;When Venus is the evening-star, her horns
are turned towards the east, and the sun sets before,
and to the westward of her. When she is a morn-
ing-star, her horns are turned towards the west, and
the sun rises after, or to the east of her; in both
cases, the horns are always turned from the sun.
When she is at her greatest elongation, half the en-
lightened hemisphere will face the earth, and her disc

1nbsp; These greatest elongations vary much at different times, from
the elliptic nature of the orbits ; those of Mercury vary from 28quot;
^Q' to 18° J those of Venus from 48° to 45°.

appear« aS the moon does in the quarters ; but when
in any part between that and her inferior conjunction,
she appears horned, and between her greatest elon-
gation and superior conjunction, her appearance is
gibbous.

33.nbsp;What has been said of the planet Venus, is
also true with respect to Mercury, with this differ-
ence, that he is direct, stationary, amp;c. so much more
frequently, as his revolutions round the sun are per-
formed in a shorter space of time.¹

34.nbsp;The apparent motion of the sun, arising from
the earth's annual motion in its orbit, is as follows:
Id fig. 7, S represents the sun, T the earth in its
orbit Tt, and RQ the concave sphere of the fixed
stars. Whilst the earth is moving in its orbit from
T to t, the sun seems to move through the starry
arch from Q to R, which measures the angle R S Q,
equal to the angle T S t, so that the celerity of the
apparent motion of the sun depends upon the cele-
rity of the angular motion of the earth, with respect
to the center of the sun. In a whole revolution of
the earth, the sun also seems to run through a whole
circle,

35.nbsp;The earth moves round the sun between the
orbits of Venus and Mars, in 365 d. 5 h, 49 m.
Besides this annual motion, it turns round its own axis
in 24 solar h.; its axis is constantly inclined in an

1nbsp; Tlie interval between tv/o successive conjunctions of Mer-
cury is about 115 d. of which 93 are progressive and 22 retro-
grade.

The interval between two conjunctions of Venus is about 584
days, during 542 of which her motion is progressive.

angle of deg. to the plane of the earth's orbit, or
the ecliptic, and keeps continually parallel to itself in
every part of its revolution.

In fig. 8, S represents the sun, A B C D the orbit
of the earth ; in the periphery of which, the centre
of the earth is carried round the sun, according to
the order of the signs, or in consequentia. f S ill:
represents the equinoctial colure, 25 S VJ, the solsti-
tial colure; the circle in each, abed, represents
the earth in the four cardinal points of its orbit; in
which d c separates the enlightened part c b d of the
earth's disc, from d a c, the obscure part of it.

The plane of the earth's annual orbit, A BCD,
extended every way to the sphere of the fixed stars,
would describe the celestial ecliptic, which would
coincide with the terrestrial ecliptic, here represented
by each of the circles abed; in which c, is the
pole of the ecliptic, P the pole of the world, or of
the equator : in all these projections, ae is the equa-
tor, t the tropic of Cancer, L the path or vertex of
London ; and the circles cutting each other in P, the
pole of the world, are circles of right ascension
in the celestial, and of longitude in the terrestrial
sphere.

30. As the sun always enlightens one half of the
earth's globe at the same time, the line d c, that
divides the illuminated from the obscure part of the
earth's disc, is called the edge of the disc.

P a, P d, P b, P c, represent so much of the earth's
axis as falls within these projections ; these may be
called the. line of direction of the earth's aîdis, which
is constantly carried round the annual orbit, always
parallel to itself.

better understood by observing tig. 9, in whicll
a b C d represents the earth's orbit, seen ut a dis-
tance ; the eye supposed to be elevated a little above
the plane of it. The earth is here represented in
the first point of each of the twelve signs, as marked
in the figure, with the twelve montlis annexed: e
the pole, and ed the axis of the ecliptic, always per-
pendicular to the plane of the orbit. P the north
pole of the world, P m its axis, about which the
earth's daily motion is made from west to east.
PCE shews the angle of its inclination, which pre-
serves its parallelism through every part of its
orbit.

38.nbsp;When the earth is in the first point of Libra,
the sun then appears in tlie opposite point of the
ecliptic at Aries, about the 2'2d of September, N. S.
and when the earth is in Aries, the sun will then
appear in Libra about the 1 Qth of March ; at which
time of the year the edge of the enlightened hemis-
phere is parallel to the solstitial colure, fig. 8, and
passes through the two poles of the world, dividing
every parallel to the equator into two equal parts;
whence the diurnal parallel of every inhabitant on
the surface of the earth will, at either of these sea-
sons, be half in the illuminated, and half in the ob-
scure part of the earth ; consequently the day and
night will be equal in all places.

39.nbsp;Conceive the earth to have moved from iiCh
Libra to Vjquot; Capricorn, its line of direction keeping
its parallelism will now coincide with the solstitial
colure, fig. 8, and the edge of the disc will be per-
pendicular thereto, and pass through e, the pole of
the ecliptic. In this situation of the earth, all places
within the northern polar circle are illuminated

Uirougbont the whole diurnal revolution ; at which
time their inhabitants see the sun longer than '24 h.;
but those which lie under the polar circle touch the
edge of the disc, and therefore their inhabitants only
see the sun skim quite round their horizon at its first
a^jpearance; every other parallel intersects the edge
of the disc; and as the illuminated part of each is
much greater than the obscure part, the days are
consequently at this season, of the summer solstice,
nliich happens about the 21st of June, longer than
the nights. While the earth is moving from Libra,
through Capricorn to_ Aries, the north pole P, being
in thequot; illuminated hemisphere, will have six months
continual day ; but while the earth passes from Aries
through Cancer to Libra, the north pole will be in
the obscure part, and have continual night; the south
pole of the globe at the same time enjoying con-
tinual day.

40. When the earth is at Cancer, the sun appears
at Capricorn. At tliis season the nights will as much
exceed the days, as the days exceed the nights, when
the earth was in the opposite point of her orbit; for
the nocturnal arches, or obscure part of their paths,
are here equal to the illuminated parts, when the
earth was at Capricorn ; and the illuminated part
is here no more than the obscure part was in that
place.

41. By suiTjmer, is meant the time in which the
earth is moving in her orbit from the vernal to the
autumnal equinox : and by winter, the time in which

it is passing from the autumnal to the vernal equi-
nox. Upon the globe it is evident- that the ecliptic
is divided into six northern and six southern signs,
and that it intersects the equator at the points marked
T and dZh:. In our summer, the sun's apparent mo-
tion is through the six northern, and in winter
through the six southern signs ; yet the sun is ] 86 d.
11 h. 51m. in passing through the six first, and
only 178 d. 17 h. 58 m.^ in passing through the six
last. Their difference 7 d. 17 h. 53 m. is the length
of time by which our summer exceeds the winter.

42. In fig. l6, A BCD represents the earth's
orbit; S the sun in one of its foci: when the earth
is at B, the sun appears at H in the first point of
Aries ; and whilst the earth moves from B, through
C to D, the sun appears to run through the six
northern signs, T b O 25 SI lU to ii at F. When
the earth is at D, the sun appears at F in the first
point of Libra; and as the earth moves from D
through A to B, the sun appears to run through the
six southern signs, ii tiJi ƒ Vy xsr to Aries at H.
Hence the line F H, drawn from the first point of
If, through the sun at S, to the first point of
divides the ecliptic into two equal parts; but the
same line* divides the earth's elliptical orbit A B C D
into two unequal parts, (the sun not being in the
centre, but in one of the foci of this orbit;) the
greater part B C D, is that which the earth describes
in summer, whilst the sun appears in the northern
signs ; the lesser part is D A B, which the earth de-
scribes in winter, whilst the sun appears in the
southern signs. C, the earth's aphelion, where it
moves the slowest, is in the greater part; A, its

43. The sun's apparent diameter Is greater in our
winter than in summer, caused by the earth being
nearer to the sun, when in its perihelion at A in winter,
than it is in the summer, when in its aphelion at C ;
which is its greatest distance. The sun's apparent
diameter in winter is 32 m. 47 sec., in summer 31m,
40 sec.

If the mean distance of the earth from the sun be
called 1000, Its eccentricity will be 17its greatest
distance 1017gt; and its least distance 983,

• We thus see the reason why the seasons are of unequal length ;
for the summer and whiter months can never be equally divided
but in the particular case of the coincidence of the perihelion of
the earth's orbit with one or other of the equinoxes. The peri-
helion does not remain stationary when once determined, but ha$
a progressive motion in the ecliptic according to the order of the
signs, performing a complete revolution in about 20,000 years. It
is a remarkable circumstance that this coincid nee of the perihe-
lion and aphelion, with the equinoctial points, took place about thç
period at which chronologists place the creation of the world, or
about 4000 years before the christian aera : in consequence of this,
the heat and light of the sun was then equally divided between the
two hemispheres of the terrestrial globe, but as the perigee con-
tinued to advance on the ecliptic, the northern hemisphere gra-
dually obtained the greatest share, and about the year 1250 the
difference was a maximum, since that period it has continued to
diminish by insensible degrees, and will do so till the ysar 6470,
when a perfect equality will again subsist between the two hemis-
pheres, after which the southern hemisphere will obtain the ad-
vantage of having the greater share of the heat of the sun, which
advantage it will continue to possess for a similar period of 10,000
years,

agree in many respects with those of the inferior
ones, which have been already explained.

45.nbsp;If the mean distance of the earth from the
smi be called 1000, the mean distance of Mars is
1523,¹ its periodical time 686 d. 23 h., its eccentri-
city 141, and it turns round its axis in '24 h. 40 m.
The planet Mars appears much larger and brighter
when it is in opposition to the sun, than when it is in
conjunction with him.'f Mars appears gibbous, when
it is in quadrature, but full and round in conjunction

46.nbsp;Jupiter is the largest of all the planets, see fig.
13, he revolves in Q h, 56 rn. about his axis, which
is nearly at right angles to the plane of his orbit, in
which he moves about the sun in somewhat less than
Î2 years, or 4332 d. 12h. His mean distance from
the sun is 5201, and eccentricity 250. Several rpots
have been seen on Jupiter's surface, which appears to
be surrounded by several belts, or girdles, parallel to
his equator : these vary in breadth and distance from
one another. See fig. 13.

47.nbsp;Saturn is the farthest of all the planets from
the sun ; his mean distance is 9538, eccentricity 547 ;
he is 29-^ years in moving through his orbit round
the sun, or 10759 7 h.j It is not yet known

1nbsp; The time of its synodical revolution or period between twe
oppositions is 780 d. of which it is 707 d. progressive, and 73 re-
trograde ; its arc of rétrogradation varies from 10° to 18°.

% It is the opinion of Dr. Herschel that Saturn revolves on its
axis in 10 h. 16 m., and that its ring revolves in 10 h. 32 m. ; the
ring is likewise now known to be double or to consist of two con-
centric rings.

whether Saturn turns round his axis or not; but he
is attended with a broad thin ring, as represented in
fig. 12. The edge of this ring reflects httle or none
of the sun's hght to us : the planes of it reflect the
light of the sun in the same manner in which the
planet does. The plane of the ring is inclined to
the plane of the ecliptic at an angle of about 31 deg.
If we suppose the diameter of Saturn to be divided
into four equal parts, the diameter of the ring will be
about nine such parts. .The distance of the inner
edge of this ring, from the body of the planet, is
equal to the breadth of the ring. Through this
«pace, between the planet and his ring, the tixed stars
may sometimes.be seen.

48. The plane of Saturn's ring is parallel to itself
in every part of its orbit. If the plane of the ring be
produced to the sphere of the fixed stars, it will cut
Saturn's heliocentric orbit in two opposite points,
called the nodes of the ring. As Saturn passes from
the ascending to the descending node of his ring,
the northern side of the plane of the ring is turned
towards the sun; as it moves from the descending
to the ascending node of the ring, the southern side
of its plane is towards the sun. When Saturn's ring
appears elliptical, as in fig. 12, the parts about its
longest axis reaching beyond the planet's disc, are
callad ansce, which a little before and after the dis-
appearance of the ring, are unequal in magnitude.
When Saturn is in the heliocentric place of either of
the nodes of his ring, its plane produced passes
through the sun, and then the ring becomes invisible
to us.*

• The ring may likewise disappear from two other causes : its
plane maj pass dirough the place of a spectator on the earth, when,

The superior planets are someti^nes in conjunction
with the sun, sometimes in quadrature, and some-
times in opposition.nbsp;.

49.nbsp;When the earth is in such a station, that a
line drawn from a superior planet to the earth becomes
a tangent to the earth's orbit, the superior planet ap-
pears^tationary. If the earth be at a or g, fig. 10,
on ], and the planet at 1; I g, and I a, are tangents
to the earth's orbit; in which places the planet
seems to stand still, or to have no geocentric motion.

50.nbsp;When a superior planet, fig. 10, is movmg
from one of its apparent stations A, through its con-
junction D to G, its geocentric motion is direct.

Fig. 10. Whilst the earth is moving from a, through
d to g, a superior planet at I appears to move in AD G,
the concave sphere of the heavens, from A, through
its conjunction D, to its other station G ; whence its
apparent motion seen from the earth is direct, or in
consequentia, which is from west to east, according

51.nbsp;Observe in fig. 10, that one end a, of the hne
a I A, drawn from the earth at a, through the planet s
place at I, to the concave starry sphere AD G, .at-
tends the earth, as it moves through abcdefg;
and the middle of it is supposed to turn round upon
the planet as a centre at 1, the other end A will then
mark out the planet's apparent motion in the heavens.
So that the arch ABCDEFG, will be that which

thP edsre only being presented, it will not be visible except in the
powerful telescopes of Dr. 1 lerschel. Sometimes the plane of the
rms nasses between the suu and the earth, when the dark part-is

the planet appears to describe; and therefore the
order of the letters expresses its motion in conse-
quentia.

52.nbsp;When a superior planet is passing from one
station to the other through the opposition, its geo-
centric motion is retrograde.

As the earth is passing from g, fig. i ], through k
to a, the planet at I appears to move from G, through
Kits opposition, to A; in this case, the apparent
motion of the planet at I, seen from the earth, is re-
trograde, or m antecedentia, that is, from east to west,
or contrary to the order of the signs. If the end g
of the line g I G, fig. n, attends the earth through
g m 1 k n h a, and the middle of this line turns round
upon the planet at I, the other end G will describe
the arch G M L K N H A, which is contrary to the

53.nbsp;The time of the retrogression of Mars is about
3 months ; of Jupiter 4 months ; and of Saturn 4J-
months.

The planets viewed through a telescope are strip-
ped of their adventitious rays, and appear like circu-
lar planes, of a determinate magnitude, whose dia-
meters may be measured by a micrometer.
■ 54. The superior planets are sometimes nearer our
earth than at other times ; whence they appear larger
or less, according to their different distances from us.
And as they are nearer to us than the fixed stars,
they may pass between us and some of the stars : and
as they go round the sun in orbits larger than that of
the earth, they always turn much the greatest part
of their illuminated hemisphere towards the earth
and therefore appear at all times round, or full'

* It may be observed as a general rule, that the planets move
slower in describing their retrograde arcs than when tliey are pro-
gressive, and their apparent magnitudes are then likewise greater ;
but there is this difference in the inferior and superior planets, that
in the former, the planet is always in conjunction with the sun in
the middle of the retrograde arc ; and in the latter, they are al-
ways in oppo!gt;ition. In the middle of their progressive arcs they
are miiversally in conjunction wilh the sun, and in the case of an
inferior planet, this is calFed the superior conjunction.—The far-
ther a superior planet is from the sun, the smaller is its arc of ré-
trogradation, bat the greater number of days it employs to de-
scribe it : thus the arc of retrogradaiion of Uranus is only 4°, while
that of Jupiter is 10° ; but Jupiter describes this arc of 10°
in 120 days, where.is Uranus employs 142 days in describing
the retrograde arc of 4°.

Astronomers had long observed that a greater interval e.xisted
between the orbits of Mars and Jupiter, than suited the apparent
regularity of the system j but as no theory suggested any absolute
necessity for this space to be occupied by a i evolving body, not
much importance was ever attached to this circumstance. It is
now found that this space is occupied by a number of smaller bo-
dies, which appear to be much less even than the smallest satellites
of the system. These bodies all revolve at nearly the same mean
distance from the sun, (nainely, about 250 millions of miles,) and
in orbits very considerably inclined to each other, and to the eclip^
tic. The diameter of the largest of them does not exceed 200
miles, and some are estimated by Dr. Herschelquot; much less ; they
have likewise a nebulous, indistinct appearance, like comets. This
and some other circumstances induced Mr. Olbers to conjecture,
that these bodies w; re only fragments of a large planet which once
revolved in an orbit now common to them all, and that this origi-
nal planet has been broken to pieces by some internal explosion
of the nature of our volcanoes.—Ceres was discovered by Piazzi,
at Palermo, Jiine I, 1801 : Pallas by Olbers, March 28, 1802 ;
Juno by Harding, Sept. 1, 1804; Vesta by Olbers, March 29,
1807-

55.nbsp;Three of the primary planets, viz:, the Earth,
Jupiter, and Saturn in their revolutions round the
sun, are attended with lesser planets, which move
round each of their respective primaries, according
to the order of the signs.

56.nbsp;Moves round the earth in an orbit, whose se-
midiameter is about 60i semidiameters of the earth ;
its eccentricity of the earth's semidiameters ; the
plane of the earth's orbit, produced to cut the plane
of the ecliptic, makes an angle with it of about 54-
deg. The points wherein it intersects the ecliptic
are called the moon's nodes; these nodes have a
slow regressive motion of 19° : 9'43quot; in a year,
which carries thein round the ecliptic, contrary to
the order of the signs, in ] 8 y. 234 d. The moon's
periodical time is 27 d. 7 h. 43 m. and her rotation
round her axis is performed in the same time.f Her

To which may now be added Uranus, or the Georgian,
t The moon, independently of its phases will present nearly
the same phenomena in a month, as the sun is observed to do in
the course of a year : twice in the month she will be in the equa-
tor, and will-then rise in the east, set in the west, and continue
twelve hours above the horizon ; when at its greatest declination
south its meridian altitude will be less than that of the equator by
the whole of its declination, it will rise south of the east, and its
continuance above the horizon v,-ill be much less than twelve
hours, sometimes only seven, its diurnal course resenibling that of
the sun on the shortest day ; on the contrary, when it has arrived
at its greatest distance north, its meridian altitude greatly exceeds
that of the equator, it rises to the north of the east, and continues
nearly seventeen hours above the horizon, its diurnal path nearly
resembling that of the sun on the longest day.

eccentricity and inclination are both variable. The
orbit which the moon describes round the earth is el-
liptical, the earth being in one of its foci ; and when
the moon is at her greatest distance from the earth, or
in her higher apsis, she is said to be in apogao ; and
when in her lower apsis, or least distance, in perigceo.

57.nbsp;When the moon is at A, fig. 14, in conjunc-
tion with the sun at S, and the earth at T, it is called
New Moon ; and when in opposition at E, it is called
Full Moon. The syzigies of the moon is a common
term to express both its conjunction and opposition.

58.nbsp;The moon's ascending node is called the Dra-
gon's Head, and is thus marked ; its descending
node the Dragon's Tail

59.nbsp;A periodical month contains 27 d. 7 h. 43 m.
in which time the moon describes her orbit; a syno-
dical month contains 29 d. 12 h. 43 m. 3 s. which is
the time that passss between one new or full moon
and the next of the same name which succeeds it;
this is longer than a periodical month about 2 d. 5 h.

60.nbsp;In fig. 15, S represents the sun, AB part of
the earth's orbit, ML represents a diameter of;the
moon's orbit, when the earth is at C; and m 1
another diameter, parallel to M L of the same orbit, ,
when the earth is removed to D. Whilst the earth
is at C, and the moon at L, in conjunction with the
sun, as the earth moves from C to D, and the moon's
orbit moves with it, the diameter M L will then be
in the position m 1 ; so that when the moon has de-
scribed its orbit it will be at 1; hut when the sun
being at S, the moon will not yet be in conjunction ;
therefore the periodical month is completed before
the synodical, and before the moon can come into
conjunction with the sun. When the earth is at D

she must move from 1 to e, in the diameter g e;
whence, besides going round her orbit, she must de-
scribe the arc 1 e, consequently the synodical is
longer than the periodical month by the quantity of
the arc 1 e.

We do not see the moon at the conjunc-
tion, but at the opposition her whole disc is en-
lightened.

In fig. 14, aTb represents a part of the earths
orbit, S the sun, T the earth, ACEG the moon's
orbit. If the moon is at A, it will be on the same
side of the earth with the the sun, or in conjunction ;
and the sun will then be beyond the moon : there-
fore the sun does not shine on that hemisphere of
the moon towards us ; whence to us her whole disc

62.nbsp;When the moon is at E, it will be m opposi-
tion, and the earth between it and the sun ; eonse-'
quently that hemisphere which is visible to us, wil
be the same hemisphere upon which the sun shines,
therefore her whole disc towards us will be enlight-
ened, or the moon will be full.

63.nbsp;Fig. 14. The moon's disc is half enlightened
when she is near the quadratures at C or G, her ap-
parent distance from the sun at S being then gO deg.:
when the moon is between the conjunction at A,
and either of the quadratures G or C, the illuminated
part of it appears horned, as atH^andB. When
between the full at E, and the quadratures G or C,
the disc appears gibbous, as at D and F. When the
moon is at A, it is new ; as she moves from A to C,
it is said to be in the first quarter; from C to E, m
the second quarter ; from thence to G, m the third
quarter; and from G to A again, In the last quarter.

After the new moon, her horns are turned towards
the east, and before new moon towards the west;
and when she is horned, that part of her disc upon
which the sun does not shine, has yet hght enough
to make it faintly visible.¹

The same side of the moon is always turned to-
wards the earth, and her surface is not smooth, but
uneven and mountainous, as may be seen with the
assistance of a telescope, either in the first or last
quarter.

64.nbsp;The distance of Jupiter's innermost satellite
from his center is 5.667 semidiameters of the planet;
the second, 9.017; the third, 14.381; and the
fourth, 25.299 semidiameters.

The periodical time of Jupiter's first satellite is 1 d.
18 h. 27 m. 34 sec. The second is 3 d. 13 h. 13 m.
42 sec. The third is 7 d. 3 h. 42 m. 3d sec. And
the fourth is l6d. ]6h. 32 m. 9 sec.

65.nbsp;The plane of the orbit of every secondary
planet is parallel to itself in every part of the orbit of
its primary. The orbits of all Jupiter's satellites are
nearly, but, not exactly, in the same plane; which
produced makes an angle with the orbit of Jupiter
of abo^t 3°; the second deviates a little from the rest.

66.nbsp;A satellite in one of its nodes appears in the
orbit of its primary : in all other parts of its orbit it
has latitude.

1nbsp; This faint light, by which we sometimes can distinguish the
remaining portion of the moon'? disk, is occasioned by the reflected
light of the earth ; and as the land reflects more light than th«
■water, it has been observed that this appearance is more visible
■when the continental parts of the earth are opposite the moon,
than when the great ocean is in the same situatioi.

If the plane of any circle produced passes through
the eye, it appears to be a straight line ; consequently
every circle, viewed obliquely, will appear elliptical;
so that

When a satellite is in its node, at the same time
that its primary's heliocentric place is in the same
degree of the ecliptic witli it, and the earth in its geo-
centfic node ; at that time the orbit of the satellite
appears a straight line. When the primary is in any
other part of his orbit, the satellite's orbit will appear
an ellipsis, whose shortest axis increases in proportion
as the primary is farther distant from the satellite's
node.

The orbit of the earth is so small, when compared
to those of Jupiter and Saturn, that in whatever part
of her orbit she may happen to be, when either of
these planets are in the nodes of their satellites,
these last will appear to describe lines very nearly
straight

67. When a satellite is in that semicircle which is
farthest froin the earth, its geocentric motion is di-
rect ; when it is in that nearest to the earth, its geo-
centric motion is retrograde.

Any satellite is at its greatest elongation from its
primary, when a line, supposed to be drawn from the
earth through the satellite, is a tangent to the satel-
lite's orbit.

In fig. 17- B a C represents a part of Jupiter's or-
bit, N ALM, the earth's orbit, S the sun, DGFH
the orbit of Jupiter's outermost satellite. When the
earth is at A, and the satellite at E or D, in the tan-
gent line AE or AD, then this satellite, seen from
the earth at A, will appear at a greater distance

68. Every satellite appears in conjunction with its
primary, when it is between the earth and its pri-
mary ; and also, when the primary is between the
earth and satellite ; the first is called its inferior, the
last its superior conjunction.

The apparent motion of any satellite is direct, as it
passes from O, fig. 17, its greatest elongation, through
P, its superior conjunction, to E, its greatest elon-
gation on the other side ; its geocentric motion seen
from the earth at A, being then from west to east,
in consequentia, or according to the order of the signs.

Any satellite's apparent motion is retrograde, as
it passes from E, its greatest elongation on one side
of its primary, through H, the inferior conjunction,
to D, its greatest elongation on the other side ; it is
therefore pi am, that its motion seen.from the earth
at A, is from east to west, in antecedentia, or con-
trary to the order of the signs.
* 69. The satellites are seen sometimes to the west,
and sometimes to the east of their respective prima-
ries : they cannot be seen in their superior conjunc-
tion, and are seldom distinguished from their primary
in their inferior conjunction.

70. The distance of Saturn's innermost satellite
from the center of the primary, is 1,93 semidiara,eters
of the ring,, the second 2,47, the third 3,47, the
fourth 8,00, and the distance of the fifthnbsp;se-

The periodical time of Saturn's, innermoi^t satejlite
is 1 d.. 21 h. la m, 27 sec. The second, 2 d. h.
41 m. 11 sec. The third, 4 d. 12 h. 25 m. i^i sec.

The fourth, 15 d. 22 h. 41m. 14 sec. And the
fifth satellite's periodical time is 79 d. 7 h. 48 m.*

71.nbsp;The satelhtes of Jupiter and Saturn cast a
shadow upon their primary, which may be seen to
pass over the disc of the planet like a spot; they
also frequently fall into the shadow of their prima-
ries, and are eclipsed; which may be observed by the
help of a telescope.

72.nbsp;Fig. 12, 13, represent the different magni-
tudes of the primary and secondary planets, with the
proportion which they bear to each other, and to a
globe of twelve inches diameter, which is supposed
to represent the sun.-f-

* Two more satellites have since been discovered by Herschel:
tlieir periodic times are . . d. h. m.

The mean distances of the seven satellites, expressed in semidia
meters of the planet, are , . i.— 3.08

Uranus has six satellites: their mean distances, in seniidia-
meters of the planet, are as follow: 1.—13.12

73.nbsp;Is the change of their apparent places, when
viewed from different stations.

The diurnal parallax is the change of the apparent
jplace of a fixed star or planet, or of any celestial body,
arising from its being viewed on the surface, or from
the centre of the earth. The fixed stars have no
diurnal parallax, the moon a considerable one: that
of the planets is greater or less, according to their
distances.

74.nbsp;In fig. 18, I AK represents the earth, T its
center, A B the sensible, T L the real horizon of a
spectator upon the earth at A, M the moon, S the
sun, both in the sensible horizon: if seen from A,
they will appear in the horizon at B ; but if seen
from T, the center of the earth, they would appear
amongst the fixed stars at C and D; that is, the moon
would appear in the line TM D, and the sun in the
line T S C : these are called their true places ; the
arch B C is called the sun's parallax, and B D that of
the moon. The angles BSC, and B M D, are
called the parallactic ajigles, which are respectively
equal to the angles A S T, and A M T ? under which,
AT, a semidiameter of the earth passing through A,
the place of the spectator, would appear, if seen from
the sun or moon.

75.nbsp;If a planet is above the horizon at E, its true
place seen from T, the center of the earth is at F, its
apparent place at G, and its parallax is F G. Hence
it is plain, that the higher the planet is elevated
above the horizon, the less is its parallax ; and when
it is directly over the head of the spectator at H, it
will have no parallax at all; its apparent place in the

heavens being Z, whether it be seen from A or T.¹
It is observable, that the apparent place G, of a
planet at E, seen from the earth at A, is always lower
or farther from the zenith Z, than F, its true place
seen from T, except when the planet is vertical, or
at H • so that the horizontal parallax is greatest

In fig. 18. W L represents the horizon, VT an
arch of the equator, ciUting the horizon at T ,^T P
the axis of the world, and P the celestial pole, L the
zenith, ZX a vertical circle, R the planet's apparent
place therein, if seen from the earth's surface ; and
y its apparent place in the same vertical, if it coUld
be seen from the earth's center: then R Y is its pa-
rallax P R O is a secondary of the equator, passing
through the planet, and PYQ, another seco^ndary,
parsing through its apparent place at Y ; whence its
declination, seen from the center, is O R, and from
the surface Q Y ; the difference N Y, between Q Y
and Q N, is the parallax of declination. When the
planet is at R, the secondary PRO passes through
the point O of its right ascension upon the equator,

1nbsp; This is upon the supposition that the earth is spherical. From
the-elliptical form of the terrestrial meridian, the direction ot a

ihe earth ; hence it arises, that the moon, when m he zenith, has
nevertheless a small parallax, which must be attended to m exact
observations-

bot the secondary P Y Q passes through Y, the
planet's apparent place, and Q its right ascension
upon the equator ; whence the parallax R Y makes
a difference, or parallax, Q O, in right ascension.

77.nbsp;If a be the apparent place of a planet upon the
meridian ZVW, when seen from the surface, and
b when viewed from the center of the earth, ab is
its diurnal parallax in a vertical circle ZW to the
horizon ; but this same circle is also a secondary to
the equator, whence there can be no parallax of right
ascension.

Now suppose P the pole of VT, which is now
called an arch of the ecliptic, cutting the horizon
WL in T, ZX a vertical circle, let RY be the
planet's parallax, PRO a secondary of the ecliptic
passing through the planet, when seen at R from the
surface of the earth ; P Y Q another secondary,
passing through it, if it could be viewed from the
earth's center, so as to appear at Y ; when at R, its
latitude is R O, when at Y, its latitude is Q Y, the
difference N Y is the parallax of latitude.

78.nbsp;When the planet appears at R in P R O, the
secondary of the ecliptic, the point O is its longitude
from the first point of Aries ; but when at Y in the
secondary P Y Q, Q is the point of its longitude ;
whence the difference Q O is the parallax of lon-
gitude.

But if the planet be in a vertical circle Z W, which
passes through P, the pole of the ecliptic, it can only
have a parallax of latitude, and none of longitude.
Let a b be the parallax of latitude ; whence from
either station, a b will be its parallax of latitude ; and
as there can pass but one secondary through both,
there can be no parallax of longitude.

The annual parallax of any heavenly body arises-
from its being seen from the earth when it is in dif- quot;
ferent parts of its orbit.

79- If a ray of light enters a transparent medium
obliquely, it does not pass straight on, but is bent at
the point at which it enters: this bending; is called
refraction.

In fig. 19. AC represents the surface of the earth,
T its center, B P a part of the atmosphere, H E K
the sphere of the fixed stars, A F the sensible hori-
zon, G a planet, G D a ray of light proceeding from
G to D, where it enters our atmosphere, and is re-
fracted towards the line D T, which is perpendicular
to the surface of the atmosphere : and as the upper
air is rarer than that near the earth, the ray is conti-
nually entering a denser medium, and is every mo-
ment bent towards T, which causes it to describe a
curve as D A, and to enter a spectator's eye at A
as if 'it came from E, a point above G. And as an
object always appears in that line in which it enters
the eye, the planet will appear at E, higher than its
true place, and frequently above the horizon A F,
when its true place is below it at G.

The greatest refraction is when the planet, amp;c.
is seen in the horizon, being 33 min. When its
altitiide is 20 deg. the refraction is 2 min. 14 sec.: at
40 deg. of altitude it is 58 sec.: at 60 deg. of alti-
tude it is 29 sec. and so becomes insensible, as the
altitude .increases.

80 An eclipse is a deficiency of light in the
heavenly bodies In an eclipse of the stin, its light

is intercepted from the sight of the inhabitants of
any part of the earth, by the moon passing between
them and the sun; and as its disc is either partly,
or wholly covered, it is called a partial or total
eclipse.

An eclipse of the moon is caused by her passing
through the shadow of the earth, whereby she is
deprived of the sun's light.

The sun can never be cclipsed but at the titne of
New Moon ; neither can tliere be an eclipse of the
moon, but at the time of the full moon : In the
iirst-case, the new moon must be within )8 de-
grees, in the last, the full moon within 12 degrees,
of one of her nodes.

These luminaries are not eclipsed every new and
full moon, because the moon's motion is not in the
plane of the ecliptic, in which the sun and earth al-
ways are.

Hence the moon's latitude is oftentimes so much
increased at the titne of the new moon, that her
shadow does not touch the earth ; and at the time
of lull moon, she as frequently passes by the earth's
shadow without entering into it: but when the
moon's latitude is inconsiderable, which only hap-
pens when she is within the limits above mentioned,
she then appears either in or near the ecliptic.

Let H G, fig. 20, represent the path of the moon
EF, the plane of the ecliptic, in which the center
of the earth's shadow always moves ; N, the node
of the moon's orbit; A, B, C, D, represents four
places of the earth's shadow in the ecliptic : when
her shadow is at A, and the moon passing by at I,
she will not enter into the shadow ; but when the
full moon is nearer to the node at K, only part of

her globe passes through the shadovv B, and that
part becomes dark: this is called a partial eclipse.
When the full moon is at M, she enters into the
shadovv C; in passing through it, she becomes
wholly darkened at L, and leaves the shadow at O.
This is called a total eclipse : and when the moon's
center passes through that of the shadow, which
can only happen at the very time she is in the node
at N, it is called a central eclipse.

We have not yet mentioned the atmosphere,
which requires our consideration, while we are treat-
ing of lunar eclipses; for the shadow of the earth
does not reach the moon. In fig. 21, T represents
the earth, B C D B g f its atmosphere, A. B, A B,
rays proceeding from the sun at S, touching the at-
mosphere at B and B; these go straight on, and ter-
minate the shadow of the atmosphere at H. The
moon is constantly enlightened by the sun's rkys
until she enters this shadow, when she becomes
fainter, as she continues to move between ABH
and ABH.

The raj's which enter the atmosphere obliquely,
are refracted, and bent into curves that touch the
earth ; all the light between F f and G g, is inter-
cepted by the earth ; and the rays C E, D E, ter-
minate the earth's shadow.

The light between F f, and A B, is refracted by
the atmosphere, and diffused between C E, and
A B, and continued beyond E, the point of the
earth's shadow: whence it is plain, that the light
proceeding from the sun becomes continually weaker,
the farther it is from the earth ; so that the sha-
dow of the atmosphere is but a weak light, and

The shadow of the atmosphere is conical, be--
cause the diameter of the sun is greater than that of
the earth. This cone does not reach so far as the
planet Mars : but the diameter of the shadow, in
the place where it cuts the moon's orbit, is not ^th
less than the earth's diameter.

A solar eclipse happens, when the new moon is
in or near the node. In fig. 12, S represents the
sun, M the moon, her shadow falling upon D C, a
part of the earth's circumference, which is surrounded
by a penumbra. Beyond A and F, the earth is illu-
minated by an entire hemisphere of the sun. As you
move from A to C, or from F to D, the light is con-
tinually diminishing; and near C and D, the rays
come to the earth only from a small point of the
sun's surface.

This diminished light, which surrounds the sha-
dow every way, is called the penumbra. An observer
at B or E can only see half the sun's diameter, the
rest being hidden by the interposition of the moon.
If the observer moves from B to C, or from E to D,
the sun. will be more and more withdrawn from his
sight, until it becomes wholly invisible in the shadow
itself; whence it is plain that there may be a solar
eclipse, although the shadow of the moon does not
touch the earth, if the penumbra comes to its surface.

When the moon's shadow falls upon the earth,quot; it
is called a total eclipse of the sun ; if the penumbra
pnly reaches the earth, it is called a partial eclipse of
the sun : with respect to particular places, it is said
to be total where the shadow passes; central, where
the center of the moon covers that of the sun ; and
partial, where the penumbra only goes by, as is re-
presented in fig. 23.

The wider the shadow G D, fig. 22, Is, the longer
the sun will be totally eclipsed, and a larger space of
the earth will be under the shadow ; but its breadth
will vary, as the distance of the moon from the earth,
and of the earth from the sun, varies ; for when the
earth is in perihelion, and the moon in apogee, that is,
at its greatest distance from the earth, the shadow of
the moon does not reach the earth, and the moon
does not cover the sun; this is called an annular
eclipse, as is represented in fig. 24.

If tha periphery of a semi-circle be turned round
its diameter as an axis, it will generate the surface of
a globe or sphere, and the center of the semi-circle
will be the center of the globe : it therefore follows,
that as all the points in the circumference of the
semi-circle are at an equal distance from its center,
so all the points of a globe, thus generated, must be
the same.

82.nbsp;Any straight line passing through the center
of a globe, being terminated by its surface, is called
a diameter; and that diameter about which the globe
turns, is called its axis; the extremities of which are
called the poles of the globe.

83.nbsp;There are two artificial globes. That on
which the surface of the earth is represented, is
called the terrestrial globe.

84.nbsp;The other on which the face of the starry
sphere is delineated, is called the celestial globe.

85.nbsp;In the use of the terrestrial globe, we are to
consider ourselves standing upon some part of its

surface, and that its motion represents the real
diurnal motion of the earth, which is from west to
east.

86.nbsp;In the use of the celestial globe, we are to
suppose ourselves at the center, and that its motion
represents the apparent diurnal motion of the hea-
vens, which is from east to west.

87.nbsp;Note, The stars being delineated upon the
convex surface of the celestial globe, we must sup-
pose ourselves at the center ; because under such
a supposition they would appear, as they naturally
do, in the concave surface of the heavens.

88.nbsp;Several circles are described upon the surface
of each globe. Those whose planes pass through
the center of the globe, are called great circles ; some
of which are graduated into sOo degrees, QO of which
make a quadrant.

89.nbsp;Those circles whose planes do not pass
through the center of the globe, are called lesser
circles.

90.nbsp;Our new terrestrial and celestial globes, fig. 1,
and fig. 25, are each of them suspended at their poles
in a strong brass circle N Z S N, and turn therein
upon two iron pins, which are the axis of the globe.
They have each a thin brass semi-circle NHS move-
able about the poles, with a small thin sliding circle
thereon.

91.nbsp;On the terrestrial globe, fig. 1, this semi-
circle N H S is a moveable meridian, and its small
sliding circle H, the visible horizon of any particular
place to which it is set. But,

92.nbsp;On the celestial globe, fig. 25, this semi-
circle ]Sf H S is a moveable circle of declination, and
its small circle H, an artilicial sun or jilanet.

g3. Each globe hatha brass wire circle, TWY,
placed at the limits of the crepusculum, or twilight,
which, together with the globe, is set in a wooden
frame : the upper part B C is covered with a broad
paper circle, whose plane divides the globe into two
hemispheres, and the whole is supported by a neat
pillar and claw, with a magnetic needle in a compass
box at M.

94.nbsp;On our new terrestrial globe, the division of
the face of the earth into land and water is accu-
rately laid down from the latest and best astronomi-
cal, geographical, and nautical discoveries. There
are also many additional circles, as well as the
rhomb-lines, for the greater ease and convenience in
solving all the necessary geographical and nautical
problems.

95.nbsp;On the surface of our new celestial globe, all
the southern constellations, lately observed at the
Cape fcf Good-Hope by M. de la Caille, and all the
stars in Mr. Flamsted's British Catalogue, are accu-
rately laid down, and marked with Greek and Roman
letters of reference, in imitation of Bayer. Upon
each side of the ecliptic are drawn eight parallel cir-
cles at the distance of one degree from each other,
including a space of sixteen degrees, called the
zodiac; these are crossed at right angles with seg-
ments of great circles at every fifth degree of the
ecliptic, for the readier noting the place of the moon
or any planet upon the globe.

g6. We have also inserted from Ulugh Beigh.,
printed at Oxford, A.D. 1665, the manazil al kamer,
i. e. the mansions of the moon of the Arabian astro-
nomers ; which are so called, because they observed
the moon to be in or near one of these every night.

during her monthly course round the earth, to each
of which the Arabian characters are affixed. They
may be of very great use to beginners to teach
them the names of the stars, as well as to mariners
for the same purpose ; who may have occasion to
observe the distance of the moon from a fixed star,
in the new method of discovering the longitude at
sea. They will likewise serve to shew, how the
moon passes from star to star in the course of
one or several nights, which is a very curious and
useful amusement; and as they are a division of the
heavens different from any thing the Greeks were
acquainted with, and therefore not borrowed from
them, and as we do not know they were ever inserted
to any globs before, we hope we have with propriety
placed them on our new celestial globe. See Cos-
tard's Hist, of Astronomy, p. 40.

the broad paper circle ,B C on thje surface of
the wooden framb whttch supports the brass
meridian

innermost of which is divided into 3So degrees, and
numbered into four quadrants, beginning at the east
and west points, and proceeding each way to 90
degrees at the north and south points ; these are the
four cardinal points of the horizon. The second
circular space contains, at equal distances, the thirty-
two points of the mariner's compass. Another cir-
cular space is divided into twelve equal parts, repre-
senting the twelve signs of the zodiac; these are
again subdivided into 30 degrees each, between which
are engraved their nam«s and characters. This space

is connected with a fourth, which c ntains the kalen-
dar of months and days ; each day, on the new
eighteen-incti globes, being divided into four parts,
expressing the four cardinal points of the day, accord-
ing to the Julia a reckoning ; by virhich means the
sun's place is very nearly obtained for the three com-
mon years after bissextile, and the intercalary day
inserted with ut confusion. Whence we derive the
following

. Problem I. To find the suns place any day in the
year on the broad paper circle.

98.nbsp;Consider whether the year in which you seek
the sun's place is bessextile, or the first, second, or
third year after.

99.nbsp;If it be the first year after bissextile, those
divisions, to which the numbers for the days of the
month are affixed, are the respective days for each
month of that year at noon ; opposite to which, in
the circle of twelve signs, is the sun's place.

100.nbsp;If it be the second year after bissextile, the
first quarter of a day backwards, or towards the left
hand, is the day of the month for that year ; against
which, as before, is the sun's place.

101.nbsp;If it be the third year after bissextile, half a
day backwards is the day of the month for that year,
opposite to which is the sun's place.

102.nbsp;If the year in which you seek the sun's place
is bissextile, then three quarters of a day backwards
is the day of the month from the 1st of January to
the 28th day of February inclusive. The intercalary,
or 29th day, is three fourths of a day to the left hand
from the 1st of March ; and on the 1st of March
itself is one quarter of a day forward, from the

division marked 1 ; and so for every day in the
remaining part of the leap-year; against each of
which is found the sun's place.

In this manner the intercalary day is very well in-
troduced every fourth year into the kalendar, and the
sun's place very nearly obtained according to the
Julian reckoning. Thus:

the points of the horizon ; in this case it represents
the rational horizon of any partictdar place, which is
an imaginary great circle in the sphere of the heavens,
dividing the visible from the invisible hemisphere.
This is supposed to be parallel to a lesser circle,
called the sensible horizon, whose plane inay be con-
ceived to touch the surface of the globe at that placef
upon which an observer stands, and to terminate his
sight when he views the heavens round about. The
extent of the sensible or visible horizon is greater or
less, as we stand higher or lower.

103. Another use we shall make of this circle is to
represent the circle of illumination, or that circle
which separates day from night.

A third use to which this circle may be applied,
is to represent the plane of the ecliptic. All of which
shall be illustrated in their proper places.

In all positions of the celestial globe, this broad
paper surface is the plane of the horizon, and distin-
iguishes the visible from the invisible part of the
heavens.

Note, As this circle occasionally represents va-
rious' great circles of the sphere, we have given it
the name of broad paper circle, to prevent the rea-
der from considering it as an horizon, when it
really represents the plane of the earth's illuminated
disc, amp;c.

The north-side of the wooden frame ought to be
placed directly towards the north-side of the heavens,
which is readily done by the mariner's compass under
our new globes.

104.nbsp;There are two notches in the broad woodea
circle (Art. 97) upon the plane of which the broad
paper circle is placed, which receive the strong brass
circle : the body of the globe, being suspended at
two opposite points in this circle, turns round therein
on its iron poles, one of which N represents the
north, and the other S the south pole.

105.nbsp;One side of this strong brass circle is gra-
duated into four quadrants, each containing go de-
grees. The numbers on two of these quadrants
increase from the equator towards the poles; the
numbers on the other two increase from the poles
towards the equator.

quot; The reason why two quadrants of the meridian
quot; are numbered from the equator, and the other
quot; two from the poles, is because the first of these
quot; two shew the distance of any point on the globe
quot; from the equator or equinoctial, and the other
quot; serves to elevate the globe to the latitude of any
quot; place.quot;

105. The strong brass circle of the celestial globe
is called the meridian, because the sun's center is
direatly opposite thereto at noon.

107.nbsp;On the strong-brass circle of our new terres-
trial globe, and about 23-|. degrees on each side oX.
the north pole, the days of each month are laid dowrr
according to the sun's declination. If any day of the
month is placed in the plane of the horizon, it will
shew the sun's declination for that day upon the other
side of the brass meridian ; and this brass circle is
so contrived, that the globe may be placed in the
position of a direct or right sphere, (which is, when
the north and south poles are placed in the plane of
the broad paper circle) and also that the south pole
may be elevated above the plane of the broad paper
surface, with as much ease as the north pole. A cir-
cumstance which we thought not unworthy of our at-
tention in the construction of our new globes.

108.nbsp;The graduated side of the strong brass circle,
encompassing our new terrestrial globe, faces the
west; being most agreeable to the real diurnal
motion of the earth, which is from west to east.

lOQ. But that which surrounds the celestial globe,
faces the east, as the apparent diurnal motion of the
heavens is from east to west.

110. In all inclinations of either globe, the north
pole should be directed towards the north point of
the heavens, which the mariner's compass at M,
placed under each of the globes, will enable us to d»
with the greatest readiness.

and minutes of time, but the equator, upon the sur-
face of either globe ; it being not only the most
natural, but the largest circle that can possibly be.
-applied for that purpose. This is done by a semi-
circular wire M F placed in the plane of the
equator, carrying two indices; one of which, I, is
occasionally to be used to point out the time.

As the first meridian in our new globes passes
through London, it therefore becomes the XII o'clock
hour circle ; and this falls upon the intersection of
the equator and ecliptic at the first point of Aries;
the other Xllth hour circle passes through the oppo-
site intersection at the first point of Libra.

Remember, when the globe shall be hereafter
rectified for London, or any other place, on the same
meridian with it, that then the graduated side of th«
strong brass meridian is the horary index itself.

It may happen, that the globe shall be so rectified
as that the two points of XII o'clock will fall in, or
so near, the east and west points of the broad paper
circle, that neither of the horary indices can be
applied thereto, in such a case either of these points
themselves will be the horary index.

112.nbsp;The hours and minutes are graduated below
the degrees of the equator on either globe ; and as

113.nbsp;The motion of the terrestrial globe is from
west to east, the horary numbers increase according
to the direction of that motion.

114.nbsp;The motion of the celestial globe being
from east to west, the horary numbers increase m
that direction.

may be called a proper or a moveable meridian. It
is graduated each v^^ay to go degrees from the equator
to either pole.

J16. To this semi-circle on the new celestial globe,
%. 25, is fitted a small thin brass circle H, about
half an inch diameter, which slides from pole to pole;
when we consider the sun's apparent diurnal motion,
we call it an artificial sun.

117.nbsp;But to the thin semi-circle applied to the new
terrestrial globe, fig. is fitted a small thin circle
H, about two inches diameter, that slides from pole
to pole ; which is divided into a few of the points
af the mariner's compass, and is called a terrestrial or
visible horizon.

118.nbsp;Is a thin narrow flexible slip of brass, that
will bend to the surface of the globe ; it has a nut
with a fiducial line upon it, which may be readily
applied to the divisions on the strong brass meridian
of either globe ; one of its edges is graduated into
go degrees, and continued to 20 degrees below the
horizon. Upon the terrestrial globe, its use is to
shew the distance of places ; and when applied to
the celestial globe, it shews the distance between two
stars. If affixed to the zenith or pole of the horizon,
it shews the altitude of any point upon the globe, its
graduations being numbered upwards from the hori-
zon to 90 degrees, and downwards to 20 degrees for
the depression of any celestial object. It will repre-
sent any vertical circle passing through the pole of
the horizon, in its motion round the zenith point,
as well as the prime vertical, which passes through

through the east and west points of the horizon.
Upon both globes it occasionally shews the distance
of every secondary to the horizon; and has other usee,
which will be hereafter shewn.

119.nbsp;Note, When we speak of bringing any point,
or place to the strong brass meridian, we mean that
it should be brought to its graduated side, which is pro-
perly the meridian.

Also, ivhen we speak of bringing the moveable meri~
dian, quadrant of altitude, or any other thin flexible
circle, to any point or place; we mean that their gra-
duated edges should be brought to that point, or place.

120.nbsp;We may imagine as many as we please upon
the surface of the earth, and conceive them to be ex-
tended to the sphere of the heavens, marking thereon
concentric circles.

1.21. The planes of all great circles pass through
the center, and divide the globe into two equal hemis-
pheres : a small circle divides the surface of a globe
into two unequal parts ; all circles are supposed to be
divided into 300 degrees.

We shall begin with the description of the equator,.
this being the most eminent great circle on eithep
globe.

122. Is 90 degrees distant from the two poles of
the globe; and is so called, because when the sun
appears to pass vertically over this circle, the days

123.nbsp;This plane of the equator passes through the
middle of the globe at right angles to the polar axis.

On our new globes it is graduated into 36o de-
grees ; upon the terrestrial globe, the numbers in-
crease from the meridian of London westward, and
proceed quite round to 36o.

124.nbsp;They are also numbered from the same meri-
dian eastAvard by an upper row of figures, for the ease
of those who use the Enghsh tables of the latitude
and longitude of places.

}25. On our new celestial globes the equatorial
degrees are numbered from the first point of Aries
eastward, to 300 degrees.

120. Close under the degrees, on either globe, is
graduated a circle of hovirs and minutes.

127.nbsp;On the celestial globe, the hours increase
eastward from Aries to XII at Libra, where they
begin again in the same direction, and proceed to XII
at Aries.

128.nbsp;But the horary numbers under the equator of
the terrestrial globe, increase by twice twelve hours
westward, from the meridian of London, to the same
again.

129.nbsp;In every position of the globe, except that
of a parallel sphere, the plane of the equator cuts
the eastern and western points of the broad paper
circle, when considered either as an horizon, the
ecliptic, or circle of illumination.

And as the globe is turned about, it always keeps
to one point of the strong brass circle, in which, as
hath been observed, the degrees are numbered both
ways from the equator, that the distance of latitude

north or south of any point on the sj^rface of the
globe may be more easily computed. Whence arises
the following

130.nbsp;Bring the place to the graduated siSe of the
strong brass meridian ; the degree it then cuts shews
its distances from the equator, which on the terres-
trial globe is called latitude.nbsp;/

Thus London has deg. 32 min. of north lati-
tude; Constantinople, 41 deg. of north latitude; ' ~~
Quebec, in Canada, 46 deg. 55 min. of north lati-
tude ; and the Cape of Good Hope, 34 deg. southnbsp;'
latitude.

131.nbsp;Suppose the given place London ; turn the
globe round, and all those places which pass under
tte »ame point of the strong brass meridian are iu
the same latitude.

Suppose London and Rome, find the lati-
tude of each place by Prob. ii. Art. 130. Their
difFerertce is the answer.

tion, find his place in the ecliptic by Prob. i. Art. 98,
amp;c. Then bring that point of the ecliptic line upon
the globe under the strong brass meridian, and the
degree which it cuts is the sun's declination for that
day. Or,

Upon the terrestrial globe, that parallel which
passes through the point of the ecliptic answering
to the day of the month, will shew the sun's decli-
tion, counting the number of parallels from the
equator. Also,

On the celestial globe, seek the day of the month
close under the ecliptic line itself, against which is
the sun's place; bring that point under the strong
brass meridian, and the degree that stands over it is
» the sun's declination for that day. Thus on the 23d
of May the sun's declination will be about 10 deg.

134. Secondly, Bring the star to the strong brass
meridian on the celestial globe, and the degree it
stands under is its distance from the equator, and this
distance is called the star's declination, which may
be either north or south, according to the side of the
equator on which the star is situated.

Thus the declination of the star Arcturus, marked «
in the constellation Bootes, has about 20 deg. 30 min.
north declination ; and that of SyriuS in Canis Major,
or the Dog star, marked a, has about 16 deg. 30
min. south declination.

135. Hence we see, that the latitude of places on
the earth, and the declination of the sun and stars, See.

m the heavens, have but one idea, the meaning óf
which is no more than their distance (either of places
on the terrestrialj br of the luminaries in the celestial
spheres) from the equator.

The latitude of a fixed star always continues the
same, but that of the sun, moon, and planets, varies.

136.nbsp;Those stars, whose declinations are equal to
the latitude of any place upon the earth, are called
correspondents to that place; and pass once in every
24 hours vertically to tile inhabitants of such latitude:
that is, those stars appear in their zenitb, or are
directly over their heads. Hence the following

Problem VI. To find what stars pass óver or
nearly over tlie zenith of any place.

137.nbsp;Find the latitude of the place by Prob. ii. Art.
98, upon the terrestrial globe, which is the distance
of that place from the equator; then turning the
celestial globe, all those stars which pass under the
strong brass meridian at the same distance from the
equatorj will pass directly over the heads of those
inhabitants, and therefore become celettial corres-
pondents to all those who live under the same parallel
of latitude.

Thus the star marked y of the second magnitude
in the head of the Dragon is 51 deg. 32 min. distant
from the celestial equator, so is London at the
same distance from the terrestrial equator i therefore
the declination of this sta.r is equal to the latitude of
London, and consequently it becomes our celestial

The star marked « of the second magnitude int.
I^ersêus's sidegt; called Algenib, passes over the zenith

of those inhabitants in France who Hve 14 min. of
one degree south of Paris ; it also passes nearly over
the zenith of St. George's Bay in Newfoundland.

138 Are great circles drawn upon globes from
one pole to the other, and crossing the equator at
right angles. Upon our new terrestrial globe there
are twenty-four of these meridians, which are also
hoor-circles, being 15 degrees from each other.

Thus 15 degrees on the equator are equal to one
hour, and each single degree equal to four minutes
of time. Only four meridians which are also called
colures, are drawn upon the surface of the celestial
globe.

There are no places on the surface of
the earth, or spaces in the apparent sphere of the
heavens, through which meridians may Hot be con-
ceived to pass; consequently all points on the ter-
restrial or celestial spheres have their meridians. So
that they only (properly speaking) live under the same
meridian, that are under the same semi-circle, on the
same side of the poles.

This variety of meridians on the globes is supplied
by the thin brass semi-circle, which being moveable
about the poles, may be set to every individual point
of the equator. Whence we call it a moveable meri-
dian, Art 115. ■

140. All those halves of great circles, that are
dravt-n from pole to pole, are the meridians of those
places through which they pass, and being perpendi-
cular to the plnne of the equator, are called seconda-
ries thereto.

141. One of these meridians on our new terres-
rial globe passes through London, and is called a
first meridian ; because from that point which is
marked y, where it crosses the equator, the degrees
of longitude, as well as the hours and minutes of
time, begin.

The opposite meridian to this crosses the great
Pacific Ocean, and passes through the first point of
Libra, marked upon the globe.

This meridian is graduated from pole to pole, and
its numbers increase from the equator each way to
the pole. One particular use to which it may be ap-
plied, and for which it was at first designed, is to
solve some of the cases in spherical trigonometry with
ease and propriety, as will be seen hereafter.

Some geographers make their first meridian pass
through the isle of Per, or Ferro.

142. The longitude of any place is that point
or degree upon the equator, which is crossed by
the meridian of that place, reckoned from a first
meridian.

Bring the moveable meridian to the place, and that
degree on the equator which it cuts, is its longitude
from London, in degrees and minutes, or that hour
and minute is its longitude expressed in time.

Or if we bring the place to the strong brass meri-
dian, that will cut the equator in the longitude as
before.

Thus Boston in new England is about 7« degrees
west of London; Cape Comorin in the East Indies
232° west of London ; or the longitude of the first

143.nbsp;The method of reckoning longitude always
westward from the first meridian is most natural,
because it is agreeable to the real motion of the
earth ;

But the common method is to reckon it half round
the globe eastward, and the other half westward
from the first meridian, ending either way at 180
degrees.

Nole. The numbers nearest the equator increase
westward from the meridian of London quite
round the globe to 300, over which another set of
numbers is engraved, which increase the contrary way,
by which means the longitude may be reckoned upon
the equator either east or west.

144.nbsp;It is mid-day or noon to all places in the
same meridian at the same time.

Thus London, Oran, Cape Goast-castle in the
Mediterranean, and Mundfort on the Gold-coast,
have their noon nearly at the same time ; Boston in
New England about 4 h. 42 min. later ; and Cape
(Comorin .18 h. 48 min. later.

145.nbsp;The difference of longitude of any two places,
js the quantity of an angle at the pole made by the
jneridians of those places; which angle is measured
ppon the equator.

J46. Bring the moveable meridian to one of the
places, aqd the other place under the strong brass
pircle, they then contain the required angle; the

measure or quantity of which is the number of de-
grees counted on the equator between these two
brass meridians.

Problem VIII. Tof nd what places have mid-
day, or the sun, upon their ?neridian, at any given
hour of the day in any place proposed.

As the real diurnal motion of the earth, here
represented by the terrestrial globe, is from west
to 6SSt

All places to the eastward of any particular meri-
dian must necessarily pass by the sun, before the
meridian of any other place to the westward of that
particular meridian can arrive at it.

148.nbsp;And therefore as the first meridian on our
new terrestrial globe passes through London, if the
proposed place be London, as in this case, bring the
^iven hour, which is placed on our globes, to the
east of London if it be in the morning, but to the
west of London if it be in the afternoon, to the
graduated side of the strong brass meridian; and all
those places which lie directly under it, hav^e noon,
or the sun, upon their meridian, when it is X o'clock
at London.

Thus having brought the Xth hour on the equa-
. tor to the eastward of London under the divided side
of the strong brass meridian, it will be found to p.iss
over the eastern side of Lapland, and the eastern ex-
tremity of the Gulf of Findland, Petersburgh in
Kussia, to cross a part of Moldavia and the Black
Sea, thence it passes over a part of Turkey, and goes
I

between the islands of Candia and Cyprus in the
Mediterranean, thence over the middle of Egypt
through the eastern side of Africa, and across the
bay of Lorenzo; all which places have the sun
on their meridian when it is X o'clock in the morn-
ing at London.

^ 149. Secondly, Let the hour proposed be IV
o'clock in the afternoon,at Port-Royal in Jamaica.

Bring Port Royal in Jamaica to the strong brass
meridian, and set the horary index to that XII which
is most deviated.; - thenquot;turn the globe from west to
east, untillhe horary index points to IV o'clock, and
the strong brass meridian will pass over the western
side of the Isle Pasares in the Pacific Ocean, and the
eastern side of the isle La Messa, thence it crosses
the equator, and passes nearly over the islands Men-
doca and Dominica, which places have the sun on
their meridian when it is IV o'clock in the afternoon
at Port-Royal in Jamaica.

150. Thirdly, Let the proposed hour be 30 min.
past V o'clock in the morning at Cape Pasaro in the
island of Sicily.

Bring Cape Pasaro to the strong brass meridian,
set the horary index to that XII which is most elevat-
ed, and turn the globe westward, because the pro-
posed time is in the morning, till the horary index
points to 5 h. 30 min. and you'll find the strong brass
meridian to pass over the middle of Siberia, Chinese
Tartary, the kingdom of China, Canton in China, the
middle of the island of Borneo, he. at all which
places it is noon, (they having the sun upon their
meridian at the same time) when it is half an hour
past V o'clock in the morning at Cape Pesaro in
bicttv.

Problem IX. To find what hour it is at any
place proposed when it is noon at any given place.

151.nbsp;Bring the proposed place mider the strong
brass meridian, and set the horary index to XII, then
turning the globe, bring the given place to the meri-.
dian, and the hour required will be shewn by the
horary index upon the equator. If the proposed
place be to the eastward of the given place, the answer
will be, afternoon ; but if to the westward of it, the
answer is, before noon.

Thus when it is noon at London, it is 49 minutes
past XII at Rome, and 32 minutes past VII in the
evening at Canton in China, and also 15 minutes
past vil o'clock in the morning at Quebec in' Cana-
da, and this at one and the same instant of time.

Problem X. At any given t¥ine of the day in the
place where you are, io find the Imtr at any other
place proposed.

152.nbsp;Bring the proposed place under the strong
brass meridian, and set the horary index to the given
time ; then turn the globe till the place where you
are is under the brass meridian, and the horary index
will point to the hour and minute required.

Thus suppose vvs are at London at IX o'clock in
the morning, what time of the day is it then at
Canton in China? Answer, 31 minutes past IV in
the afternoon.

Also, when it is IX in the evening at London, it
is about 15 minutes past IV oV-lock in the afternoon
at Quebec in Canada.

Problem XI. The latitude and longitude of any
place being known, to find that place upon the globe-,
or if it be not inserted, to find its place, and fix the
center of the artificial horizon thereon.

153.nbsp;The latitude of Smyrna in Asia is 38 deg.
28 min. north, its longitude 17 deg. 30 min. east
of London.

Bring 27 deg. 30 min. on the equator counted
eastward of our first meridian to the strong brass cir-
de, and under 38 deg. 28 min. on the north side of
the equator, you will find Smyrna.

The latitude of Cape Lorenzo in Peru is 1 deg.
2 min. south, and longitude 80 deg. 17 min. west
of London : this place is not inserted upon the globe.
Therefore bring the graduated edge of the moveable
meridian to 80 deg. 17 min. counted westward on
the equator, and slide the diameter of the artificial
horizon to l deg. 2 min. south ; and its center will
be correctly placed on that point of the globe, where
the Cape of Lorenzo.ought to have been placed.

The four last problems depend entirely on the
knowledge of the longitude and difierence of longi-
tude of places.

154.nbsp;Is that graduated circle which crosses the
equator in a« angle of about 23i degrees; and this
angle is called the obliquity of the ecliptic.

This circle is divided into 12 equal parts, each of
which contains 30 degrees ; the beginning of each
12th part is marked with the usual characters, which
^vith their names are as follow:

the equator, are called equinoctial points, and are
marked with these charrcters T and ii at the begin-
ning of Aries and Libra.

marked with the characters 25 and VJquot;, which two
points are called the solstices ; the first is the summer
solstice, the second that of the' winter, to all the
inhabitants upon the north side of the equator; but
directly contrary to those on the south side of it.

Although the ecliptic does not properly belong to
the earth, yet we have placed it upon our terrestrial
globe according to ancient custom ; it being useful
in some particular cases ; it is chiejfly to be regarded
npon the celestial globe.

157. The longitude of the stars and planets is
reckoned upon the ecliptic ; the numbers beginning

at the first point of Aries T? where the ecliptic cros-
ses the equator, and increasing according to the
order of the signs.

138. The latitude of the stars and planets is deter-
mined by their distance from the ecliptic upon a secon-
dary or great circle passing through its poles, and
crossing it at right angles.

159.nbsp;Twenty-four of these circular lines, which
cross the ecliptic at right angles^ being fifteen degrees
from each other, are drawn upon the sm face of our
celestial globe; which being produced both ways,
those on one side meet in a point on the northern
polar circle, and those on the other meet in a point
on the southern polar circle.

160.nbsp;The points determined by the meeting of
these circles are called the poles of the ecliptic, one
north, and other south.

161.nbsp;The longitude of the stars hath been observ-
ed to increase about a degree in 72 years, which is
called the precession of the equinox.

162.nbsp;On the surface of the celestial globe are
represented by a variety of human and other figures,
to which the stars that are either in or near them
are referred.

The several systems of stars, which are applied to
those images, are called constellations. Twelve of
these are represented on the ecliptic circle, and extend
both northward and southward from it. So many
of those stars as fall within the limits of 8 degrees
on both sides of the ecliptic circle, together with such
parts of their images as are contained within the

aforesaid bounds, constitute a kind of broad hoop,
belt or girdle, which is called the zodiac.

The names and the respective characters of the
twelve signs of the ecliptic may be learned by inspec-
tion on the surface of the broad paper circle; and the

163.nbsp;The zodiac is represented by eight circles
parallel to the ecliptic, on each side thereof; these
drcles are one degree distant from each other, so
that the whole breadth of the zodiac is 16 degrees.

164.nbsp;Amongst these parallels, the latitude of the
planets is reckoned; and in their apparent motion
they never exceed-the limits of the zodiac.

165.nbsp;On each side of the zodiac, as was observed,
other eonstellations are distinguished ; those on the
north side are called northern, and those on the south
side of it, southern constellations.

166.nbsp;All the stars which compose these constel-
lations are supposed to increase their longitude con-
tinually • upon which supposition, the whole starry
firmament has a slow motion fmm west to east;
insomuch that the first star m the constellation of
Aries, which appeared in the vernal intersection of
trhe equator and ecliptic in the time of Meton the
Athenian, upwards of IQOO years ago, is now remov-
ed about 30 degrees from it.

To represent this motion upon the celestial globe,
elevate the north pole, so that its axis may be perpen-
dicular to the pkne of the broad paper- circle, and the
equator will then be in the same plane; let these
represent the ecliptic, and then the poles of the globe
will also represent those of the ecliptic ; the echptiG
line upon the globe will at the same time represent
the equator, inclined in an angle of degrees to

the broad paper circle, now called the ecliptic, and
cutting it in two points, which are called the equinoc-
tial intersections.

Now if you turn the globe slowly round upon its
axis from east to west, while it is in this positioi^,
these points of intersection will move round the same
way; and the inclination of the circle, which in shew-
ing this motion represents the equinoctial, will not
be altered by such a revolution of the intersecting or
equinoctial points. This motion is called the pre-
cession of the equinoxes, because it carries the
equinoctial points backwards amongst the fixed stars.

The poles of the world seem tcf describe a circle,
from east to west, round the poles of the ecliptic,
arising from the precession of the equinox. This
motion of the poles is easily represented by the above
position of the globe, in which, if the reader remem-
bers, the broad paper circle represents the ecliptic,
and the axis of the globe being perpendicular thereto
represents the axis of the ecliptic; and the two points,
where the circular lines meet, described in Art. 15^,
160, will now represent the poles of the worlds
whence as the globe is slowly turned from east to
westy these points will revolve the same way about
the poles of the globe, which are hece supposed to
represent the poles of the ecliptic. The axis of the
world may revolve as above, although its situation
with respect to the ecliptic be not altered; for the
points, here supposed to represent the poles of the
world, will always keep the same distance from the
broad paper circle, which represents the ecliptic in
this situation of the globe.*

167.nbsp;From the difFerent degrees of brightness ia
the stars, some appear to be greater than others, or
nearer to us; on our celestial globe, they are distin-
guished into seven different magnitudes.

168.nbsp;The daily rotation of the earth about its axis
is one of the most essential points which a beginner
ought to have in view; for every particular meridian
thereon is successively turned towards every point
in the heavens, and as it were describes circles in
the celestial sphere, perpendicular to the axis of the
earth, and parallel to each other; by which means
the fixed stars seem to have an apparent diurnal
motion,

169.nbsp;Except those two points in the starry firma-
ment, into which the earth's axis, supposed to be so
far extended, would fall; these two points are called
the celestial poles, which correspond with our terres-
trial north and south poles.

the real diurnal motion of the earth and the apparent
diurnal motion of the heavens are represented by them
Art. 85, 86, and thence all problems solved as readily
in south as in north latitudes, and in places on or
near the equator ; by which means we are enabled
to shew, how the vicissitude of days and nights,
their various alterations in length, the duration of the
twilight, are really made by the earth's daily
motion, upon the principles of the Pythagorean or

concave sphere of the fixed stars, se n q s se the globe
of the earth, whose axis n s is supposed to be extend-
ed to N S, in the sphere of the fixed stars ; all the
stars seem to revolve upon these two points as poles.

If the plane of the earth's equator se z q c ae is con-
ceived to be extended to the starry firmament, it will
point out the celestial equator M ^ Q^X

N represents the celestial, and n the terrestrial
north pole, S and s thé south pole.

171. Fig. 26. That circle which any star seems
to describe in twenty-four hours is called its parallel:
thus, suppose a right line drawn from C the center
of the earth, through any point d of its sur-
face, and extended to D in the starry firmament, by
means of the earth's daily rotative motion, the extre-
mity D of the line C D will describe the celestial
parallel GxDx G, corresponding to the terrestrial
parallel gd, of the point d. If D C be supposed to be
extended to H, the opposite side of the starry firma-
ment, it will describe another parallel equal to the
former.

Those circular lines upon the terrestrial globes,
which are described from the poles, on either side of
the equator, are parallel to it, and are called paral-
lels of latitude, but on the celestial globe they are
called parallels of declination.

There are four principal lesser circles parallel to
the equator, which divide the globe into five unequal
parts,called Zones; these are the two tropics, and the
two polar circles.

We have already shewn, that the distance of
any parallel from the equator, measured in the
arch of a great circle on the terrestrial sphere, is
its latitude ; and on the celestial sphere, its declina-
nation. Art. 135,

172. If the sun, moon, a fixed star, or planet,
is situated in any parallel between the equator M Q,
fig.- 26, and the north pole N, it is said to have
north declination ; but if towards the south pole S,
south declination.

Thus the two parallels G D, and H I, have the
same declination : because they are equally distant
from JE Q th^ equator ; the first hath north, the
last south declination.

Hence we must observe, that a celestial parallel
G X D, and its correspondent g x d upon the earth,
are two parallel circles, being similar elements of a
cone, whose axis is that of the earth, and apex C,
the center of the earth. Therefore the plane of a
terrestrial parallel cannot be the same with its cor-
respondent celestial parallel ; only the plane of the
celestial equatornbsp;is the same with

that of the terrestrial ae z q, because these two
planes are produced by the same radius C Q, per-
pendicular to the axis N S, on which the earth or
the heavens are supposed to turn.

If by the earth's daily rotative motion, a star D
passes over the zenith d of any inhabitant of the
earth, that star is the celestial parallel, which cor-
responds to the terrestrial parallel of the observer ;
for the distance of the celestial parallel GD, con-
tains the same number of degrees from JE Q, the
celestial equator, as that of the inhabitant's parallel
g d does from se q, the terrestrial equator.

Therefore the measure of the arch of any in-
habitant's distance from the terrestrial equator,
which is called the latitude of the place, is si-
milar and equal in the number of degrees, to
that fixed star's declination, which passes over his
zenith.

If the inhabitant changes his situation either
north or south, the different declinations of those
stars which pass over his zenith, at the several
places of his removal, will shew his advance to-
wards or regress from the equator.

Whence any place upon th« earth may be repre-
sented by its corresponding zenith point, in the ap-
parent concavity of the starry sphere; as shall be
hereafter shewn.

173.nbsp;Upon our new terrestrial globe, there are
twenty-three parallels drawn at the distance of one
degree from each other, on both sides the equator ;
which, with two other parallels at 234- degrees
distance, include the ecliptic circle; these two are
called the tropics. That on the north side of the
equator is , called the tropic of Cancer ; and the
other, which is on the south side of it, the tropic
of Capricorn.

174.nbsp;The space between these two tropics, which
contains about 47 degrees, was called by the anci-
ents, the torrid zone.

The two polar circles are placed at the same dis-
tance from the poles, that the two tropics are from
the equator.

These include 234- degrees on each side of their
respective poles, and consequently contain 47 de-

175.nbsp;The space contained within the northern
polar circle, was by the ancients called the north
frigid zone, and that within the southern polar cir-
clc, the south frigid zone.

176.nbsp;The spaces between either polar circle, and
its nearest tropic, which contain about 43 degrees
each, were called by the ancients the two temperate
zones.

177.nbsp;Whenever any parallel passes through tvi^o
places on the terrestrial globe, these places have the
same latitude.

Also all those stars which are in the same pa-
rallel upon the celestial globe, have the same de-
clination.

And.as the ecliptic is inclined to the equator in an
angle of 234- degrees, and is included between the
tropics, every parallel in the torrid zone must ne-
cessarily cross the ecliptic in two places ; which two
points shew the sun's place, when he is vertical to
the inhabitants of that parallel; and the days of the
month upon the broad paper circle answering to
those points of the ecliptic, are the days on which
the sun passes directly over their heads at noon, and
are called their two midsummer days : whence the
inhabitants of the torrid zone have two summers
and two winters every year.

Hence as the earth's progressive, or rather ap-
parent annual motion, seems to be in the celestial
ecliptic, the sun's declination is thereby changed
gradually every day. Therefore on our new ter^
restrial globe, as mentioned in Art. 173, we have
drawn parallels through the whole space of the

torrid zone, and the two spaces within the polar
circles, to give a general and clear idea of the Sim's
apparent passage from one tropic to another.

178.nbsp;Are circular lines drawn on the celestial
globe from pole to pole, (as meridians are npon
the terrestrial globe) crossing the equator at
right angles, and being secondaries to it. Art.
140.

179.nbsp;The two celestial meridians which pass
through the first point of T and making together
one |reat circle, are represented by the circle
^ T K B, in fig. 26, and are called the .equi-
noctial colure. the points marked T and ^ are
called the equinoxes, or equinoctial points. •

1^0. The two celestial meridians represented by
the circle NtESQN, passing through the sol-
stitial points (marked ss and VJ) of Cancer and Ca-
pcicorn, are called the solstitial colure.

181. These colures cut each other at right
angles in the poles of the world, and divide the
celestial equator, ecliptic, and zodiac, into four
equal parts,- which points determine the four
seasons of the year. See Art. 34 to 41, and Art.
187-

The equinoctial colure only passes through the
poles of the world at n and s. But,

-phe solstitial colure passes through the poles of
the world at n and s, and also through the poles of
the ecliptic at B and K, fig. 26.

Whence it happens in every daily rotation of the
jfarth about its axis, that the solstitial and equi-

noctial colures are twice blended with every
meridian upon the surface of the earth : conse-
quently, each pole of the ecliptic appears to pass,
once every day, over all the meridians of the ter-
restrial sphere.

182. All those circular lines that are, or may be
supposed, drawn on the celestial globe, which pass
through the poles, cutting the equator at right
angles, are called circles of declination ; because the
declination of those- points or stars through which
they pass, or the distance of those stars from the
equator, is measured upon these circles : and this is
done by bringing the divided edge of the moveable

Hence the thin brass semi-circle. Art. 1.15, which
we call the moveable meridian, is also a moveable
circle of declination.

arctic and antarctic cincles, or circles op
perpetual apparition and occultation.

183. The largest parallel of latitude on the ter-
restrial globe, as well as the largest circle of decli-
nation on the celestial, that appears entire above the
horizon of any place in north latitude, was called by
the ancients the arctic circle, or circle of perpetual
apparition.

Between the arctic circle and the north pole in
the celestial sphere, are contained all those stars
which never set at that place, and seem to us, by
the rotative motion of the earth, to be perpetually
carried round above our horizon in circles parallel to
the equator- ■

and the largest parallel of declination on Ae ce-
lestial globe, which is entirely hid below the ho-
rizon of any place, were hy the ancients called
the antarctic circle, or circle of perpetual oc-
cultation.

This circle includes all the stars which never
rise in that place to an inhabitant of the north-
ern hemisphere, but are perpetually below the
horizon.

All arctic circles touch their horizons in the north
point, and all antarctic circles touch their horizons
in the south point ; which point, in the terrestrial
and celestial spheres, is the intersection of the
meridian and horizon.

If the elevation of the pole be 45 degrees, the
most elevated part either of the arctic or antarctic
circle, will be'in the zenith of the place.

If the pole's elevation be less than 45 degrees,
the zenith point of those places will fall without
its arctic or antarctic circle. If greater, it will fall
within.

Therefore the nearer any place is to the equator,
the lesser will its arctic and antarctic circles be ; and
on the contrary, the farther any place is from the
equator, the greater they are. So that.

At the poles, the equator may be considered as
both an arctic and antarctic circle, because its plane
is coincident with that of the horizon.

But at the equator (that is, in a right sphere)
there is neither arctic nor antarctic circle.

They who live under the northern polar circle,
have the tropic of Cancer for their arctic, and that
of Capricorn for their antarctic circle.

Hence, whether these circles fall within or with-
out the tropics, their distance from the zenith of
any place is ever equal to the difference between the
pole's elevation, and that of the equator above the

may be as many arctic and antarctic circles, as
there are individual points upon any one meri-
dian, between the north and south poles of the
earth.

184. Many authors have mistaken these muta-
ble circles, and have given their names to the im-
mutable polar circles, which last arc arctic and
antarctic circles, in one particular case only, as has
been shewn.

185. Arises from the earth's annual motion in
tlie ecliptic, the inclination of its axis, and its al-
ways moving parallel to itself. .

Imagine the plane of the earth's orbit'extended
as far as the fixed stars, it will there mark out the
circle S5, VJ, X, So, which we call the celestial
ecliptic; see fig. 26.

From this comparison of the earth's orbit with
the celestial ecliptic, is derived the ancient rule to
find the sun's place, if we first find the earth's place^
either by observation or calculation ; six signs
added to or subtracted from it gives the stin's true
place in the ecliptic. Consequently it is the same

when we consider the daily motion of the earth
about her equatorial axis, represented by the ter-
restrial globe, whether we suppose the earth, or
the sun, to have an annual motion.

It is also the same thing in the use of the ce-
lestial globe, whether we suppose the earth to turn
upon her equatorial axis, or the starry sphere to
revolve upon the extremities of the same axis ex-
tended to the heavens : the result in either case will
be the same, provided we conceive ourselves at the
center of the globe.

180. We shall therefore suppose the sun's ap-
parent annual motion to be in the plane of the ce-
lestial ecliptic, Art. 34 to 41, and in his passage
through it, describing by a ray connecting the
centers of the earth and sun, a different circle of
declination, parallel to the equator every day.
Whereby all who inhabit any of those places on
the earth which are situated between the terrestrial
tropic of Cancer represented in fig. 26, by 25, e,
and the terrestrial tropic of Capricorn represented
by h, V5', have the sun at the time he is de-
scribing their parallel, in their zenith ; or directly
vertical, or over their heads, which happens twice '
every year.

. 187. Whence the inhabitants of those places,
as well as mariners who pass between the tro-
pics, have a corresponding zenith point, where
their latitude is equal to tiie sun's parallel of de-
clination, from the sun by day, and from the stars
by night.

It is easily conceived, that if the planes of the
equator and ecliptic were united in one continued
plane, a central solar r'ay, connecting the centers of

the earth and sun, would by the earth's diurnal mor
tion describe the equator every day ; but, as we
have before observed, the sun does apparently de-
describe a different parallel every day :. wherefore
the ecliptic and equator are inclined to each other in
an angle confirmed by observation of about 23 deg.
29 min.

Let the sun's apparent annual motion be repre-
sented by the circle g5, T, fig- 26, which
bisects the celestial equator ^ Q T ^ the
points and T ; the first of these is called the
autumnal, the second the vernal, equinoctial point.

When the sun is in he appears to describe the
equator, at which time he has no declination ; and
as he proceeds gradually from =2= towards VJ, his
southern declination continually increases, and he
describes less and less parallels, till he appears in
and describes the tropic of Capricorn ; being then
at his greatest southern declination, viz. at his
greatest distance .from the eqttator southerly, and

and the parallels he describes'are greater and greater, -
■ until he comes to Aries, or the vernal equinox, and
again has no declination, describing the equator as
before.

As he advances from thence towards 05, the de-
clination increases, and the parallels described are
less and less, until he arrives at 55, or the summer
solstice ; being then at his greatest northern decli-
nation, describing the tropic of Cancer.

Thence proceeding forwards towards the de-
clination continually decreases, and the parallels
described increase till the sun's arrival at the next

succeeding autumnal equinox ; where he again de-
scribes the equator, having no declination ; and
completes the length of a mean solar tropical year,
containing 365 d. 5 h. 4Q mm.

What we have said with respect to summer and
winter solstices, is to be understood with relation to
those places which lie between the equator and the
north pole ; but to the places between the equator
^ - ^ ^ and south pole the contrary happens.

We have been thus particular in our description
of the sun's apparent annual motion, for the use of
beginners; and we hope this consideration will plead
in our behalf, if we should appear tedious or trifling
to those who are masters of the subject.

But what has been said, might yet be more clearly
illustrated by an orrery or a tellurian, which shews
the annual and diurnal motions of the earth, and
parallelism of its axis, amp;c. and by the different po-
sitions of the earth's axis, with respect to her en-
lightened disc, will make it appear to the eye as it
is really understood by astronomers; and then we
may with more propriety repair to the use of the
globe itself.

188. Describe a circle A B C D, fig. 8, with chalk
upon the floor, as large as the room will admit ef,
that the globe may be moved round upon it: divide
this circle into twelve parts, and mark them with the
characters of the twelve signs, as they .^re. engraved
in fig. 8, or upon the broad paper circle ; placing 35

in the west: the mariner's compass under the globe
will direct the situation of these points, if the va-
riation of the magnetic needle be attended to.

Note. At London , the variation is between 10
and '21 degrees from the north westward.

Elevate the north pole of the globe, so that 664-
degrees on the strong brass meridian may coincide
with the surface of the broad paper circle, and this
circle will then represent the plane of the ecliptic, as
mentioned in Article 103.

Set a small table or stool over the center of the
chalked circle to represent the sun, and place the
terrestrial globe upon its circumference over the
point marked VJ, with the north pole facing the ima-
ginary sun, and the north end of the needle point-
ing to the variation : this is the position of the earth
with respect to the sun at the time of the summer
solstice about the 2,1st of June: and the earth's
axis, by this rectification of the globe, is inclined to
the plane of the large chalked circle, as well as to
the plane of the broad paper circle, in an an angle
of 23i degrees; a line or string passing from the
center of the imaginary sun to that of the globe,
will represent a central solar ray connecting the
centers' of the earth and sun : this ray will fall up-
on the first point of Cancer, and describe that circle,
shewing it to be the sun's place upon the terrestrial
ecliptic, which is the same as if the sun's place, by
extending the string, was referred to the opposite
side of the chalked circle, here representing the
earth's path in the heavens.

of the globe, it will also pass through the sun's
center, and the points of Cancer and Capricorn in
the terrestrial and celestial ecliptic; the central
solar ray in this position of the earth is also in that
plane ; this can never happen but at the times of
the solstice.

If another plane be conceived to pass through the
center of the globe at right angles to the central
solar ray, it will divide the globe into two hemis-
pheres ; that next the center of the chalked circle
will represent the earth's illuminated disc, the con-
trary side of the same plane will at the same time
shew the obscure hemisphere.

The intelligent reader, for the use of,his pupils,
may realize this second plane by cutting aw^y a
semicircle from a sheet of card paste-board, with
a radius of about IJ- tenth of an inch greater than
that of thegoble itself; if this plane be applied to
66-I- degrees upon the, strong brass meridian, it will
be in the pole of the ecliptic; and in every situation
of the globe round the circumference of the chalked
circle, it will afford a lively and lasting ide^ of the
annual and diurnal motion of the earth, of the vari-
ovis phaepomena arising from the parallelism of the
earth's axis, and in particular the daily change of
the sun's declination, and the parallels thereby
described.

Let the globe be removed from VJ to and the
needle pointing to the variation as before will pre-
sarve the parallelism of the earth's axis; then it will
be plain, that the string or central .^lar ray will f^]!
upon, the first point of Leo, six signs distant from,^
but opposite to the sign upon which the globi;

stands: the central solar ray will now describe tbe
20th parallel of north declination, which will be
about the 23d of July.

If the globe be moved in this manner from point
to point round the circumference of the chalked
circle, and care be taken at every removal that the
north end of the magnetic needle, when settled,
points to the degree of the variation, the north pole
of the globe will be observed to recede from thelme
connecting the centers of the earth and sun, until
the globe is placed upon the point Cancer: after
which, it will at every removal tend more and more
towards the said line, till it comes to Capricorn
again.

189. If the place be in north latitude, raise the
north pole; if in south latitude, raise the south
pole, until the degree of the given latitude, reckoned
on the strong brass meridian under the elevated
pole, cuts the plane of the broad paper circle; then
this circle will represent the horizon of that place.

190.nbsp;After the former rectification, bring the de-
grees of the sun's place in the ecliptic line upon the
globe to the strong brass meridian, and set the
horary index to that Xllth hour upon the equator

191.nbsp;Or, if the sun's place is to be retamed, to
answer various conclusions, bring the graduated

edge of the moveable meridian to the degree of the
sun's place in the ecliptic, upon the celestial globe,
and slide the wire which crosses the center of the ar-
tificial sun thereto : then bring its center, which is
the intersection of the aforesaid wire, and graduated
edge of the moveable meridian, under the strong
brass meridian as before, and set the horary index
to that XII on the equator which is most elevated.

After the first rectification, screw the nut
of the quadrant of altitude so many degrees from
the equator, reckoned on the strong brass me-
ridian towards the elevated pole, as that pole is
raised above the plane of the broad paper circle,
and that point will represent the zenith of the
place.

Note. The zenith and nadir are the poles of
the horizon, the former being a point directly
over our heads, and the latter, one directly under
our feet.

193. If you are doubtful whether the proper
point of the brass meridian is correctly cut, when
set by the eye, apply a card cut in the shape of fig.
27, to the place, flat upon the broad paper circle,
and it will be truly adjusted.*

If, when the globe is in this state, we look on
the opposite side, the plane of the horizon will cut
the strong brass meridian at the complement of the
latitude, which is also the elevation of the equator
above the horizon.

Problem XIII. To find the moon's mean place
npon the celestial globe, her age and day of the
month being known.

104 The moon increases her longitude in the,
ecliptic everv day about 13 deg. 10 min. by which
means she' crosses the meridian of any place
about 60 minutes later than she did the pre-
ceding day.

Thus if her place be in the 12th degree of
Taurus any day at noon, it will be 25 deg. 10 mm.

It is new moon when the sun and moon have
' the same longitude, or are in or near the same

the given day of the month in any common alma-
nack, the number of days elapsed is the moon's

The equator on our new celestial globe is di-
vided by large dots into 29^ equal parts, each ot
which is directed by a short dotted line, to a num-
ber marked in Roman figures, expressing the several
days of the moon's age.

globe to 90 degrees, and then the equator will be
in the plane of, and coincide with the broad paper
circle; bring the first point of'Aries, marked ^
on the globe, to the day of the new moon on the
said broad paper circle, which answers to the sun's
place for that day ; and the day of the moon's age
will stand against the sign and degree of the
moon's mean place ; to which set the artificial moon
upon the ecliptic on the globe.

But if you are provided with an ephemeris,*
that will give the moon's latitude and place in the
ecliptic; first note her place in the ecliptic upon
the globe, and then counting so many degrees
amongst the parallels in the zodiac, either above or
below the ecliptic, as her latitude is north or
south upon the given day, and that will be the
point which represents the true place of the moon
for that time, to which apply the artificial moon'.

igQ. Note. TJie artificial moon is a small thin
piece of brass in form of a crescent, having two
holes a and b, fig. 28, through which a small
string of silk twist is put, that it may slip back-
wards or forwards upon it.

To one end c of this silk string is tied a small
piece of brass dec with three holes at dec.

The manner of putting it upon the globe is this :
first put the crescent a b, on the string; and the
piece of brass, by passing the string through the
two holes d, e, the string being as yet left free.
The two ends of the string being loose, pass the
end F round the north pole of the globe, in a
groove made for that purpose, and tie it into a
loose loop like Fg, then put the other.end of the

string G c round the south pole, and tie it fast to
the hole at c,: then by pulling the piece dec up-
wards, the string may be tightened on any part of
the globe, and pushing it downwards will slacken
it, that it may be removed to any other place, and
then tightened again.

Problem XIV. To represent the apparent di-
urnal motion of the sun, moon, and stars, on the
celestial globe.

igy. Find the sun's place in the ecliptic, by Pro-
blem i. Art. 98, and to that point on the eeliptie
line which is drawn upon the globe, set the center
of the artificial sun. Also,

Find the moon's place by Problem xiii. Art. I944
and set the center of the artificial moon upon it.

Rectify the globe to the latitude, sun's place,
and zenith, by Problem xii. Art. 189, 190, and

The globe being turned round its axis from east-
to west, will represent the apparent motion of the
sun, moon, and stars, for that day.

] 98. When the center of the artificial sun is in
the plane of the horizon on the eastern side, ths
horary index shews upon the equator the time of
sun rising.

199. All those stars which are then in the
plane of the horizon on the eastern side, are at
the same instant of time rising with the sun, and
those on the western side of the horizon, are then
setting.

200. And when the center of the artificial moon
comes to the horizon on the eastern side, the
horary index will point to the hour and minute of

And those stars on the eastern edge ot the ho-
rizon are then rising with her, whilst at the same
time all the stars, cut by the western edge, are
setting.

act. That degree and minute of the equator
which is cut by the plane of the horizon, at the
same time that the center of the artificial sun,
moon, or any star, is also cut by the said plane,
is the very point of the equator, which rises with
either of them, and is called the sun, moon, or
star's oblique ascension.

202.nbsp;As the sun ascends in the heavens till it
culminates, or comes under the graduated side of
the strong brass meridian, the horary indtex will
successively point to the hours before noon ; but
when it is under it, the horary index points at
XII o'clock, and that degree and minute on the
equator, which is then cut by the brass meridian,
is called the sun's right ascension, that is, its dis-
tance from the first point of Aries, reckoned in de-
grees, minutes, amp;c. upon the equator.

203.nbsp;At the same time, that degree of the brass
meridian, which is directly,over the artificial sun,
is his declination. Art. 133, for that day.

The same is to be observed of the moon or any
staV as they ascend in the heavens, till they cul-
minate or come under the meridian,, the horary

index constantly pointing to the hour of. the day
or night ; their right ascension and declination
are also shewn in the same manner as i that of the
sun.

204.nbsp;Whilst the sun descends from the merii
dian westward, the horary index successively shews
the hours after noon.

And when the center of the artificial sun is in
the plane of the horizon on the western side, the
horary index shews the time of sun setting; and
that point of the equator which is then cut by the
plane of the horizon, is the point which sets with
the sun, and is called his oblique descension.

205.nbsp;The number of degrees on the equator
contained between the points of his oblique as--
cension, and right ascension, or between the points
of his right ascension, and oblique descension, is
called his ascensional difference.nbsp;-

Observe the same with respect to the moon or
any star: as they descend from the meridian west-
ward, the horary index will successively shew the
time of their arrival at any given point, their
setting, oblique descension, and ascensional differ-*
ence, in the same manner as before described in
relation to the sun.

The rising, culminating, settingj See.- of any
planet may be obtained, if the place of the planet,
its longitude and latitude being taken from an
ephemeris, be ascertained ; and an artificial planet
set thereto, in the manner in which we have di-
rected the artificial moon to be placed upon the
globe. Art. 196, or this last may ocGfeSionally repre-
sent a. planet.nbsp;, i

gtile, being the first year after bissextile, the sun's
place will be H, 27 deg. 22 min. the moon's place
1, 18 deg. O min. her latitude north Odeg. 30 min.
The full moon about of an hour past Vill o'clock
in the morning ; to which places, if the artificial sua
and moon be set, a beginner may readily exercise
himself in finding the proper answers agreeable to
these data, by the directions in this problem.

200. The globe remaining rectified as in the last
problem, the uppermost point represents a point in
the heavens directly over our heads, which is called
the zenith: and as the brass quadrant is moveable
about its upper end as a center, when that center
is fixed to the latitude of the place upon the strong
brass meridian, it will be in the zenith, and the
beginning of its graduations will coincide with the
plane of the broad paper circle, which in these cases
represents the horizon of the place.

If the quadrant be moved about the globe, its
first division will describe the horizon. And,

At the same time, all its intermediate divisions
will describe circles parallel to the horizon ; the
point marked 10 describes a parallel of 10 degrees,
the point marked 20 a parallel of 20 degrees, and
so of any other point.

207. These circles parallel to the horizon are
called parallels of altitude, because they shew the
elevation of the sun, moon, stars, or planets, above
the plane of the horizon :

208. Set the center of the artificial sun to his
place in the echptic upgn the globe ; and rectify it
to the latitude and zenith, by Problem xii. Art.
189, amp;c.; bring the center of the artificial sun
under the strong brass meridian, and set the hour
index to that XII which is most elevated ; turn
the globe to the given hour, and move the graduated
edge of the quadrant to the center of the artificial
sun; and that degree on the quadrant which is
cut by the sun's center, is the sun's height at that
time.

The artificial sun being brought under the strong
brass meridian, and the quadrant laid upon its cen-
ter, will shew its meridian, or greatest altitude, for
that day.

If the sun be in the equator, his greatest oi
meridian altitude is equal to the elevation of the
equator, which is always equal to the co-latitude of
the place.

209. An azimuth circle in astronomy,
very same as a circle of position in geography ; they
being secondaries to the horizon, or great circles
passing through the zenith of any place, and crossing
the horizon at right angles: either in the heavens,
called aaimuths : or on the eafth, cirsleS oS position.

Any azimuth circle may be represented by the
quadrant of altitude, when the center upon
which it turns is screwed to that point of the
strong brass meridian, which answers to the lati-
tude of the place, and the place brought into the
zenith.

Suppose at London, if you bring the divided
edge of the quadrant to 10 degrees on the inner
edge of the broad paper circle, it will represent an
azimuth circle of 10 degrees; if you set it to 20,
it will represent an azimuth circle of, 20 degrees ï
and so of any other.

If the quadrant of altitude be set to 0 degree,
that is either upon the east or west points of the
broad paper circle, it will then represent that se-
condary to the horizon, or azimuthal circle, which
is called the prime vertical.

%\0. Rectify the globe to the latitude and sun's
place. Art. IBQ, igo, then turn it to the given
hour, and bring the divided edge of the quadrant
of altitude to the sun's place in the ecliptic, or to
the center of any star, and it will cross the horizon
the azimuth required.

The distance of that point of the horizon, in
which the sun appears to rise or set, counted
from the prime vertical, Art. 200, or east and
west- points of the horizon, is called the sun's
j^jnplitude.

211. The angle of position is that formed be-
tween the meridian of one of the places, and a
great circle passing through the other place.

Rectify the globe to the latitude and zenith of
one of the places, Art. IBQ, I92, bring that place
to the strong brass meridian, set the graduated
edge of the quadrant to the other place, and the
number of degrees contained between it and the
strong brass meridian, is the measure of the angle

''Hence it is plain, that the line of position. Or
azimuth, is not the same from either place to the
other, as the romb-lines are.

212. The bearing of one sea-port from another
is determined by a kind of spiral called a romb-
line passing from one to the other, so as to make
enull angles with all the meridians it passeth by;
therefore if both places are situated on the same
parallel of latitude, their bearing is either east or
west from each «ther; if they are upon the same

meridian, they bear north and south from one
another; if they he upon a romb-line, their bearing
is the same with it; if they do not, observe to
which romb-line the two places are nearest parallel,
and that will shew the bearing sought.

Thus the bearing of the Lizard Point from the
island of Bermudas is nearly E. N. E.; and that of
Bermudas from the Lizard is W. S. W. ; both nearly
upon the same romb, but in contrary directions.

213. Is that position of the globe, in which the
poles are in the zenith and nadir, its axis at right
angles to the equator and horizon, which coin-
cide ; and consequently those circles which are
parallel to the equator, are also parallel to the
horizon.

The inhabitants of this sphere, if any there be,
must live upon the two terrestrial poles, and will
have but one day and one night throughout the
year ; and the moon, during half her monthly
course, will never rise, and during the other half
will never set: all the fixed stars, visible to those
people, will describe circles every day parallel to
their horizon.

214. Is that in which the inhabitants see both
poles in their horizon, the equator passing through
their zenith and nadir, and all the circles parallel
to the equinoctial perpendicular to their horizon.

These people live upon the terrestrial equator,
consequently all the heavenly bodies will always
rise and set perpendicularly to them ; and their
days and nights will be of an equal length through-
out the year.

215. Hath one of the poles of the globe above,
the other under the horizon; the equator in all the
cases of this sphere is half above, and half below
the horizon, and all its parallel circles cut the ho-
rizon obliquely.

That arch of any parallel of declination in the
celestial, or of latitude in the terrestrial sphere
that is above the horizon, is called th^ diurnal
arch. And

The remaining part of it, which is below the ho-
rizon, is called the nocturnal arch.

These arches, with respect to the sun's apparent
motion, determine the different length of days and
nights.

The inhabitants of this sphere are those who live
on all parts of the earth, except those at the poles
and upon the equator.

That light which we have from the sun before it
rises, and after it sets, is called the twilight.

216. The morning-twilight, or day-break, begins
when the sun comes within 18 degrees of the ho-
rizon, and continues till sun-rising.

For this purpose on our new globes, a wire circle
is fixed 18 degrees below the surface of the broad
paper circle ; so that

All those places which are above the wire circle
will have the twilight, but it will be dark to all
places below it.

At the time of winter solstice, when the whole
space within the northern polar circle is out of the
sun's light, the greater part of it enjoys the benefit
of twilight; there being only about degrees
round the pole that .will be totally dark.

We have here only considered the twilight re-
flected to us from the earth's atmosphere by the
sun himself; besides which the body of the sun
is always encompassed with a sphere of light, which
being of a larger circumference than the sun, must
rise before him, and set after him ; which conse-
quently lengthens the twilight by illuminating our
air, when the sun is depressed too low to reach it
with his own light: this seems to be the cause,
why the sun is preceded by a luminous segment of a
circle in the east before his rising, difFerent from
that light reflected by the atmosphere from the body
of the sun ; the like to which may be observed in
the west after sun-set.

217. We have already shewn how the earth's
diurpal motion is represented by the motion of the

terrestrial globe about its axis from west to east;
and that the horary index will point upon the equator
the 24 hours of one diurnal rotation, or any part of
that time.

The broad paper circle, under this consideration,
will be now employed to represent a plane supposed
to pass through the center of the earth, perpen-
dicular to a central solar ray : or in other words,
perpendicular to a line supposed to be drawn from
the center of the sun to that of the earth at all
times of the year.

In which case, the broad paper circle divides that
half of the earth's surface, which is illuminated by
the sun's rays, from the other hemisphere which is
not enlightened.

218. That the globe may appear to be so en-
lightened, conceive a sun painted on the ceiling of
the room in which you are, directly over the ter-
restrial globe, and of the same diameter; from
whence imagine an infinite number of parallel rays
falling perpendicularly downwards upon the upper
surface of the globe, which here represents the il-
luminated hemisphere of the earth's enlightened disc.

Whence it is plain, that the central solar ray is
the only one which passes through the centers of
the sun and earth, as well as the only ray thai can
po!=sibly be perpendicular to the earth's surface ; all
other solar parallel rays will fall more and more
oblique, as they are fartKer from the central ray,
till their arrival at the edge of the enlighteiied disc,
here represented by the inner edge of the broad
paper circle, where they w,ill become parallel to
the horizons of all places then under the said edge
of the disc.

In one diurnal revolution of the earth, the central
solar ray describes the parallel of the sun's declina-
tion ; or rather that parallel, to the inhabitants of
which the sun that day will pass directly veitical, or
over their heads.

From this application of the terrestrial globe, we
see the natural cause of the different altitudes of
the sun at different times of the day, and at different
seasons of the year; which arise from the earth's
daily rotative and progressive motion, amp;c.

When we view the globe in this position, we at
once see the situation of all places in the illuminated
hemisphere, whose inhabitants enjoy the light of
the day, while at the same time all those places be-
low the broad paper circle are deprived of the sun's
light, and have only twilight so far as the wire circle,
and all below that, have total darkness, when the
moon does not shine on them.

And by observing the angles made by the meri-
dians, drawn on the globe, cutting any parallel of la-
titude at the edge of the broad paper circle, with the
strong brass meridian, we see the semi-diurnal arches
continually decrease from the elevated pole, till they
Gome to the opposite part of the earth's enlightened
disc.

Problem XVII. To rectify the terrestrial globe,
that the enlightened half of the earth's surface may
be all above the broad paper circle for any time of
the year; the sun being supposed in the zenith.

219. On the backside of the strong brass meridian,
3nd on each side of the north pole, are graduated, ia

Bring the day of the month to coincide with thé
broad paper circle, and the terrestrial globe is
rectified.

When the globe is thus rectified, that degree and
minute upon the graduated side of the brass meri-
dian, which is then cut by the plane of the broad
paper circle, is the distance of the shade of extu-
berancy upon the earth's disc, reckoned from the
pole, and is equal to the sun's declination for that
day; and is therefore also equal to the latitude,
counted from the equator, of all those places to
which the sun is vertical; and this point on the
brass rnericlian represents the central solar ray de-
scribing the parallel of the day.

If now the globe be turned from west to east, ali
those places which arrive at the western edge of the
broad paper circle are passing out of the twilight
into the sun's light; and the sun then appears rising

At the same time, if you look upon the eastern
edge of the broad paper circle, it will cut all those
places which are then passing from the sun's light
into the twilight; whose inhabitants will see the sun
setting, and enjoy the twilight, until they arrive at
the wire circle, which is placed 18 degrees below the
illuminated disc, at which time they enter into total
darkness.

The graduated side of the strong brass meridian
shews, at the same time, all those places which have
mid-day or noon.

ticufar place is brougTit under the strong brass meri-
dian, it will shew, as you turn the globe from west
to east, the precise time of sun rising, setting, amp;;c.
at that place.

The horary index will also shew how long a pi - ce
is moving from the west to the east side of the illu-
minated disc, here represented by the broad paper
circle, and thence the length of the day and night;
it will also point out the length of the twilight, by
shewing the time in which the place is passing from
the twilight circle to the edge of the disc on the
western side, or from the edge of the disd to that
circle on the eastern side ; and thereby determining
the length of its whole artificial day.

We shall proceed to exemplify these particu-
lars at the times of equinox and solstice.

220. The sun has no declination at the times of
equinox, consequently there must be no elevation of
the poles.

Bring the day of the month on the backside of the
strong brass ciple, in which the sun enters the first
point of Aries or Libra, into the plane of the broad
paper circle, and t,hen the two poles of the globe will
be in that plane also ; and all those circlesquot; which are
parallel to the equator will cut the p];ine of that
broad circle at right angles, and the globe will then
represent a right sphere.

If you now turn the globe from west to east, it will
plainly appear, that all places upon its surface are
twelve hours above the broad paper circle, and as

many below it ; which shews, that the nights are
equal to the days to all the inhabitants of the earth ;
that is, they are illuminated by the sun's rays twelve
hours : whence these are called the equinoctial sea-
sons, two of which occur in every year ; the first is
the autumnal, the second the vernal equinox.

At these times the sun appears to rise and set at
the same instant to all places in the same meridian.

But their twilight is longer as their situation is
nearer to either pole ; in so much that within 18
degrees of the poles, their twilight is twelve hours,
consequently there is no dark night in those places
at the times of equinox : when at the same time
those places under the equator have only one hour
and i'2, minutes twilight ; so that their artificial day
is about I4h'. 2'Jm. at these two seasons of the year.

Thus, if London and Mundford on the Gold
Coast, be brought to the strong brass meridian, the
graduated side of which is i^i this casé the horary
index; (though in other cases the hour,index is to
be set to that XII which is most elevated ;) if
then they be brought to the west side of the broad
paper circle, the index \yijl .point to VI o'clock for
sun-rising, and to VI for sun setting, when these
places are brought to the eastern side..

Also, if London be turned from the west towards
the east, and the hour index be set to XII as before,
jf you turn it.,till the, island of Jamaica comes to the
niericiian, it will shew qn- tlie equator, the hour af-
ter noon at .London, v^'hen it is noon at Jamaica ; or
that London passes under the meridian about 5h,
4 min. before Jamaica arrives at it.

221.nbsp;Rectify the globe to the extremity of thfc
lt;Jivisions for the. month of June, or to 33^
degrees north declination; then that part of the
fcarth's surface, which is within the northeri» polar
circle, will be all illuminated by the sun, and the in-
habitants thereof will have continual day.

But all that space which is contained within the
southern polar circle, will be at the same time in the
shade, and have continual night.

222.nbsp;In this position 'of the globe, we see how
the diurnal arches of the parallels of latitude de-
crease, as they are more and more distant from the
elevated pole.

233. If any place be brought under the strong
brass meridian, and the horary index be set to that
XII which is most elevated, and if that place be
brought to the western side of the broad paper circle,
the hour index will shew the time of sun rising;
and when moved to the eastern edge, the index
points to the time of sun-settiug ; the length of the
day is obtained by the time shewn by th^e horary
index, while the globe is turned from the west to
the east side of the illuminated disc.

Thus it will be found that at London the sun rises
about 15 minutes before IV in the morning, and sets
about 15 minutes after VIII at night.

We also see, that at the time when the sun rises
at London, it rises at the island of Sicily in the Me-
diterranean, and at the island of Madagascar.

And that at the time when the sun sets at London,
it is setting at the island of Madeira, and at Cape
Horn.

And when it is sun-setting at the island of Borneo
in the East Indies, the sun is rising at Florida in
America.

22.4. Rectify the globe to the extremity of the
divisions for the month of December, or to 23^. de-
grees south declination.

At this season it will be apparent, that the whole
space within the southern polar circle is in the sun's
light, and enjoys continual day ; whilst that of the
northern polar circle is in the shade, and has conti-
nual night.

Then if the globe be turned as before, the horary
index will shew, that at the several place« before

mentioned, their days will be respectively equal, to
what their nights were at the time of the summer
solstice.

It will appear to be sun-setting at the time it was
then sun-rising ; and oh the contrary, sun-rising at
the time it then appeared to set.

225.nbsp;As has been described Art. 117, is a small
brass circle with one diameter that passes through'
Its center ; its circumference is divided into eight
parts, which are marked with the initial letters of the
mariner's compass, the four cardinal points of the
horizon being distinguished from the rest; this may
be slipped from pole to pole on the moveable meri-
dian, and by this means be set to any place upon
the globe.

When the center of it is set to any particular
place, the situation of any other places is seen with
respect to that place; that is, whether they be east,
west, north, or south ; thus it represents the sensible
horizon.

It will also shew, why the sun appears at difFerent
altitudes and azimuths, although he is supposed to
be always in the same place.

Problem XXI. The sun's altitude, as observed
with a terrestrial or visible horizon.

226.nbsp;The altitude of the sun. is greater or less,
according as one of the parallel right lines or rays,
coming from the sun to us, is farther from, or nearer
to, our horizon.

Apply the terrestrial horizon to London, the sim
being supposed in the zenith, or on the ceiling di-
rectly over the globe.

If then from London a line pass vertically up-
wards, the sun will be seen from London in that
line.

At sun rising, when London is brought to the
west edge of the broad, paper circle, the supjiosed
line wilfbe parallel to the terrestrial horizon, and
from London will be then seen in the horizon.

As the globe is gradually turned from the west to-
wards the east, the horizon will recede from the line
which passes perpendicularly upwards ; for the hne in
which the snn was then seen, seems to glide farther
and farther from the terrestrial horizon j fciiat is, the
sun's altitude increases as- gradually as that line de-
clines from the terrestrial horizon.

When the horizon, and the line which goes from
London vertically upwards, are arrived at the strong
brass meridian, the sun is then at his greatest or
meridian altitude for that day ; then the lina and ho-
rizon are at the laigest angle they can make that
day with each other.

After which, the motion of the globe being con-
tinued, this angle between the terrestrial horizon and
the line, which goes from London vertically upwards,
continually decreases, until London arrives at the
eastern edge of the broad paper circle ; its horizon
then becomes vertical again, and parallel to the line
which goes vertically upwards, and will then appear
in the horizon, and be seen to set.

227.nbsp;Rectify the globe to the time of winter sol-
stice, Art. 224, and place the center of the visible
horizon on London.

When London is at the graduated edge of the
strong brass meridian, the line which goes vertically
upwards, makes an angle of about 15 degrees; this
is the sun's meridian altitude at that season to the
inhabitants of London.

228.nbsp;If the globe be rectified to the time of equi-
nox, Art. 220, the horizon will be farther separated
from the line wiiich goes vertically upwards, and
makes a greater angle therewith, it being about 384-
degrees; this is the sun's meridian altitude at the
time of equinox at London.

229.nbsp;Again rectify the globe to the summer sol-
stice, Art. 221, and you will find the visible horizon
recede farther from the line which goes from London
vertically upwards ; and the angle it then makes with
the horizon is about 62 degrees, which shews the
sun's meridian altitude at the time of the summer
solstice.

230. Add the sun's declination to the elevation of
the equator, if the latitude of the place and declina-
tion of the sun are both on the same side.

58	36
38	28
23	29

61 5?

231. Add the sun's declination to, and subtract it
from the elevation of the equator, their sum and
difference will be the sun's meridian altitudes, when
he hath the same declination either north or south..

Thus, to and from the elevation of the equator
Add and subtract the sun's declination

232.nbsp;Imagine the sun, as we have done before, to
be painted on the ceiling directiy over the globe.
Art. 218, and a line going vertically upwards towards
the sun from any place on the surface of the globe:

If to tliat place you .''pply the visible horizon, that
point of it which a vertical line is nearest to at any
time, shews the sun's azimuth at that time : and we
must also observe, that that point of the terresfial
or visible horizon, to which a. vertical line is nearest,
is always the most elevated point.

233.nbsp;Kectify the globe to the position of a right
sphere. Art. 2\4, and apply the visible horizon to
London. When London is at the western edge of
the bro;id paper circle, which situation represents the
time when the sun appears to rise, the eastern point
of the visible horizon being then most elevated,
shews that the sun at his rising is due east.

Turn tlie globe till London comes to the eastern
side of tlie paper circle, then the western point of
the visible horizon will be most elevated, and shew
that the sun sets due west.

If the globe be rectified into the position of an
oblique sphere. Art. 2]5, and London be brought to
the eastern or western side of the broad paper circle
the vertical line will depart more or less from the
east and west points : in which cases the sun is said
to have more or less amplitude either north or south
as this departure tends to either of those two car-
dinal points.

As the gjobe is turned to any particular time of
the day, we shall have the sun's azimuth upon that
jjoiat of the visible horizon which is most elevated;

and this will be the point wherein a line going to-
wards the sun is nearest to a vertical line; thus it
a line going towards the sun, be nearest the south-
east point, the sun is then, said to have 45 degrees
azimuth eastward, that point being 45 degrees from
the meridian.

when London is brought to the strong brass meri-
dian, the most elevated point of the visible horizon
will always be the south point of it, which shews
that the sun, at all seasons of the year, will appear
to the south of the terrestrial horizon m all places
included in the northern temperate zone; but to
the north of it at those places within the southern
temperate zone.

235. the ancient distinction of the dif-
FERRENT places on the earth, ACCORDING
to the diversity of the shadows of upright

Problem XXV. The ascii, or those who on a cer-
tain day project no shade at noon.

236. Rectify the globe by Problem xix. Art. 221,
to the time of the summer solstice, and apply the
terrestrial horizon to any place situated on the tropic
of Cancer, as Canton in China, and observe the sun s
meridian altitude with it, by bringing its center un-
der the strong brass meridian. Art. 226, it wiH then
appear, that a line going vertically upwards, will be
perpendicular to it, consequently the sun will be at
t^hat time directly over the heads of the inhabitants
of Canton, and project no shadow; therefore they are
ascii their noon shadow being dijectly under them,

At all other times of the day, their shadow is
projected, in the morning directly westward, and in
the evening direptjy eastward.

The same thing wiJi happen to all the inhabitants,
who live between the tropic of Canper and that of
Capricorn, if the terrestrial horizon be gradually
removed from parallel to parallel within these ümit«,
and the globe rectified according to the day of the
month as before directed; by bringing the sensible
horizon tQ the strong brass meridian, to observe the
sun's meridian altitude, we shall find him appear to
he QO degrees high, or vertical, at noon, tq every
place betwepn the tropics; all the inhabitants being
ascii twice a year, except those on the tropics them-
selves, who are ascii pnly once a year.

Problem XXVI. TAe inhabitants of all places
letiveen the tropics of Cancer and Capricorn, are not
only asciif but amphiscii,- whose noon-shadows are
projected sometimes towards the north, at other times
towards the south.

237. Place the sensible horizon on the equator,
and rectify the globe to the time of the equinox. Art.
220, at which time the equatorial irjliabitants are
ascii at noon, having the sun full east of them all
the morning, and full west all the afternoon.

The eastern point of the sensiiaie horizon wi}l be
^^Ivvays uppermost, or most elevated, as the globe is
moved from wegt to east, till it comes to the strong
brass meridian ; and after it has passed this, the
western point will be most elevated.

The sepsible horizon remaining on the equator,
jrectify the globe the time of the Rummer solstice,

Art. -221, and you will find the north point at noon
will be most elevated ; which plainly shews, that the
itihabitants of the equator will see the sun full north
at that season, and that their shade will be projected
southwards.

2SS. If the globe be rectified to the winter sol-
stice, Art. 224, the south point will be most elevated,
and the .nhab.tants will see the sun on their south
side, which will project their shadows northwards.

239. Heteroscii, are those who live between the
tropics and polar circles, whose noon-shadows are

Those in north latitude have their noon-shadows
projected northwards; the sun at that time being

shadows projected southwards; the meridian sun
always appearing to them in the north.

240 Periscii are those who live within the polar
circles^ the sun going continually round them, their
shadow must necessarily go round them also.

If the sensible or terrestrial horizon be applied to
any of these places, and the globe rectified accord-
ing to the preceding directions, it will shew, that the
sun appears to be more elevated at one time of the
day than at another; and also, which way at all
times the noon and other shadows are cast.

24J. Antoeci are two opposite nations, lying in
or near the same meridian, one of them in north,
the other in south latitude ; they have both the same
longitude, and equal latitude, but on opposite sides
of the equator: they have opposite seasons of the
year, but the same hours of the day.

sides of the globe, in the same parallel of latitude,
having the same seasons of the year, and opposite
hours of the day.

243.nbsp;Antipodes are two nations diametrically
opposite, which have opposite seasons as well as op-
posite hours.

A straight line passing from one to the other
must consequently pass through the center, and
therefore become a diameter of the globe.

These are exemplified by rectifying the globe into
the position of a right sphere. Art. 220, and bring-
ing the nations under consideration to the edge of
the broad paper circle. Thus,

Tlgt;e inhabitants of the eastern parts of Chili are
Antceci to those of New England ; whose Perioeci
live in the northern parts of China, who are also
antipodes to the inhabitants of Chili.

We shall now proceed to exemplify the former
precepts in a few particular problems.

Peoblem XXVII. Tojind all those places on the
globe over whose zenith the sun will pass on any
given day.

244.nbsp;Rectify the terrestrial globe, Art. 21 g, by
bringing the given day of the month, on the bLk-
side of the strong brass meridian, to coincide with
the plane of the broad paper circle, and observe the
elevation of the pole on the other side ; and that
degree counted from the equator on the strong brass
meridian, towards the elevated pole, is the point

over which the sun is vertical. Now turning the
globe, all those places which pass under this point,
have the sun direciK vertical on the given day.

Thus bring the 1 Uh day of May, into the plane
of the broad paper circle, and the said plane will cut
18 degrees for the elevation of the pole, wnich is
equafto the sun's declination for that day ; which
counted or. the strong brass meridian towards the
elevated pole, is the point over which the sun will be
vertical. Now turning the globe round, we shall
find that A.nalagm, one of ,tiie Ladroue islands, the
northern part o. Manilla, the middle ofSiam, a ^-eat
part of Afric, apd St. Anthony one ot the Cape
Verd Isle ,, the southern side of the islands Porto-
Rico and Domingo, and the northern part of the
island of Jamaica, amp;c. have all of them the sun m

Hence wlien the sun's declination is equal to the
latitude of any place inahe torrid zone, the sun will
be vertical to those inhabitants that day.

Probi em XXVIII. To find the swis declination,
and thence the parallel of latitude corresponding
therewith, upon the terrestrial globe.

245. Find the sun's place upon the broad paper
circle for any given day, Art. 98, and seek that place
in the ecliptic line upon the globe ; this will shew
the parallel of the sun's declination amorg the dot-
ted lines, which is also the corresponding parallel of
latitude ; therefore all those places through which
this parallel passes, have the sun in their zenith at
poonon the given day.

Problem XXIX. To find those two days on
which the sun will be vertical to any place between
the tropics.

246.nbsp;That parallel of declination which passes
through the given place, will cut the ecliptic line
upon the glebe in two points, which denote the
sun's place, against which, on the broad paper circle,
are the days and months required.

Problem XXX. The day and hour at any place
being given, to find where the sun is vertical at
that time.

247.nbsp;Let thé given place be London, and time
the nth day of May at 4 minutes past V in the
afternoon.

Rectify the globe to the day of the month. Art.
QJQ, and you have the sun's declination 18 degrees
ilorth : bring London to the meridian, and set the
horary index to XII, turn the globe till the index
points to the given hour on the equator, 4 minutes
past V, then Port- Royal in Jamaica will be under
the 18th degree of the strong brass meridian, which
is the place vk-here the sun is vertical at that in-
stant.

one place being given, to find all those places in
which the sun is then rising, setting on the meridian^
and where he is vp-tical; likewise those places in
which it is midnight, twilight, and darknight, at the
same instant; as well as those places in which the

twilight is beginning and ending-, and also to find
the sun's altitude at any hour in the illuminated, and'
his depression in the obscure, hemisphere.

248. Rectify the globe to the day of the month.
Art. 219, on the backside of the strong brass meri-
dian, and the sun's declination for that day, which is
equal to the elevation of the pole, is given upon the
graduated side of the brass meridian, by its coinci-
dence with the plane of the broad paper circle;
bring the given place to the strong brass meridian,
and set the horary index to XII, upon the equator,
turn the globe from west to east, until the horary
index points to the given time. Then

All those places, which lie in the plane of the
western side of the broad paper circle see the sua
rising, and at the same time those on the eastern

It is then noon to all the inhabitants of those
places under the upper half of the graduated side
of tl.e strong brass meridian, whilst at the same
time those under the lower half have midnight.

All those places, which are then between the up-
per surface of the broad paper circle, and the wire
circle under it, are in the twilight; which begins ta
all those places on the western side that are imme-
diately under the wire circle, to which it is the dawn-
ing of the day ; its end is at all those places in the
plane of the paper circle, on which the sun has just
begun to rise.

The contrary happens on the eastern side; tne
twilight is jquot;st beginning to those places in which
the Tun is setting, and its end is at the place just
under the wire circle.

And all those places which are under the twilight
wire circle have dark night, unless the moon i a-
Vourahle to them.

All places in the illuminated hemisphere have the
sun's altitude equal to their distance from the edge
of the enlightened disc, which is known by fixing
the quadrant of altitude to the zenith, and laying its
graduated edge over any particular place.

The sun's depression is obtained in the same man-
ner by fixing the center of the quadrant at the
nadir.

PuoBLEM XXXII. To find the time of the sun's
rising and setting, ihe length of day and night, on any
day in the year, in any place whose latitude lies be-
tween the polar circles, and also the length of the
shortest day and night in any of those latitudes, and
in ivhat climate they are.

249. Rectify the celestial globe to the latitude of
the given place. Art. isg, bring the artificial sun to
his place in the ecliptic for the given day of the
month ; and then bring its center under the strong
brass meridian, and set the horary index to that XII

Then bring the center of the artificial sun to the
eastern part of the broad paper circle, which in this
case represents the horizon, and the horary index
shews the time of the sun-rising ; turn the artificial
sun to the western side, and the horary index will
shew t;he time of the sun-setting.

Double the time of sun-rising is the length of
the night, and the double of that of sun-setting is
the length of the day.

Thus on the 5th day of June, the sun rises at
3 h, 40 min. and sets at 8 h. 20 min. by doubling
each number it will appear, that the length of this
day is l6h. 40 min. and that of the night 7 h.
20 min.

The longest day at all places in north latitude, is
when the sun is in the first point of Cancer. And,

The longest day to those in south latitude, is when
the sun is in the first point of Capricorn.

Wherefore the globe being rectified as above,
and the artificial sun placed to the first point of
Cancer, and brought to the eastern edge of the
broad paper circle, and the horary index being set
to that XII which is most elevated, on turning the
globe from east to west, until the artificial sun co-
incides with the western edge, the number of hours
counted, which are passed over by the horary ia-
dex, is the length of the longest day ; their comple-
ment to twenty-four hours gives the length of the
shortest night.

250. If twelve hours be subtracted from the
length of the longest day, and the remaining hours
doubled, you obtain the climate mentioned by anci-
ent historians : and if you take half the climate, and
add thereto twelve hours, you obtain the length of
the longest day in that climate ; this holds good for
every climate between the polar circles.

A climate is a space upon the surface of the earth,
contained between two parallels of latitude, so far
distant from each other, that the longest day in one
di tiers half an hour from the longest day in the
other parallel.

The climates are reckoned from the equator to
the polar circle, where the longest day is twenty-

four hours ; from the polar circle towards the pole
the climates are said to increase by a whole natural
day, till they come to a parallel under which the
longest day is fifteen natural days, or half a month,
from this the climates are reckoned by half months,
or whole months, in the length of the artifici;il day,
till they come to the pole iteelf, under which the day
is six months long.,

Prob£km XXXIII. To find all those places
within the polar circles, on which the sun begins to
shine, the time he shines constantly, when he begins
to disappear, the length of his absence, as well as
the first and last day of his appearance to those
inhabitants-, the day of the month, or latitude of
the place being given,

251. Bring the given day of the month on the
backside of the strong brass meridian, to the plane
of the broad paper circle, the sun is just then be-
ginning to shine on all those places which are in
that parallel, just touched by the edge of the broad
paper circle ; and will for several days seem to
skim all around, and but a little above the horizon,
just as it appears to us at its setting; but with this
observable difference, that whereas our setting sun
appears in one part of the horizon only, by them
it is seen in every part thereof; from west to south,
thence east to north, and so to the west again.

Or if the latitude was given, elevate the globe
to that latitude, and on the backside of the strong
brass meridian you obtain the day of the month,
then all the other requisites are answered as
above.

As the two concentric spaces which contain the
days of the month on the back of the strong
brass meridian, are graduated to shew the opposite
days of the year, at 180 degrees distance; when
the given day is brought to coincide with the broad
paper circle, it shews when the sun begins to shine
on that parallel, which is the first day of its ap-
pearance above the horizon of that parallel :' and
the plane of the said broad paper circle cuts the day
of the month on the opposite concentric space,
when the sun begins to disappear to those inhabi-
tants ; thus the length of the longest day is ob-
tained, by reckoning the number of days between
the two opposite days found as above; and their
difference from 305 days gives the length of their
longest night.

252. Elevate the celestial globe to the latitude,
and set the center of the artificial sun to his place
upon the ecliptic line on the globe for the given
day, and bring its center to the strong brass meri-
dian, placing the horary index to that XII which is
most elevated; then turn the globe till the artificial
sun cuts the eastern edge of the horizon, and the
liorary index will shew the time of sun-rising; turn
It to the western side, and you obtain the hour of
sun-setting.

The length of the day and night will be ob-
tained, by doubling the time of sun-rising and
setting, as before.

Pkoblem XXXV. To find the length of the
longest and shortest days in any latitude.

253.nbsp;Elevate the globe according to the latitude.
Art. 189, and place the center of the artificial sun
for the longest day upon the first point of Cancer,
but for the shortest day on the first point of Capri-
corn, then proceed as in the last Problem.

But if the place hath south latitude, the sun is
is in the first point of Capricorn on their longest
day, and in tlie first point of Cancer on their short-
est day.nbsp;, , , . ,

Problem XXXVI. To find the latitude of a
place, in which its longest day may he of any given
length betiveen twelve and tiuenty-four hours.

254.nbsp;Set the artificial sun to the first point of
Cancer ; bring its center to the strong brass me-
ridian, and set the horary index to XII; turn the
globe till it points to half the number of the given
hotirs and minutes ; then elevate or depress the pole,
till the artificial sun coincides with the horizon,
and that elevatiovi of the pole is the latitude re-
quired.

altitude over both places, and the number of de-
grees between them is their distance, which is
reduced to geographical miles, by reckoning 6o to
a degree, or to English miles by reckoning OQ-i to
one degree.

If both places lie under the same meridian their
difference of latitude is the distance required.

If they are in the same parallel of latitude, their
difference of longitude is the distance sought.

Problem XXXVIII. To find all those places
ivhich are at the same distance from a given place.

256. Rectify the globe by Problem xii. Art. isg.
and bring the given place to the strong brass meri-
dian, over which screw the center upon which the
quadrant of altitude turns ; now move the quadrant
round, and all those places that are cut by any one
pomt on the quadrant are equally distant from the
given place.

Problem XXXIX. To shew at one view upon
the terrestrial globe for any given place, the smis
meridian altitude, his amplitude, or point of the
compass, on which he rises and sets every day in
the year.

_ 257. Rectify the globe to the latitude of the
given place. Art. I89, bring that place to the strong
brass meridian, and set the horary index to XII,
screw the quadrant of altitude to the zenith of the
horizon, and bring it to the brass meridian, you
will then at one view see the sun's meridian altitude
on every degree of the sun's declination for the

whole year, cut by the graduated edge of the qu^
drant of altitude, on the dotted parallels ; these
dotted parallels at the same instant also cut the
edge of the broad paper circle now representing the
horizon, in the point of the compass or amplitude,
on which the sun is seen to rise on the east, or t®
set on the west side of the horizon, for every degree
of declination throughout the year.

If you trace any of those parallels to the ecliptic
line, you have the sun's place when he is upon that
declination, and thence the day and month upon the
horizon.

Also, the knowledge of the sun's place in the
ecliptic line, shews the sun's declination for that
time amongst the dotted parallels.

Problem XL. To shew at one view upon the.
terrestrial globe the length of the days and nights at
any particular place, for all times of the year.

258. Rectify the globe to the latitude of the
place. Art. I89, and the broad paper circle will
represent the horizon: and the upper part of the
dotted parallels of declination, which are here
also parallels of latitude, will represent the diurnal
arches.

Whence we may obtain the number of hours
each of them contains, which is the solution of the
Problem. To illustrate which,

Elevate the globe to the position of a right
sphere, Art. 214, and you will, with one glance of
the eye, see that all the dotted parallels of decli-
nation, as well as the equator itself, are cut by the
horizon into two equal parts.

Therefore the inhabitants on the equinoctial line
have their days and nights twelve hours long; that
is, the sun is never more nor ever less than twelve
hours above their horizon, during his apparent pas-
sage from the tropic of Cancer to the tropic of Ca-
pricorn, and thence to Cancer again.

All the fixed stars have the same apparent motion
to the equatorial inhabitants ; that is, they rise and
set, continue above, and are depressed below, the
horizon of any place upon the equator, exactly
twelve hours.

Raise the north pole of the globe a few degrees
of latitude at a time, and you will seethe diurnal
arches will increase in length, until the pole is
elevated to 664- degrees above the horizon : then
the parallel of the sun's greatest declination will
be as far from the equator as the place itself is from
the pole ; and this parallel is the tropic of Cancer,
which will just touch the horizon in the north
point.

And on the contrary, we may observe, that the
southern parallels of declination continually shorten,
as the northern ones lengthen, until they come to
the tropic of Capricorn.

Rectify the globe to the latitude of London 514-
degrees north : when the sun is in the tropic of
Cancer, the day is about l6i hours; as he recedes
from thence, the days shorten, as the length of the
diurnal arches of the parallels shortens, until the
sun comes to Capricorn, and then the days are at
the shortest, being of the same, length with the
nights, when the sun was in Cancer, viz. about 74.
hours.

polar circle, and you will find, when the sun is in
Cancer, he touches the horizon on that day without
setting, being completely twenty-four hours above
the horizon : and when he is in Capricorn, he
once appears in the horizon, but does not rise for
the space of twenty-four hours ; when he is upon
any other parallel of declination, the days are longer
or shorter, as that parallel is nearer to, or farther
from, the equator.

Elevate the globe to the latitude of 80 degrees
north, at which time let the sun's declination be
10 degrees north, he then apparently seems to turn
round above the horizon without setting, and
never sets from this point to Cancer, until in his
return, after he has again passed this parallel of
declination.

In the same manner, when his declination is
10 degrees south, he is just seen at noon in the
horizon, and disappears from that time in his
southerly motion, till his return to the same point.

Elevate the north pole to QO degrees, or in the
zenith, then the globe will be in the position of a
parallel sphere, (Art. 210,) and the equinoctial line
will coincide with the plane of the horizon : con-
sequently all the northern parallels are above, and
all the southern parallels below the horizon ; there-
fore the polar inhabitants, if any there be, have
but one day and one night throughout the year;
their dav, when the sun is in his northern ; and
their night, when he is in his southern, de-
clination.

This method of rectifying the globe for north,
latitude holds good in south latitude also, by ele-
vating the south pole.

PiiOBLEM XLI. To Jind what constellation any
remarhahle star, seen in the firmament, belongs to.

259. Bring the snn's place in the ecliptic for
that day to the strong brass meridiari, and set the
horary index to that XII which is most elevatod,
the celestial globe being rectified to the latitude,
turn the globe till^ it points to the present hour ;
and by the help of the mariner's compass, and at-
tending to the variation, which at London is between
23 and 24 deg. from the north, westward, set the
north pole of the globe towards the north pole of

The star upon the globe, (if yon conceive your-
self in the center,) which directs towards that
point in the heavens, in which the star you want to
know is seen, is the star required.

At the same time, by comparing the stars in the
heavens with those upon the globe, the other stars
and their constellations may be easily known;
whereby you will be enabled, any star-light night,
to point out many of those stars called correspond-
ents to various places on the earth.

Problem XLII- To find at what hour any
hnown star passes the meridian on any day in the
year.

260. Rectify the globe to the latitude, (Art. I89,)
and set the artificial sun to his place in the ecliptic:
bring its center under the strong brass meridian,
and set the horary index to XII ; then turn the
globe till the star comes to the meridian ; and the

horary index will point upon the equator to the
hour on which that star will be upon the south part
of the meridian.

If you turn the globe on till the center of the
artificial sun is under that graduated side of the
brass meridian, which is below the elevated pole,
all those stars, which are then cut by that side of
the meridian above the said pole, will pass the me-
ridian at midnight.

Problem XLIII. To Jind on ivhat day of the
year any star passes the meridian at any proposed
hour of the night.

261. Bring the star to the strong brass meridian,
and set the horary index to the proposed hour;
then turn the globe till the index points to XII,
and that degree on the ecliptic, which is cut by the
meridian, is the sun's place, against which, in the
kalendar upon the broad paper circle, is the day of
the month.

262. We shall solve this problem for the time
of the autumnal equinox ; because that intersection
of the equator and ecliptic will be directly under
the depressed part of the meridian about midnight;
and then the opposite intersection will be elevated
above the horizon : and also because our first me-
ridian upon the terrestrial globe passing through
London, and the first point of Aries, when both
globes are rectified to the latitude of London, and

to the sun's place by Problem xii. Art. ISQ, 102,
and the first point of Aries is brought under the
graduated side of each of their meridians, we shall
have the corresponding face of the heavens and the
earth represented, as they are with respcct to each
other at that time, and the principal circles of each
sphere will correspond wifh each other.

The horizon is then distinguished, if we begin
-from the.north, and count westward, by the follow-
ing constellations : the hounds and waist of Bootes,
the northern crown, the head of Hercules, the
shoulders of Serpentarius, and Sobieski's shield;
it passes a little below the feet of Antinous, .md
through those of Capricorn, through the Sculptor's
frame, Eridanus, the star Rigell in Orion's foot,
the head of Monoceros, the Crab, the head of the
little Lion, and lower part of the great Bear.

The meridian is then represented by the equi-
noctial colure, which passes through the star
marked in the tail of the little bear, under tha
north pole, the pole star, one of the stars in the
back of Cassiopea's chair marked (3, tlie head of
Andromeda, the bright star in the wing of Pegasus
marked f, and the extremity of the tail of the
whale.

That part of the equator, which is then above
the horizon, is distinguished on the western side
by the northern part of Sobieski's shield, the
shoulder of Antmous, the head tind vessel of
Aquarius, the belly of the western fish in Pisces;
it passes through the head of the whale, and a
bright star marked ^ in the corner of his mouth,
and thence through the star marked ^ in the belt of

That half of the ecliptic which is then above the
horizon, if we begin from the western side, pre-
sents to our view Capricornus, Aquarius, Pisces,
Aries, Taurus, Gemini, and a part of the constella-
tion Cancer.

Tlie solstitial colure, fmm the western side,
passes through Cerberus, and the hand of Her-
culcs, thence by the western side of the consrella-
tion Lyra, and through the dragon's head and
body, through the pole point,under the polar star,
to the east of Aanga, through the star marked r,
in the foot of Castor, and through the hand and

The northern polar circle, from that part of the
ineridian under the elevated pole, advancing to-
wards the west, passes through the shoulder of the
great bear, thence a little to the north of the star
marked a in the dragon's tail, the great knot of
the dragon, the middle of the body of Cepheus,
the northern part of Cassiopea, and base of her
throne, through Camelopardalus, and the head of the
great bear.

The tropic of Cancer, from the western edge
of the horizon, passes under the arm of Her-
cules, under the Vulture, through the goose
and fox, which is under the beak and wing of the
swan, under the star called Sheat inarked |3 in Pe-
gasus, under the head of Andromeda, and through
the star marked lt;p in the fish of the constellation
Pisces, above the bright star in the head of the
ram inarked through the Pleiades, between the

horns of the bull, and through a grOup of stars at
the foot of Castor, thence above a star marked
between Castor and PoUux, and so through a part
of the constellation Cancer, where it disappears by
passing under the eastern part of the horizon.

The tropic of Capricorn, from the westein side of
the horizon, passes through the belly, arid under
the tail of Capricorn, thence under Aquanus, through
a star in Eridanus marked c, thence under the belly of
the whale, through the base of the chen;ical fur-
nace, whence it goes under the hare at the feet of
Orion, being there depressed under the horizon.

The southern polar circle is invisible to the inha-
bitants of London, by being under our horizon.

TO FIND THE TIME OP THE SUN S ENTEY INTO THE
FIRST POINT OF LIBRA OR ARIES ; AND THENCE
THAT POINT IN THE EaUATOR TO WHICH THE
SUN is VERTICAL AT EITHER OF THOSE TIMES.

263. This requires the knowledge of a meridian
that shall pass through that point in the equator, to
which the sun is vertical at the times of equinox;
but as this point is variable, a fixed meridian must
be first obtained.

In Anno Domini 1753, the late Rev. Dr. Bradley
observed the sun to enter Libra September 22d.
]0h. 24 min. afternoon, new stile, at the Royal
Observatory at Greenwich.

As the earth's diurnal motion is from west to
east, it causes all places to the east of any other
place to pass first under the sun ; therefore when
the meridian of Greenwich passed under the sun

that day, he was not then arrived at the intersecting
point of the earth's equator and celestial ecliptic,
but wanted JOh. 24 min. which is equal to 156
degrees.

Whence the fixed or first meridian sought is thus
obtained, and lies lOh. 24 min. in time, or 156
equatorial degrees west of the Royal Observatory at
Greenwich.nbsp;v

This meridian is marked by a dotted line on our
new terrestrial globe; it passes through the Great
Pacific sea, and crosses one of the Isles of St. Ber-
nard, and the Isles des Mouches.

The next thing to be considered is the nearest
mean length of a tropical year, which is a deter-
minate space or interval of time between the sun's
apparent passage from, one point of the ecliptic,
until he returns to the same point again, or from
one equinox to the same again, be it either vernal
or autumnal.

We take for our radix the autumnal equinox.
Anno 706 of the Julian period, which we call
Anno Mundi O, and compute from Thursday, Oct.
25th, oh. O min. or noon, the sun being then
supposed to be in the first point of Libra on the
meridian before mentioned, and vertical to that
point of the equator, which lies 156 degrees west
of Greenwich.

And also in the meridian of Greenwich, Oct.
25tb, lOh. 24 min. upon the 298th day from the
calends of January.

The tropical year thus reckoned exceeds the
Egyptian year 5h. 49 min. and is but 11 minutes
short of the Julian year ; so much being annually

allowed for the retKocession of the equinox, con-
sequently the mean length of a tropical year, is
365 d. 5 h. 49 min.

We are induced to measure time by this quantity^
because astronomers unanimously agree, that the
earth passes through all the signs of the ecliptic, so
as to complete the circle in 365 d. 5h. 49 min.

See the respective tables of Rudolphus, Tycho
Brahe, Cassini, Sir Jonas More, Mr. Flamsted,
Dr.' Halley, Mr. Meyer, and Mr. Maskclyne;
whereby it will appear that

completes the circle, and not one second of time
more or less can be produced from any tables
extant.

And the difference between calculating downwards
from the epoch A. J. P. 706, and calculating back-
wards in the modern practice, from the various epochs
in the most celebrated tables, is, that in those last

The equinoxes resiularly fall every year 5h. 49min.
later in the day, than in the preceding year, and at
the end of every annual motion of the earth, the
equinoctial intersection changes its meridian west-
ward of that in which it fell the year before, just
87 deg. 15 min.

264. First, Find the number of years from the
radix : if the given year is before the Christian
j^ira, sitbtract it from 4008; the remainder is
the year from the radix.

Secondly, If any year since the Christian ^ra be
given, add it to 4007, their sum is the year from
the radix.

Thirdly, Collect the days, hours, and minutes of
retrocession and autumnal equinoxes from the
table, according to the number of years from the
radix, in thousands, hundreds, tens, and units ;
add these into two sums, the first will be the retro-
cession, the second the time of the equinox in
that meridian, \vhich lies 156 degrees west of

Greenwich Observatory ; to which add lOh. 24tn.
and yoa obtain the time at Greenwich.

This method wiil serve for any other meridian
also, if you add its difference in time from the
fixed meridian.

Solar tropical years thus reckoned begin and end
at the autumnal equinox, and all Julian years begin
and end at the kalends of January.¹

In comparing solar tropical years,with Julian
years, by which we still compute time, observe,
that the last nine months of any solar tropical year
answer to the first nine months of that Julian year
with which it is compared; and that the first three
months of the next succeeding tropical year answer
to the three last months of that same Julian year
with which it is compared.

The 2g8th day from the kalends of January,
which was, Thursday in the 706th year of the
Julian period, the sun entered Libra at noon ; at
which instant it was lOh. 24min. past noon at
Greenwich.

In all calculations of autumnal equinoxes, we take
the same 2g8th day, or October 23th m the radical
year O, for our epoch.

And to gain the day of the month in which the
equinox must happen since the radix.

Add the number of days, hours, and minutes in
the retrocession, to the days, hours, and minutes
of the equinox in the fixed meridian, and you obtain
the Julian days and hours from the radix.

1nbsp; The kalends of Jannaiy begin from the noon of the pre-
ceding day i that is, from the noon of the day before the first of
January.

Add the epoch 298 to the days of the tropical
reduction, and'^ from their sum subtract the entire
days of the Julian reduction, the remainder is the
number of days from the kalends ot January old
stile ; add thereto eleven days, and you obtain the
number of days from the said kalends of January
new stile; from which if you deduct the nearest
less number in the table of months (which numbers
express the last days of each month) the residue is
the day of the succeeding month.

But when the sum of the Julian reduction con-
tains eighteen hours above entire days, it is a
bissextile year; then one day more must be added
to the entire Julian days before the subtraction is
made.

When Jthere are no hours in the Julian reduction,
that is the first year after a bissextile ; if six hours,
the second ; if twelve hours, the third ; and when
eighteen hours above entire days, it is the bissextile
year.

And when the last result exceeds 12 hours, add
J to the days, and subtract. 12 from the hours, and
you change the time from astronomical to the civil
reckoning.

To gain the time of the equinox on any other
meridian, add the difference of meridians to the
time found in the first meridian. Thus for London
or Greenwich we add 10 h. 24 min.; for Paris,
10h. 33 min. 20 sec.; for Alexandria in Egypt,
'12h. 25 min. amp;c.

7 ; if O remains, it is Thursday ; if 1, Friday ; 2,
Saturday; and 3, Sunday; and so on to 6, which
is Wednesday, as in the table ef week-days.

206. First find the autumnal equinox for the
same year in which the vernal equinox is required ;
and from it subtract 186 deg. 11 h. 5l min. which
is the distance in time from Aries to Libra; their
difference will be the time of the vernal equinox
required. •

The day of the month, and week-day found as
above, we obtain the literal character for that day
as follows i

In the table of months stand the literal characterSj
that are placed against the first day of each month in
any common almanack.

And whatever letter stands against the first day
of any month, the 8th, I5th) 22d, and 29th days
of that month, are all characterised with the
same.

the day of the month and WEEK-day given, to
find its LITERAL character and dominical
letter for that year.

The literal character for the first of September,
is F ; so is the 22d, and Tuesday in the pre-
sent question. Look on the circle of week-day
characters, call F Tuesday, G Wednesday, A
Thursday, and so on to Sunday which falls upon
D the last of the two dominical letters for that
year, serving from the intercalary day to the year s

Therefore the two dominical letters for the bissex-
tile year 1772 are-E D new stile.

The'literal character for the 1st of March is D,
so is the fifteenth, and the 20th being 5 days more,
f we count from D, which happens to be the do-
minical letter, to E Monday the l6th, we shall find

If the dominical letters were required'for old
stile, m these examples the first would be the nth
of September 1772, whose literal character is
thus found: F the 1st day of September, and also
tne 8th, G the gtb, A the 10th, and B the
nth and by the following calculus Tuesday,
^herefore AC are the dominical letters old J,]

268. Required the autumnal equinox at Alex-
andria in Egypt, in the 146th year before the
Christian ^Era.

269. To find the time of the vernal equinox in
the same year, and at the same place.

Frgm the autumnal equinox, Sept. 26, a kal. Jan. 269 12 23
subtract the distance in time between T and £!: 186 11 51

the sun in the 1st point of Aries at Alexandria \
before Christ 146 years, Marchnbsp;J

^ , , 572 2109318nbsp;18 0
Jul. days 1—319 because of the 18 h. bissextile year.

172. Having found the autumnal and vernal
equinoxes for the bissextile year, A. D. 1768, we
obtain them for the three following years by con-
tinually adding thereto 5 h. 49 min. Thus

Tropical days 735 to the tropical time 2110735 14 SI
,nbsp;^«onbsp;retrocession-1-nbsp;44 J

From the autumnal equinox, Sept. 22, ^ kal. J™- 265 0 55
^nbsp;dist. from Aries to Libra 186 11 51

We find the two equinoxes in the three next sue
ceeding common years, as in the preceding example,
by the continual addition of 5 hours, 4Q minutes.

By this method of calculation, we avoid any mis-
take that might happen, with respect to the interca-
lary day; because we find the autumnal equinox
first, and thence the vernal eqoinox, which always
falls after the intercalary day, and also because tro*
pical tinae has no bissextile years.

275. Divide the seconds of time by 4, the quo-
tier)t is minutes, and remainder so many times 13
seconds.

Divide the minutes by 4, the quotient is degrees,
pnd remainder so many times 15 minutes.

Reduce llh. 35 min. 27. sec. of time into de,
grees, minutes, amp;c. of the equator.

276. Divide seconds by 15, the quotient if
seconds, and remainder so many times 4 thirds.

Divide minutes by J 5, the quotient is minutes,
and remainder so many times 4 seconds.

Divide the degrees by 15, the quotient is hours,
and remainder so many times 4 minutes.

Reduce 173 deg, 51 min. 45 sec. of the equator,
into hours, minutes, and seconds of time.

We are now prepared to solve the latter part of
the last problem, which is as follows.

which it is noon at the time of annbsp;equinox, as well
as that point upon the equator, to which the sun is
vertical at that time.

111. Having found the time of an equinox by
the preceding, or any other method of calculation.

as in the first example, we find the sun entered the
first point of Aries, at Alexandria in Egypt, March
24th, oh. 32 min.

Therefore bring Alexandria under the graduated
side of the strong brass meridian, and set the ho-
rary index to XII upon the equator; turn the
globe from west to east until 32 minutes of time,
or 8 degrees of the equator, have passed under
the horary index, where stop the globe; then all
those places under the said graduated side of the
Strong brass meridian will have noon, and that de-
gree of the equator, which is then under the meri-
dian, is the point to which the sun was at that
instant vertical, and is the intersecting point of the
equator and ecliptic, or that terrestrial meridian
which governs the passage of the first point of Aries
for that year.

the VERNAL EftUINOX, A.D. 1772, WILL FALLON
THE iqth DAY OF MAR'CH, AT 13 H. 4 MIN. WHICH
REDUCED TO the DEGREES AND MINUTES OF THE
EaUATOR, IS ettual to 196 degrees.

278. Bring London to the strong brass meridian,
and set the horary index to XII, (in this case the
graduated side is the horary index,) turn the globe
from west to east until 13 h. 4 min of time, or 196
degrees of the equator, have passed under the horary
index, where stop the globe; the ]96th degree of
the equator will now be found under the graduated
side of the brass meridian, and is that point on which

the sun will be vertical at noon; at which instant
it will be 13 h. 4 min. past noon at London or
Greenwich.

The meridian passing through this point, will be
seen to pass a little eastward of Kamkatska through
the Pacific Sea across the Island Dicerta, thence
east of the isle Tanmago, and through the western
part of New Zealand ; all which places will have
noon at the instant of that vernal equinox.

THE AUTUMNAL EOUINOX, a. B. 1772, WILL HAP-
PEN SEPTEMBER 22, O H. 55 MIN. AT LONDON,
THE 55 MIN. BEING EQUAL TO 13 deg. 45 MIN.
of the equatok.nbsp;/

279. Bring t^ondon to the graduated side of the
strong brass meridian, and set the horary index to
XII, turn the globe from west to east, until 53
minutes of time, or 13 deg. 45 min. of the equator
have passed under the horary index, where stop the
globe ; here, as in the last example, the 13th degree
and 45th minute is that point upon the equator to
which the sun is vertical, and the meridian passing
through this point, lies under the graduated side of
the strong brass meridian ; which passes over the
middle of Greenland, and through the Atlantic
Ocean to the east of TenerifFe, a little to the west
of Ascension Island, and thence through the Eihio-
pic Ocean, at which places it will be noon at the
time of this autumnal equinox.

OF THE NATUBAI. AGREEMENT BETWEEN THE CELES-
TIAL AND TERRESTRIAL SPHERES ; OR, HOW TO
GAIN A PERFECT IDEA OF THE SITUATION AND
DISTANCE OF ALL PLACES UPON THE EARTH, BY
THE SUN AND STARS,

280, That part of the firmament which is in the
zenith of London is perpendicular to half the
globe of the earth ; which half comprehends almost
gll the habitable land of Europe, Asia, Africa, and
America, with their coasts, capes, land, and seas ;
since under the other celestial hemisphere, which
we do not see at the same time, there are only very

The inhabitants of Great Britain and Ireland
nearly see the same half of the firmament adorned
with stars and planets, which at all times supply
the place of an immense map of the world ; and
shew our terrestrial hemisphere by the stars, convey-
ing the correspondent marks of the two continents

The sun, by his apparent daily motion, seems to
describe a kind of spiral, in passing from one tropic
to the other and back again, continually changing
his declination, and every day describing a difFerent
parallel, Art. 371.

Forty-seven of these diurnal parallels are drawn
on our new terrestrial globe, Art. 177, 178, between
the tropics of Cancer and Capricorn, representing
the parallels for every degree of the sun's decli-
nation.nbsp;• 1 •

change in the sun's declination, to go back to Art.
185, and read from thence to the ISQth Art.

Which being done, it will be easy to conceive,
that the sun being in any one of these parallels, must
necessarily cast his perpendicular rays that day upon
the heads of the inhabitants of those places through
' which that parallel of declination passes.

Nole. Although these 47 parallels are here called
parallels of declination, they are also parallels of
latitude upon the terrestrial globe.

The sun being perpendicularly over any one of
these distant cities or principalities, at the time of
our observation, if a plumb-line be held up be-
tween the observer and the sun, so as to pass
through or before the sun's center, it will cut the
visible horizon in a point, that will fix the bearing
or passage in a right line from the observer to that
place, upon which the sun is then vertical.

A point thus noted upon the visible horizon may
be seen at all times, and represent the same bearing,
independent of the sun and stars, and that in such
a conspicuous manner as to render this knowledge
always entertaining, useful, and interesting.

The stars at night perform the same more copi-
ously, by pointing out to our senses the distance of

many remote provinces, at one and the same instant
of time, from our own zenith.

Hence we are in possession of a most extensive
field, wherein we may correct and improve our

PiIoBlem XLVI. To find the solar correspond-
ence to a fixed point upon the earth, when the sun is
seen by an observer situated upon any other point of
its surface.

281. Let the observer be in London (or in any
of the country places within thirty miles of it)
upon the 10th day of March, at 10 minutes past
XI o'clock in the morning.

Rectify the globe, by bringing the 10th of March,
engraved on the back of the strong brass meridian,
to the plane of the broad paper circle; find the
sun's place,- against the day of the month in the
kalendar, which will be about 20deg. 10 min. in
Pisces; seek these degrees and minutes in the
sign Pisces upon the ecliptic line on the globe,
and you will find it fall upon the fourth parallel of
south declination : to all the inhabitants on this
parallel, the sun will be vertical that day. Now
bring llh. 10 min. on the equator to the gra-
duated side of the strong brass meridian, and

you will find it cut the fourth southern parallel
upon the city of Loango, on the western coast of
Africa.

Therefore if you look at the sun 10 minutes
past XI in the morning at London, you will tbea
see him at the instant he is directly over thé heads
of the inhabitants of the city of Loango in Africa;
at the same time, your ideas are made sensible of
the comparative distance, which you see in the
firmament between the zenith of London, under
which you stand, and the sun, which is then in
the zenith of Loango ; also if at the time of your
observation, you cause a plumb-line to be held up
between you and the center of the sun, and cast
your eye down towards the most distant part of.
your sensible horizon, the plumb-line will cut a
point thereon, which, if remembered, will always
shew you the true bearing or point of the compass,
in a direct line from your situation,, to that of
Loango.

Elevate the globe to the latitude of London,
that the broad paper circle may represent your
horizon ; screw the nut of the quadrant of alti-
tude in the zenith, that is, upon 51 deg. 32 miu.
counted from the equator towards the elevated
pole, bring London under that point, and lay the
graduated edge of the quadrant upon Loango,
which will cut the bearing 15 degrees, reckoned
from the south towards, the east, or between the
points S. E. and S. by E. ; now separate the
quadrant from the globe, and lay its graduated
edge upon i/oango and Loudon, so that the be-

ginning of the graduation may he upon one of the
places, then the other will cut 50 degrees, which
is equal to 3360 geographical miles, or 38^2
English miles, the distance between London and
Loango.

To elucidate this example, we shall trace the
sun's verticity over that part of this day's parallel of
declination, which is included between the rising
and setting sun at London for that day.

Imagine, as we have before supposed, an image of
the sun to be painted upon the ceiling of the roomj
directly over the terrestrial globe.

Let the globe be rectified to the 10th of March,
place the center of the artificial horizon upon
London, and bring it into a coincidence with the
west side of the plane of the broad paper circlcj
now representing the edge of the earth's illuminated
disc; we shall then have the position of the earth
with respect to the sun for that day; when the in-
habitants of London will be leaving the twilight,
and passing into the first point of day, or sun-rising,
at about 18 minutes past VI in the morning, cut
by the graduated side of the strong brass meridian
on the hour line under the equator; at this time,
the meridian will likewise cross the fourth parallel
of south declination, in the Indian ocean, between
the island of Sumatra and the Maldive Isles; if
we look upon the sun that morning at the instant of
his rising, we shall see that his distance from our
zenith will then be QO degrees, he being in our ho-
rizon, which is equal to 5400 geographical Or 6l55
English miles, the distance from London to that
part of the Indian Sea ; turn the globe from west
to east, until 8h. 12 min. are under the horary

index, which in this case is the strong brass meri-
dian, and it will cut the isle Macarenhas, to which
the sun will then be perpendicular; at J- past IX
he will be perpendicular to the coast of Zanguebar,
his central ray passing between Monibacca and
Pemba; thence it passes over the kingdoms of
Monomugi, Macoco, Congo, amp;c. until he. is per-
pendicular to the city of Loango, upon the western
coast of Africa, at lib, 10 min. the same morn-
ing ; immediately after which, his perpendicular
rays are absorbed in the Ethiopic Ocean, over
which he is 3 h. 22 min. in passing to Fort St.
Lucar, on the eastern coast of America, at 32 mi-
nutes past II in the afternoon ; thence he proceeds
to send forth his perpendicular rays over the heads
of the inhabitants of Brazil, across the vast country
of the Amazons and Peru, in the decline of our
evening, until his arrival over Cape Blanco on tlie
western side of South America, a little before he
sets to the inhabitants of London, which is about
40 minutes past V o'clock.

282. Every rectification being observed as in the
first example; Q. What is the place upon which
the sun is a correspondent at 48 minutes past VI in
the evening of the 18th of May, the sun's place
being about l/deg. 40 min. in Taurus, or nearly
vertical to the 17th parallel of north declination on
that day ? Turn the globe from west to east, until
London has passed the strong brass meridian, and
stop vvhen its graduated side is directly over
48 min. afternoon, and it will cut the 17th

parallel of north declination, the city of Acapulco
on the western coast of Mexico, over which the
snn will then be vertical.

283. Let the oBserver be at Cape Clear on the
western coast of Ireland, on the l6th day of July,
at 54 minutes past VIII in the morning.

The sun's place being in the 24th degree of Can-
cer, which on the globe falls upon the 21st parallel

Bring Cape Clear to the graduated side of the
strong brass meridian, and set the horary index ta
XII, turn the globe till 8 h. 54 min. amongst the
morning hours are under the horary index, and you
will find the graduated side of the strong brass me-
ridian to cut the 2lst parallel of north declination
upon Farrat in Nubia, on the western coast of
the lied Sea.

184. Let the observer be at Rome on the 20th
day of November, at 37 minutes past x in the
morning.

The sun being about 284- degrees in Scorpio,
which falls to the southward of the 20th parallel of
south declination,

brass meridian, and set the horary index to XII,
turn the globe to have loh. 37 min. under the
horary index, and the said graduated side will then
cut, under the 20th parallel of south declination,
the city of Sofalo ia the kingdom of Quiteri, to
the south of Monomotapa, on the eastern coast of
Africa.

We apprehend these four examples are suf-
ficient to give the reader a clear idea of the solar
correspondents to all places within the torrid zone,
and to enable him to discover some thousands
more.

Although we can have but one solar correspond-
ent at the same time, yet, as in the first example,
we can trace him through his diurnal parallel for
every hour and minute of the day, and so also
upon every day in the year.

Nothing can be easier or more intelligible than
this method of improving the mind, by represent-
ing to the eyes the distance from our own zenith
to that of every spot of land and sea within the
tropics; when at every single observation we have
it also in our power to note the bearing of each of
these places upon our visible horizon, which may be
referred to at all times, when the sun is not in that
parallel.

Let us now change the scene, and proceed from
the consideration of the sun, to that of the stars ;
which will present to our view a copious field of
geographical knowledge; many of these may be
seen at one and the same instant of time, when
they are in the zenith of so many different places
upon-the earth, and then immediately afterwards re-

285. The knowledge of the celestial correspond-
ents discovers a new system of astronomical geo-
lt;Traphy. The perfect agreement between the ce-
lestial and terrestrial spheres constitutes this ys-
tem ; which may with very little trouble be under-
stood, by making the study of one a guide to the
knowledge of the other ; the object of this corres-
pondeHce is the continual variation between the
parts of the celestial and terrestrial spheres.

Geography alone being easier than astronomy, has
generally a particular place in the education of
young students, who seldom leave their juvenile
studies without gaining some idea of the four
quarters of the world, a slight notion of the situa-
tion of places with respect to each other, and a
sketch of the principal empires ; but generally
without any application to the terrestrial, and
scarce ever a comparison of that with the celestial
globe; and without feeling a lively curiosity to be-
come acquainted with these necessary and improving

To facilitate the study of geography, it has al-
ways been necessary to lay maps and charts before a
pupil, which are generally separate plans of difFerent
countries. But what idea do these alFord of the
vast extent of the earth, of its spherical form, or of
the proportionable distances, real bearings, kc. of
the empires, kingdoms, and states on the habitable,
part of our terrestrial globe I

How much more intelligible and just are the
proportionable distances of the fixed stars, when
compared with the natural distances of the several
places upon the earth, over which they dart their
perpendicular rays ; thereby constituting this new
system of astronomical geography, by ocular de-
monstration ? They are faithful testimonies of the
vast extent of the universe, and they declare the
distance, bearing, and situation of all places upon
the earth.

By these means, together with the assistance
of maps and charts, such a copious and clear idea
of geography will be attained, and its natural prin-
ciples so firmly established, as never to be erased.

The consequences to be drawn from these prin-
ciples are entirely in favour of the harmony between
the celestial and terrestrial spheres.

186. This point determines the apparent daily
motion of the heavens, and fixes the continual dif-
ference in the course of the sun and stars.

The knowledge of that particular point on the
terrestrial equator, where its intersection with the
celestial efcliptic happens to fall at the time of a
vernal equinox, points out that place npon the earth
to which the sun is vertical at that time ; and from
the knowledge of this we obtain the time of its pas-
sage over any meridian upon the globe, for every
day of the year.

The conformity of the degrees of right ascension,
with those of terrestrial longitude, happens but upon
one moment of the 24 hoûrs, in a natural day ;

when the first point of Aries is on the meridian of
London, the first degree of right ascension is on
this meridian also ; and the signal to confirm this
is, when a star of the second magnitude marked y
near the extremity of the wing of Pegasus, is upon
the meridian ; at that instant, the equinoctial colure
will he upon the meridian also; for this colure
passes through the first point of Aries and that star.
This is the moment, in which each of the 360
degrees of right ascension in the celestial sphere,
is perpendicular to every like degree of terrestrial
longitude ; at which time there is a perfect parallel-
ism and perpendicular correspondence of all the cir-
cles, points, and lines, in both spheres.

To this we have paid a particular regard, in the
construction of our new globes, by numbering the
degrees on the equator of the terrestrial globe,
with an upper row of figures in the same direction,
as those of right ascension are numbered upon the
celestial globe.

If from that instant of time, when the star y of
Pegasus is upon the meridian, we conceive the stars
to be immoveable, and that we, together with the
globe of the earth, are turned from west to east
vipon the equatorial axis, we shall pereeive our own
meridian to pass successively under every degree and
star on the celestial equator,

287. And that the reader may thoroughly under-
stand what is meant by this uniformity in the two
spheres, let him imagine the celestial globe to be
delineated upon glass, or any other transparent mat-
ter, which shall invest or surround the terrestrial
globe, but in such a manner, that either may be
turned about upon the poles of the world, whilst
the other remains fi;ced_; and suppose the first point

of Aries, on the investing globe, to be placed upon
the first point of Aries on the terrestrial globe,
(which point is in the meridian of London,) they
will then represent that situation of the heavens
and the earth we have been just describing, on
that instant when the first point of Aries is upon
the meridian ; and then every star on the celestial
will lie upon every particular place of the terrestrial
globe, to which it is a correspondent; each star will
then have the degree of its right ascension directly
upon the corresponding degree of terrestrial longi-
tude ; their declination will also be the same ,with
the latitude of those places upon which they lie.

Now if the reader conceives the celestial invest-
ing globe to be fixed, and the terrestrial globe to
be^ gradually turned from west to east, he will
readily understand, as the meridian of London
passes from one degree to another under the in-
vesting sphere, that every star thereon becomes a
correspondent to another place upon the earth ;
and so oi?, until the earth has completed one di-
urnal revolution, or till all the stars, by their ap-
parent daily motion, have passed over every mCr-
ridian of the terrestrial globe. Hence arises an
amazing variety in the harmony of both spheres.

If the sun and a star pass the meridian on any
particular day, the next day the star will precede
the sun about tour minutes ; in two days the ac-
celeration of the star with respect to the sun will be
about8 minutes; in 4 days, l6 minutes, in 8 days, ,
32 minutes, and in 15 days the apparent motion of
the star will be accelerated one hour ; whilst the
sun, with respect to the star, will seem to be re-
tarded one hour ; in one month the star will be

two hours before the sun, in three months six hours,
in six months tweh^e hours, and in one year twenty-
four hours.

So that a year after the sun and star have crossed
the meridian together, they will meet again nearly
at the same time; but the star, instead of seeming
to make 305 revolutions, will have made 366, one
more than the earth to the sun in a year.

The right ascension of the first point of Aries,
is the complement of the sun's rig-ht ascension to
36o degrees of the equator, or to the 24 hours of
a natural day: this is the point from which, the
right ascension of the sun, stars, and planets is al-
ways reckoned.

The reader will please to observe, that in spring
and summer, the first degree of right ascension,
which is the first point of Aries, comes to the
meridian with us before noon ; there are no stars
then visible in the night, but those which follow
the first point of Libra ; that is to say, those stars
which have more than 180 degrees of right as-
cension : in autumn and winter those stars are
visible in the night, which follow the first point
of Aries, having less than 180 degrees of right
ascension.

Observe also, that the interval between the pas-
sage of the first point of Aries over the meridian
of any place, and that of the first point of Libra
over the same meridian, is not 12 complete hours,
but only 11 hours 58 minutes, to which attention
must be paid, lest these two minutes should be
n^istaken.

By the passage of the stars over the meridian,
we are taught the knowledge of those degrees cif

the equator, which are then rising and setting ;
for that degree which is setting preoedes that on
the meridian QO degrees, or six hoars; and 180
degrees or twelve hours that which is rising ; and
that degree of the equator, which is on the me-
ridian under the elevated pole, is 180 degrees
distant from that point of it which is passing the
meridian.

Problem XLVII. To find the time of the right
ascension of the first point of Aries upon any me-
ridian.

388. We have already shewn by. an easy calculus,
how to find the times of equinox to any meridian,
but we have not yet shewn their application to thé
right ascension of the first point of Aries.

The diurnal difference of right ascension, at the
time of a vernal equinox, is 3 min. 38 sec. which
we have formed into a table, intitled, quot; The horary
difference in the motion of the first point of Aries
at the time of a vernal equinox to which is an-
nexed, quot; A table of the difference of the passage of
the first point of Aries over the meridian for every
day in the year.quot;

289- Having found the time of any vernal
equinox, and transferred it from the fixed to your
own meridian by the addition of your meridian
distance.

Take out of the table of horary differences, the
motion answering to the hours and minutes of the

time of the vernal equinox, and their sum will be
the time of the passage of the first point of Aries
over that meridian; the day on which, but before,
the equinoctial intersection happens.

N. B. In taking out the numbers from this
table, reject the thirds, if they are und«r thirty ;
if they exceed thirty, add one to the minutes found
in the table.

The right ascension of the first point of Aries,
thus found for the day on which the equinox hap-
pens, holds good for the whole year, and is to be
added to the difference of the passage of the first
point of Aries over the meridian found against the
day of the month ; and their sum will be the time
of day when the first point of Aries will pass the
meridian.

Observe when the equinox falls on the 1 oth day
of March in a year which is not bissextile, to. seek
the day of the month in the right hand column of
the table ; and when it falls upon the 20th day of
March, seek the day of the month in the left hand
column, over which in either case, and under the
name of the month, you have the proper difference
of ri ght ascension to be added to that found above
for the day of the equinox.

In bissextile years, seek the day of the month
in the left hand column, to the end of February,
and for the intercalary day, or 29th of February,
take out the difference of right ascension answering
to the first of March, after which to the year's
end seek the day of the month in the right hand

first point of Aries for any day in the year, add
thereto 11 h. 58 min. and you obtain the time of
the right ascension of the first point of Libra.

August 28,

1	15	34
1	9	50
	1	59
1	11	49
1	6	7
	1	59
1	8	6
13	28	17
	1	59
13	30

These four examples are quite sufficient, if the
reader compares them with the tables and precepts.

In the Aid and 43d Problem, Art. 200, 26j, we
have shewn how to find the hour that any known
star comes to the meridian; and also to find the
time of the year any star passes the meridian at any
hour proposed, but- in that place we were not pre-
pared to apply the right ascension of the first point
of Aries, so properly for an observation of the stars,
as by the following

Problem XLVIII. To find the time of the
right ascension of any star, upon any particular
meridian, on any day in the year.

290. First find the time of the right ascension
of the first point of Aries, Art. 28S, by Problem
47, agreeable to your own meridian.

Then apply to the celestial globe, and bring the
given star under the graduated side of the strong
brass meridian, which will cut its right ascension,
or rather its distance in time or degrees, upon the
equinoctial; add this quantity expressed in^ time to
the right ascension of the first point of Aries, and
you will obtain the time of the passage of that star
over the meridian very near the truth. Thus,

The star marked y in the head of Draco, will
have 268 degrees, or 17 h. 52 min. of right as-
cension or distance from the first point of Aries,
Art. 276 ; which added to the right ascension of
that point for the 13th day of July, A. D. 1772,
gives the true time of its right ascension that even-
ing : at 10 h. 12 min. this star will be over the heads
of the inhabitants of London at that time, its de-

JVotg. In this method of working, when the
hours exceed 24, deduct 24 hours therefrom, and
you obtain the true time sought.

Problem XLIX. To rectify the celestial globe for
any time in the evening of any day in Lhe year, by
the knowledge of the time ivhen the first point of
Aries shall pass the meridian that day.

291. As the degrees and hours upon the.equinoc-
tial line on our new globes, are numbered from the
first point of Aries,

47, Art. 288, for the given day, and rectify the globe
to your latitude, Art. 189, then bring the first point
of Aries upon the globe, under the graduated side of
the strong brass meridian, and set the horary index
to the hour and minute of the passage of Aries o,
first found : turn the globe until the given hour is
under the horary index, and place it due north and
south by the mariner's compass, attending to the va-
riation of the needle, and you will have a perfect
representation of the starry firmament, not only for
that instant, but as long as you please to apply your-
self to the knowledge of the stars that evening, by
only moving the globe to any other minute under
the horary index as the time advances.

Thus, on the 25th of February, A.D. 1770, about
46 minutes after V in the evening, the star called
Al-debaran, or the Bull's-eye, will be upon the me-
ridian of London, or places adjacent; about VI
o'clock that evening, Orion will begin to pass the

ineridian, and present a glorious view to the eyes of
the observer, there being so many eminent stars in
that constellation, then successively passing over the
meridian until i past VII ; all the stars in Auriga,
or the Charioteer, will be passing the meridian at the
same time; after which Canis Major will succeed,
with Syrius, the Dog- star, at the side of his jaw ;
then Canis Minor, and Gemini, or the Twins, will
follow, and so on for the remainder of the night.—
This appearance may be observed several months, but
at different hours in the night, which may be found
by this Problem.

Also, on the 8th of May in the same year, the
first point of Aries will pass our meridian at 20 h.
58 min. 29 sec. but if we reckon the hours from mid-
night, at 58 minutes past VIII in the morning, at
which time no stars can be seen ; therefore we must
have recourse to the right ascension of the first point
of Libra, which is thus obtained:

The right ascension of the first point of Libra, ?
A. D. 1770, May 8th, at - - -j

Now in the precept to this Problem, read Libra
instead of the word Aries, and the rule will hold good
in this as well as in the first case. Therefore,

Bring the first point of Libra to the graduated
side of the strong brass meridian, and set the horary
index to 56 minutes past VIII in the evening, ti^rn

the globe until the horary index points to 10 minutes
past X o'clock, and you will tind the star called Spi-
ca Virginis, being that in tlie ear of corn she holds
in her hand, a star of the first magnitude marked «,
upon the meridian .it that time. If you then look
at the firmament, you will see the constellations Can-
cer, Leo minor, Leo major, the great Bear, with the
head and wings of Virgo on the western side of the
meridian ; and on the eastern side thereof, the Ba-
lance, Scorpio, Bootes, Hercules, amp;c. successively
following the first point of Libra in their passage
over the meridian.

292. Before we attempt an observation of this
kind, a signal or warning star must be first obtained ;
that is, such a star is to be sought, as shall have the
same or nearly the same quantity, either in degrees
or time of right ascension, reckoned from the first
point of Aries, as the place, over which any other
star shall then happen to be a correspondent, shall
have of longitude, reckoned eastward of London.

It has been shewn, that declination in the celestial,
and latitude on the terrestrial, globe, mean one and
the same thing, both being measured by their dis-
tance from the equator ; consequently, if the decli-
oation of any star is equal to the latitude of any
place, that star, by a line conceived to be drawn
from it to the center of the earth, will describe the
parallel of that place ; whence it becomes a corre-
spondent, not only to that particular place, but also
to all those places which lie in the same parallel of
latitude, by passing perpendicularly over them all

once every 24 hours. But as a preparation, we must
first shew, by the following problems, how to find
those places to which any star -is a correspondent,
and those stars which are correspondents to any
place.

293. First find the declination of the star on the
celestial globe by Problem V. Art. 55, and remember
whether it be north or south ; count the same num-
ber of degrees upon the strong brass meridian of the
terrestrial globe the same way from the equator, and
note the place by holding the edge of a card thereto;
turn the globe from east to west, and all those places
which pass under that point, will be correspondents
to that star, because they will be in the line passing
from the center of the earth through the very place
upon its surface, to which the star is at that time

of Draco, is 51 deg. 32 min. equal to the latitude of
London; therefore this brilliant star of the second
magnitude may be called the star of this metropolis,
without being deprived of its own name ; it may
likewise take the name of aiiy othei- place in the pa-
rallel of London.

The reverse of this Probletn, being to find all th^
stars which are correspondents to any place, is so
easy as to require no farther explication, than that of
applying first to the terrestrial globe.

The apparent diurnal motion of one star only,
will successively shew its perpendicularity to varioils
countries, as will appear by

A GENERAL DESCRIPTION OP THE PASSAGE OP THE
STAR MARKED y IN THE HEAD OF THE CONSTEL-
LATION DRACO, OVER THE, PARALLEL OF LONDON.

294. This eminent star traces t,he parallel of Lon-
don, and is a star of perpetual apparitio.n to the in-
habitants of the Britannic isles ; it cames upon the
meridian of London with the 268th degree of right
ascension, and is at that time directly perpendicular
to, or over the heads of, the people of this city, two
minutes of an hour after its warning star marked k
in the milky way, has passed the meridian.

Note. This star marked k is the southernmost of
a group of five stars, situated between the shoulder
of Serpentarius and Sobieski's shield, which in the
firmament appear in the form of a Roman V, as may
be seen upon the globe.

The declination of our correspondent star y in
the head of Draco, is 51 deg. 32 min. equal to the
latitude of London; with which apply to the terres-
trial globe, and bring London to the graduated side
of the strong brass meridian, and set the edge of a
card thereto, holding it to the brass meridian with
your right hand, while you gradually turn the globe
from west to east with the other hand, and that point
of the card which is upon the globe will then repre-
sent the intersection of that line upon the surface of
the earth, which we have supposed to pass from the
center of the earth to the star; and as this point,
though at rest, passes over the parallel of London
upon the globe, so does the central ray, proceeding
from the star, really pass over every point of land

and sea, upon that part of the earth which is cir-
cumscribed by the parallel of London.

Thus you will see the star marked y, in the head
of Draco, pass from London over the road to Bristol,
and dart its perpendicular rays upon that city; then
crossing the sea, it reaches Ireland between Kinsale
and Cork, and leaving that kingdom, will shine over
the Atlantic Ocean, until it is perpendicular to the
north cape of Newfoundland ; whence it.will be ver-
tical to Eskimos, and pass between lake Achona and
northern coast of the gulph of St. Lawrence, then
it will cross St. James's Bay, Kristino, amp;c. and pass
westward over a vast space of land but little known
to the Europeans ; thence it will leave the western
coast of North America, to shine upon the northern
part of the Pacitic Ocean, until it is perpendicular to
several islands, one of which is called St. Abrahani ;
it crosses the southern land of Kamkatska, and the
island Sangalien ; thence it becomes perpendicular to
the continent near Telmen on the east side of Mon-
gales in Chinese Tartary, and so proceeds to cast its
perpendicular rays over a vast country in Asia, being
sometimes a zenith point to the Chinese, at other
times to the Russian Tartars, and passing over Biel-
gorod, becomes vertical to Muscovy, Poland, Ger-
many, andZealattd, and so crosses the sea again to re-
turn to its perpendicularity ov gt; the city of London ;
. all which is performed by the earth's diurnal motion
in so short a time as twenty-three hours and fifty-six
minutes. ■ '

When a beginner has been thus exercised wjth
f^e general passage^ of two or three principal stars
over their correspondent parallels on different parts

of the earth, his ideas will be so greatly improved,
that maps and charts may then be laid before him
with propriety, in order to confirm him in the know-
ledge of the particular parts of those very parallels,
of which he has already attained a general idea
upon the globe.

PitoBi-EM LI. To Jind «a signal, or ivarning
star, that shall be upon or near the meridian of an
observer, at the time any known star is perpendicular
to any place on its corresponding parallel.

295. Bring the given place to the graduated side
of the strong brass meridian on the terrestrial globe,
and it will cut the degrees of its longitude, reckoned
eastward from London, upon the upper row of
figures over the equator ; then

Apply to the celestial globe, and set the given
star under the graduated side of the strong brass
meridian, which will cut the degree of its right as-
cension on the equinoctial.

If the situation of the observer is west of the
given place, subtract the terrestrial longitude from
the right ascension of the star ; if east, add the
longitude, and move the celestial globe, till the
sum or residue thereof is under the graduated side
of the strong brass meridian, and then that side
will be directly over those stars which are upon,
or have just passed, or are not quite come up, to
the observer's meridian, at the moment the given
star is vertical to the place proposed; either of
which will correctly answer the present purpose, and
become the signal or warning star ; that upon its

Thus let the observer be in or near London, and
the bright star in Lyra, or the harp, of the first
magnitude, be given, it is called Vega, and marked
this star is a correspondent to the south
west cape of the island of Sardinia in the Medi-

The longitude of this cape from London ^is 9
degrees, and the right aScension of the star Vega
js 'gt;77 degrees j as London is west of Sardmia ; 9
dei-ees subtracted from 277 degrees, leaves 268
degrees of right ascension, to which the celestial
g4e being set, the graduated side of the strong
brr^s meridian will be found directly over the star
^ in Draco, and also over a star of the fourth
magnitude in one of the heads of Cerberus. These
a-e eminent signals, and both upon the meridian,
when at the same time the star marked m
the knee of Hercules, will have passed the me-
ridian about two minutes of an hour, and^ the star
marked P, of the fourth magnitude, m the milky
way, will want about two minutes of an hour of

An observer at Sardinia may note the same with
respect to the- distance and bearing of London
from him.

To excite students who have an aspiring emula-
tion to improve themselves in this extensive science
of geography and astronomy, the principal requi-
sites whereby they may acquire universal know-
ledge, we shall proceed to illustrate this system of
the natural agreement between the celestial and
terrestrial spheres, by a few interesting examples.

when the star marked y in the head op dracq
js perpendicular to the city of london, thr
twelve following stars may ee seen prom
^ thence at the same time, when they will
also be perpendicular to as many places
upon the earth.

296. The signal or Warding star is y in the
head of Draco, which comes upon the meridiail
with the 268th degree of right ascension ; it will
be vertical to the city of London two minutes of
time after the star marked k, in the milky way,
near the equinox, has passed the meridian, at which
time the twelve following stars will be vertical to the
places they sta«d against:—

The use of a warning star is to point out the true
time of the phœnomenon, which is to be first nearly
found by obtaining the time of the right ascension of
that star for the evening on which the observation
is intended to be made.

The right ascension and declination of the star«
were found in round numbers upon the celestial
globe^ and written in two columns, inclosing the
names of the stars ; the columns for the names of
the correspondent places being left blank for their
insertion afterwards :

Next, as the longitude on our new terrestrial
globes is numbered both ways from the meridian of
London, whatever the right ascension of the signal
star may happen to be, that point of the celestial
sphere is likewise considered to be upon the meri-
dian of London. Therefore,

To gain the longitude in the last column of
the table, if the given stars were east of the sig-
nal, the right ascension of the warning star was
subtracted from the right ascension of the given
star.

But the west longitude was obtained by sub-
tracting the right ascension of the given stars from
that of the signal.

The reverse of this example is to find what stars
will be perpendicular to any place upon the earth,
a warning star being known, that shall be upon the
meridian of an observer, when the stars to be
sought shall be vertical to the places assigned, which
the reader will easily perform from what has been
already said.

When a star is known to be perpendicular to any
assigned place, its (xsrrespondence to that terrestrial
point may be equally affirmed, to all those who can
see it at that instant from any part of the earth, or
sea, they may then happen to be upon.

If an observer in Palmyra, another in the middl«
of the Mogul's empire, a third at Levata in Africa,
and a fourth at Chapa in Mexico, should look at
the star y, in the head of Draco, the moment it is
in the zenith of London, they will see its cor-
respondence to that metropolis at one and the
same instant of time; their hour only will be dif-
ferent according to the difference of the meridians,
as those places are situated either east or west from
London.

The signal or warning star tp each of these
places, is the perpendicularity of that star expressed
in the preceding catalogue of twelve stars.

From the observation under either of these stars
in the catalogue, may be seen the other tvaelve
Btars, when they are shining over the heads of
the inhabitants of all the other countries therein
named.

This constitutes the system of astronomical geo-
graphy before spoken of. It affords us a real as-
sistance from the heavens, whereby we not only
see the marvellous distances of a multitude of
celestial bodies, composing that part of the univtrse,
which we are permitted to behold ; but it also
enables us to comprehend the distances and bearings
of the most remote countries from that point of the
earth upon which we stand.

head of Castor, is upon the meridian of London
with the 110th degree of right ascension, the
twelve following correspondents will be vertical to
the places annexed :—

P.Wales fort. Hud--)
son's Bay J
Twightees, S. of7
Lake Michiganj
Eskimos between^
L. Otter and L.
Pitetibi, North
America
Cape Risher, G.

298. When the bright star marked a in the ear
of corn which the Virgin holds in her hand,
called Spica Virginis, is upon the meridian of Lon-
don with ] 98 degrees of right ascension, the fol-
lowing twelve stars will be vertical to the several
places in the following table :—

299. When the 289th degree of right ascension
is upon the meridian of London, signified by one
nainute of an hour after the star marked S in the
southern wing of the Eagle has passed the me-
ridian, then the twelve following places will have
the annexed stars in their zenith:—

Fro. Sea near Islequot;)
WarduSjLaponia^
Between Sio and
Ampaia, Zan-
guebar
Russia, 4° E. of
Moscow

300. When the star marked 6 in the side of the
Whale is upon the ineridian of Londdn, with 18
degrees of right ascension, the twelve following stars
will be in the. zenith of the annexed places :—

The stars in this example may be seen in the
month« of October, November, and December.

301. Wiien the moon is at or near the full,
about the time of an autumnal equinox, she rises
nearly at the same hour for several nights together:
this phoenomenon is called the harvest moon.

To account for this upon the celestial globe, set
tX\e artificial sun upon the first point of Libra, where
the sun must necessarily be at every autumnal equi-
nox, and place the artificial moon upon the first point
of Aries, where she must be, if a full moon should
happen at that time.

Rectify the globe to the position of a right sphere,
Art. 214, which answers to the inhabitants of the
equator ; bring the center of the artificial sun to the
western edge of the broad paper circle, and the ho-
rary index in this case being the graduated edge of
the strong brass meridian, will cut the time of the
sun's setting, and the moon's rising; hence it is ob-
vious the moon will rise when the sun sets, which
will be at VI o'clock, because they are both sup{»sed
to be in the celestial equator, but in opposite signs.
Therefore on that day the same phoenomenon will
happen in all latitudes between the equator and
either pole.

But as the moon's motion in her orbit, which we
shall at present consider as coincident wifti the eclip-
' tie, is about 13 deg. 10 min. every day, which retards
her diurnal motion about 51 min. 56 sec, of time
with respect to the first point of Aries, this daily dif-

fference as it relates to the sun is generally reckoned
at 48 minutes of time, or two minutes for every
hour.

Let us now enquire upon the globe, what time thé
moon will rise the next night after the autumnal
equinox, at which the sun will have advanced onö
degree in Libra, and the moon 13 deg. 10 min. in
Aries, which is 12 degrees more than the sun has
done in the same time : therefore place the center of
the artificial sun upon the first degree of Libra, and
the artificial moon on 13 deg. 10 min. of Aries, the
globe being rectified as before to the position of a
right sphere, bring the artificial sun under the gradu-
ated side of the strong brass meridian, and set the
horary index to XII, turn the globe until the artifi-
cial sun coincides with the western side of the broad
paper circle, the horary index will shew he sets
tliat evening at VI o'clock, and the globe being turn-
ed till the artificial moon coincides with the eastern
side of the broad paper circle, the horary index will
shew the moon's rising that evening to be about 48
minutes past VI o'clock, with 5 degrees of amplitude
northerly, as she is now entered into the northern
half of the ecliptic.

Now elevate the north pole of the globe to the
latitude of London, every other rectification remain-
ing the same, and bring the artificial moon to the
east side of the horizon, and the horary index will
point to 20 minutes past VI, her time of rising ; and
her amplitude at that time will be about 8 degrees, 3
degrees more than at the equator the same evening.

If we thus investigate the time of the moon's ris-
ing for two or three nights together, before and after

The reason is, that the full moons which happen
at this time of the year, are ascending from the
southern into the northern signs of the zodiac:
whence the moon describes a parallel to the equator
every night more northerly, which increases her ris-
ing amplitudes considerably, and more so as the lati-
tude is greater, as in the present example ; hence it
is plain, that the nearer any celestial,object ia.to either
pole, the sooner it ascends the horizon.

Every thing remaining as before, if we elevate the
north pole of the globe to 664- degrees, which is the
latitude of the northern polar circle, and bring the
artificial moon to the east side of the horizon, she
will be found to rise about the same time that the
sun sets the evening after the autumnal full moon,
which is about VI o'clock, at A^hich time her place
and amplitude will be about degrees.

In this position of the globe, if the artificial moon
be removed 13 deg. 10 min. upon the ecliptic, which
is her mean motion therein for one day, and so on
for fourteen nights together, she will be seen to rise
within the space of one hour during that time, which
will be clear on observing that half the ecliptic rises

What has been said with rcspect to north latitudes
is equally applicable to south latitudes.

In like manner the new moons in spring rise near-
ly at the Sitmc hour for several nights successively,

while the full moons rise later by a greater difference
than at any other time of the year, because at this
time of the year the new moons are in the ascending,
and the full moons in the descending signs.

This phœnomenon varies in difFerent years : the
moon's Orbit being inclined to the ecliptic about 5
degrees, and the line of nodes continually moving
retrograde, the inclination of her orbit to the equa-
tor will be greater sometimes than at others, which
prevents her hastening to the northward, or descend-
ing southward in each revolution with equal pace.

Problem LIII. To find the time of the yea;r
in ivhich a star rises or sets cosmically or achroni-
cally.

302. The cosmical rising and setting of a star, is
when a star rises with the sun, or sets at the time
the sun is rising.

The achronical rising or setting of a kar, is when
a star rises or sets at the time the sun is setting.

Elevate the pole of the celestial globe to the lati-
tude of the place, and bring the star to the eastern
edge of the broad paper circle, and observe what de-
gree of the ecliptic rises with it, which seek in the
kalendar on the broad paper circle, against which is
the day of the month whereon that star rises cos-
mically.

Turn the globe till the star coincides with the
western edge of the horizon, and that degree of the
ecliptic which is cut by the eastern side, gives the
day of the month when the star sets cosmically ; so
likewise against the degree which sets with the star,
you have the day of the month of its achronical set-

ting, and if you bring it to the eastern side of the
horizon, that degree of the ecliptic then cut by the
western side of the broad paper circle sought in the
kalendar, will shew the day of the month when
the star rises achronically.

303, When a star is first visible in the morning,
after having been so near the sun as to be hid by the
splendor of its rays, it is said to rise heliacally.

When a star is immersed in the evening, or hid
by the sun's rays, it is said to set heliacally.

Elevate the pole of the celestial globe to the lati-
tude of the place, bring the star to the eastern side
of the broad paper circle, fix the quadrant of altitude
to the zenith, and apply its graduated edge to the
western side in such a manner that its 12th degree
above the horizon may cut the ecliptic, the point
opposite to this will be 12 degrees below the broad
paper circle on the eastern side, and is the sun's
place in the ecliptic at the time a star of the first
magnitude rises heliacally ; seek this point in the
kalendar, or upon the ecliptic line on the globe,
against which you will find the day of the year when
that star rises heliacally.

To find the heliacal setting, bring the star to the
western side of the horizon, and turn the quadrant
of altitude on the eastern side, till the 12th degree
cuts the ecliptic; its- opposite point is the sun's
place, which sought either upon the kalendar ov
ecliptic line, gives the day of the year when the star
sets heliacally..

Stars- of the first magnitude, according to Ptolemy,
rise or set heliacally, when they are 12 degrees dis-
tant from the sun; that is, when the star is rising,
the sun must be depressed in the perpendicular be-
low the horizon 12 degrees, that the star may be far
enough from the sun's rays to be seen before he
rises.

Stars of the second magnitude require the sun's
depression thirteen degrees, and those of the third
magnitude fourteen degrees, amp;c.

THE MANAZIL AL KAMER OF THE ARABIAN ASTRO-
NOMERS, ¹ PROM ULUGH EEIGH, PUBLISHED AT
OXPOKD, 1665.

304. The manazil al kamer of the Arabian astro-
nomers, are XXVIII; they are so called, i. e. the
mansions of the moon, because they observed the
moon to be in or near one of these every night dur-
ing her monthly course round the earth: they are
these that follow, to which upon the globe the
Arabian characters are affixed, but omitted here for
the want of an Arabian type.

i.nbsp;y// Sheratdn, these are the first and second stars
of Aries, or the stars in the Ram's horns, marked
(3 and y, with 1, ([ , signifying the first mansion of
the moon, which the reader will please to remem-
ber once for all.

ii.nbsp;Botein, the stars in the Ram's belly, according
to Ulugh Beigh ; by Bayer, and on our globe,
» and f.

VII.nbsp;Al Dira, the two bright stars, one in the head
of Castor, the other in Pollux, marked « and (3.

VIII.nbsp;Al Nethrah, the nebul®, or group of stars in
Cancer, marked £, called by the Greeks lt;px.rvn, i. e.
Pragsepe.

XV.nbsp;Al Gaphr, three stars in the skirt of the robe
of Virgo, marked (p »- k.

XVI.nbsp;Al Zubana, that is Libra ; the northern scale
is called Zubdnah Al Shemali, and is the star mar-
ked |3 ; the southern scale, marked is called Zu-
bdnah al Genubi] Shemali signifies northern, and
Genubi southern ; they are exactly miscalled on
the common globes of modern construction.

XVIII.nbsp;Al Kalb, the Scorpion's heart, marked «
more fully, Kalb Al Ahrab. The word Antares,
if it is not a corruption, has no signification, and
is therefore omitted.

XIX.nbsp;Al Shaulah, the Scorpion's tail, or the star
marked A. The word Lesath we have omitted,
being another pronunciation of Ldamp;ah, the true
name is Shaulah.

XX.nbsp;Al Ndaim, these are eight stars in Sagittary,
marked y ^ i x a- (p Ulugh Beigh makes them
only three, i. e. y a- xp.

XXI.nbsp;Al Beldah, this is that part of the Horse in
Sagittary, where there are no stars drawn, and if
there be any in that part of the heavens, it is
thought they are only telescopic stars.

XXVII.nbsp;Al Pherg al Muaechir, these are two stars,
one in the head of Andromeda, marked the
other in the wing of Pegasus, marked y.

This is a division of the heavens, different from
any thing the Greeks were acquainted with, and
therefore was not borrowed from them.

305. Bring the sun's place in the ecliptic on the
celestial globe, to the graduated side of the strong
brass meridian, and set the horary index to that XII
which is most elevated ; turn the globe, till the star
marked y in Cassiopea's hip, is under the graduated
side of the strong brass meridian, with about 11 de-
grees of right ascension ; at which time the polar
star, in the extremity of the tail of the little bear,
will be above the pole, and upon the meridian also.
If you find in this application of the globe, that the
horary index points to any hour of the day, when
the globe is rectified to the latitude of your.situation,
turn the globe again, till the st?r marked £, called
Alioth, being the first in the tail of the great Bear,
is under the graduated side of the strong brass
meridian, and then the polar star will likewise be
upon the meridian, with about IQl degrees of right
ascension, but under the north pole, and the horary
index will point out the time of the night, when this
phcEUomenqn is to happen ; before which you are to
have the following apparatus properly prepared, that
you may be ready to attend the observation, that is^
to find your meridian line.

Suspend two plumb lines, and let their weights be
immersed in water, to prevent their vibrating, but

in such a manner that the string of one of them may
be directly between the polar star and the string of
the other. After this adjustment of the two strings,
if they remain untouched till the next day at noon,
a meridian line may be obtained at any window iü
the house which has a southern aspect, by suspend-
ing lines as above from the ceiling; that next the
window may be fixed, but tbe other should be move-
able in a direction nearly east and west; the weights
of these ought also to be immersed in water : then,
if two persons attend a little before noon on the next
day, one of them at the two first plumb lines which
were adjusted to the polar star, and the other at the
two plumb lines in the house which are then to be
adjusted, each of them holding a sheet of white
paper in their hands, to receive the shadow of the
two strings cast thereon by the sun ; the first obser-
ver is to give a signal to the second of the instant
the two shadows on his paper are united in one and
the same line, at which time the sun will be precisely
upon the meridian. The other observer in the
house is likewise to attend with diligence, and as the
sun is coming nearer and nearer to the meridian, he
is constantly to remove his moveable plumb line, and
keep the shadows of his two strings always united in
one distinct shadow, that his observation may be
complete, when his assistant gives the definitive
signal.

If this be repeated four or five times, a very accu-
rate meridian line may be obtained, and may be drawn
on the window, the floor, or a pavement, by their
shadow when united by the sun's rays, and the plumb
lines may be occasionally suspended from two fixed

For the use of the curious it will not be improper
to observe, that the late Dr. Bradley found that the
distance of the star marked « at the extremity of
the tail of the little Bear, from the polar point, was
1 deg. 1 min. SQ sec. on the first of January, A. d.
1751, old style ; at the same time its right ascension
was 10° 45' 15quot;, equal to 43 min 1 sec. of time;
and as the right ascension increases 1 min. l6sec.
every ten years, its right ascension may be obtained
for any succeeding year ; and having the sun's right
ascension in time also, subtract the last from the
first ; by adding 24 hours to the right ascension of
the pole star when it is less than the sun's, the re-
mainder will be the time of the star's coming to the
meridian.

306. As time flows with great regularity, it is
impossible to measure it accurately, and compare its
several intervals with each other, but by the motion
of some of the heavenly bodies, whose progress is as
uniform and regular as itself.

Ancient astronomers looked upon the sun to be
sufficiently regular for this purpose ; but by the ac-
curate observations ot later astronomers, it is found
that neither the days, nor even the hours, as measur-
ed by the sun's apparent motion, are of an equal
length, on two accounts :

1st, A natural or solar day of 24 hours, is that space
of time the sun takes up in passing from any particu-
lar meridian to the same again*; and one revolution
of the earth, with respect to a fixed star, is performed
in 23 hours, 56 minutes, 4 seconds; therefore the
unequal progression of the earth through her ellip-
tical orbit, (as she takes almost eight days more to
run through the northern half of the ecliptic, than
she does to pass through the southern,) is the reason
that the length of the day is not exactly equal to the
time in which the earth performs its rotation about
its axis.

2dly, From the obliquity of the ecliptic to the
equator, on which last we measure time ; and as
equal portions of one do not correspond to equal por-
tions of the other, the apparent motion of the sun
would not be uniform; or, in other words, those
points of the equator which come to the meridian,
with the place of the sun on different days, would
not be at equal distances from each other.

This last is easily seen upon the globe, by bringing
every tenth degree of the ecliptic to the graduated
side of the strong brass meridian, and you will find
that each tenth degree on the equator will not come
thither with it, but in the following order from f
to 25, every tenth degree of the ecliptic comes sooner
to the strong brass meridian than their correspond-
ing lOths on the equator ; those in the second quad-
rant of the ecliptic, from 25 to =Ci:, come later, from
i^i: to yj* sooner, and from Vy to Aries later, whilst
those at the beginning of each quadrant come to the
meridian at the same time; therefore the sun and
clock would be equal at these four times, if th^ sun
was not longer in passing through one half {^f the

ecliptic than the other, and the two inequalities jotn-
ed together, compose that difference which is called
the equation of time.'

These causes are independent of each other; some-
times they agree, and at other times are contrary to
one another.

The time marked out by an uniform motion is
called true time, and that shewn by the sun is called
apparent or solar time, and their difference is the
equation of time.

WE NOW proceed to SHEW how the tereesteial
GLOBE WILL REPRESENT THE REAL PHCENOMENA
RELATING TO THE EARTH, WHEN ACTUALLY COM-
PARED WITH THE REFULGENT RAYS EMITTED
I'-ROM THE GREAT SPHERE OF DAY.

307. The meridians on our new terrestrial globes,
being secondaries to the equator, are also hour circles,
gnd are marked as such with Roman figures under
the equator, and at the polar circles. But observe,
there is a difference in the figures placed to the same
hour circle ; if it cuts the Illd hour upon the polar
circles, it will cut the IXth hour upon the equator,
which is six hours later, and so of all the rest.

Through the great Pacific sea, and the intersection
of Libra, is drawn a broad meridian from pole to
pole, it passes through the Xllth hour upon the
equator, and the Vlth hour upon each of the polar
circles; this hour circle is graduated into degrees
and parts, and numbered from the equator towards
cither pole.

There is another broad meridian passing through
the Pacific sea, at the IXth hour upon the equator,
and the Illd hour upon each polar circle; this con^

tains only one quadrant, or go degrees, the numbers
annexed to it begin at the northern polar circle, and
end at the tropic of Capricorn.

Here we must likewise observe, there are 23 con-
centric circles drawn upon the terrestrial globe with-
in the northern and southern polar circles, which for
the future we shall call polar parallels ; they are plac-
ed at the distance of one degree from each other,
and represent the parallels of the sun's declination,
but in a different manner from the 47 parallels be-
tween the tropics.

The following Problems require the globe to be
placed upon a plane that is level, or truly horizontal,
which is easily attained, if the floor, pavement,
gravel-walk in the garden, amp;c. should not happen to
be horizontal.

A flat seasoned board, or any box which is about
two feet broad, or two feet square, if the top be per-
fectly flat, will answer the purpose, the upper surface
of either may be set truly horizontal, by the help of
a pocket spirit level, or plumb rule, if you raise or
depress this or that side by a wedge or two, as the
spirit level shall direct; if you have a meridian line
drawn on the place over which you substitute this
horizontal plane, it may be readily transferred from
thence to the surface just levelled ; this being done,
we are prepared for the solution of the following
Problems.

Pboblem LVII. To observe the suns altitude
hy the terrestrial globe, when he shines bright, or
»'hen he can but Just be discerned through a cloud.

that caused by the sphericity of the globe, here-
tofore called the edge of the earth's enlightened
disc, and there represented by the broad paper
circle, but here realized by the natural light of the
sun itself.

Elevate the north pole of the globe to 66i degrees,
bring that meridian or hour circle, which passes
through the IXth hour upon the equator, under the
graduated side of the strong brass meridian, the globe
being now set upon the horizontal plane; turn it
about thereon, frame and all, that the shadow ot the
strong brass meridian may fall directly under itself,
or in other words, that the shade of its graduated face
may fall exactly upon the aforesaid hour circle; at
that instant the shade of extub'erancy will touch
the true degree of the sun's altitude upon that
meridian, which passes through the IXth hour
upon the equator, reckoned from the polar circle,
the most elevated part of which will then be in the
zenith of the place where this operation is per-
formed, and is the same v^'hether it should happen
to be either in north or south latitude.

Thus we may, in an easy and natural manner,
obtain the altitude of the sun, at any time of the
day, by the terrestrial globe; for it. is very plain,
when the sun rises, he brushes the zenith and
nadir of the globe by his rays ; and as he always
illuminates half of it, (or a few minutes more, as
his globe is considerably larger than that of the
earth,) therefore when the sun is risen a degree
higher, he must necessarily illuminate a degree
beyond the zenith, and so on proportionably from
time to time.

But as the illuminated part is somewhat more
than half, deduct 13 minutes from the shade of
extuberancy, and you have the sun's altitude with
tolerable exactness.

If you have any doubt how far the - shade of ex-
tuberancy exactly reaches, hold a pin, or your fin-
ger, on the globe, between the sun and point in
dispute, and where the shade of either is lost, will
be the point sought.

309. Turn the meridian of the globe toward the
sun, as before, or direct it so that it may lie in
the same plane with it, which may be done if you
have but the least glimpse of the sun through a
cloud; hold a string in both hands, it having first
been put between the strong brass meridian and
the globe : stretch it at right angles to the me-
ridian, and apply your face near to the globe,
moving your eye lower and lower, till you can but
just see the sun: then bring the string held as
before to this point upon the globe, that it may
just obscure the sun from your sight, and the de-
gree on the aforesaid hour circle, which the string
then lies upon, will be the sun's altitude required,
for his rays would shew the same point if he shone
out bright.

Note. The moon's altitude may be observed by
either of these methods, and the altitude of any star
by the last of them.

Problem LVIIL To place the terrestrial globe
in the suns rays, that it may represent the natural
position of the earth, either by a meridian line, or
tvithout it.

310. If you have a meridian Hne, set the north
and south points of the broad paper circle directly
over it, the north pole of the globe being elevated
to the latitude of the place, and standing upon a
level plane, bring the place you are in under the
graduated side of the strong brass-ineridian, then
the poles and parallel circles upon the globe will,
without sensible error, correspond with those in
the heavens, and each point, kingdom, and state,
will be turned towards the real one which it re-
presents.

If you have no meridian line, then the day of
the month being known, find the sun's declination
as before instructed, which will direct you to the
parallel of the day, amongst the polar parallels,
reckoned from either pole towards the polar circle;
which you are to remember.

Set the globe upon your horizontal plane in the
sun-shine, and put it nearly north and south by
the mariner's compass, it being first elevated to
the latitude of the place, and the place itself
brought under the graduated side of the strong
brass meridian: then move the frame and globe
together, till the shade of extuberancy, or term
of illumination, just touches the polar parallel for
the day, and the globe will be settled as before
and if accurately performed, the variation cf the

ftiagnetical needle will be shewn by the degree to
which it points in the compass box.

And here observe, if the parallel for the day
should not happen to fall on any one of those
drawn upon the globe, you are to estimate a pro-
portionable part between them, and reckon that,
the parallel of the day; If we had drawn more,
the globe would have been confused.

The reason of this operation isj that as the stiri
illuminates half the globe, the shade of extube-
fancy will constantly be 90 degrees from the point
wherein the sun is verticah

If the sun be in the equator, the shade and il-
lumination must terminate in the poles of the
world; and when he is in any other diurnal pa-
rallel, the terms of illumination must fall short of,
or go beyond either pole, as many degrees as the
parallel which the sun describes that day, is distarrf
from the equator ; therefore when the shade of ex-
tuberancy touches the polar parallel for the day,
the artificial globe will be in the same position^
with respect to the sun, as the earth really is, and
will be illuminated in the same manner.

Pkoblem LIX. To find naturally the sun^s de-
clination, diurnal parallel, and his place thereon.

311. The globe being set upon an horizontal
plane, and adjusted by a meridian line or otherwise,
observe upon which or between which polar parallel
the term of illumination falls; its distance from
the pole is the degree of the sun's declination:
»eckon this distance from the equator among the

larger parallels, and you have the parallel .which
the sun describes that, day ; upon whieh it you
move a card, cut in the form of a double square,
until its shadow falls under itself, you will obtaiu
the very place upon that parallel over which the
sun is vertical at any hour of that day, if you set
the place you are in under the graduated side ot

Note. The moon's declination, diurnal parallel
and place, may be found in the same manner.
Likewise when the sun does not shine bright, his
declination, Uc. may be found by an application m

312. If a gi'eat circle at right angles to the ho-
rizon passes through the zenith and nadir, and
also through the sun's center, its distance from
the meridian in the.morning or evening of any
day reckoned upon the degrees on the mner edge
. of the broad paper circle, will give the azimuth

313 Elevate either pole to the position of a
naraUei sphere, by bringing the north pole in
Lrth latitude, and the south pole in south lati-
tude into the zenith of the broad paper circle,
having first placed the globe upon your meridian
line or by the other method before prescribed ;

tiold up a plumb line so that it may pass freely
near the outward edge of the broad paper circle,
and move it so that the shadow of the string may
fall upon the elevated pole ; then cast your eye
immediately to its shadow on the broad paper cir^
cle,^ and the degree it there falls upon is the
sun's-azimuth at that time, which may be rec-
koned from either the south or north points of
the horizon^

314. If you have only a glimpse, or faint sight
of the sun, the globe being adjusted as before.
Stand on the shady side, and hold the plumb line
on that side also, and move it till it cuts the sun's
center, and the elevated pole at the same time,
then cast your eye towards the broad paper circle,
and the degree it there cuts is the sun's azimuth,
which must be reckoned from the opposite cardinal
point.

Pkoblem LXI. To shew that in some places of
the earth's surface, the sun iviU he twice on the same
azimuth in the morning, twice on the same azimuth
in the afternoon ; or, in othei tuords,

315. When the declination of the sun exceeds
the latitude of any place, on either side of the
equator, the sun will be on the same azimuth twice
in the morning, and twice in the afternoon.

Thus, suppose the globe rectified to the latitude
of Antigua^ which is in about 17 deg. of north

latitude, and the sun to be in the beginning of
Cancer, or to have the greatest north declination ;
set the quadrant of altitude to the 21st degree north
of the east in the horizon, and turn the globe upon
its axis, the sun's center will be on that azimuth
at 6h. 30 min. and also at 10 h. 30 min. in the
morning. At 8h. 30 min. the sun will be as it
were stationary with respect to its azimuth for some
time ; as will appear by placing the quadrant of al-
titude to the 17th degree north of the east in the
horizon. If the quadrant be set to the same
degrees north of the west, the sun's center will «
cross it twice as it appfoaches the horizon in the
afternoon.

This appearance will happen more or less to all
places situated in the torrid zone, whenever the
sun's declination exceeds their latitude; and from
hence we may infer, that the shadow of a dial,
whosfe gnomon is erected perpendicular to an ho-
rizontal plane, must necessarily go back several de-
grees on the same day.

But as this can only happen within the torrid
zone, and as Jerusalem lies about 8 degrees to the
north of the tropic of Cancer, the retrocession of
the shadow on the dial of Ahaz at Jerusalem
was, in the strictest signification of the word, mi-
raculous.

PeoblBM LXII. To observe the hour of the day
in the most natural manner, when the terrestrial globe
is properly placed in the sun-shine.

operation with respect to the hour, three of which
are here inserted, being general to all the inhabi-
tants of the earth ; a fourth is added peculiar to
those of London, which will answer, without sen-
sible error, at any place not exceeding the distance
of 60 miles from this capital.

317.nbsp;Having rectified the globe as before di-
rected, and placed it upon an horizontal plane over
yeur meridian line, or by the other method, hold a
long pin upon the illuminated pole in the directiori
of the polar axis, and its shadow will shew the hour
of the day amongst the polar parallels.

The axis of the globe being the common section
of the hour circles, is in the plane of each ; and
as we suppose the globe to be properly adjusted,
they will correspond with those in the heavens;
therefore the shade of a pin, which is the axis con-
tinued, must .fall upon the true hour circle,

318.nbsp;Tie a small string with a noose round the
elevated pole, stretch its other end beyond the globe,
and move it so that the shadow of the string may
fall upon the depressed axis; at that instant its
shadow upon the equator wiH give the solar hour to
a minute.

But remember, that either the autumnal or
»ernal equinoctial colure must first be placed un-
der the graduated side of the strong brass meridian

before you observe the hour, each of these being
marked upon the equator with the hour XII.

The string in this last case being moved into the
plane of the sun, corresponds with the true hour
circle, and consequently gives the true hour.

319. Every thing being rectified as before, look
where the shade of extuberancy cuts the equator,
the colure being under the graduated side of the
Strong brass meridian, and you obtain the hour in
two places upon the equator, one of them going
before, and the other following the sun.

The reason is, that the shade of extuberancy
being a great circle, cuts the equator in half, and
the sun, in whatsoever parallel of declination he
may happen to be, is always in the pole of the
shade ; consequently the confines of light and shade
livill shew the true hour of the day.

4thly, peculiar to the inhabitants of lon-
don, and its envikons, within the distance
of sixty miles.

320. The globe being every way adjusted as
before, and London brought under the graduated
side of the strong brass meridian, hold up a plumb
line, so that its sliadow may fall upon the zenith
point, (which in this case is London itself,) and
the shadow of the string will cut the parallel of the

day upon that point to which the -sun is then ver-
tical, and that hour circle upon which this inter-
section falls, is the hour of the day; and as the
meridians are drawn within the tropics at 20 mi-
nutes distance from each other, the point cut by
the intersection of the string upon the parallel of
the day, being so near the equator, may, by a glance
of the observer's eye, be referred thereto, and the
true time obtained to a minute.

Thei plumb line thus moved is the azimuth,
which, by cutting the parallel of the day, gives the
sun's place, and consequently the hour circle which
intersects it.

From this last operation results a coroJbry, that
gives a second way of rectifying the globe to the
sun's rays.

If the azimuth and shade of the illuminated axis
agree in the hour when the globe is rectified, then
making them thus to agree must rectify the globe.

321. Move the globe till the shadow of the
plumb line, which passes through the zenith, cuts
the same hour on the parallel quot;of the day, that the
shade of the pin held in the direction of the axis
falls upon, amongst the polar parallels, and the
globe is rectified,

The reason is, that the shadow of the axis re-
presents an hour circle; and by its agreement in
the same hour, which the shadow of the azimuth

string points out, by its intersection on the parallel
of the day, it shews the sun to be in the plane of
the said parallel; which can never happen in the
morning on the eastern side of the globe, nor in
the evening on the western side of it, but when thé
globe is rectified.

This rectification of the globe, is only placing it
in such a manner that the principal great circles,
and points, may concur and fall in with those of
the heavens.

The many advantages arising from these capital
problems relating to the placing of the globe in the

sun's rays, an intelligent reader will easily discern,
and readily extend to his own as well as to the be-
nefit of his pupil.

322.nbsp;Rectify the celestial globe to the latitude
and sun's place. Art. I89, 190, find the place of
Venus by an ephemeris, and set the artificial moon
to that place in the zodiac, which will represent
the planet; bring the artificial sun to the eastern
edge of the horizon ; if Venus is then elevated,
she will rise before the sun, and be a morning star •
but if she is depressed below the horizon, she must
then consequently follow the sun, and become an
evening star.

Problem LXIV. To find at what time of the
night any planet may be viewed with a reflecting te-
lescope.

and sun's place. Art. I89, 190, s^k the planet's
place and latitude in an ephemeris; to which place
in the zodiac set the artificial moon to represent
the planet, and it will shew its place in the heavens;
bring the planet's representative to the eastern side
of the horizon, and the horary index will shew the
time of its rising; if the artificial sun is thea
elevated^ the planet will not be visible at that time
by means of his superior light; therefore turn the
globe from east to west until the artificial sun is
depressed below the circle of twilight, Art. 93, and
216, where stop the globe, and screw the nut of
the quadrant of altitude in the zenith. Art. 192,
lay its graduated edge on the center of the planet,
and it will shew in the horizon the azimuth or
point of the compass, on which the planet may
then be viewed in the heavens; the horary index
will at the same time point out the hour of the
night. When the planet comes to the strong brass
meridian, the index will shew the time of its pas-
sage over that celestial circle ; and at the western
edge of the horizon, the time of its setting will
likewise be obtained.

Problem LXV. To find what azimuth the
moon is upon at any place when it is flood or high
■water^; and thence the high tide for any day of the
moons age at the same place.

324. Having observed the hour and minute of
high water about the time of new or full moon,
rectify the globe to the latitude and sun's place.
Art. 189,nbsp;the moon's place and latitude

and screw the quadrant of altitude in the zenith ;
turn the globe till the horary index points to the
time of flood, and lay the quadrant over the center
of the artificial moon, and it will cut the horizon
in the point of the compass upon which the moon
was, and the degrees on the horizon contained be-
tween the strong brass meridian and the quadrant,
will be the moon's azimuth from the south.

325. Rectify the globe to the latitude and zenith,
find the moon's place by an ephemeris for the given
day of her age, or day of the month; and set the
artificial moon to that place in the zodiac; put the
quadrant of altitude to the azimuth before found,
^nd turn the globe till the center of the artificial
moon is under its graduated edge, and the horary
index will point to the time of the day on which it
will be high water.

326.nbsp;A spherical triangle is formed upon the
surface of a globe by the intersection of the three
great circles.

327.nbsp;A spherical angle is the intersection of two
great circles that incline to one another ; the quan-
tity of any spherical angle is measured by a third
great circle, intercepted between the legs of the
angle, at 90 degrees distance from the, intersecting
point.

328.nbsp;A right angled spherical triangle hath one
right angle, the sides about which are called legs^
and the side opposite to it the hypothenuse.

329.nbsp;An oblique angled spherical triangle has its
angles greater or less than 90 degrees: the solution
of spherical triangles consists in finding the measure
of its sides and angles.

330.nbsp;The sides of any spherical triangle may be
changed into angles, and the angles into sides; if
for any one side, and its opposite angle, their com-
plement to a semicircle be taken.

331.nbsp;Fig. 30. Elevate the pole P to 42° 12', the
quantity of the given leg AC, and number thé
same quantity on the strong brass meridian from
JE., the equator, to Z, the zenith; there fix the
quadrant of altitude. Bring that meridian which
passes through London under the brass meridian,
and count 64° 40', the measure of the hypothenuse,
on the quadrant downwards from Z to G, and move
it till the point G intersects the equator, and the
triangle ZGM will be formed.

The side MZ represents the given side AC,
the hypothenuse BC is represented by the arch
ZG, the required side AB is represented by GjE
an arch of the equator, its measure 54° 43', be-
tween M and G, is the quantity sought; the angle
ACB, is represented by the angle GZJE, and its
measure is found on the arch A O of the horizon
equal to 64° 35'.

332.nbsp;To find the other angle A B C* having ob-
tained the measure of the side B A, 54° 43',
elevate the pole P agreeable thereto, and reckofi
the same from iE toZ-} there fijt the quadrant of

altitude; number the other leg AC, 42° 12' from
yE to G on the equator, (the meridian passing
through London remaining as before,) and to that
point bring the quadrant of altitude; then the arch
A O, on the horizon, will contain 48° 00', the
measure of the angle JEZG, equal to ABC, the
angle sought.

333. Fig. 33. Place P p the poles of the globe
in the horizon H O, and fix the quadrant of alti-
tude to Z the zenith ; number 64° 35', the meastire
of the given angle, upon the horizon from M
to F; move the quadrant to the point F, and
thereon count 64° 40', the quantity of the hypo-
thenuse from Z downwards to G, to which point
bnng that graduated meridian which passes through
Libra i-, and the triangle GZ will be formed.

Z G an arch of the quadrant of altitude repre-
sents the hypothenuse ; Z an arch of the equator
represents the required side AC equal to 42° 12',
and G ii: an arch of the meridian ; P p equal to

Now having found the side A B, adjacent to the
required angle A B C, its measure may be found
by Art. 332.

334. Fig. 30. Elevate the pole P, to 54° 43',
the quantity of the given leg B A; count the
same from M to Z, and fix the quadrant at Z;
bring that meridian which passes through London
under the strong brass meridian, and reckon the
given angle 48° 00', from O to A, on the ho-
rizon ; bring the quadrant to A, and the triangle
ZGM will be formed.

We have the measure of the- required side C A
upon ^ G an arch of the equator, equal to 42° 12',
and the hypothenuse B C, upon G Z, an arch of
the quadrant, equal to 04° 40', the angle ACB
trjiy If found by Art. 332. ^

335. Fig. 30. Elevate the globe to the quantity
of either given leg as AC, 42° 12', number the
same from JE to Z, and fix the quadrant at Z,
set the meridian which passes through London
under the strong brass meridian, and count the
other given leg A B, 54® 43', upon the equator
from iE to G, bring the quadrant to G, and the
triangle Z G ^ will be formed.

The arch Z G on the quadrant of altitude 64° 40'
is equal to B C the hypothenuse, the arch O A,
64° 35' on the horizon, is the measure of the angle
GZ^, equal to the required angle ABC. The
other angle may he found by Art. 332.

336.nbsp;In this fifth case, we must have recourse
to Art. 330, and then we shall have an oblique
angled spherical triangle a be, %. 31, whose side
a b is equal to the angle A C B of the given tri^
angle; the side be, equal to the angle ABC;
and the side a c, equal to the complement of the
right angle to 180 degrees, which must therefore
necessarily be-go degrees.

337.nbsp;Fig. 30. Number 48® OO' the side be of
this second triangle, from P, the pole of the globe
to Z, and there fix the quadrant of altitude ; then
bring the point Z into the zenith. Art. 1^2, and
count 90quot; 00' the quantity of the side a c, from P
the pole to G, upon that meridian which passes
through ; number the side a b, 64° 35' upon
the quadrant of altitude downwards from Z to Ggt;
then move the globe and the quadrant, until these
quantities meet in one point at G, and the triangle
PZG will be formed.

The arch M G, on the equator, will give the
measure of the angle ^ P G 34° 43', equal to the
required side A B; and the arch A O, in the ho-
rizon, that of the angle GZJE 64° 40', which is
the complement of the angle PZG to ISO de-
grees, and is equal to the hypothenuse B C: thus
having obtained the measures of two of the re-
quired sides, we have sufficient data to find the
third side A C, either by the first or second of the
preceding cases. Art. 331, 383.

Problem LXXI. Ttvo sides and an angle op'^
posite to one of them being given, to find the rest.

338.nbsp;Fig. 30. Count the side BC 83° 13', on
the strong brass meridian from P to Z; fix the
quadrant of altitude at Z, and bring that point
into the zenith; and from Z downwards to G^
number 56quot; 40'; where make a mark for the ex-
tent of the other side CD, and reckon its opposite
angle D B C, 48° 31', on the equator from the
point iCt at G eastward, towards M., where slop
the globe, and bring the mark upon the quadrant
to coincide at G with the meridian PG, which
passes through then the arch P G will contain
114° 3o', the measure of the required side BD;
and the arch H A in the horizon J 25° 20', will be
the measure of the angle BCD; the other angle
p GZ, equal to the required angle B D Cgt; may be
found by Art. 332, in changing the sides upon the
globe. Or,

xenith, over which the quadrant of altitude is to
be fixed, and lay its graduated edge upon the point
just marked ; it will shew in the horizon, between
the strong brass meridian and quadrant, Qlquot; 51',
the measure of the required angle P G Z, equal to
the angle B D C.

Problem LXXII. Two angles and a side op-
posite to one of them being given, to find the rest.

840. Fig. 30. Reckon the angle BDC, 62° 51',
which is opposite to the given side upon the
equator from eastwards, and bring that point to
iE; count the given side BC, 83° 13' upon the
quadrant of altitude from Z downwards to G,
where make a mark, and number the other given
angle BCD 125° 30', in the horizon from H to
A. • set the lower end of the quadrant to the point
A' and hold it there while you slide the pole of
the globe higher or lower, until the mark on the
quadrant at G, intersects that meridian which passes
through and at the same time, that the nut
at the upper end of it may be exactly in the ze-
nith, where fix it, and the triangle PZG will be
formed.

The arch V Z, of the strong brass meridian,
contains 56quot; 40', the quantity of the required side
CD, and the arch PG 114° 30', is equal to the
other required side B D, the angle D B C may be
found by Art. 332, or 339.

341. Fig. 30. Count the side CD 56° 40'from
P to Z on the strong brass meridian; bring the
point Z into the zenith, and to it fix the quadrant
of altitude, and number from Z downwards to G
the quantity of the side BC 83® 13', and there
make a mark ; then count the given angle BCD
125° 30', on the horizon from H to A, and to A
bring the quadrant ; lastly, bring the meridian
which passes through ii to the point G marked
on the quadrant, and the arch P G, J]4° 30' will
be the measure of the required side B D, and
the equatorial arch ./EG, 63° 51' is the measure
of the angle BDC, equal to the angle GPZ:
the other angle miy be found as before shewn.
Art. 332, 339.nbsp;^

342. Fig, 30. Number the side C D, 56quot; 40',
from P to Z, and bring Z into the zenith, and fix
the quadrant there also ; count the angle B D C,
62° 51' on the equator, from to JE ; number the
angle BCD, 125° 30' upon the horizon from H
to A, and bring the quadrant to A; then P G,
114° 30', will he equal to B D the required side,
G Z 8?'° 13'equal to the other required side B C,
and the angle PGZ equal to the angle DBC,
may be found by Art. 332, 339.

343. Fig. 30. Number the sPde C D 50° 40',
on the strong brass meridian from P to Z, bring
Z into tlje zenith, and to it fix the quadrant of
altitude ; coimt the side B D, 114° SO' on the
meridian, which passes through from P to G,
and the side C B 83® 13' upon the quadrant from
Z downwards to G, tnen move the globe and qua-
drant, until the two last points coincide. The
arch HA 125° 20' on the horizon will be the
measure of the angle PZG, equal to the required
angle BCD, the arch tES of the equator 82° 15',
is the measure of, the angle GPZ, equal to the
angle B D C. Thus having found two of the re-
quired angles, the third may be found by Art. 332,

344. This case may be resolved as the fifth
case of right angled spherical triangles. Art. 336,
by converting the angles into sides, then finding
the angles as in the last problem, where the angles
in the converted triangle will be the sides required
in this.

and oblique angled spherical triangles, we proceelt;J
to shew the extensive use of the globes in the so-
lution of a few of the principal astronomical pro-
blems, according to Dr. Flamsted's doctrine of the
sphere; and as we do not know these have ever yet
been applied to the globes, hope the reader will
think them both entertaining and useful.

Problem LXXVII, Given, the suns place in
the ecliptic in y 12° 15'. The inclination of the
planes of the equator and ecliptic, 23° 20'.

To find the sun's right ascension from the first
point of Aries, the suns distance from the north
pole of the world, and the angle, which the meridian,
passing through the sun at thctt place,-makes with
the ecliptic.

345. Fig. 34, The circular space marked SB, ii,
Vy, y, represents the ecliptic, e its pole, P the
north pole of the world, elevated 664- degrees above
the first point of 55, The eye is supposed to be
placed directly over the point e, vvhen the reader
compares this figure with the globe.

Make a mark ©, at 12° 15' in Taurus, to re-
present the sun's place in the ecliptic, and turn the
globe till that meridian which passes through iis
intersects the point Q ; it will then represent the
sun's meridian at that time.

The globe being thus rectified, we have between
the sun's proper meridian P Q, and the solstitial
colure S5 P here represented by the strong brass

meridian, with the arch © 05, a spherical triangle
G 25 P, right angled at 55, in which we have the
following data. See fig. 34.

25 P 66° 31', the complement of P e, 23^29',
the distance of the poles of the equator and ecliptic.

To find the angle 25 P O, the complement of
O P Tgt; the sun's right ascension from the first
point of Aries, Art. 202.

The angle S5 O P, which is the angle that the
meridian passing by the sun makes with the ecliptic.

We obtain the measure of the first, by numbering
the degrees upon the equator, between the strong
brass meridian, and that which passes through rit,
which are equal to 50quot; 12', its complement; 39quot; 48'
is the sun's right ascension, which is that angle at the
pole formed by the proper meridian © P with the

Note. This arch of the equator could not be re-
presented in fig. 34, it being under the broad paper
circle ; but the reader will see it plainly when the
globe is thus rectified.

The quantity of the second postulatum, which is
the sun's distance from the nearest pole, is found by
inspection, 74° 27' upon the arch P © of that me-
ridian passing through its compleujent P i, equal
to 15° 33', is the distance of the north pole from
the edge of the illuminated disc, represented upon
the globe, as in fig. 34, by the semicircle f e g,
the black line f e being the quadrant of altitude,
and the other dotted half eg bei»g supposed ; or.

if the reader pleases, he may represent it with a
string. This complement P i is, by Dr Flamsted,
called the reflection, and is ever equal to the sun's
declination.

Lastly, the measure of the angle 25 © P, is ob-
tained by screwing the quadrant to e the pole and
zenith point of the ecliptic, and counting QO degrees
from O to f; thither bring its lower end, then will
the arch © i be a quadrant also; and the quantity
72° 10', counted from f to i, upon the quadrant of
altitude, is the measure of the required angle
25 © P, formed by the meridian i P Q with the
«cliptic 0 2S

Problem LXXVIII. Given, the sun's place in
the ecHplic, y J2° lb', the reflection or declination
J5° 33', and latitude of the place, suppose London,
51quot; 32'.

To find the time of the suns rising aaid setting;
the length of the day and night; the amplitude of
the rising-sun from the east, and of the setting-sun
sfrom the west; and that of the path of our vertex in
the edge of the illuminated disc.

346. Fig. 35. Elevate P, the pole of the globe,
to 15° 33', the sun's declination, above the plane of
B d G i, the circle of Illumination : count the same
quaiitity from ^ the equator to ©, at which point
fix the quadrant of altitude ; this point will represent
the sun's place ; make a mark upon the globe on
that iTieridian which passes through ii at 51° 32'
the given latitude; this will express a point in the
path of the vertex of London : bring this point to
the edge of the disc at B, and set the lower end of

the quadrant thereto: B is that point in the disc
from which the sun is Seen to rise, or where the
vertex of London in its diurnal motion from west
to east, passes out of the obscure into the en-
lightened part of the disc ; i Pd is the sun's proper
meridian, which is represented in this by the strong
brass meridian. O is the place at which the vertex
of London arrives at noon, being 51° 33' from JE
the equator at O, and G the place in the disc, from
which the sun is seen to set, or where the vertex
passes out of the illuminated into the obscure part
of the disc. B 0 G is the diurnal, and G—B, on
the other side of the disc, (not here represented, but
to be seen upon the globe) is the nocturnal part of
the path of London.

If you bring the mark on that meridian which
passes through =2= to the point G, and the quadrant
of altitude to the same point, it will be plain that
we shall have two triangles formed on each side of
i P O, the sun's proper meridian, viz. © PB, BiP,
on the oriental or ascending side, and 0 PG, iPG,
on the occidental or descending side.

In either of these four triangles there are sufficient
data to find what is required in this problem. In
the triangles © P B, Q P G, are given, © P in
both, the sun's distance from the pole, P B, equal
to P G, the distance of the vertex from the pole,
which is always equal to the complement ^ the
latitude, with the sides © B, © G, each equal to
go degrees.

To find the angle P B ©, or P G ©, the sun's
amplitude from the north, when rising or setting;
and the angle © P B, or ©PG, the time before,
noon. But as the two last mentioned angles are

obtuse, we chuse to resolve this problem by one of
the two lesser triangles P B I, P G I, each of them
being right angled at i, in which are given, P i,
the reflection, ] 5° 33', equal to the declination,
B P, equal to P G, 38® 28', the distance of the
pole from the vertex.

To find the angle PBi, or PGi, the comple-
ment of O B i, or 0 G i, the sun's amplitude at
rising or setting from the east or west, and the
angle i P B, equal to the angle i P G, which are
formed between the sun's proper meridian, and
that which passes through the vertex at sun-rising
or setting: this changed into time, expresses the
time from midnight, of sun-rising and setting. The
side B i is called the amplitude of the path of Lon-
don in the edge of the disc, and these are obtained
from the globe as follows:

The measure of the angle B P i is obtained by
inspection, reckoning from ii upon the equator to
the strong brass meridian, which is 96° 31': if re-
duced to time, it is 4 h. 38 min. in the morning,
at which time the sun rises at London, when he is
in y 12° 15', and consequently sets at 7 h. 22 min.
afternoon. See Art. 249.

The quantity 35° 38' of the required side B i,
is obtained by inspection between B and i, upon the
edge of the disc.

The measure of the angle P B i may be attained
as follows: every thing else remaining as before,
bring the graduated edge of the moveable meridian
to the first point of T on the ecliptic ; then count
the complement 54° 22' of the side B i, from i to x,
where make a mark ; and count the complement of
BP, 51° 32' from P to y, upon the moveable me«

ridian, where make another mark ; remove the
quadrant of altitude, and apply it between these two
marks, and the quantity 25quot; 31' is the measure of
the ang-le PB i. Art. 327. This is the sun's ampli-
tude from the east, or N. E. 3° l' easterly.

Problem LXXIX. Given, the latitude of the
place 51° 32', or rather its complement 38° 28',
tvhich is the distance of the path of the vertex from
the pole, aitd the sun's distance from the pole, 74° 27',
which is the complement of his declination 16° 33'.

To find the suns distance from the vertex at the
hour of six, and ids amplitude at that time.

347. Fig. 35. Elevate P, the pole of the globe,
to 15° 53', the declination ; bring the moveable me-
ridian to that which passes through London; slide
the artificial horizon to 51° 32', the latitude of the
place, and turn the globe till the sixth hour upon
the equator comes under the graduated side of the
strong brass meridian ; then the moveable meridian,
together with that which passes through wiU
represent the six o'clock hour-circle F K P A g ;
fix the quadrant of altitude to 15° 33', at the point
O, counted from M the equator; turn the qua-
drant to the point K, which represents the center of
the artificial horizon, and the proper triangles will
be formed.

In the right angled spherical triangles AP©,
K P O J angled at P, are given P K, equal to
PA, 38° 28', the distance of the vertex from the
pole, O P. the path's distance from the pole
74° 27'. To find O K, or O A, the sun's dist-
ance from the vertex at the hour of six, and either

of the angles, 0 A P, or 0 K P, the sun's azimuth
from the north at the same time.

It is plain that P 0, being the sun's proper me-
ridian, FPg at right angles to it, must be the
hour-circle of .^ix in the morning and evening,
and that the sun rises, when the vertex B comes in
the western edge of the sun's enlightened disc.
Therefore it must be at K, at six o'clock in the
morning; at noon the vertex will be at O, upon
O P, the sun's proper meridian; and at six in tbe
evening it will be at A, upon the six o'clock hour-
circle again ; and when the vertex arrives at G,
Bpon the eastern edge of the disc, the sun will be
seen to set westward of the vertex.

The required side © K, which is the sun's di-
stance from the vertex, is found by counting the
quantity 77° 33' upon the qtiadrant, from © to K;
and the angle © K P, 80° 11'; the sun's azimuth
from the north may be measured by producing the
side K ©, to go degrees from K to m, (Art. 327.)
the side K P being already produced on the ether
side of the strong brass meridian, K P is known to
be 38° 28'; therefore count its complement 51° 32',
from P to n, upon that meridian which parses
through and there make a mark ; now remove
the quadrant of altitude to cut the opposite point
of the horizon to that at which it stood before,
and count thereon from © downwards 12° 07' to
m, where make another mark; then an arch of a
great circle applied to these two marks will give
S0° 11', the sun's azimuth from the north.

Note. A flexible semicircle'of position, if ap-
plied with the quadrant of altitude, will be fouud
useful in this and many other cases.

Problem LXXX. To Jind the suns distance
from the vertex when due east or west, and the hour,
or time from noon, when he shall be in either of
these points.

348. Fig. 35. The north pole of the globe being
eievfited to the sun's declination, as in the» last
problem, and the quadra.it fixed at O as before,
tre moveable meridian placed on that of London,
and the center of the artificial horizon set to the
same point; turn the globe so that the graduated
edge of the quadrant may he upon the east and.
west points of the artificial horizon, and the tri-
angle O K P will be formed ; in which is given
O P, the sun's distance from the pole 74° 27';
P K the distance of the path from the pole 38*^ 21';
0 K, the sun's distance from the vertex, when due
east and west, may be found by inspection, count-
ing from © to K upon the quadrant, 70° o': the
measure of the angle ©PK is also obtained upon
the equator, counting from that point where it is
crossed by the quadrant of altitude, to its inter-
section with the graduated side of the strong brass
meridian, 77° 53', in time 5 h, 9 min. from noon,
which is 51 min. past six in the morning; or at
9 win. past five in the afternoon, when the sun is
due east or west.

The sun's distance 70° O' from the vertex as
found above, when due east or west subtracted from
90 degrees, leaves 20 degrees, which is its altitude
abcgt;ve the horizon at either of these times, for
0 v, © w are quadrants, from which if we take
© K in the first, or O A in the second, it is

Problem LXXXI. Given the hour from noow,
viz. 8 in the morning, which is 4 hours from noon,
and the suns distance from the pole, 74° 27'.

34Q. Fig. 33. Elevate P the pole of the globe to
the sun's declination, 15° 33', set the moveable me-
ridian to the vertex of London, and slide the center
of the artificial horizon to that point at K, and turn

the globe, until the eighth hour-circle marked upon
the equator comes under the graduated side of the
strong brass meridian ; the quadrant of altitude
being fixed at i:he point G as before, turn it to the
point K, and the triangle G P K will be formed ;
in which is given the ingle K P G, four hours from
noon, PK, 38° 28' the distance of the path from
the pole ; Q K, the sun's distance from the vertex
will then be found, by inspection on the quadrant,
counting from G to K 50° 20'.

Problem LXXXIL Given the sun's distance
from, the pole 74° 27', the latitude of the place
51° 32', and the sun's distance from the vertex by
observation, 46° ii'.

To find the time of the day when that observation
vias made, and the azimuth upon which the sun was
at that time.

350. Fig. 35. Elevate P the pole of the globe, to
15° 33', the complement of the sun's distance from
the pole; bring the moveable meridian to the vertex

of London, and slide the center of the artificial
horizon to that point: then screw the quadrant to
O the zenith of the illuminated disc, and bring it«
graduated edge to London ; and move the globe and
quadrant, that the vertex may cut the quadrant at
46° 1 J', the observed distance counted from © toK;
and an obhque angled triangle O K P will be formed
upon the globe, in which we have three sides given,
O P, 74° 27' the sun's distance from the pole, O K
his observed distance from the vertex 46° 11' in the
morning, and K P 38° 28' the distance of the pole
from the vertex: to find the angle K P 0, count
the quantity contained upon the equator, between
the moveable and strong brass meridians, which
will be found 36° 23', or 2 h. 25 min. in time
from noon, which is 35 minutes past 9 o'clock in
the morning.

The angle P K O may be measured by producing
the arches which include the angle to the distance
of 90 degrees from the angular point as in Art. 332,
or by Art. 339, and it will be found 127° 40', or
11 points of the compass from the north, reckoned
round by the east, or S E b E, 3° 35' southerly.

If the observation had been made in the afternoon,
at the same height or distance from the vertex, the
answers would have been the same, but in a contrary
direction.

By this problem we may regulate our clocks at
any time of the day, without staying till the sua
comes to the meridian ; if the sun's altitude be taken
by a large quadrant, and you note the time by the
clock when the observation was taken, and the true
time answering thereto be found as above, or by
calculation, the difference between this and the time

pointed out by the clock at the instant of observation
^11 shew how much the clock is before or behind the
solar apparent time.

Problem LXXXIII. Given, the htiittde of the
'phce 51° 32', the suns place y 12° 15', the suns
right ascension, 39° 48', at one o clock afternoon, being
ihe time when an ohservation was made :

To find what point of the ecliptic culminates upon
ihe meridian, which is the highest point of it, or the
gOth degree from the points wherein it intersects the
horizon, and consequently those polnis iht ntst l-ves ; the
distance of the nonagesimal and mid heavm points
from the vertex \ and the angle made by the vertical
circle paising through the sun at that time with the
ecliptic.

351. Fig. 34. Elevate P the pole of the globe to
66-l degrees, count the same quantity from M the
equator to e, there fix the quadrant of altitude;
this point e, will then be the pole of the broad
paper circle marked T ® — Y^j ^^hich now repre-
sents the ecliptic, in which at © put a mark, at
y 12° 15', for the place of the sun; bring the
graduated edge of the moveable meridian first to
the vertex of the given place, in this example Lon-
don, and bring the center of the artificial horizon
thereto; next set it to the point marked O, and the
horary index to that Xllth hour upon the equator
which is most elevated, and turn the globe until the
given time one hour from noon comes under the
horary index. Then set the graduated edge of th»
quadrant of altitude to the vertex at E, and the
globe will be rectified fgr a solution of this peoblem,
3

E, is that point in the path on which the vertex,
is at one o'clock afternoon ; D, that point of the
ecliptic which then culminates upon the meridian
E O 95, the angle made by E O the vertical circle
then passing through the sun with the ecliptic ;
the point T in the ecliptic, which is cut by the
quadrant of altitude passing through E, is evidently
the nearest point to the vertex, or the highest or
nonagesimal point of it. ET is the distance of
the point T from the vertex E, and ED the di-
stance of D from the vertex, which is the point then
culminating upon the meridian.

In the triangle D 35 P, is given the angle 25 P D,
the complement of T P D, which is the right ascen-
sion of the mid-heaven, the sun's given right ascen-
sion 48', agreeable to the sun's place y 12° 15',
at noon, to which the addition of 15° for one hour
after noon, as we did above in rectifying the globe,
makes the angle T PD 54° 48' the present right
ascension of the mid-heaven, and PED the me-
ridian at that time ; P 5E 66° 31', and the angle
at 25 right.

I. To find 25 D, the complement of f D, the
longitude of PD the mid-heaven from the first
point of Xgt; which is obtained on the ecliptic here
represented by the broad paper circle between points
25 and D, 32° 54', or between T »quot;d D, 57° 6',
the longitude itself, which is 27 deg. 6 min. in
Taurus. P is that point of the ecliptic which cul-
minates upon the meridian at that time ; whence we
may readily find what points of the ecliptic rise and
set .It that time,

The quantity 70° 27' contained between P the
pole of the globe, and D upon the moveable me-
ridian, is the distance of D the mid-heaven point
from the pole; if we deduct P E 38.28, or count
the quantity between D and E, we shall have
31° 59', the distance of the point D in the ecliptic
which now culminates on the meridian from the
vertex E, its complement to 90 degrees being 58° l'
is the height of the ecliptic at this time, or the
inclination of the ecliptic to the horizon of the
place.

II. To find 25 T, the complement of T T,
tvhich is the longitude of the nonagesimal, andTE
its distance from the vertex.

In the oblique angled spherical triangle PeE,
are given P e 23° 29', the distance of the poles of
the equator and ecliptic, PE, 38° 28' the co-lati-
tude with the included angle ePE 144° 48', the
complement of 35° 12' the distance of the mid-
heaven from the first point of S5 to 180 degrees.
The measure of this angle is obtained upon the
equator between the strong brass, and the moveable
meridians.

To find the angle PeE, as it is included between
05 e, the strong brass meridian, and e T the qua-
drant ; we have its measure 24° 44' upon the arch
03 T of the ecliptic, its complement 65° 16' is T T,
the longitude of the nonagesimal from the first
point of^Aries, or H 5° 16' its distance ET from
the vertex E, is gained on the quadrant of altitude

3l0 2', the complement of which 58° 58' is the
altitude of the ecliptic above the horizon at this
time; or it is the feiigle which the planes of the

ecliptic and horizon make with each other ; as T
is the highest point of the ecliptic at this time,
and its longitude in IJ 5° iamp;, three signs or 00
degrees counted on the broad paper circle fcbm T
towards x will give tl^ 5° 16' for that point of the
ecliptic which is then rising, and the same quantity
counted from T towards y will fall upon ^ 5° 16'
which point is then setting,

III. To find the angle EOT, being that which a
vertical circle E O passing through the sun at that
time makes with the ecliptic; this is called the
parallactic angle.

To represent this angle upon the globe, it is ne-
cessary to have a flexible slip of brass, or a slip of
parchment about the breadth of the quadrant of
altitude, with the divisions inscribed on it with a
pen ; if this slip be applied to the point O, and its
graduated edge laid over the vertex E, and ex-
tended to the quadrant of altitude first removed to
X 90 degrees from O, it will intersect the quadrant
at w; the quantity upon the quadrant, from x
to w, will be 56° IQquot;, the measure of the paral-
lactic angle EOT. The result of this problem is
as follows :

That point of the ecliptic which culminates dn
the meridian is in a 27° 6', its distance from the
vertex 3i° 59', the highest or nonagesimal point of
the ecliptic, n 5° 16', its distance from the vertex
31' 2', the rising point of the ecliptic rrj^ 5° 16', its
setting point ^ 5° 16', the distance of the nona-
gesimal from the mid-heaven 8° 10', and the paral-
lactic angle at this time 56° 59',

Problem LXXXIV. Given, the latitude of the
place, right ascension and declination of any point of
the ecliptic, or of a fixed star :

To find its rising or setting amplitude, its ascen-
sional difference, and thence its oblique ascension.

352. Fig. 36. Elevate P, the pole of the globe
to 51quot; 32', the latitude of London ; then the diurnal
parallel of the first point of Cancer will be repre-
sented by 25 F, the tropic of that name, marked
25 e F, in fig. 36, bring the first point of 25 on
the ecliptic, hne to the graduated edge of the strong
brass meridian, and e will be the point where it
rises ; to this point bring the graduated edge of the
moveable meridian, represented in the figure by
P e g p, then a e, upon the horizon at H O, or the
angle aZe, from the angular point Z m, the zenith
will be its rising amplitude, from the ease at Aries,
towards the north point of the horizon at o, and
a g, determined by the moveable meridian, which
now represents a circle of right ascension passing
through the points e and g, and the horizon its
ascensional difference, which subtracted from its
right, leaves its oblique ascension.

The ascensional difi^erence is the difference be-
tween that point of the equator, which culminates
upon the meridian, with the first point of Cancer,
and that other point of the equator which rises
with it above the horizon ; it is here subtracted,
to find the oblique ascension ; because that point of
the equator which rises with the first point of Can-
cer, comes to the horizon before the point of itP

In the triangle age, we have ge, the northern
declination of the point e, in the diurnal parallel
of the first point of .Cancer, equal to 23° 29', the
angle g amp; e, which is the inclination of the planes
of JEQ the equator, and HO the horizon, with
the angle at g right. Whence upon the horizon
we obtain between a and e, 39° 50', the rising
amplitude of the first point of 25, which is N E b E,
and 5° 20' more. Upon the equator, from a to g,
we find 33° 9', the ascensional difference of the first
point of Cancer: which subtracted from OOdeg. the
right ascension of that point, leaves 56° 51', its ob-
lique ascension.

Every thing else npon the globe remaining the
same, if we bring the moveable meridian to the
point n, where the tropic of Capricorn intersects
the horizon, 'we shall have another triangle 3 b n,
equal to the former, wherein the first point of Ca-
jiricorn has the same amplitude 23° 29' from a, in
the east, to n, towards H, the south part of the
horizon, that the former triangle had towards the
north ; and this added to the right ascension of the
first point of Capricorn, 270'' 00', gives its oblique
ascension 303° 09', because that point of the equator
which rises with the first point of Capricorn comes
to the horizon after the point of its right as-
cension, or that with which it culminates upon the
meridian.

353. Note.. Every star which rises with any
point of the ecliptic, has the same oblique ascension

Bootes, of the fourth magnitude, which is repre-
sented in fig. 30. at the point having its north
declination of 17° 21', its ascensional difterence a f,
rises above the horizon with the same point of the
equator with which e, in the diurnal parallel ot the
first point of Cancer, rises. So that having its right
ascension 204=, and declination 17quot; 21', its ascen-
sional difference and oblique ascension may be foAind
in the triangle a f , in the same manner in which
the former were found in the triangle age.

As the ascensional difference is subtracted from
the right ascension to find the oblique ascension, if
it be added to the right ascension it will give the
oblique descension. For that point of the equator
which sets with the diurnal parallel of the first
point of Cancer, comes to the horizon before the
point of its right ascension, or that with which it
culminates upon the meridian. Hence we have
another method of finding the length of the day at
London, or elsewhere, when the sun is in the first
point of Cancer, or any other parallel of his de-
clination, viz.

354. Subtract the sun's ascensional difference m
time from six in the morning, the residue is the
time of his rising ; add it to six in the evening, and
it gives the time of his setting ; then doubling the
first, you obtain the length of the night, and the
double of the last will be the length of the day.
And after this manner all these particulars may be
found to every interniediate point of the ecliptic in

As the rising and setting of some of the principal
fixed stars are mentioned by ancient writers, as
' criteria by which to judge of the commencement

of seasons, and the beginning of times set apart
for rehgion, husbandry, politics. Sec. we have
judged it necessary to add the following problems,
as a farther elucidation of the two former. Art,
302, and 303.

Problem LXXXV. Given, the latitude of the
place, the points of the ecliptic luith which a star
rises or sets, and the altitude of the nonagesimal,
when those points are upon the horizon :

To find in what points of the ecliptic the sun must
he to make the star when rising or setting appear just
free from the solar rays ; and thence the times of its
heliacal rising and setting.

355. Fig. 36. Elevate P, the pole of the globe,
to the latitude of the place, and fix the quadrant of
altitude in the zenith at Z, and H O will represent
the horizon. Turn the globe until the given star
just appears at ^ in the edge of the horizon, and
a will be that point of the ecliptic in which the
sun must be when the star rises and sets with it s
Let us suppose the star at ^ to be of the first mag-
nitude, which requires that the sun should be de-
pressed 12 degrees below the horizon, that the star
may appear free from the solar rays: having noted
the point a, on the ecliptic, move the quadrant
until the 12th degree below the horizon intersects
the ecliptic at s, then Z s will represent a verti-
cal circle, in which the sun at s is depressed 12
degrees.

So in the triangle aC5, right angled at L, we
have the sides CS, 12 degrees, the requisite de-

pression of the sun below the horizon, to free the
star from his rays, or that point of the ecliptic at
S, to make the star at X first heliacally visible when
it rises, or from which we may see upon the other
side of the globe when it sets heliacally.

The angle SaC is the altitude of the nonagesi-
mal, or inclination of the planes of the ecliptic and
horizon ; and the angle at C right, being formed
by the intersection of a vertical circle with the
horizon : the measure of the angle SaC, is ob-
tained by inspection on the hrass meridian from O
to VJquot;, the point in which the tropic of Capricorn

cuts that circle; the side a S, being an arch of the
ecliptic, through which the sun passes, from the
time the star at v rises with him to its heliacal
rising, or an arch of the same quantity on the
other side of the globe, through which the sun
must have passed from the time when the star set
heliaeally, to its setting with the sun, which, as in
the former case, added to the point of the ecliptic,
in which the sun is when the star rises with him,
gives the point he is in at its heliacal rising ; and
in the latter case subtracted from that point of the
ecliptic the sun is in when the star sets with him,
leaves the point he is in at the same star's heliacal
setting.

Thus having found the points of the eclipticquot; in
which the sun must be when any star rises or sets
heliacally, against those points in the kalendar, on
the horizon,quot; you obtain the month and day.

As the distances of the fixed stars from one
another have been found the same in all ages, it
is probable they have no real motion of precession.

but only an apparent one, caused by the retroces-
sion of the equinoctial points, \vhich are found to
recede from their ancient stations at the rate of 50
seconds every year ; this alters their longitude,
but their latitude does not vary : hence their places
being once determined to a known year, their lon-
gitudes may be ascertained for any time past or to
come, by the solequot; subtraction or addition of so
many times 50 seconds, as there are years between
that to which the given star is rectified, and that to
which it is required; or knowing the quantity of
precession from any former period, the distance
thereof in time may be obtained, by reducing it
into seconds, and dividing the result by 50, the
quotient will give the number of years, as in the
following examples:

The regular change in the precession of the fixed
stars, or rather the constant retrogression of the
equinoctial points, seems to cause an irregular va-
riation in their right ascensions and declinations,
more or less, according to their distances from the
pole of the ecliptic. Whence it may not be im.
proper to shew how these may be found, as the
cosmical, achronical, and heliacal risings and
settings of the fixed stars, found by the precedmg
problems, have respect only to the present age :
and the following problem, with which I shall
conclude this treatise, will shew the reader how to
determine the ancient place of any star agreeable
to the time of ancient authors, if their authority
may be depended on.

Elevate the celestial globe to 664- degrees, bring
the pole of the ecliptic into the zenith, and there
fix the quadrant of altitude ; apply its graduated
edge to the given star, and it will cut its present
longitude, either on the ecliptic or broad paper
circle, which in this position of the globe coincide
with each other : make a rnark on the quadrant,
at-the latitude of the given star,, and remove it to
its ancient longitude, as found above; then bring
the graduated edge of the moveable meridian to the
mark just made upon the quadrant of altitude, and
set the center of the artificial sun to that point
which will then represent the ancient place of the
given star. That point of the moveable meridian,
upon which the center of the artificial sun was
placed, is its ancient declination ; and that point of
the equator, cut by its graduated edge, is its an-
cient right ascension.

The globe being thus rectified to the place and
precession of any particular star, as given us by
ancient authors, the times of the year when such
star rose or set, either cosmically, achronically, or
heliacally, may he thus obtained by the preceding
problems, agreeable to the period of the author
under consideration.

a TABLE OF THE HORARY DIFFERENCE IN THE MO-
TION OF THE FIRST POINT OF ARIES, AT THE
TIME OF A VERNAL EQUINOX.

a TABLE OP THE DIFFERENCE OP THE PASSAGE OP
THE FIRST POINT OF ARIES OVER THE MERIDIAN,
FOR EVERY DAY IN THE YEAR.

	O	O	Length	Twi-
	Rising.	Setting.	ofDay.	hght.
	h. m.	h. m.	h. m.	h. na.
Cape Horn	S 44	3 16	6 32	2 35
Cape of Good Hope	7 09	, 4. 51	9 42	1 43
Rio de Janeiro in Bra- quot;i
zii, near the tropic V	6 42	5 19	10 38	1 23
o' Capricorn j
The island ofSt.Tho-T. mas at the equator. S	6 0	6 0	12 0	1 20
Cape Lucas, the south- ^
ernranst point of Ca- f lifornia,at the tropic ^	5 12	6 48	13 36	1 35
of Cancer. )

sec.	min.	deg. h.	h. min. sec.
15)45(3quot;	15)51(3'	15(173(11	11 32 0
45	45	15	0 3 24
	—	—	0 0 3
e	6=24quot;	23
		15	11 35 27aniw.
	t	8=32'

Right ascension T Qj	4	23 52
Decem. lO,	Ö	22 58
■		1 6
Right ascension T Q,	6	lt;24 4
Example IV.
A. D. 1772, equinox March IQ.	h.	min.sec.
Bissextile year.	h.	min.sec.
Feb. 28,	1	13 S5
		1 59

Right A sc.	*		Deel, and Lat.			West Lon.
267è	Knee of Hercules		i	37	Carthagena, Old Spain Frontiers of Mo-' roccoandTar- •	Ok
1671	Wrist of Hercules		1	30i	Carthagena, Old Spain Frontiers of Mo-' roccoandTar- •	Oh
261 198 175 191	Ras albagus, Ser-quot;1 pentarius J Spica Virginis Deneb Alasad/ Lion's tail Alioth, 1st in tail Great Bear	[	ot » 8 1	12è 10 16 57	gua 3 Kingdom Kom-\ bergrada, Africa ƒ Peru, S. America Chapa in Mexico Isle Belchier, Hudson's Bay	7 70 93 77

Right Asc.		Deel, and Lat.			East Lon.
277	Vega, in Lyra		38j	S. W. Cape, Isle'	0
	Vega, in Lyra			of Sardinia	y
290	Atair, Eagle's neck	»	8	Frontiers of Benin'
	Atair, Eagle's neck			and Nigritia, Africa	17
290	Swan's beak, A1-' bireo	8	27i	Mid.LevatainTa-' gua, Africa	22
308	Deneb, Swan's' rump	»	44J	Palmyra	40
34.3	Sheat, in Pegasus	e	27	Middle of Mogul's!	75
	Swan's So. Wing			Empire j	75
309	Swan's So. Wing	f	331	Frontiers of Tur-T
309				key in Asia, and gt; Desert Arabia J	41

Right		Deel, and			East
Asc.		Lat.			Lon.
132	Great Bear's foot	»	47	Middle of Hungary	22
139	Hydra's heart	«	8	Kingdom Massey,7	29
				Africa j	29
143	Corner^ of the' Lion's mouth	lt;	25	Nahassa, in Egypt	33
149	Regulus, Lion's' heart	ÛC.	13	Abyssinia, Africa	39
176	Third in the Sq.		53	0»tiakis, S.Wpart	66
176	Great Bear	y	53	of Siberia	66
192	N.WingofVirgo'		12	Sea 2° E. of Pon-'	82
	Vindematrix		12	dicherry	82

Right		Deel.			W.
Right	.	and			Lon.
Asc.		Lat.
206	The star in thequot;)		20	Sea 2° S. Capequot;	83
206	« leg of Bootes J		20	Corrente, Cuba
219	Somhemgt;icaleof1 Libra J	ft	15	Collao, in Peru	70
226	Jiorthern Scale	ß	8	Amazonia, America	63
	1 of Libra	ß	8	Amazonia, America	53
2^6	A star in Scorpio	tr	25	Paraguay, America	53
240	H^nd of Ser- :		3	N.'W. part of Brazil	49
267 ■	pentarius knee of Hercules		37	N.of St. Michael,quot; in the Azores

Right Asc,		Deel, and Lat.			• W. Lon.
290 294 308 324 331 _ 341	The Swan's beak FirstiatheSwan's } wing f Deneb, in thequot; Swan's rump Side of Cepheus Head of Cepheus Fomahaut, mouth 1 of Pisces Notius j	e s u s s lt;x	28 44 44 70 56 30	Gulph Mexico, 3° S. Misisippi Lake Michigan^ Canada New England Cumberland' near Baffin's Bay N. Sea, E. of La- brador Middle of the At- lantic Ocean	88 84 70 57 4r 37
c- Eastward.
Right Asc.		Deel, and Lat.			E. Lon,
.27 42 43 S3 96 lia	Almaak, foot of Andromeda Shoulder of Perseus Menkar, Whale'squot; iriouth fhe Pleiad« North foot tsffollux Prpcyon, little Dog	y i y a y k	41 52 3 23 16 6	Sea coastof Sardinia Brisac Luthania Bake Bake, Africa Frontiers ofEgypt? anii Nubia J Golconda, Asia Seal°N.W.Achem-l Sumatra ƒ	9 24 25 35 78 94

Years.	D.	H.	M.	Days.	H.	M.
6000	■ 45	20	0	2191454	4	0
5000	38	4	40	1826211	19	20
4000	30	13	20	1460969	10	40
3000	22	22	0	1095727	2	0
2000	15	6	40	730484	17	20
1000	7	15	20	365242	8	40
900	6	21	0	328718	3	0
800	6	2	40	2.92193	21	20
700	5	8	20	255669	15	40
600	4	14	0	219145	10	0
500	3	19	40	182621	4	20
400	3	1	20	146096	22	40
300	2	7	0	109572	17	0
200	1	12	40	73048	11	20
100	0	18	20	36524	5	40
90	0	16	30	32871	19	30
80	0	14	40	29219	9	20
70	0	12	50	25566	23	10
60	0	11	0	21914	13	O4
50	0	9	10	18262.	2	50
40	0	7	20	14609	16	40
30	0	5	30	10957	6	30
20	0	3	40	7304	20	20
10	0	1	50	3652	10	10
9	0	1	39	3287	4	21
8	0	1	28	S.921	22	32
7	0	1	17	2556	16	43
6	0	1	6	2191	10	54
5	0	0	55	1826	5	5
4	0	0	44	1460	23	16
3	0	0	33	1095	17	27
2'	0	0	22	730	11	38
1	0	0	11	365	5	49

£ S B ^ O	JS . ■y a		m « b 'rt 3 a, a gt;gt;« O
A	31	January .	31
D	28	February	59
D	31	March	90
G	30	April	120
B	31	May	151
E	30	June	181
G	31	July	212
C	31	August	243
F	30	September	273
A	31	October	304
D	30	November	334
F	31	December	365

M.	s.	///	M.	s.
h.	M.	s.	h.	M.	s:
1	0	9	31	4	42
2	0	18	32	4	51
3	0	27	33	5	0
4	0	36	34	5	9
£	0	45	35	5	18
• 6	0	54,	36	5	27
7	1	4	37	5	36
8	1	13	38	5	45
9	1	22	39	.5	54
10	1	31	40	6	3
11	1	40	'41	6	12
12	1	49	42	6	21
13	1	58	43	6	31
14	2	6	44	6	40
-15, '	2	16	45	6	49
l6	2	25	46	6	58
17	2	34	47	7	•7
18	2	43	48	7	16
1.9	2	53	49	7	25
20	3	2	50	7	34
21	3	11	51	7	43
22	3	20	52	7	52
23	3	29	53	8	0
24	3	38	54	8	8
25	3	47	55	8	17
26	3	56	56	8	25
27	4	4	57	8	35
28	4	12	58	8	45
29	4	22	59	8	55
30	4	32	60	9	5

Days.	January.	February,	March.	Days.
1 ■ 2 3 4 5	H. M. S. 5 10 53 6 28 2 4 4 57 40 53 16	H. M. S. 2 58 46 54 42 50 39 46 37 42 36	H. M. S. 1 9 50 6 7 2 24 0 58 41 54 58	1 2 3 4
6 7 8 9 10	48 53 44 31 40 9 35 47 31 26	38 36 34 36 30 37 26 39 22. 42	51 16 47 34 43 52 40 11 36 30	5 6 7 8 9
11 12 13 14 15	27 6 22 46 18 27 14 9 9 51	18 45 14 50 10 55 7 1 3 7	32 50 29 10 25 31 21 52 18 13	10 11 12 13 14
16 17 18 19 20	5 33 1 17 3 57 2 52 47 ■ 48 33	1 59 14 i 55 22 51 32 47 42 43 52	14 34 10 55 7 16 3 38 0 0 0	15 16 17 18 39
21 22 23 21 25	44 19 40 6 35 54 34 43 27 33	40 3 36 14 32 26 28 39 ■ 24 52	23 56 22 52 44 49 6 45 28 41 50	20 21 -22 33 24
26 27 28 29 30 31	23 24 19 15 15 7 11 0 6 54 2 49	21 6 17 20 13 35	38 12 34 34 30 56 27 18 23 40 20 2	25 26 27 28 29 30 —____

Days.	April.			May.			June.			Days.
	H.	M.	S.	H.	M.	S.	H.	M.	S.
1	23	16	24	21	25	12	19	22	28
2		12	46		21	23		18	22	1
3		Q	8		17	33		14	16	2
4		5	29		13	43		10	9	3
5		1	50		9	52		6	2	4
6	22	58	11		6	0		1	55	5
7		54	33		O	8	18	57	48	6
8		50	54	20	58	16		53	40	7
9		4,7	14,		54,	2.-3		49	32	8
10		43	35		50	30		45	24	9
11		39	55		46	35		41	15	10
12		36	14		42	40		37	6	11
13		32	33		38	44		32	57	12
J4		28	52		34	49		28	48	13
15		25	11		30	51		24	39	14
		21	30		26	54.		20	29	15
17		17	47		22	56		16	20	16
18		14	4		IS	58		12	11	17
19		10	21		14	59		8	1	18
20		6	38		11	0		3	51	19
21		2	54		7	0	17	59	42	20
22	21	59	11		2	59		55	33	21
23		.55	26	19	58	59		51	23	22
24		51	41		54	58		47	14	23
25		47	55		50	56		43	4	24
26		44.	9		46	53		38	55	25
27		40	23		42	50		34	46	26
^ t 2S		36	36		38	46		30	37	27
29		32	48		34	42		26	29	28
30		29	0		30	38		22	20	29
		29			26	33				30

Days.	July.		August.			September.			Days.
	H.	M. S.	H.	M.	S.	H.	M.	-S.
1	17	18 11	15	13	26	13	17	22
2		14 3		9	33		13	45	1 -
3		9 56		5	41		10	8	2
4		5 48		1	49		6	31	3
5		1 41	14	57	58		2	54	4
6	16	57 34		54	8	12	59	17	5 u
7		53 28		50	18		55	40	6
8		49 22		46	29		52	4	7
9		45 17		42	40		48	28	8
10		41 J2		38	52		44	52	9
11		37 7		35	5		41	16	10
12		33 2		31	18		37	40	11
13		28 58		37	32		34	4	12
14		24 55		23	46		30	29	13
15		20 52		20	1		26	54	14
16		l6 49		16	l6		23	18	15
17		12 47		12	32		19	43	16
18		8 46		S	48		l6	7	17
19		4 45		5	5		12	31	18
20		0 45		I	22		8	56	19
21	15	56 45	13	57	40		5	20	20
22		52 46		53	58		1	44	21
23		48 48		50	16	11	58	8	2\|2
24		44 49		46	35		54	32	23
25		40 51		42	55		50	56	24
26		36 54		39	)4		47	20	25
27		32 67		35	35		43	44	26
2g		29 2		31	55		40	7	27
29		6		?8	17		36	30	28
30		91 12		24	38		32	53	29
31		17 18		21	0				30

Days.	October.			November.			December.			Days.
	H.	M.	S.	H.	M.	S.	H.	M.	S.
1	11	V9	15	9	32	50	7	28	50
2		25	37		28	55		24	29	1
3		21	59		24	58		20	8	2
4		18	20		21	0		15	47	3
5		14	42		17	2		11	25	4
6		11	3		13	3		7	3	5
7		7	23		.9	3		2	40	6
S		3	43		5	2	6	58	17	7
g		0	2		J	0		53	54	8
10	10	56	21	8	56	57		49	30	9
11		52	40		52	53		45	6	10
12		48	58		48	49		40	41	11
13		45	16		44	44		56	15	12
14		41	33		40	38		31	50	13
15		37	50		36	31		27	24	14
16		34	6		32	23		22	58	15
17		30	21		28	14		13	32	16
18		26	36		24	5		14	5	17
1.9		22	50		19	54		9	39	18
20		19	4		15	44		5	13	19
?1		15	17		11	32		0	46	20
22'		11	29		7	19	5	56	19	21
2amp;		7	40		3	5		51	52	2?
		3	51	7	58	51		47	25	23
25	lt;	O	2		54	36		42	59	24
26	9	S6	11		50	SO		38	33	25
27	1	52	20		46	4		34	6	26
28		48	27		41	47		29	40	27
29		44.	34		37	29		25	14	28
30		40	41		33	13		20	48	29
31		36	47					16	23	30