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1827
THE NEW
AMERICAN GRAMMAR
OF THE
ELEMENTS OF ASTRONOMY,
on AN IMPROVED PLAN:
IN THREE BOOKS.
I. THE USE of THE TERRESTRIAL GLope. IN
* THE SOLUTION OF GEOGRAPHICAL AND
ASTRONOMICAL PROBLEMS.
II. THE USE OF THE CELESTIAL GLOBE IN THE
SOLUTION OF PROBLEMS, RELATIVE TO
THE SUN, PLANETS, AND FIXED STARs.
III. THE SOLAR SYSTEM, AND THE FIRMAMENT
G) F FIXED STARS.
THE WHOLE
Systematically flrranged and Scientifically Illustrated;
witH SEVERAL CUTS AND ENGRAVINGs ;
AND ADAPTED TO THE INSTRUCTION OF YOUTH IN
SCHOOLS AND ACADEMIES.
-e Os-
By JAMEs RYAN;
AUTHOR of “AN ELEMENTARY TREATISE on ALGEBRA,
THEORETICAL AND PRACTICAL,” ETC. -a < *********~ x4.
—s (9G-
JNEW YORK : .*
PUBLISHED BY COULINS AND HANNAW.
No. 230 Pearl-street.
1827.
Southern District of JW8w-York, ss
BE IT REMEMBERED, That on the 22d day of October, A. D. 1825,
in the 50th year of the Independence of the United States of America,
James Ryan, of the said District, hath deposited in this office the title of a
Book, the right whereof he claims as author, in the words following, to wit:
The New American Grammar of the Elements of Astronomy, on an im-
§. plan; in three books I. The use of the Terrestrial, Globgºin the
olution of Geographical and Astronomical Problems. , Il. The use of the
Celestial Globe in the Solution of Problems relative to the Sun, Planets, and
Fixed Stars. III. The Solar System, and the Firmament of Fixed Stars.
The whole systematically arranged and scientifically illustrated; with
several cuts and engravings ; and adapted to the instruction of youth in
schools and academies. By James Ryan, author of “An Elémentary Trea-
tise on Algebra, Theoretical and Practical,” &c.
In conformity to the Act of Congress of the United States, entitled “An
Act for the encouragement of Learning, by securing the copies of Maps,
Charts, and Books, to the authors and proprietors of such copies, during the
time therein mentioned.” And also to an Act, entitled “ }. Act, supple-
mentary to an Act, entitled an Act for the encouragement of Learning, by
securing the copies of Maps, ('harts, and Books, to the authors and pro-
prietors of such copies, during the times therein mentioned, and extending the
benefits thereof to the arts of designing, engraving, and etching historical
and other Mºs - -
JAMES DILL, Clerk of the Southern District of JNew-York.
%2
4.
contents.
ſº
2
J.
*
*
§
In
&
VII.
VIII.
IX.
i
3-3-4-
~(~&t.
gº
duction, - . - - - - wº
*sº
Book THE FIRST.
- of THE TERRESTRIAL GLOBE.
Definitions and preliminary remarks, tºº
Of the great circles on the Terrestrial Globe,
Of the smail circles on the Terrestrial Globe,
Of the Wooden Horizon, and other appen-
dages to the Terrestrial Globe, - -
Definitions and terms belonging to the Ter-
restrial Globe, - - - =
Of Latitude and Longitude. Division of
the Earth into Zones and Climates, *
Of the natural and artificial division of Time,
Positions of the Sphere. Names assigned
to persons from their different situations
on the Globe, &c. tº gº sº
Astronomical and Geographical Problems
performed by the Terrestrial Globe, -
Questions to exercise the learner in the fore-
going Problems, – sº gº tº
mº
BOOK II.
OF THE CELESTIAL, GLOBE,
Definitions and terms melonging to the Ce.
lestial Globe, tºº gº -
Of the Fixed Stars. Division of the Stars
into Constellations, 8.c. tº º º
Of the Zodiacal Cons ellations, and fables
relative to them, - gº tºº - -
Of the Northern Constellations, and fables
relative to them, - tºº * * = tº
Of the Southern Constellations, and fables
relative to them, - - - - tºº
On the position of the Constellations and
principal Stars in the Heavens, - -
Astronomical Problems performed by the
Celestial Globe, - * * * *g
PAGE.
i
13
17
20
27
3S
39
134
IWe CONTENTS.
CHAP. . - PAGE.
Questions for the examination of the stu- .
dent in the preceding problems, - - 226
==
BOOK III.
of THE SOLAR systEM, AND THE FIRMAMENT OF FIXED,
STARs.
I. Of the bodies which compose the Solar Sys-
tem, - - see . Pºº " sº - - 231
II. Explanation of Astronomical terms, - 239
II. Of the Sun, - * * * gº? – , , - 248
IV. Of the Geocentric motions of the Planets 257
W. Of Mercury, - - - - - - 274
VI. Of Venus, - tºº tºº - - - - - 279
VII. Of the Earth, , , - - - - - - 286
VIII. Of Mars, - - - A - - - - - - 299
IX. Of the new planets, or asteroids, Westa,
Juno, Ceres, and Pallas, - - - 304
X. Of Jupiter, and its satellites, - . . - ... - 310
|XI. Of Saturn, of its rings and satellites, - 316
XII. Of Uranus, and his satellites, - - - 320
XIII. Of the Moon, gº — . . - - 325
XIV. Of Tides, – - - - - 335
XV. Of Refraction, Parallax, &c. .. - 340
XVI. Of Eclipses, - - - - - 348
XVII. Of Comets, - - - - - - 356
XVIII. Of the Firmament of Fixed Stars, - - 366
- m
IIST OF ENGRAVINGS.
ENGRAV. .
I. Popular illustration of the constellation
Canis Major, to face, - tº - - 180
II. Popular illustration of the constellation
Ersa Maj r, - - - - - - 184
III., Relative sizes of the Planets, - - - - 238
IV. Telescopic appearances of Venus, - - 279
W. Telescopic ºppearances of Mars, - - 299
WI. Telescopic appearances of Jupiter, - 310
VII. Telescopic appearance of the Moon, ~ 325

VIII. The Comet & f 1811, gº tº º . 353
THE NEw
AMERICAN GRAMMAR
OF THE
ELEMENTS OF ASTRONOMY
emm-mm-º-º-º:
INTRODUCTION.
Definitions and Fundamental Principles.
1. As TRoNoMy is a mixed mathematical science,
which treats of the heavenly bodies, their motions,
periods, eclipses, magnitudes, distances, and other
phenomena. *
The determination of their magnitudes, distances, and the
orbits which they describe, is called plane or pure Astrono-
my; and the investigations of the causes of their motions,
is called physical Astronomy. *
2. All bodies are necessarily extended, and there-
fore are found existing under figure or shape, which
is the boundary of extension. -
3. Extension has three dimensions; length,
breadth, and thickness.
4. A line is length without breadth. The ex-
tremities of a line are called points. A point there-
fore has no extension. - -
5. A straight line, or right line, is the shortest
distance from one point to another. e -
6. Every line which is neither a straight line nor
composed of straight lines, is called a curve line.
2 A. -
2. GRAMIMAR OF ASTRONOMIY’.
7. A surface is that which has length and breadth.
without thickness. -
8. A plane is a surface, in which if any two
points be joined by a straight line, the whole of
that line will be in the surface. -
9. Every surface which is neither a plane nor
composed of planes, is called a cuvre surface.
10. A solid is that which unites the three dimen-
sions of extension.
11. The inclination of two limes to each other is
called an angle.
12. When two straight lines, lying in the same
plane, may be produced both ways indefinitely,
without meeting, they are parallel.
13. When a plane surface is bounded by an uni-
form curve line, such that all straight lines drawn to
it from a certain point in the plane, are equal, the
surface is called a circle. *.
A circle is usually described with a pair of compasses;
one point of which is fixed, whilst the other is turned round
to the place where the motion first began. The fixed point
is called the centre of the circle; and the curve line des.
cribed by the other point is called the circumference.
14. The term circle also often implies the cir-
cumference, and not the circular surface ; and half
the circumference of a circle is usually called a
semicircle. - .#
15. Any portion of the circumference of a circle
is called an arc; and one-fourth of the circum-
ference of a circle is usually called a quadrant.
16. The circumference of every circle is divided
into 360 equal parts, called degrees; and of which
the symbol is 120 or 79, if 12 or 7 be their number.
Each degree is also divided into 60 equal parts,
called minutes ; and of which the symbol is 14, or
9', if 14 or 9 be their number ; and, finally, each
\
INTRODUCTION. 3
minute is divided into 60 equal parts, called seconds;
and of which the symbol is 7" or 30", if 7 or 30 be
their number.
Thus, if AD be
equal to one-fourth
of the circumfer-
ence of the circle
ABDE; then AD
contains 90 de-
grees, or symboli-
i...º". E
If AB be equal
to one-seventh of
the circumference
ABDEFA, AB=
3600 divided by 7,
equal to 51925'42"
—H #X 1", which is
read 51 degrees 25
minutes 42 seconds plus six-seventh of one second.
17. An angle subtended by the fourth part of the
circumference of a circle, or by an arc of 90 de-
grees, is called a right angle.
Thus, the angle ACD is a right angle, if the arc AD sub-
tending it, contains 90 degrees. g
18. An angle subtended by an arc less than 90
degrees, is called an acule angle.
Thus, the angle ACB, subtended by the arc AB, which is
less than 90 degrees, is an acute angle.
19. An angle subtended by an arc greater than
90 degrees, is called an obtuse angle. g
Thus, the angle FCD, which is subtended by the arc FD
greater than 90 degrees, is called an obtuse angle.
20. It is proper to observe, that in most of the
French scientific treatises, that have of late years
been published, the circumference of every circle
is divided first into 400 equal parts or degrees; then

$ ,' GRATWIMAR OF ASTRONOMY.
-each degree into 100 equal parts or minutes; and,
finally, each minute into 100 equal parts or seconds. .
So that a French degree is less than an American, in the
proportion of 90 to 100; a French minute less than an-Ame-
rican, in the proportion of 90 × 60 to 100×100; and a French
second less than an American, in the proportion of 90 × 60 ×
60 to 100 × 100 × 100. Hence, if n be the number of French
degrees, the corresponding number of American equals
n—#, which form points to an easy arithmetical operation
for finding the number of degrees in the American scale
from the number in the French scale, since from the pro
posed number we must subtract the same, after the decimal
point has been removed one place to the left.
EXAMPLES.
1. What number of degrees, minutes, and se-
conds, in the American scale, correspond to 100
degrees in the French scale 2
100
10
90° Answer.
2. What number of degrees, minutes, &c. in the
American scale, correspond to 91° 25' in the
French scale 2
9
5
!
5
*
*-* *
S
;
i
2
2
2
"7.5
30.0
Ans. 820 7' 30". .
3. What number of degrees, minutes, &c. in the
American scale, correspond to 35° 0735, to 180°,
$o 2009, and to 360°, in the French scale 2
Ans. 31° 33'58", 1629, 1809, and 324°,
BOOK THE FIRST.
tº cººl
a-s-s-s-s-s-s
A.
OF THE TERRESTRIAL GLOBE.
CHAPTER I.
9efinitions and Preliminary Remarks.
1. A GLoBE, or SPHERE, is a round body, every
part of whose surface is equally distant from a
point within, called its centre.
2. Artificial Globes are of two kinds, terrestrial
and celestial.
The artificial globes are oſ considerable use in geography
and astronomy, by serving to give a lively representation of
their principal objects, and for performing and illustrating
many of their operations in a manner easy to be perceived
by the senses, and so as to be conceived even without any
knowledge of the mathematical grounds of those sciences.
3. The terrestrial globe exhibits a representation
of the different countries, republics, empires, king-
doms, chief towns, oceans, seas, lakes, rivers, &c.
truly delineated on it, according to their relative
situations on the real globe of the earth.
The true figure of the earth, which is an oblate spheroid
(a figure formed by the revolution of an ellipsis, which ap-
proaches nearly to a circle, round its shorter axis or conju-
gate diameter,) shall be explained in a subsequent part of
this work; but here the figure of the earth is supposed to be
a perfect sphere, since there is no other figure which can give
so exact an idea of its true shape.
V- T
*
:6 GRAMINIAR OF ASTRONOMY.
4. The celestial globe is an artificial representa-
tion of the heavens, on which the stars are laid down
in their natural situations.
As the stars are drawn on a convex surface, whereas their
natural appearance is in a concave one; in using this globe,
the student is supposed to be situated in the centre of it,
and viewing the stars in the concave surface.
5. The awls of the earth is an imaginary straight
line passing through its centre, and upon which it
is supposed to revolve. -
6. The poles of the earth are the extremities of
its aris at the earth’s surface; one of which is
called the north pole, and the other the south pole.
If the axis of the earth be produced to the heavens, the
points in which it cuts the celestial sphere, are called the
celestial poles, or, by way of eminence, the poles of the world.
7. The avis of the terrestrial globe is a straight
line, which passes through its centre from north to
south, and is represented by the wire on which it
turns. * -
8. The revolution of the globe upon this axis
shows the manner in which the earth performs its
diurnal rotation from west to east.
From this circumstance arises the apparent diurnal mo-
.tion of all the heavenly bodies from east to west.
9. This diurnal or daily motion of the earth is
the occasion of day and night; and its annual mo-
tion round the Sun, (in popular language called the
sun's course in the ecliptic,) causes the beautiful
diversity of seasons.
When we reflect on the diurnal motion to which all the
heavenly bodies are subject, we cannot but recognise the ex-
istence of one general cause which moves them, or which
seems to move them round the earth; and, as LAPLACE re-
marks in his System of the World, since the heavenly bodies
present the same appearances to us, whether the firmament
carries them round the earth, considered as immoveable, or
\
or THE TERRESTRIAL GLoBE. ºf
whether the earth itself revolves in a contrary direction; it
seems much more natural to admit this latter motion, and
to regard that of the heavens as only apparent.
Carried on with a velocity which is common to every
thing that surrounds us, we are in the case of a spectator
placed in a ship that is in motion. He fancies himself at
rest, and the shores, the hills, and all the objects placed out
of the vessel, appear to him to move. But on comparing the
extent of the shore, the plains, and the height of the moun-
tains, with the smallness of his vessel, he recognises that
the apparent motion of these objects, arises from the real
-motion of himself. The numberless stars which fill the ce-
Festial regions, are relatively to the earth what the shores and
the hills are to the vessel; and the same reasons which con
vince the navigator of the reality of his own motion, prove
to us the motion of the earth. The diurnal and annual mo–
:tions of the earth shall be fully illustrated in the Third Book.
QUESTIONS.
What is a globe or sphere 2. -
How many kinds of artificial globes are there,
and what are they called 2 - -
What does the terrestrial globe represent?
What does the celestial globe represent 2
What is the axis of the earth 2 *
What are the poles of the earth, and what are
they called 2 -
What is the axis of the artificial globe, and what
does the revolution of the globe on this axis show 2
What is the occasion of day and night?
What is the cause of the beautiful diversity of
Seasons? - * * -
-*-
CHAPTER II.
Of the great circles on the terrestrial globe.
1. Circles which divide a globe into two equal
parts, are called great circles. -
& - GRAMMAR OF ASTRONOMY.
2. The pole of any great circle is a point on the
surface of the globe, 90 degrees distant from every
part of that circle of which it is the pole.
Hence every great circle has two poles diametrically op-
posite to each other. -
3. The great circles on the terrestrial globe, which
divide it into two equal parts, are the equator, the
ecliptic, and the meridians. •. &
4. The equator is a great circle of the earth,
equidistant from the poles, and divides the globe into
two hemispheres, called the northern and southern.
The latitudes of places are counted from the equator
northward and southward, and the longitudes of places are
reckoned upon it, eastward and westward from the first
meridian.
5. The equator, when referred to the heavens,
is called the equinoctial, because when the sun ap-
pears in it, the days and nights are equal all over
the world, (the poles excepted;) that is, 12 hours
each. . - - .
'#'his is on the supposition that there is no refraction.
6. The ecliptic is that great circle in which the
sun makes his apparent annual progress among the
fixed stars; or it is the real path of the earth round
the sun. .
The ecliptic cuts the equator in an angle of 23°28'; the
points of intersection, Aries and Libra, are called the equi-
noctial points; and the points Cancer and Capricorn, where
it meets the tropics, are called the solstitial points.
The angle which the ecliptic makes with the equator, is
called the obliquity of the ecliptic.
7. The ecliptic is usually divided into 12 equal
parts, called signs, each containing 30 American
degrees. , -
ºf
OF THE TERRESTRIAL GLOBE. 9
The sum makes his apparent annual progress through the
ecliptic at the rate of 59'8" 2, (or nearly a degree,) in a day.
8. The division of the signs commences at the
first point of Aries, which is one of the equinoctial
points, and they are numbered according to the sun’s
apparent motion in the ecliptic. -
9. The names of the signs, with their corres-
ponding characters, and the days on which the Sun
enters each of them, according as they are repre-
sented on Wilson's flmerican Globes, are, * -
Signs. Marks. Days in which the sun enters
each of them. &
Aries, 20th of March.
Taurus, § 19th of April.
Gemini, II 21st of May.
Cancer, 9.5 21st of June.
Leo, & 23d of July.
Virgo, iſ, 23d of August.
Libra, ~~ 23d of September.
Scorpio, [ſ] 23d of October.
Sagittarius, £ 22d of November.
Capricornus, WP 22d of December.
Aquarius, * 19th of January.
Pisces, 19th of February.
The former six signs lie on the north side of the equator,
and are called northern signs; when the sun is in any of
these signs, his declination is north. The latter six signs
lie on the south side of the equator, and are called southern
signs; when the sum is in any of these signs, his declination
is south. It is also proper to observe that, when the sun
enters the signs Aries or Libra, his declination is nothing.
10. The meridians are great circles passing
through the poles, and cutting the equator at right
angles. - +
Every place upon the earth is supposed to have a meri-
dian passing through it, though, to prevent confusion, there
are, in general, only twelve drawn on the artificial globe.
}{
}() GRAMMAR OF ASTRONOMY.
11. It is proper to observe that, though the me-
ridians completely invest the globe; they are usual-
ly, and very properly called only semicircles, which
is the property, of the meridian of any place, the
other half of the same circle being called the oppo-
site meridian. -
Meridians, according to this acceptation, are also called
Mines of longitude.
f
\
12. To supply the place of other meridians, th
globe is hung in a large brass circle, which is usual-
ly called the brazen meridian, or sometimes, by way
of distinction, the universal meridian, or only the
meridian.
The brazen meridian is divided into 360 degrees. On one
half of the meridian, these degrees are numbered from 0 to
90, from the equator towards the poles, and are used for
finding the latitudes of places. On the other half of the
meridian they are numbered from the poles towards the
equator, and are used in the elevation of the poles.
13. The brazen meridian, which may be made to
coincide with the meridian of any place, divides the
globe into two equal hemispheres, called the eastern
and western.
Hence, east and west are only relative terms with respect
to places situated on the earth: for instance, London is east
of New-York, and west of Paris; consequently, with re-
spect to the meridian of New-York, London is in the eastern
hemisphere; and with respect to the meridian of Paris,
London is in the western hemisphere.
14. When the sum comes to the meridian of any
place, not within the polar circles, it is noon or
mid-day at that place. t
15. The first meridian is that from which geo-
graphers begin to reckon the longitudes of places.
16. The English and Americans count the lon-
OF THE TERRESTRIAL GLOBE, 11
gitudes of places from the meridian of London; and
the French from the meridian of Paris.
Hence, in American, as well as in English maps and
globes, the first meridian is a semicircle supposed to pass
through London, or the observatory at Greenwich.
17. The meridional circles that pass through the
equinoctial and solstitial points, are called colures;
the former being called the equinoctial, and the lat-
ter the solstitial colure. * -
The first determines the equinoxes, the second shows the
solstices; and by dividing the ecliptic into four equal parts,
they also designate the four seasons of the year.
QUESTIONS.
What is a great circle 2
What are the poles of a great circle 2
How many great circles are there drawn on the
globe, and what are they called 2
What is the equator, and what is its use 2
Why is the equator, when referred to the heavens,
called the equinoctial 2
What is the ecliptic, and in what angle does it in-
tersect the equator 2 -
What are the principal points of the ecliptic, and
what are they called 2 -
What are the meridians, and in what angle do
they cut the equator 2 | º
What are the meridians, when considered as limes
of longitude 2
What is the brazen meridian 2
What is the first meridian 2 -
From what meridian do the Americans count the
longitude 2 -
What are the colures, and into how many parts
do they divide the ecliptic 2
$2. GRAMMAR OF ASTRONOMY. .
CHAPTER III.
Of the small circles on the terrestrial globe.
1. Circles which divide a globe into two unequal
parts, are called small circles. *
2. The small circles on the terrestrial globe, which
divide it into two unequal parts, are the tropics, polar
circles, parallels of lalitude, &c.
3. The tropics are two small circles parallel to the
equator at the distance of 23° 28′ from it; the
northern is called the tropic of Cancer, and the
southern the tropic of Capricorn.
Two planes are parallel when, being produced ever so ſac,
they do not meet. - -
4. The polar circles are two small circles parallel
to the equator, at the distance of 66° 32' from it, ol
230 28 from each pole. -
5. Parallels of latilude are small circles drawn
through every ten degrees of latitude, on the ter-
restrial globe, parallel to the equator.
Every place on the globe is supposed to have a parallel
of latitude drawn through it, though there are only sixteen
drawn on Wilson’s terrestrial globe. When the parallels
of latitude are referred to the heavens, they correspond to
the parallels of declination.
6. Parallels of altitude, commonly called fllma-
canters, are imaginary circles parallel to the hori-
zon, and serve to show the height of the Sun, moon,
Or StarS. - s
These circles are not drawn on the globe, but they may
he described ſor any latitude by the quadrant of altitude.
OF THE TERRESTRIAL GI, OBE. l3
QUESTIONs.
What is a small circle, and how many are usually
drawn on the globe 2 - k
What are the tropics, and how far do they extend
from the equator 2 . . . *
What distance are the polar circles from the
poles, and what distance are they from the equator 2
What are the parallels of latitude, and how many
are generally drawn on the globe 2 - *
What circles are called almacanters, and what do
the parallels of altitude show ! --
*sºmsºmº-s-s
ÖHAPTER IV.
of the wooden horizon, and other appendages to the
terrestrial globe. -
1. The horizon is a great circle which separates
the visible half of the heavens from the invisible ;
the earth being considered as a point in the centre
of the sphere of the fixed stars. . . . . . .
2. Horizon, when applied to the earth, is either
sensible or rational. .
3. The sensible, or visible, horizon is the circle"
which bounds our view, where the sky appears to
touch the earth or sea. * ,
The sensible horizon extends only a few miles; for in-
stance, the mean diameter of the earth, being, (according to
Dr. JAdrain’s computation,) 7920 miles, and the circum-
ference 24880 miles; if a.man of 6 feet high were to stand
on the earth where the surface is spherical, or on the surface
of the sea, the utmost extent of his view on the earth or sea,
would be 3 miles nearly. Thus, 7920 miles is equal to
41817600 feet, to which add 6 feet, and the sum will be
41817606, this multiplied by 6, gives 250905636; then by
extracting the square root of this last number, we shall find
G) .
rtº
14 GRAMMAR OF ASTRONG MY.
15840 very nearly ; which is equal to 3 miles, the distance
which a man 6 feet high can see straight forward, admitting
there is nothing to intercept his view. * *
4. The rational, or true horizon, is an imaginary
plane passing through the centre of the earth, pa-
rallel to the sensible horizon. -
The rational horizon determines the rising of the sun,
stars, and planets. t
5. The wooden horizon, circumscribing the ter-
restrial globe, represents the rational horizon on the
real globe of the earth. - * x
6. The wooden horizon is divided into several
concentric circles: On Wilson’s terrestrial globe
they are arranged in the following order:—
The first circle is marked amplitude, and is numbered
from the east towards the north and south, ſrom 0 to 90 de-
grees; and from the west towards the north and south in the
same manner. -
The second circle is marked azimuth, and is reckoned from
the north and south points of the horizon towards the east
and west from 0 to 90 degrees.
The third circle contains the thirty-two points of the come
pass, divided into half and quarter points.
The fourth circle contains the twelve signs of the ecliptic,
(usually called the signs of the Zodiac,) with the figure and
character of each sign. -
The fifth circle contains the degrees of the signs, each
sign comprehending 80 degrees, as has been already observed.
The sixth circle contains the days of the month answering
to each degree of the sun's place in the ecliptic.
The seventh circle contains the equation of time, or the
difference of time, shown by a well regulated clock and a
correct sun-dial. When the clock ought to be faster than
the dial, the number of minutes expressing the difference at
noon, has the sign--, which is read plus, or more, before it;
and when the clock or watch ought to be slower, the num-
ber of minutes in the difference has the sign —, less, or
minus, before it. - -
The eighth circle contains the 12 calender months of the
year
of THE TERRESTRIAL GLOBE. '. I5
7. The amplitude of any object in the heavens, is
an arc of the horizon, contained between the centre
of the object when rising, or setting, and the east or
west points of the horizon. Or, it is the distance
which the sun or a star, rises from the east, and sets
from the west, and is used to find the variation of
the compass at sea. , ,
In our summer, the sun rises to the north of the east, and
sets to the north of the west; and in the winter, it rises to
the south of the east, and sets to the south of the west, ex-
cept at the time of the equinoxes. - • ,
r
8. The quadrant of altitude is a thin slip of brass
divided upwards from 0 to 90 degrees; and down-
wards from 0 to 18 degrees, and, when used, is ge-
nerally screwed to the brass meridian. ... •
The upper divisions are used to determine the distances
of places on the earth, the distances of the celestial bodies,
their altitudes, &c.; and the lower divisions are applied to
finding the beginning, end, and duration of twilight.
9. The hour circles are two small circles on the
globe, placed at the north and south poles, having
the hours of the day delineated upon them, with an
index to each, pointing to any particular time.
10. The indewes are two moveable pointers fixed
at the north and south poles, which are the centres
of the hour circles. .
11. Every hour answers to 15 degrees of the
equator, and distance is by that means reduced into
time at pleasure. . . . . t
Hence every degree answers to four minutes of time,
every half degree to two minutes, and every quarter degree
to one minute. . - .
- ! r •
12. The compass, usually called the Mariner’s
Compass, is a representation of the horizon, and
consists of a circular brass box, which contains a
paper card, divided into 32 equal parts, and fixed
£6 GRAMMAR OF ASTRONOMY.
on a magnetical needle that generally turns towards
the north. Each point of the compass contains 11°
15', or 11% degrees, being the 32d part of 360
degrees. . . .
The compass is used for setting the terrestrial globe north
and south; but care must be taken to make a proper allow-
ance for the variation. The compass is also used by sea-
men to direct and ascertain the course of their ships.
13. It is proper to observe, that the needle does
not always point directly north, and that it is also
subject to a small variation: its deviation, from the
north point of the horizon is called its declination;
and the change of its declination, is properly called
the variation of the needle. This term, however,
is usually used to signify the declination itself.
At present, at London, the north end of the needle points
about 24; degrees towards the west of the true north point
of the horizon, but at the North Cape it points only about 1°
towards the west; while in some parts of Davis's Straits its
direction is more than 64 points towards the west, and at
Cape Horn it points about 22 degrees towards the east of
the truth north. When the north point of the compass is to
the east of the true north point of the horizon, the declination
is called east; if it be to the west, the declination is west.
t - QUESTIONs.
‘What is the horizon 2 ‘. * #
What is the distinction between the rational and
sensible horizon 2 -
What is the wooden 'horizon, and how is it di-
vided ?. . . * -
What is the amplitude of a celestial object, and
what is its principal use ! -
What is the quadrant of altitude, how is it di-
vided, and what is its use 2 *
What are the hour circles, and where are they
situated on the globe 2. - w
What is the compass, how is it divided, and what
is its use on the globe 2
f
Does the needle always point directly north 2
'OF THE TERRESTRIAL GLOBE. 17
What is the deviation of the needle from the north
point of the horizon called 2
What are the indexes, and where are they fixed 2
How many degrees of the equator answers to an
hour, and how many minutes of time corresponds
to a degree ? --
CHAPTER v.
Befinitions and terms belonging to the terrestrial globe.
1. The east, west, north, and south points of the
horizon, are called cardinal points.
When the days and nights are equal, that is, when the
sun is in the equinoctial; the point of the horizon where the
sun rises is called the east; and the point where he sets is
called the west; the point of the horizon towards which the
sum appears at noon to those situated in the northern hemis-
phere, is called the south ; and the point of the horizon di-
rectly opposite to the south is called the north.
2. The equinoctial and solstitial points are called
the cardinal points of the ecliptic ; and the cardinal
signs are Aries, Cancer, Libra, and Capricorn.
The time when the sun is at the equinoctial point, in his
passage from the south to the north side of the equator,
is called the vernal equinoa: ; and the time when he is at the
other equinoctial point, is called the autumnal equinoa:. . .
The time when the sun is at the northern solstitial point,
is called the summer solstice ; and the time when he is at
the southern solstitial point, is called the winter solstice.
3. The cardinal points in the heavens are the
zenith, the nadir, and the points where the sunrises
and sets. *
4. It is found by experiment that the plumb line,
when the plummet is freely suspended, and is at
Qº
#8 GRAMMAR OF ASTRONOMY.
rest, is perpendicular to the free surface of still
Water. ... } .* -
Hence, a straight line in the direction of gravity at any
place on the earth's surface, is also perpendicular both to
the sensible and rational horizons of that place. -
5. If at any place on the earth's surface a straight
line, in the direction of gravity, be produced both
ways to the heavens, the point in which it cuts the
celestial sphere; exactly over our heads, is called the
zenith of the place ; and the point in which it cuts
the opposite part of the sphere, or directly under
our feet, is called the nadir.
Hence, the zenith is the elevated pole of our rational
horizon, and the nadir, being diametrically opposite to the
zenith, is the depressed pole.
6. Azimuth, or vertical circles, are imaginary great
circles passing through the zenith and nadir, and
cutting the horizon at right angles.
The altitudes of the heavenly bodies are measured on
these circles: they may be represented by screwing the
quadrant of altitude on the zenith of any place, and making
the other end move along the horizon of the globe.
7. That azimuth circle which passes through the
east and west points of the horizon, is called the
prime vertical.
This circle is always at right angles with the brass meri-
dian, which may be considered as another vertical circle
passing through the north and south points of the horizon.
8. The azimuth of any object in the heavens is
an arc of the horizon, contained between a vertical
circle passing through the object, and the north or
south points of the horizon. s
The azimuth of the sun, at any particular hour, is used
at sea for finding the variation of the compass.
Qi' 'I' iſ E TE}tl&ESTRIAL GLOBE. 19
9. The allitude of any object in the heavens
is an arc of a vertical circle, contained between the
centre of the object and the horizon. When the
object is on the meridian, this arc is called the me-
ridian altitude. . . . w
10. The zenith distance of any celestial object is
an arc of a vertical circle, contained between the
centre of that object and the zenith; or, it is what
the altitude of the object wants of 90 degrees.
When the sun is on the meridian, this arc is called
the meridian zonith distance.
11. The polar distance of any celestial object is
an arc of a meridian, contained between the centre
of that object and the pole of the equinoctial."
questions. ) -
What are the cardinal points of the horizon 2
What are the cardinal points of the ecliptic, and
what are the cardinal signs 2 . .
What are the cardinal points in the heavens 2
What is the zenith, and of what circle is it the
pole 2 * * ,
What is the nadir, and of what circle is it the
pole 2 . 4.
What are the azimuth or vertical circles, and
what is their use 2 - -
What is the prime vertical ?
What is the azimuth of a celestial object?
What is the altitude of any object in the heavens,
and what is the meridian altitude of the sun, a star,
or planet 2 * s
What is the zenith distance of a celestial object?
What is the polar distance of a celestial object?
\
20 GRAMIMAR OF ASTRONOMY.
CHAPTER VI.
6f latitude and longitude. Division of the earth into
- zones and climates. t
* 1. The arc of the meridian contained between
the zenith of a place and the equator, is called the
latitude of the place. . . - -
The latitude of a place, on the terrestrial globe,
is measured on the brass meridian, from the equator
towards the north or south pole. &
1f the place lies in the northern hemisphere, it is said
to have north latitude; and iſ it lies in the southern hemis
phere, it is said to have south latitude: so that the latitude
of any place will be greater or less, according as it is farther
from, or nearer to the equator. Hence the latitude under
the equator is nothing, and the latitude increases gradually
as we advance towards either of the poles, where it is 90
degrees, or the greatest possible; as will appear evident
from consulting the globe. - t
It is also obvious that a greatnumber of places may have
the same latitude; for if a circle be supposed to be drawn
through any point of the meridian, parallel to the equator,
all the places which lie under that parallel will be equally:
distant from the equator, and consequently must have the
same latitude. * * .
2. The angular distancé of a place, on the sur-
face of the earth, measured upon a secondary to the
equator, is called the reduced latitude of the place.
Secondaries to a great circle are great circles, which pass
through its poles, and which are perpendicular to that great
circle : thus, the meridians are secondaries to the equator
or equinoctial. z }
It may be also observed, that the true latitude of a place,
as defined in the preceding article, would be equal to the re-
duced latitude of the same place, if the figure of the earth
were truly spherical. The difference between the true and
reduced latitudes shall be pointed out, when we come to
consider the true figure of the earth.
OF THE TERRESTRIAL GLOBE. 21
3. Longitude of a place is its distance east or
west from the first meridian, reckoned in degrees,
minutes, &c. upon the equator. - ,
The choice of a first meridian has been a matter of consi– .
derable embarrassment both to astronomers and geographers,
and even yet they aré not perfectly agreed in their determi-
nation. The French formerly made their first meridiaſ, pass
through the island of Ferro, one of the Câmaries; and the
Dutch fixed upon another of those islands, called Teneriffe,
as the proper situation for this purpose. But the English;
as has been already observed, make their first meridian pass.
over London, or rather over Greenwich, on account of the
observatory being at that place. , r g”
This disagreement amongst astronomers of different na-
tions is not, however, to be considered as a matter of much
importance; for whichever is regarded as the first meridian,
the rest may be easily deduced from it, by noting the dif-
ferent points where they intersect the equator, and finding
the difference. - - - - -
Though it is very natural to suppose, that astronomers
and geographers would assume as the first meridian that
which passes through the metropolis of their own country;
the Americans, on account of having no public observatory,
are still under the necessity of referring the longitudes of
places to the meridian of London. -
. 4. It is proper to observe, that the greatest lon-
gitude a place can have, is 180 degrees; and that
the longitudé of any place lying under the first
meridian will be nothing. e
A great number of places may also have the same longi-
tude; for if a meridian be supposed to be drawn through any
point upon the globe, all places lying under that meridian,
when reſerred to the equator, will be at an equal distance
from the first meridian, and consequently their longitude
must be the same. -
5. The declination of a heavenly body is its
distance north or south of the equator, or equinoc-
tial, reckoned in degrees and minutes, upon a se-
condary to it drawn through the body. -
Hence, the declination of a celestial body is similar to
22 GRAMMAR OF ASTRONOMY.
the latitude of a place on the terrestrial globe; and the great-
est declination the sun can have, north or south, is 23° 28′.
6. A division of the earth contained between two
parallels of latitude, is called a zone.
7. The two tropics and two polar circles divide
the globe into five zones. . .
8. That part of the earth contained between the
3ropics, is called the torrid zone. The breadth of
this zone is therefore equal to twice the greatest
declination of the sun, or obliquity of the ecliptic,
equal to 46° 56', or twice 23° 28′. g
The torridzone experiences only two seasons, the one dry,
the other rainy. The former is looked upon as the summer,
the latter as the winter of these climates; but they are in di-
rectopposition to the celestialwinter and summer, for the rain
always accompanies the sum, so that, when that luminary is
in the northern signs, the countries to the north of the equa-
tor have their rainy season. It appears that the presence of
the sun in the zenith of a country, continually heats and rari-
fies its atmosphere. The equilibrium is every moment sub-
verted, the cold air of countries, nearer the poles is inces-
Santly attracted, it condenses the vapours suspended in the
atmosphere, and thus occasions almost continual rains. The
countries of the torrid zone, where no vapours rise into the
air, are never visited by the rainy season. Local circum-
stances, particularly high chains of mountains, which either
arrest or alter the course of the monsoons and winds, exer-
cise such influence over the physical seasons of the torrid .
zone, that frequently an interval of not more than several
leagues separates summer from winter. In other places
- there are two rainy seasons, which are distinguished by the
names of great and little. ---- &
The heatis almostalways the same within 10 or 15 degrees
of the equator; but towards the tropics, we feel a difference
between the temperature which prevails at the moment the
Sun is in the zenith, and that which obtains, when in the op-
posite solstice, the solar rays ſakling under an angle of more
than 47 degrees. We may, therefore, with Polybius, divide
the torrid zone into three others. The equatorial zone, pro-
perly so called, is temperate, compared with the zone of the
tropic of Cancer, composed of the hottest and least habitable
of THE TERRESTRIAL GLOBE. 23.
regions of the earth. The greatestnatural heatever observed,
which is 35 degrees of Reaumer, or 111 degrees Fahrenheit,
has been at Bagdad, at 33° of latitude. The zone of the tropic
of Capricorn contains but little land; but it appears to ex-
perience momentary heats of extreme intensity.
Most of the ancients, disregarding the observations of Po-
& lybius, conceived that the heat continued to increase from the
tropic towards the equator. Hence they concluded that the
middle of the zone was uninhabitable. It is now ascertained
that many circumstances combine to establish even there a
temperature that is supportable. The clouds; the greatrains;
the nights naturally very cool, their duration being equal to
that of the days; a strong evaporation; the vast expanse of
the sea; the proximity of very high mountains, covered with
perpetual snow; the trade winds, and the periodical inunda-
tions, equally contribute to diminish the heat. This is the
reason why, in the torrid zones, we meet with all kinds of
climates. The plains are burnt up by the heat of the sun.
All the eastern coasts of the great continents, fanned by the
trade winds, enjoy a mild temperature. The elevated districts
are even cold; the valley of Quito is always green; and per-
haps the interior of Africa contains more than one region
which nature has gifted with the same privilege. Nothing
equals the majestic beauty of the summer in the torrid zone.
The sun rises vertically; it traverses in an instant the burn-
ing clouds of the east, and fills the heavens with a light
whose effulgent splendour is unobscured by a single shade.
The moon shines here with a more brilliant, lustre, Venus
blazes with purer and more vivid rays, and the milky way
glitters with augmented brightness. To this magnificence of
the heavens, we must add, the serenity of the air, the smooth-
mess of the waves, the luxuriance of vegetation, the gigantic
forms of plants and animals, all nature more grand, more
animated, and yet less inconstant and less changeable.
9. Those parts of the earth contained between the
tropics and polar circles, are called the two tempe-
rate zones: each of which is, therefore, 43°4' broad.
The north temperate zone extends from the
tropic of Cancer to the arctic circle ; and the south
temperate zone from the tropic of Capricorn to the
antarctic circle. -
The temperate zones enjoy the mild and varied charms of
24 º GRAMMAI8, Ol' ASTRONOMY.
spring and autumn, the moderate heat of summer, and the
salutary rigours of winter. This succession of four seasons
is not known beyond the tropics, nor towards the poles.
Even that part of the north temperate zone which lies be-
tween the tropic of Cancer and the 35th degree of latitude,
in many places resembles the torrid zone. Until we come
towards the 40th degree, the ſrost in the plains is neither
intense nor of long duration; and it is equally unusual to see
snow fall there. Elevated countries feel, all the rigours of
winter—and the trees even in the plains lose their foliage,
and remain stripped of verdure during the months of No-
vember and December. . . .
It is from the 40th to the 60th degree, that the succession
of the four seasons is most regular and most perceptible,
without, however, endangering the health of man: JMalte-
Brun observes, though, perhaps, not properly, that it is within
these latitudes we must look for the nations that are most
distinguished for knowledge and civilization, and those who
display the greatest courage by sea and land. It would ap-
pear, that in countries where there is no summer, the inha-
bitants are destitute of genius, or, at least, of intelligence and
taste; while in those regions where there is no winter, true
valour, constancy, and loyalty, as well as other civil and
military virtues, are almost unknown. But, let us remember
that it is man himself, who has in a great measure created
these salubrious climates: France, Germany, and England,
not more than twenty ages ago, resembled Canada and
Chinese Tartary, countries situated, as well as those portions
of the earth, at a mean distance between the equator and the
pole. Even the physical climate of that portion of the United
States, situated about the 41st degree of north latitude, has,
in less than half a century, undergone a very great change:
for instance, in the city of New-York, for several years past,
we have experienced mild winters, having had very little
frost, and no long continuance of snow. 'l'his is principally
owing to the clearing of ſorests; the cultivation of the soil;
and the rapid improvement in the surrounding country; so
that, in all probability, our climate may be in a few ages,
as mild as that which is now experienced by those countries,
situated in the same, latitude in Europe. -
11. Those parts of the earth included within the
polar circles, are called the two frigid zones. The
north frigid zone extends from the north pole to
of THE TERRESTRIAL GLOBE. 25
the arctic circle, and the South frigid zone from the
south pole to the antarctic circle. -
Beyond the 60th degree, and as far as the 78th, (which, as
JM. JMalte-Brun remarks, appears to be the limit of the habi-
table earth in the northern hemisphere,) only two seasons
are generally known; a long and rigorous winter, succeeded
often suddenly by insupportable heats. The power of the
solar beams, though ſeeble, from the obliquity of their di-
rection, accumulates during the days, which are extremely
long, and produces effects which might be expected only in
the torrid zone. There have been examples, of forests
having been set on fire, and of the pitch melting on the
sides of ships. In winter, on the contrary, brandy has been
frozen in heated rooms; the earth has been ſound frozen to
the depth of 100 feet; and mercury, congealed in the ther-
mometer, leaves the degree of cold indeterminate. We
speak here of extreme cases and of the zone in general.
For, in some places, a southern exposure, and the neigh-
bourhood of the ocean, soften the climate to an almost in-
credible degree. Bergen in Norway, and the whole of the
adjoining coast, between 60 and 62 degrees of latitude,
has a very rainy winter, but seldom snow or frost—that sea-
son of the year is there less rigorous, and requires less fuel
than at Craconia, or Prague, or Vionna, in ſlustria, between
the 48th and 50th degrees of latitude. The ſrigid zone enjoys
an atmospheric calm, which is unknown in temperate re-
gions—it has no storm, no hail; scarcely a tempest—the
splendours of the aurora borealis, reflected ſrom the snow,
dispel the darkness of the polar night. The heat of the sun
from his long continuance above the horizon, astonishingly
accelerates the growth of vegetation. In three days, or
rather three times twenty-four hours, the snow is melted
and the ſlowers begin to blow. The succession of physical
zones is not equal in the two hemispheres: for, in the
arctic seas, we scarcely meet with the large floating masses
of ice beſore we arrive at the 70th degree, nor the stationa-
ry fields, until towards the 75th or 80th degrees of latitude;
while, in the antarctic seas, both occur at from 50 to 60 de-
grees southern latitude. In the island of Terra del Fuego,
in that of Sandwich, and in several others situated towards
the 54th and 59th degrees of south latitude, the mountains
even in the southern summer remain covered with Snow
quite to the shores of the sea.
().
º
, 26 GRAMMAR OF ASTRONOMY.
This diminution of heat appears to cease all at once be
tween the 30th and 40th degrees of latitude; for hot winds
arise from the interior of New Holland, whilst the mountains
of Van Dieman's Land remain covered with perpetual
snow; thus there is felt in these latitudes the most sudden
transition from a Suffocating heat to a very sensible cold.
See, for farther information, respecting the causes of this
phenomenon, J.M. JMalte-Brun's System of Geography.
12. Climate, in a geographical sense, is a part
of the surface of the earth contained between two
Small circles parallel to the equator; and of such
a breadth, as that the longest day in the parallel
nearer the pole, exceeds the longest day in that next
the equator, by half an hour, in the torrid and tem-
perate zones; or by one month in the frigid zones.
13. Physical climate comprehends the degree of
heat and cold, the drought, the humidity, and the sa-
lubrity, which occur in any given region of the earth.
The causes of physical climate are mine in number:
1st, The action of the sun upon the atmosphere. 2d, The
interior temperature of the globe. 3d, 'The elevation of the
earth above the level of the ocean. 4th, The general incli-
nation of the surface, and its local exposure. 5th, The
position of its mountains relatively to the cardinal points.
6th, The neighbourhood of great seas, and their relative
situation. 7th, The geological nature of the soil. 8th, The
degree of cultivation and population at which a country has
arrived. 9th, The prevalent winds. JM. JMalte-Brun, Book
XVII. . - -
QUESTIONS. - * e
What is the true latitude of a place on the ter-
restrial globe 2 -
What is the reduced latitude of a place on the
surface of the earth 2 - -
What is the longitude of a place, and how is it
reckoned 2 --- - -
What is the greatest longitude a placé can have 2
What is the declination of a heavenly body, and
how is it reckoned 2
of THE TERRESTRIAL GLOBE. 27
What is a zone, and into how many zones is the
earth divided ? a *
What is the situation, and what is the extent of
the torrid zone? .
Where are the two temperate zones situated, and
what is the extent of each 2 -
Where are the two frigid zones situated, and
what is the extent of each 2 ...”
What is a climate in a geographical sense, and
what is a physical climate 2
->{}º-
- CHAPTER. VII.
of the Natural and flrtificial Divisions of Time.
1. Time relatively to us, is the impression which
a series of objects leaves upon the memory, and of
which we are certain the existence has been suc-
cessive. - . . .
Absolute, true, and mathematical time, of itself, and from
its own nature, flows equally without regard to any thing ex-- . .
ternal, and by another name is called duration: relative, ap-
parent, and common time, is some sensible and external
(whether accurate or unequable) measure of duration by
the means of motion, which is commonly used instead of
true time; such as an hour, a day, a month, a year.
2. Mankind have universally agreed to make
use of the diurnal and annual motions of the sun,
for the purpose of measuring time.
It is proper to observe, that whenever the motion of the
Sun is spoken of, it is not to be understood in a positive
sense, as if he actually removed from one part of space to
another, but only as an appearance occasioned by the real
motion of the earth in a contrary direction. The pheno-
mena are exactly the same; and astronomers sometimes
mention one, and sometimes the other, according as they
find it most convenient for their purpose.
28 GRAMMAR or ASTRONOMY.
3. The interval of time from the sun's centre
leaving any meridian to its returning to the same
again, is called a true solar day; and is counted
twenty-four hours without interruption; that is, in
numerical succession from 1 to 24.
This is usually called an astronomical day, because astro-
nomers reckon their day from noon: It is also called a matu-
ral day, because it is of the same length in all latitudes.
True solar time is that which is shown by a true sun-dial.
4. A mean solar day is the time elapsed from 12
o'clock at noon on any day, to 12 o'clock at noon
on the next day, as shown by a perfectly well regu-
lated clock or watch.
The time shown by a well regulated clock, or watch, and
a true sun-dial, is never the same but on or about the 15th
of floril, the 15th of June, the 1st of September, and the 24th
of December. The clock, if it goes equally and true, will
be faster than the sun from the 24th of December till the
15th of April; from that time till the 15th of June the sum
will be faster than the clock; from the 15th of June till 1st
of September the clock will be again faster than the sun;
and from thence to the 24th of December the sun will be
faster than the clock. - .
The difference between the true solar noon, as shown by a
true sun-dial, and the mean solar noon as shown by an equal-
ly going clock, is the greatest about the 3d of November;
the time shown by the clock being then 16 minutes and
15.9 second slower than the time shown by the sun-dial.
Though the difference between the true and mean solar
noons about the 3d of November, is 16 minutes and a quar-
ter nearly; we are not however to infer that the difference
between the mean solar day and true solar day, is equal to
the same; for, in ſact, they are nearly equal at that time,
as may be readily seen from the Nautical Almanac for the
present year. -
The difference between mean and apparent time, usually
called the equalion of time, depends upon two causes, the
obliquity of the ecliptic with respect to the equator, and the
unequal motion of the earth in an elliptical orbit. The ef-
fects of both these causes shall be fully considered in a
Subsequent part of this work.
of THE TERRESTRIAL GLOBE. 29
5. The civil day is from midnight to midnight
again, the first twelve hours are the morning hours,
and the last twelve the afternoon hours.
The astronomical day begins at the noon of the civil day;
for instance, May 13th, at 4 o’clock in the aſternoon, accord-
ing to the civil account, will be the same as the astronomical
account; but supposing it was 4 o’clock in the morning of
May 19th, according to the civil account, it would be May
12th, 16 hours by the astronomical way of reckoning.
In civil life, according to Laplace, the day is the interval
of time which elapses between the rising and setting of the
sun, and is variable according to the different latitudes of
places: the night is the time which the sun remains below
the horizon, and varies in like manner.
6. The time in which any star appears to re-
volve from the meridian to the meridian again ; or,
which amounts to the same thing, the time in which
the earth makes one complete revolution on its
axis, is called a sideredl day, which is twenty-three
hours, fifty-six minutes, four and one-tenth seconds
of mean solar time. &
A sidereal day is, therefore, less than a mean solar day, by
3 minutes 55.9 seconds. . This difference is occasioned by
the immense distance of the fixed stars; for the earth’s orbit,
when compared with this distance, is but a point; and there-
fore any meridian will revolve from a fixed star to that star
again, in exactly the same time as if the earth had only a
diurnal motion, and was to remain for ever in the same part
of its orbit. -
But this is not the case with respect to the sum ; for as the
earth, at a mean daily motion, advances 59'8.2° eastward in
its orbit, and that its diurnal motion is also eastward, it is
evident that the same meridian can never be brought round
from the sun, to the sun again, by one entire revolution of
the earth upon its axis, but that it will require as much
more of another revolution as is equivalent to the space
which the earth has advanced in its orbit during that time.
So that three hundred and sixty-six terrestrial revolutions
would be exactly equal to three hundred and sixty-five
diurnal revolutions, if the equinoctial points were at rest in
the heavens. - - -
3%
30 &RAMIMAR OF ASTRONOMY.
7. A clock that is so regulated as to move
through twenty-four hours in the course of a side-
real day, is said to be regulated to sidereal time.
Astronomers have found, by comparing a certain number
of solar and sidereal days, that a mean solar day is 24 hours,
3 minutes, and 56.55 seconds of sidereal time, so that the
excess of a mean solar day above a sidereal day, is 8
minutes, 56.55 seconds in sidereal time.
8. An hour is a certain determined part of a
day, and is equal or unequal. An equal hour is .
the 24th part of a mean solar day, as shown by
well regulated clocks; unequal hours are those
measured by the returns of the Sun to the meri-
dian, or those shown by a correct Sun-dial.
Hours are divided into 60 equal parts, called minutes, a
minute into 60 º parts called seconds, a second into 60.
equal parts called thirds, &c. -
9. A sidereal hour is the 24th part of a sidereal
day, and is therefore less than an hour of mean
solar time. p
For, a mean solar day is to a sidereal day, as 24 hours is
to 23h. 56m. 4.1 seconds in mean solar time; or, as 24h.
3m. 56.555 seconds is to 24 hours in sidereal time: And,
consequently, if the length of a solar hour be taken equal
to unity or 1, a sidereal hour will be equal to .99797 in mean
solar time; or, if a sidereal hour be taken equal to unity, or
I, an hour of mean solar time will be equal to 1.0027.379 in
sidereal time. Hence, by multiplying any given portion of
sidereal time by .997.27, we shall have the corresponding
mean solar time; and, on the contrary, to reduce mean solar
time, to sidereal time, we must multiply by 1.0027.379.
10. A year, in the general extent of the word,
is a period or space of time, measured by the revo-
lution of some celestial body in its orbit.
As year denoted originally a revolution, and was not
limited to that of the sun; accordingly, we find by the oldest
accounts, that people have, at different times, expressed
other revolutions by it, particularly that of the moon; and

of THE TERItESTRIAI, GLOBE. {3}.
consequently that the years of some accounts are to be
reckoned only months, and sometimes periods of 2, or 3, or
4 months. This will assist us greatly in understanding the
accounts that certain nations give of their own antiquity,
and perhaps also of the age of men. We read expressly,
in several of the old Greek writers, that the Egyptian year,
at one period, was only a month; and we are farther told
that at other periods it was 3 months, or 4 months. -
The Egyptians boasted, almost 2000 years ago, of having
accounts of events 48000 years distance. A great deal
must be allowed to fallacy on the above account; but be-
sides this, the Egyptians had, in the time of the Greeks,
the same ambition which the Chinese have at present, and
wanted to pass themselves on that people, as these do upon
us, for the oldest inhabitants of the earth. They had also
recourse to the same means, and both the present and the
early impostors have pretended to ancient observations of
the heavenly bodies, and recounted eclipses in particular,
to vouch for the truth of their accounts. .* -
Since the time in which the solar year, or period of the
earth's revolution round the sun, has been received, we may
account with certainty; but for those remote ages, in which
we do not precisely know what is meant by the term year,
it is impossible to form any satisfactory conjecture of the
duration of time in the accounts.
11. The returns of the sun to the same equinox
mark the years, in the same manner as its returns
to the meridian mark the days. The solar year
is either astronomical or civil. .
12. The astronomical solar year is that which is
determined precisely by astronomical observations;
and is of two kinds, tropical and sidereal, or astral.
13. It is found by observation that the sun, in
consequence of its annual motion in the ecliptic,
employs three hundred and sixty-five days, five
hours, forty-eight minutes, and fifty-one seconds,
in moving from one equinox to the same again.
This period of time is called the tropical year.
This is the only proper or natural year, because it always
keeps the same seasons to the same months.
32 GRAMMAR OF ASTRONOMIY.
14. Observation also shows us that the sum ent
ploys 365 days, 6 hours, 9 minutes, and 11 seconds,
in passing from any fixed star, till it returns to the
same again. This period is called the sidereal year.
Hence, the sidereal year is 20 minutes and 20 seconds
longer than a tropical year; and it likewise follows that the
equinoctial points must have a motion along the ecliptic in
a direction contrary to the order of the signs, amounting to
50" 1, in a year: ſor, as the sun describes the whole eclip-
tic, or 360° in a year, 365d. 5h. 48m. 51sec.: 360°: : 1d;
59'8" 2, the daily mean motion of the earth, or the ap-
parent mean motion of the sun in a day; and therefore 1d :
59' 8" :: 20' 20" : 50" 1. This retrograde motion of the
equinoctial points is called the recession of the equinoc-
tial points. . -
15. That form of year which a nation has adopt-
ed for computing their time by, is called a civil
year. The ſlimerican civil year is a period of 365
days, 6 hours, which is either common or bissertile.
The common civil year is that consisting of 365
days; having seven months of 31 days each ; four
of 30 days, and one of 28 days: the bissextile,
usually called the leap year, consists of 366 days,
having one day extraordinary, called the interca-
lary, or bissextile day; and takes place every 4th
year. In this year February contains 29 days.
QUESTIONS.
What is time !
How is time measured?
What is a true solar day?
What is a mean solar day?
What is a civil day? -
What is a sidereal day, and what is its duration
in mean solar time? -
What is an hour?
What is a sidereal hour?
of THE TERRESTRIAL GLOBE. 33
What is a year?
What is a true solar year?
What is an astronomical year, and how is it di-
vided ?.
of it?
What is a sidereal year, and what is its duration?
What is a civil year, and how is the American
civil year divided? 3.
How many days does the common civil year
eonsist of, and what is the duration of the bissex-
tile or leap year? - .
•=sº-º-º-e
CHAPTER VIII.
Positions of the Sphere. Names assigned to Persons
from their ift. situations on the Globe, &c.
1. Position of the sphere, is its situation with
respect to certain circles on the surface of the earth
and the horizon. There are principally three po-
sitions of the sphere; right, parallel, and oblique.
2. A right sphere is that position of the earth
where the equator passes through the zenith and
nadir, the poles being in the rational horizon.
The inhabitants who have this position of the sphere live
at the equator; they have therefore no latitude, nor no ele-
vation of the pole. All the heavenly bodies will appear to
revolve round the earth from east to west, in circles parallel
to the equinoctial, according to their different declinations;
one half of the starry heavens will be constantly above the
horizon, and the other half below; and the sun always rises
at right angles to their horizon, making their days and
nights of equal length at all times of the year, because the
horizon bisects the circle of diurnal revolution; so that the
stars will be visible for twelve hours, and invisible for the
same space of time.
What is a tropical year, and what is the length
34 GRAMIMAR OF ASTRONOMY.,
3. J1 parallel sphere is that position of the earth
where the equator coincides with, and all its paral-
Hels are parallel to the horizon.
Hence, the poles of the world are in the zenith and madir,
while all the meridians cut the horizon at right angles. The
inhabitants of a sphere in this position, if there are any,
live at the poles; they have the greatest possible latitude;
and the stars, which are situated in the hemisphere to which
the inhabitants belong, never set, but describé circles paral-
lel to the horizon; while those stars of the contrary hemis-
phere never rise. * ,
During the time that the sun is describing the northern
signs, the inhabitants of the north pole have continual day,
and those of the south pole continual might; and while he
is describing the southern signs, the inhabitants of the
north pole have continual might, and those of the south
pole continual day.
4. An oblique sphere is that position of the earth
in which the equator and all its parallels are un-
equally divided by the horizon.
This is the most common position of the sphere, or it is
the situation which the earth has with respect to all its in-
habitants, except those at the equator and poles.
To the inhabitants of an oblique sphere, the pole of their
hemisphere is elevated above the horizon as many degrees
as are equal to the latitude, and the opposite pole is de-
pressed as much below the horizon; so }. the stars only,
at the former, are seen. The sun and all the heavenly
bodies rise and set obliquely; the seasons are variable, and
the days and nights are unequal.
5. The inhabitants of the earth have different
names assigned to them by geographers, according
to the several meridians and parallels of latitude
they lie under, and are called antoci, perioci, and
antipodes, -
6. The antaci, or antecians, are those who live
under the same meridian, or line of longitude, and
have the same degrees of latitude, but the one has
OF THE TERRESTRIAL GLOBE. 35
north and the other south latitude; as New-York
and Cape St. Antonio. *
The antoeci have noon at the same time, but contrary sea-
sons of the year; so that when it is summer with one, it is
winter with the other, &c.; consequently the length of the
days with one is equal to the length of the night with the
other. They have different poles elevated, and the stars
that never set to the one are never seen by the other.
Those who live at the equator have no antoeci.
7. The periaci, or peria:cians, are those who live
under the same parallel of latitude, but under op-
posite meridians; their difference of longitude
being 180 degrees. ~- -
The periocci have the same seasons of the year, and also
their days and mights of the same length; but when it is
moon with the one, it is midnight with the other. Those
who live at the poles of the earth, have no periocci.
8. The antipodes are those inhabitants of the
earth who live under opposite meridians, and op-
posite parallels of latitude; their difference of lon-
gitude being 180 degrees, and the one having the
same degrees of north latitude as the other has of
south latitude.
The antipodes are diametrically opposite to each other,
the zenith of the one being the nadir of the other, and, con-
sequently, they walk feet to feet; they have the same sea-
sons and length of days and nights; but all of these at con-
trary times, it being day to the one when it is night to the
other, summer to the one when it is winter to the other, &c.
9. The inhabitants of the earth have also parti-
cular names assigned to them from their shadows
falling different ways at noon, and are called ſlim-
phiscii, Heleroscii, and Periscii. -
10. Amphiscii, or ſlmphiscians, are the people
who inhabit the torrid zone; so called, because they
cast their shadows both north and south at different
– times of the year; the sun being sometimes to the
36 - GRAVIMAR OT, ASTRONOMY. "
south of them at moon, and at other times to the
north. -
When the sun is vertical, or in the zenith, which happens
twice in the year, the inhabitants have no shadow, and are
then called Ascii, or shadowless.
11. Heteroscii is a name given to the inhabitants
of the temperate zones, because they cast their
shadows at moon only one way.
Thus the shadow of an inhabitant of the north temperate
zone always falls to the north at noon, because the sun is
them directly south; and an inhabitant of the south, tem-
perate zone casts his shadow towards the south at noon, be-
cause the sun is due north at that time.
12. Periscii, or Periscians, are those people who
inhabit the frigid zones, so called because their
shadows, during a revolution of the earth on its
axis, turn quite round to all points of the compass,
without disappearing.
For as the sun does not set to the inhabitants of the frigid
zones during several revolutions of the earth on its axis,
but moves quite round; so do their shadows also.
These distinctions of the inhabitants of the earth from
the direction of their shadows, are of little, or, perhaps, of
no importance. .
13. The right ascension of the Sun, or a star, is
that degree of the equinoctial which rises with the
Sun, or a star, in a right sphere, and is reckoned
from the equinoctial point, Aries, round the globe.
14. Oblique ascension of the sun, or a star, is
that degree of the equinoctial which rises with the
Sun, or a star, in an oblique sphere, and is likewise
counted from the point Aries round the globe.
15. Oblique descension of the sun, or a star, is
that degree of the equinoctial which sets with the
sun, or a star, in an oblique sphere.
OF THE TERRESTRIAL, GLOBE. - 37
16. The ascensional or descensional difference is
the difference between the right and oblique ascen-
sion, of the difference between the right and ob-
lique descension ; and with respect to the sun, it is
the time he rises before six o'clock in the summer,
or sets before six in the winter. -
17. The longitude of the sun, which is usually
called the sun's place in the ecliptic, is reckoned
on the ecliptic from the point Aries, eastwald,
round the globe.
18. The time from the first dawn or appearance
of the morning, or between the setting of the Sun
and the last remains of day, is called the crepuscu-
lum, or twilight. - -
The twilight, it is supposed, usually begins and ends
when the sun is about 18 degrees below the horizon; for
then the stars of the 6th magnitude disappear in the morn-
ing, and appear in the evening. It is of longer duration in
the solstices than in the equinoxes, but it is longer in an
oblique sphere than in a right one; because, in those cases.
the sun, by the obliquity of his path, is longer in ascending
through 18 degrees of altitude.
19. Jingle of position between two places on the
terrestrial globe, is an angle at the zenith of one
of the places, contained by the meridian of that
place, and a vertical circle passing through the
other place. → *-
The vertical circle, as has already been observed, may be
represented by the quadrant of altitude screwed in the
zenith of one of the places, and passing over the other; and
the angle of position is usually measured on the horizon,
from the elevated pole towards the quadrant of altitude.
20. Rhumbs are the divisions of the horizon into
32 parts, usually called the points of the compass.
The ancients, according to Pliny, were acquainted only
with the four cardinal points, and the wind was said to
blow from that point to which it was nearest. -
38 GIRAMMIAR OF ASTRONOMY.
21. The path which a ship describes, while she
sails on the same point of the compass, and cuts.
all the meridians at the same angle, is called a
rhumb line. - - ; :
This angle is usually called the course, and sometimes
the proper angle of the rhumb. If the rhumb line, which
is a loa-odromic or spiral curve, be continued, it will never
return into itself so as to ſorm a circle, except it happens to
be due east and west, or due north and south; and it can
never be a straight line upon any map, except the meridians.
be parallel to each other, as in Mercator's and the plane
chart. Hence the difficulty of finding the true bearing
between two places on the terrestrial globe, or on any
map but those above mentioned. The bearing ſound by a
quadrant of altitude on a globe, is only the measure of a
spherical angle upon the surface of that globe, as defined
by the angle of position, and not the real bearing or rhumb,
as shown by the compass; if a place A bear due east from
a place B, the place B will bear due west ſrom the place
A; but this is * case when measured with a quadrant
of altitude.
QUESTIONS.
How many positions of the sphere are there 2
What is a right sphere, and what inhabitants of
the earth have this position ? - -
What is a parallel sphere, and what inhabitants
of the globe have this position ? - -
What is an oblique sphere, and what inhabitants
of the globe have this position ? . . .
What inhabitants are called antoeci to each other,
and what do you observe with respect to their lati-
tudes, longitudes, &c. 2 - -
What inhabitants are called perioeci to each
other, and what is observed with respect to their
latitudes, longitudes, hours, &c. 2 -
What are the antipodes, and what observed with .
respect to their seasons of the year, &c. 2
What parts of the globe do the amphiscii inha-
hit, and why are they so called 2
º
Q? THE TERRESTRIAL GLeBE. ... 39
When do the amphiscii obtain the name of ascii?
What parts of the globe do the heteroscii inha-
bit, and why are they so called 2
What parts of the globe do the periscii inhabit,
and why are they so called 2
What is the right ascension of the Sun ?
What is the oblique ascension of the Sun?
What is the oblique descension of the Sun ?
What is the ascensional or descensional differ-
ence 2 . . .
What is the crepusculum, or twilight, and when
does it begin or end ? -
What is an angle of position ?
What are rhumbs and rhumb lines?
-*-
CHAPTER IX.
Astronomical and Geographical Problems performed by
- the Terrestrial Globe.
- PROBLEM 1. -
..fl. Place being given, to find its Latitude and Longitude.
RULE. Bring the given place to the graduated
side of the brazen meridian, which is counted from
the equator towards the poles; the degree directly
over the place is the latitude, and the degree on the
equator, under the edge of the meridian, is the
Tongitude. - - -
The longitude is either east or west. Thus, if it be on
the east side of the first meridian, it is called east longi-
tude; if on the west side, west longitude, and is reckoned
180 degrees each way. - • *
On Wilson's American globes there are two rows of
figures on the north side of the equator. When the place
lies on the east side of the meridian of London, the longi-
40 GRAMMAR OF ASTRONOMY.
tude must be counted on the upper line; and when it is on
the west side, it must be counted on the lower lime.
It has been already observed that the places on the earth
are laid down on, the terrestrial globe, so as to answer to
their real situations: Hence the latitude and longitude of
a place on the terrestrial globe, found according to the
above rule, will be the true latitude and longitude of the
same place, situated on the real globe of the earth.
- EXAMPLES.
1. What is the latitude and longitude of New-
York, the first commercial city in America, and one
of the first in the world 2
Bring New-York to the gradu ated side of the meridian,
and it will be found under about 400 42 north of the equa-
tor, or 400. 42' north latitude ; and the intersection of the
meridian with the equator is 74° west of the meridian of
London, or 74° west longitude. Hence New-York is in
400 42 morth latitude, and 74° west longitude.
It is proper to observe that the latitudes of places cannot
be ſound on the terrestrial globe to any great degree of accu-
racy, because the brazen meridian is only graduated to de-
grees and half degrees, and seldom to less than quarter de-
grees; the same defect is in the graduation of the horizon
and quadrant of altitude ; but the equator is usually gra-
duated to degrees and minutes. Consequently, whenever the
latitude or longitude of a place is to be ſound accurately, we
must have recourse to correct tables, calculated for that pur-
pose: for instance, the latitude of New-York, found by cal-
culation, is 40°42' 40" north, and the longitude 74° 1' west.
2. Required the latitude and longitude of Wash-
ington city, the capital of the United States.
3. Find the latitude and longitude of London,
the capital of England. - a
4. Required the latitude and longitude of Co-
penhagen, the capital of Denmark.
5. What is the latitude and longitude of Paris,
the capital of France 2
6. Required the latitude and longitude of Dub-
Jim, the capital of Ireland.
OF 'THE FE RRESTRIAL, GLOBE. 4l
7. What is the latitude and longitude of Phila-
delphia, the capital of Pennsylvania 2
It may not be improper to remark, that capital, in this
work, generally implies the chief or largest city in a State;
and the seat of government, the town or city where the legis-
lature of the State meets: for instance, Harrisburg is the
seat of government of the State of Pennsylvania, and
Philadelphia the capital or chief city. -
8. What is the latitude and longitude of Madrid,
the capital of Spain 2 -
9. What is the latitude and longitude of Mos-
cow in Russia 2 .
10. What is the latitude and longitude of Can-
ton in China Ż -
14. What is the latitude and longitude of St.
Helena, an island in the Atlantic Ocean, in which
Napoleon Bonaparte was imprisoned by the allied
sovereigns of Europe, from the year 1815 till his
death in 1821 2. * - i
PROBLEM II.
To find all those places that have the same latitude as any
. given place. . -
RULE. Bring the given place to the brazen me-
ridian, and mark the degree over it; turn the globe
round, and all places passing umder the observed
degree of latitude, are those required. . .
Whenever a place is brought to the brazen meridian, the
graduated edge which is numbered from the equator towards
the poles, is always to be understood, unless the contrary
be mentioned. -
All places in the same latitude, as has been already ob-
served, have the same length of day and night, and the same
seasons of the year, though, from local circumstances,
they may not have the same atmospherical temperature.
4 :
42 GRAMMAR of ASTRONOMY.
EXAMPLES. .
1. What places have the same latitude, or nearly
the same latitude as Baltimore, the capital of Mary-
land, in latitude 39° 20' north 2 - .
.Answer. Flores, one of the Western Islands; Cagliari,
the capital of Sardinia; Port Mahon in Minorca; Sarma-
cand, once the capital of Independent Tartary ; Pekin, the
capital of China; Marietta, the oldest town in the state of
Ohio, &c. f
2. Which places have the same latitude, or
nearly the same latitude with Madrid 2 -
3. What inhabitants of the earth have the same
length of days as those of Berlin, the capital of
Prussia 2 tº .* - - .
4. What inhabitants of the earth have the same
seasons of the year as those of Ispahan, formerly
the capital of Persia?
5. Find all the places on the globe which have
no latitude, or which have nearly the same latitude
with Quito, the largest city in the Republic of Co-
lombia, famous for its great elevation, being up-
wards of 9500 feet above the level of the sea.
6. Find all the places on the globe which have
the greatest latitude, or 90 degrees. g
7. Which places have nearly the same latitude
with Havana, the capital of Cuba 2 . . .
8. Which places have nearly the same latitude
with Rio Janeiro, the capital of Brazil 2 , *
9. Which places of the earth have nearly the
same latitude with North Cape in Lapland, lati-
tude 71° 10' north-2 ... "
10. What places have nearly the same latitude
as the following places: New-York; Petersburgh,
the capital of the Russian empire; Canton in Chi-
na; Sydney, the capital of the British colony of
OF THE TERRESTRIAL GLOBE. &
*New South Wales; and Lima, the capital of
Peru? . . . . :
PROBLEM III.
To find all places on the globe that have the same lon-
. gitude as any given place.
RULE. Bring the given place to the brazen me-
ridian, them all places under the same edge of the
meridian, from the north to the south pole, have
the same longitude. .
All those places situated under the same meridian, from
the tropic of Cancer to the tropic of Capricorn, have noon
at the same time: or, if it be one, two, three, or any other
number of hours before or after noon with one particular
place, it will be the same hour with every other place
situated under the same meridian.
EXAMPLES.
1. Find all those places that have the same, or
nearly the same longitude as Lima.
The longitude of Lima is found to be 76° 50', and all the
places that have nearly the same longitude are those re-
quired. -
By proceeding according to the rule, the following places
are found to be the answer to the above example: Port
Royal and Kingston in Jamaica; Norfolk in Virginia;
Edenton in North Carolina; Baltimore in Maryland; and
Kingston in Upper Canada. - - -
2. What places have the same, or nearly the same
longitude as Stockholm, the capital of Sweden 2
3. When it is nine o'clock in the morning at
New-York, what inhabitants of the earth have the
same hour 2 -
4. Find all those places that have nearly the
same longitude as London; or, which amounts to
the same thing, find all those places that have no
longitude.
5. When it is moon at Vienna, the capital of
+44 GRAMMIAl& OF ASTRONOMY.
Austria, what inhabitants of the earth have the
same hour 2 r
6. What inhabitants of the earth have the same *.
longitude as Washington city ?
7. What inhabitants of the earth have the same
longitude as Dublin 2 .
8. What inhabitants of the earth have the
greatest longitude ; or, which amounts to the same
thing, what inhabitants have nearly the same lon-
gitude as Antipodes Island, in the South Pacific
Ocean 2 - . . -
9. Find all those places that have nearly the
same longitude as the following places: Charles-
ton, the capital of South Carolina; New-Orleans,
the capital of Louisiana; Mexico, the oldest city
in America; New-Haven, the capital of Connecti-
cut; Cincinnati, the capital of Ohio; and Pesin,
the capital of China. -
- - PROBLEM IV.
The longitude and latitude of any place being given, to
find that place on the globe.
RULE. Find the longitude of the given place
on the equator, and bring it to the brazen meri-
dian ; then under the given latitude, found on the
meridian, is the place required.
EXAMPLES. -
1. The longitude of a place is 77° 40' east, and
the latitude 28° 37' north; find that place on the
globe.
Jìnswer. Delhi, a celebrated city, and, for many years, the
capital of Hindostan. -
2. The longitude of the greatest commercial
town in Germany is 9° 55' east, and latitude 539
34 north. What is the name of that town 2
ÖF THIE I'ERRESTRIAL GLOBE. 45
3. The longitude of a town in Norway is 100
23 east, and latitude 68° 25' north. What is the
name of that town 2 ;
4. The longitude of a city, which was one of
the most populous and splendid cities of the world,
is 44° 24′ east, and latitude 23° 20' north : Where
is that city situated, and what is it called 2
5. The longitude of a remarkable cape in South
America, is 67°21'west, and latitude 55° 58' south.
What is that cape called ! -
6. The longitude of a city in South America
is 58° 24′ west, and 34° 35' south. What is that
city called, and of what country is it the capital 2
7. The longitude of a commercial city in the
United States, is 71° 4' west, and latitude 42° 23'
north. What is that city called, and of what state
is it the capital 2 t .
8. Find those cities, and other conspicuous
places, whose longitudes and latitudes are as fol-
lows: -
Latitudes. longitudes.
32° 02' N. 81 o 03' W.
30 40 N. 88 21 W.
25 42 N. 80 06 W.
36 49 S. , 73 09 W.
22 44 N. 109 54 W.
3 48 S. 102 28 E.
6 09 S. 106 52 E.
: PROBLEM. W.
To find the difference of latitude between any two given
- places. -
RULE. Find the latitude of each place, by
prob. I. Then, if both places are on the same
side of the equator, subtract the less latitude from
43 G 3.". AllMAR OF ASTRONOMY.
the greater, and the remainder will be the differ-
ence of latitude ; but, if the latitudes be one north
and the other south, add them together, and their
sum will be the difference of latitude.
Or, bring one of the places to the brazen meridian, and
mark the degree over it; then, bring the other place to the
meridian, and likewise mark the degree over.it': the number
of degrees between these two marks, countéd on the meri-
dian, will be the difference of latitude-réâuired. This rule
is not so convenient for exercising the student as the above.
EXAMPLES,
1. What is the difference of latitude between
Amsterdam, the capital of the Netherlands, and
Athens, anciently the capital of Attica in Greece 2
By bringing Amsterdam to the brazen meridian, its lati-
tude is found to be 52O 22' north; and, in like manner, the
latitude of Athens is found to be 370 58' north. Conse-
quently, their difference 4o 24' is the difference of latitude
required. we
2. What is the difference of latitude between
Copenhagen, the capital of Denmark, and Mo-
Zambique, the capital of the Portuguese possessions
on the eastern coast of Africa 2
Copenhagen being brought to the brazen meridian, its
latitude is found to be 55° 41' north; and, in like manner,
the latitude of Mozambique is found to be 15° 1' south.
Consequently, their sum 700 42' is the difference of latitude
required. *
3. Find the difference of latitude between Juan
Fermandes, in the Pacific Ocean, and Bermudas,
in the Atlantic.
4. Find the difference of latitude between Sa-
vannah, the capital of Georgia, and Candia, the
capital of the island of Candia, in the Mediterra-
I\628.11 S628. - t
OF THE TERRESTRIAL GLOBE. 47.
5. What is the difference of latitude between
Petersburgh and Detroit, the capital of Michigan
Territory 2
6. What is the difference of latitude between
Astracan in Asiatic Russia, and St. Louis, the ca-
pital of Missouri ?
7. Required the difference of latitude between
the north and south poles.
8. Required the difference of latitude between
the following places: Alexandria and the Cape of
Good Hope; London and Charleston in South
Carolina; Cadiz and Kaskaskia, the capital of Il-
linois; Cape Horn and North Cape, on the coast
of Norway; Quebec, capital of Lower Canada,
and Potosi, a city in the United Provinces of La
Plata, celebrated for the richest silver mines in the
world. , . .
PROBLEM WI.
To find the difference of longitude between any two
given places. **
RULE. Find the longitude of both places, (by
Prob I.) then, if both places are situated on the
same side of the first meridian, subtract the less
longitude from the greater, and the remainder will
be the difference of longitude; but, if the longi-
tudes be one east and the other west, add them to-
gether, and their sum, (when it does not exceed 180,)
will be the difference of longitude; and if the sum
of their longitudes should exceed 180 degrees, sub-
tract it from 360, and the remainder will be the
difference of longitude. - - .
What is usually understood by the difference of longitude
between any two places, is the nearest distance of their me-
ridians from each other, measured at the equator; hence,
the last part of the above rule is evident. -
48. GRAMMAR OF ASTRONOMY.
EXAMPLEs.
1. Find the difference of longitude between
Jłlexandria, the ancient capital of Egypt, and Rome,
a large and famous city of Italy, formerly the seat
of the Roman Empire, and the capital of the
world.
The longitude of Alexandria is found to be 300 5' east,
and the longitude of Rome 12° 28′ east; hence their differ-
ence, 17° 37', is the difference of longitude required.
2. Find the difference of longitude between
Smyrna, a city of Asia Minor, and Panama, a city
and sea-port on the isthmus of Darien.
The longitude of Smyrna is readily found to be 270 20
east, and the longitude of Panama 79° 19 west: hence
their sum, 106° 39', is the difference of longitude required.
3. Required the difference of longitude between
Jerusalem, capital of the ancient Judea, and Fez,
a large city of Morocco, in Africa, and once the
capital of all the Western Mahometan States.
4. Find the difference of longitude between
Batavia, a city in the island of Java, and the mouth.
of Columbia, or Oregon river, on the north-west
coast of America.
5. What is the difference in longitude between
St. Jago, in the Atlantic Ocean, and the Straits of
Babelmandel on the coast of Arabia 7
6. What between Cape Breton in the gulf of St.
Lawrence, and Cape Cambodia, the Southern ex-
tremity of Cambodia, in the gulf of Siam 7
7. What between Cape Farewell, the southern
extremity of Greenland, and Cape Farewell, on
the coast of New-Zealand in the Pacific Ocean 2
8. Required the difference of longitude between
the following places: Portsmouth, the capital of
OF THE 'ſ ERRE8TRIAL GI.O.B.E. 49
New-Hampshire, and the city of Jeddo in the em-
pire of Japan; Portland, the capital of Maine,
and Port Jackson, in New-Holland; St. Fee de
Bogata, a city in the Republic of Colombia, and
Kesho, the capital of the empire of Tomkin ; Nat-
chez, the capital of the State of Mississippi, and
Lassa, the capital of Tibet; Cape Comorin in Hin-
dostan, and Gondar, the capital of Abyssinia.
- - ProBLEM v11.
To find the distance between any two places on the globe.
Definition. The shortest distance between any
two places on the earth, considered as a sphere, is
an arc of a great circle contained between the twc.
places.
The length of a degree of any great circle on the surfa,
of the earth, is 69. American miles, supposing it to b,
sphere of 7920 miles in diameter, and 24880 miles in c
cumference: because, 360C:24880 miles: : 10: 69% mil
It is proper to observe that, in geography and navigat
a degree on the surface of the earth contains 60 geograph
cal miles ; hence, a geographical mile is greater than an
merican, in the proportion of 60: 69%, or of 1 : 1.15185.
It may be also remarked that an American mile is the same
as an English mile, each coniaining 5:00 American or Eng-
lish feet. - - - -
*ULF. Lay the graduated edge of the quad-
rant of altitude over the two places, so that the
division marked 0 may be on one of them, the de-
grees on the quadrant, contained between the two
places, will give their distance; and if their dis.
tance in degrees be multiplied by 60, the product
will be the distance in geographical miles; or
multiply the degrees by 69%, and the product will
be the distance in American miles. Or, take the
distance between the two places with a pair of
compasses, and that distance applied to the equa-
for will give the number of degrees between them :
#,







50 , - GRAMNIAR of ASTRONOMY.
which may be reduced to geographical and Ame-
rican miles, as before. . . . . . -
If the distance between the two places should exceed the
length of the quadrant, stretch a piece of thread over the
two places and mark their distance; the extent of the thread
between these marks, applied to the equator, from the first
meridian, will show the distance between the two places in
degrees, which may be reduced, if necessary, to Geographi-
cal and American miles, as above. •- , , , ,
- . . . ExAMPLEs. -
I. What is the nearest distance between Albany
and St. Louis - . . . . . . . . .
* ~ * - º - - * * . \ .
.Answer. The distance in degrees is 13.
| 13 distance in degrees. 13 distance in degrees.
60 . . . . . 69%
780 geographical miles. 117
. 7S
+ 1;
898% American miles.
Hence, the nearest distance is equal to 780 geographical,
or to 898, American miles. - . . . . . . .
2. What is the nearest distance between Lom-
don and Port Jackson, a bay and English settle-
ment, on the eastern coast of New-Holland, and
9 miles north of Botany Bay 2. º -
Here the distance between the two places exceeds the
quadrant of altitude; therefore, by measuring the nearest
distance with a thread, and applying that distance to the
equator, it will be found to be 154 degrees nearly.
154 distance in degrees. 154 distance in degrees,
* * Y! -
60 , . " 69%
9240 geographical miles. | 1386,
. . . . . . . 924
|| 17;
10648% American miles.









of THE TERRESTRIAL, GLOBE. 53
Jìnswer. The distance in degrees is 154; the distance in
geographical miles is 9240, and the distance in American
miles is 10643; . . . • . " }
3. What is the nearest distance between, New-
Haven, and Puebla, a considerable city in Mexico,
situated on a plain elevated more than 1000 feet
above the level of the sea 2 . . . . . .
4. What is the extent of America from Cape
Horn, the most southern extremity of Terra del
Fuego, to the Icy Cape, on the north-west coast of
America, in the Frozen Sea 2 . . . .
5. What is the extent of the United States in
Geographical and American miles, from Cape
Florida to the mouth of Columbia river; and also
the extent from the mouth of the Sabine river in
Louisiana, to the northern extremity of Maine m.
about 47; degrees north latitude 2 . . . . . . . .
6. What is the nearest distance in American
miles from the north to the south pole 2 • "
7. What is the extent of Africa in American
miles, from Cape Verd to Cape Guardafui, the most
eastern point of Africa, at the entrance into the
Red Sea 2 . . . . . .
8. What is the extent of Africa in American
miles, from the Cape of Good Hope to the Straits
of Gibraltar 2 . . . . . . . . .
9. What is the extent of Europe in American
miles, from Cape Matapan in the Morea, to the
North Cape in Lapland .
10. Suppose the tract of a ship to Canton be
(thº shortest distances) from New-York to Bermu-
das, thence to Ascension island in the Atlantic
Ocean, between Africa and Brazil, thence to St.
Helena, thence to the Cape of Good Hope, thence
to the Straits of Sunda, between Java and Suma-
oz GRAMMAR OF ASTRONOMY.
tra, thence to Canton : How many American
miles from New-York to Canton on these different
courses 2 .
Simple as the preceding problem may appear in theory,
on a superſicial view, yet, when applied to practice, the diſ-
ficulties which occur are almost insuperable. In sailing
across the trackless, ocean, or travelling through extensive
and unknown countries, our only guide is the compass; and
except two places be situated directly north and south of
each other, or upon the equator, though we may travel or
sail from one place to the other, by the compass, yet we can-
not take the shortest route, as measured by the quadrant of
altitude. - -
PRoBLEM v1.11.
.3 place being given on the globe, to find all places which are
situated at the same distance from il as &ny other given
place. . . . . . . - -
*
RULE. Bring the first given place to the brass
meridian, and screw the quadrant of altitude over
it ; next move the quadrant till its graduated edge
falls upon the other place, and mark the degree
over it; then move the quadrant entirely round,
keeping the globe in its first situation, and all places
which pass under the same degree which was ob-
served to stand over the second place, will be those
sought. - - -
Or, place one foot of a pair of compasses in one of the
given places, and extend the other ſoot to the second given
place; a circle described from the first given place, with this
extent, will pass through all the places sought. If the length
between the two given places should exceed the length of the
quadrant, or the extent of a pair of compasses, stretch a
piece of thread over the two places, with which describe a
circle as before. i
EXAMPLES. - .
1. Find all those places that are at the same, or
nearly the same distance from Paris, as the Mael-
of THE TERRESTRIAL GLOBE. 53
stroom, a dreadful whirlpool on the coast of Nor-
way, near the island of Moskoe. a
• Answer. St. Petersburg, the capital of the Russian em-
pire; Novgorod, a town in European Russia, situated in a
'beautiful plain.at the north extremity of the lake Ilmen;
Smolensk, a town in European Russia, famous for its siege
and bombardment by the French; Cherson, a town in Eu-
ropean Russia, on the river Dnieper; Milo, ancient Melos,
an island of the Mediterranean in the Grecian Archipelago;
Sidra, ancient Syrtis, a gulf on the coast of Tripoli; Gada-
mis, a town in Africa, S. W. of 'Tripoli; Mogadore, a sea-
port of Morocco, on the Atlantic; and Iceland, an island in
the Atlantic Ocean, belonging to Denmark. . s'
It may be proper to observe, that each of those places is
1380 American or English miles distant from Paris.
2. Required all those places that are at the same
distance from London as Warsaw, a city in the new
kingdom of Poland. * * . . . . .
3. What places are at the same, or nearly the
same, distance from Washington city as Archan-
gel, a city in the northern part of Russia, at the
mouth of the Dwina, a few miles from the White
Sea 2 " . . . . . . . . . . .
4. It is required to find all those places on the
globe that are at the same, or nearly the same, dis-
tance from New-York as Turin, the capital of Pied-
‘mont and of the Sardinian monarchy, finely situ-
rated on the river Po. * , I
5. It is required to find all those places that are
at the same, or nearly the same, distance from Bue-
nos Ayres, the capital of the United Provinces of
South America, situated on the bank of the Rio de
la Plata, as Madrid, in Spain. -
6. What places are at the same distance from
Mecca, a large city of Arabia, celebrated as the
birth-place of the impostor Mahomet; as Madras,
a celebrated city and fortress of the south of In-
& 5* .
54 GRAMMAR of ASTRONOMY.
dia, and capital of the British possessions in that
quarter 2 . . . . .
PROBLEM IX.
The latitude of a place being given, and its distance from
a given place, to find that place, the latitude of which
w8 gwen. * -
RULE, ! If the distance be given in American or
geographical miles, reduce them into degrees, allow-
ing 69; American, or 60 geographical miles to a de-
gree; then bring the given place to the meridian,
and screw the quadrant, of altitude over it; move
the quadrant completely round, if necessary, and
observe the places over which the degrees of dis-
tance pass; turn the globe till one of those places
falls under the given latitude on the brazen meri-
dian, and it will be the place required. . . . .
Or, having reduced the miles into degrees, take
the same number of degrees from the equator with
a pair of compasses, and with one foot of the com-
passes in the given place, and this extent of degrees,
describe a circle on the globe; turn the globe till
this circle falls under the given latitude on the me-
ridian, and you will find the place required.
it may be proper to observe that, as there are two places
on the same parallel of latitude, which are equally distant
from the given place; it is necessary to turn the globe till
two of the observed places, as in the first rule, or two points
of the circle, as in the second, fall under the given latitude
on the meridian; unless it is mentioned in the problem, that
f * place sought lies eastward or westward of the given
a08, Y. % - * , ºr *
p It is also proper to remark that it is more convenient for
students in exercising on the globes, to use the quadrant of
altitude, or a thread, than a pair of compasses, because, by .
using the quadrant or thread, the globe would be less in-
jured than if the compasses had been used. g
of THE TERRESTRIAL GLOBE. 55
EXAMPLES.
1. A place in latitude 55° 41' N. is 1770 geogra-
phical miles from Suez, a town in Egypt, on the
west coast of the Red Sea, where the ancient Ar-
sinoe is supposed to have stood; required the place
whose latitude is given 2
Dividing 1770 by 60, the quotient is 29}, which is the dis-
tance in degrees; then, bringing Suez to the meridian, screw-
ing the quadrant of altitude over it, and observing the places
that pass under the degrees of distance on the quadrant; that
is, counting 29 from the zenith, the degrees of distance on
the quadrant will therefore be 60 ; and when the lower eng
of the quadrant is moved round, the places which pass under
60% are Paris, Brussels in the Netherlands, Copenhagen,
Vologda, a city in Russia and capital of a government of the
same name, Birsk, a town in European Russia. Now, by
turning the globe round, you will find that Copenhagen is the
place sought; since it passes under the given latitude on the
meridian: It will be ſound that Birsk will also pass under
the given latitude, and it is at the given distance from Suez.
Consequently, Copenhagen and Birsk are two places which
will answer the conditions of the problem; but iſ it were
xnentioned in the problem, that the required place was west-
ward of Suez, then Copenhagen would be the answer; and
if the required place was eastward of Suez, then Birsk
would be the place sought. w
2. A place in latitude 84 degrees N. is 3660
geographical miles eastward of Boston, the capital
of Massachusetts; required the place.
3. A place in latitude 60° N. is 1273 American
or English miles from London, and it is situated in
east longitude; required the place. • *
4. A place in latitude 808 S. is 3179 American
miles from Richmond, the capital of Virginia, and
it is situated westward of the meridian of Richmond;
required the place.
5. A place in latitude 33° 2' S. is 4680 geogra-
phical miles from Montreal, a town in Lower Cana-
:56 'GRAMMAR OF ASTRONOMY.
l
'da, the second in rank in the province ; required
the place 2 -
PROBLEM x.
. . . . ! , - . . . tº ‘. . . * . . . . . f
The longitude of a place being given, and its distance from a
given place, to find that place whose longitude is given.
RULE. If the distance be given in miles, reduce
them into degrees, as in the foregoing problem;
then screw the quadrant over the given place, move
the lower end of it so far round as may be consi-
dered necessary, and observe the places passing
under the degrees of distance; bring the given lon-
' ' - . } . -* tº ~ * * . a
Igitude to the brass meridian, and you will find the
place sought under the meridian. . . . .
Or, bring the given longitude under the brass
meridian, and describe a meridian on the globe with
;a fine pencil, or in any other way that is convenient,
so as not to injure the globe; then put that part of
the graduated edge of the quadrant of altitude
which is marked 0, upon the given place, and move
the other end northward or southward, according
as the required place lies to the north or south of
the given place, till the degrees of distance cut the
given longitude; under the point of intersection
you will find the place required. . . .
Or, having reduced the miles into degrees, take the same
number of degrees ſrom the équator with a pair of compasses,
or a thread, and with one foot.of the compasses in the given
place, under the point where the other cuts the meridian
passing through the given longitude, you will find the place
required. • * - -
EXAMPLES.
1. A place in north latitude, and in 87° 40 east
kngitude, is 2940 geographical miles from Cal-
or THE TERRESTRIAL GLOBE. 57
~ 4
Cutta, a city in Bengal, and capital of all the Bri.
fish possessions in Hindostan; required the place.
Jłnswer. Gondar, in latitude 12° 30' north; and Tula, a
city of Russia, in latitude 540.11% north: So that there are
two places having nearly the same longitude, which are
equally distant from Calcutta. . . . . . . . . . . . . . º
Here, dividing .2940 by 60, the quotient will be 49, the
distance in degrees; then, by proceeding according to the
second method, which is frequently the most convenient in
practice, we shall find the above two places. If it were
mentioned, in this.example; that the required place was
southward of Calcutta, then Gondar would be.the answer;
but, if the required place was fiorthward of the given place,
Tula would be the place sought: And as the direction of the
required place is not stated, both will answer the conditions
of the problem. . . . . . . . . . . . . . . . 't
- ' ' ' ' ' … 2 . . . . . . . . . . - . . . . . . . . .
º2. A place in north latitude, and in 60 degrees
west. longitude, is .4216 English miles from Lon-
don; required the place. . . . . . . . . . .
3:. A place in north latitude, and in 74 degrees
west longitude, is 3600 geographical miles from
Venice, a city in Austrian Italy, formerly the capi-
tal of a republic, near the gulf of Venice; required
the place. . . . . . . . . . . . . . . . . .
4. A place in north latitude, and in 81 degrees
west longitude, is 5529 American miles from Adri-
anople, a city of European Turkey, in Romania;
required the place. . . . . . . . . . . . . .
5. A place in south.latitude, and, in longitude
5° 36' west, is 5190 geographical miles from Que-
bec; required the place. . . . . t * .
6. A place in longitude 31° 20' east, is 82 de-
grees, or 5667 American miles, from the mouth of
the Amazon, a river of South America and the
largest in the world, which flows into the Atlantic
Ogean under the equator; required the place.
58 GHANIMAR OF ASTIRON ONIY.
PROBLEM XI. ! )
To find the Jintact of any given place.
RULE. Bring the given place to the brass meri-
dian, and observe its latitude ; then in the opposite
hemisphere, under the same degree of latitude, you
will find the antoeci. , ſ
\
\
EXAMPLES.
\ W
1. Required the anteci of Cape Fear, the south
point of Smith's island in the mouth of Cape Fear
river, North Carolina. p
Jłnswer. Juan Fernandez, an island in the Pacific Ocean,
west of Chili, celebrated for having been the solitary resi-
dence of Alexander Selkirk for several years, from whose
adventures upon it De Foe wrote the popular novel of Ro-
binson Crusoe. l
2. Required the antoeci of Cusco, anciently the
capital of the Peruvian empire, and the seat of the
Incas. ,
3. Required the antoeci of Thebes, ancient city
and capital of Egypt, famous as “the city of an
hundred gates,” the theme and admiration of an-
cient poets and historians, and the wonder of tra-
vellers. * J. '
4. Required the antoeci of Azoph, a town in
Asiatic Russia, on the east extremity of the sea of
Azoph, at the mouth of the river Don.
f
f
PROBLEM XII.
To find the Periwei of any given place.
RULE. Bring the given place to the brass me-
ridian, and set the index of the hour circle to 12,
OF THE TERRESTRIAL GLOBE. 59
turn the globe half round, or till the index points
to the other 12, then under the latitude of the given
place you will find the perioeci.
EXAMPLES.
{ |
i. Required the perioeci of Mayze, the east cape
of Cuba, and the west point of the windward pas-
Sage. . . . ; : \ ,
Answer. Kesho, or Cachoa, the capital of Tonkin, an
empire in India, east of the Ganges. ſ
} |
2. Required the perioeci of Milledgeville, the
seat of government of the State of Georgia.
3. Required the perioeci of Albany, the seat of
government of the State of New-York.
4. Required the perioeci of Bastia, a sea-port
and city, formerly the capital of the island of Cor-
S1Ca. ; *
5. Required the periosci of Naples, a large city
in the south-west of Italy, and capital of the king-
dom of Naples. Y
y”
PROBLEM XIII.
To find the flntipodes of any given place.
RULE. Bring the given place to the brass me-
ridian, and set the index of the hour circle to 12,
turn the globe half round, or till the index points to
the other 12; then under the same degree of lati-
tude with the given place, but in the opposite he-
misphere, you will find the antipodes.
Or, find the antoeci of the given place, and the
perioeci of this will be the antipodes or point of the
globe, diametrically opposite to the first place.
|
60 GRAMMAR OF ASTRONOMY.
EXAMPLEs.
1. Required the antipodes of Trinidad, an island
near the coast of South America, the largest, most
fertile, and most beautiful of all the windward
islands, and was compared by Columbus, its disco-
verer, to a terrestrial paradise.
Answer. Sandalwood, an island in the East Indian Sea,
south of Flores and west of Timor. . . . .
When it is summer to the inhabitants of Trinidad it is
winter to those of Sandalwood, and when it is day to the one,
it is night to the other. . . . . . . . . . . . . .
2. Required the antipodes of Anguilla, the most
northern island of the Caribbees. .
3. Required the antipodes of Owhyee, an island
in the North Pacific Ocean, the most easterly and
by much the largest of the Sandwich Islands: it was
on this island that the celebrated Captain Cook was
killed by the natives, on Sunday the 14th of Feb-
ruary, 1779. . . . . . .
4. Required the antipodes of the following places:
Madrid; Malta, in the Mediterranean ; Bermudas;
Cape Horn; Havanaa ; Halifax, the capital of No-
va-Scºtia; and Avignon, a city in France, on the
river Rhone. . . . . . . .
5. What place on the earth is diametrically op-
posite to Cape Charlotte, the southern extremity of
New-Georgia, a desolate island in the South Atlan-
tic Ocean 2 . . . . .
Aſter the student has resolved the examples in the last
three problems, it may not be improper to exercise him in
finding the antaeci, perioeci, and antipodes of any given place,
by the following method. - -
{
OF THE TIGRRESTRIAL GLOBE. 61.
PROBLEM XVI.
To find the fluteci, Perioci, and flntipodes of any given
, place.
RULE. Place the two poles of the globe in the
horizon, and bring the given place to the eastern
part of the horizon; them, if the given place be in
north latitude, observe how many degrees it is to
the northward of the east point of the horizon; the
same number of degrees to the southward of the
east point will show the Antoeci; an equal number
of degrees, counted from the west point of the ho-
rizon towards the north, will show the Perioeci ;
and the same number of degrees, reckoned to-
wards the south from the west, will point out the
Antipodes. -
If the place be in south latitude, the same rule
will serve, by reading south for north, and the con-
trary. --
EXAMPLES.
1. Required the Antoeci, Perioeci, and Anti-
podes of St. Ambrose, an island in the Atlantic
Ocean, west of Chili.
Jłnswer. The Antoeci is the southern part of Florida, a
Territory belonging to the United States; the Periocci is in
the Indian Ocean, a little west of Tryal Rocks on Flinder’s
tract in 1813; and the Antipodes is a little east of Ava, a
town in Asia, and ancient capital of the Birman empire.
2. Required the Antoeci, Periosci, and Antipodes
of the following places: Falkland Islands, west of
Patagonia; Albany, the seat of government of the
State of New-York; and Cadiz, a fortified city and
sea-port in Spain. -
6
63% GRAMMAR OF ASTRONOMY.
problem xv.
To find the angle of position between any two given places:
RULE. Elevate the north or south pole, accord-
ing as the latitude is north or South, so many de-
grees above the horizon as are equal to the latitude
of one of the given places; bring that place to the
brass meridian, and screw the quadrant of altitude
upon the degree over it; next move the quadrant
till its graduated edge falls upon the other place;
then the number of degrees on the wooden hori-
zon, between the graduated edge of the quadrant
and the meridian, reckoning towards the elevated
pole, is the angle of position between the two
places. - ra
EXAMPLES,
1. What is the angle of position between New-
York and Syracuse, a sea-port in the island of Si-
cily, formerly a superb city, and flourishing repub-
lic : Archimedes, the famous geometrician, was a
native of this city. -
Jīnswer. 60 degrees from the north towards the east, the
quadrant of altitude will pass over or near the following
places: Nantucket, an island belonging to Massachusetts;
Cape Sable, the south-west point of Nova-Scotia; the north-
ern part of the Banks of Newſoundland; Bayonne, a sea-
port in France, about 3 miles from the Bay of Biscay;
Barcelona, a city in Spain; Cagliariin Sardinia; and Thebes
in Upper Egypt. Hence all these places have the same
angle of position from New-York.
2. What is the angle of position between Lyons,
a large and celebrated city of France, situated at
the conflux of the Rhone and Saone ; and Teflis,
a city of Asia on the sublime banks of the Kur, and
capital of Georgia, formerly a province of Persia,
but now belonging to the Russian empire,
of THE TERRESTRIAL GLOBE. {3
3. What is the angle of position between Leipsic,
the chief commercial city in the interior of Ger-
many; and Limerick, a large, elegant, and popu-
lous city in Ireland, on the Shannon, about 60 miles
from its mouth 2 - - ..
4. What is the angle of position between Wash-
ington city and the following conspicuous places:
Albany; Aleppo, a city of Syria; Brest, a sea-port
in France, the chief station of the French marine,
and one of the best harbours in Europe; Cork, the
second city of Ireland, on the river Lee, about 16
miles from the sea; Dresden, the capital of Saxony
in Germany, beautifully situated on both sides of
the Elbe ; Edinburgh, the metropolis of Scotland;
Frankfort on the Maine, a large city of Germany,
and now the permanent seat of the Germanic diet;
and Gibraltar, a well known promontory in the
south of Spain, on the straits which connect the At-
ſlantic with the Mediterranean.
PROBLEM xvi.
To find the bearing of one place from another.
RULE. If both places be situated in the same
parallel of latitude, their bearing is either east or
west of each other; if they be situated on the same
meridian, they bear north and south from each
other; if they be situated on the same rhumb line,
that rhumb lime is their bearing ; if they be not si-
tuated on the same thumb line, lay the quadrant of
altitude over the two places, and that rhumb line,
which is the nearest of being parallel to the quad-
rant, will be their bearing.
On some globes there are two compasses drawn on the
equator, each point of which may be called a rhumb line.
/
-64 GRAMMAR OF ASTRONOMY.
being drawn so as to cut all the meridians in equal angles.
One compass is drawn on a vacant place in the Pacific Ocean,
between America and New-Holland; and another, in a simi-
lar manner, in the Atlantic, between Africa and South Ame-
rica. There are no rhumb lines on Wilson's globes; to
avoid confusion they have given place to the several tracks
of eminent circumnavigators.
EXAMPLES.
1. What is the bearing between Bermudas and
Madeira, an island off the western coast of Africa,
justly celebrated for the excellence of its wine?
Jìnswer. Madeira and Bermudas are nearly on the same
parallel of latitude; consequently the bearing of Madeira
from Bermudas, is east. . f
Or, if the globe have no rhumb lines drawn on
it, make a small mariner's compass, and apply the
centre of it to any given place, so that the north
and south points may coincide with some meridian;
the other points will show the bearing nearly of all
the circumjacent places, to the distance of upwards
of a thousand miles, if the central place be not far
distant from the equator.
The bearing is however found much more correct from
JMercator's sailing, by the following proportion; Meridional
difference of latitude: radius :: difference of longitude: tan-
gent course. Or, the bearing may be more readily found,
by inspection only, from the tables in books on Navigation,
calculated for that purpose.
2. Required the bearing from Cape Cod Light
House, in the latitude of 42° 5' N. and longitude
700 4 W. to the island of St Mary, one of the
Western Islands, in the latitude of 36° 59' N. and
longitude of 25° 10' W.
Here, by describing a circle on a sheet of paper, or on a
card, with a radius of any convenient length, and then di-
viding its circumference into 32, or each quadrant or 4th
part into 8 equal parts, and annexing to each partits appro-
OF THE TERRESTRIAL GLOBE. 565
priate name ſound on the horizon of the globe. Any two
lines drawn through the centre, at right angles to each other,
may be first considered the E. W. N. and S. lines. These
points may be again divided into halves, quarters, &c.
Now, by bringing Cape Cod to the meridian and applying
the centre of the card over it; screw the quadrant of alti-
tude upon the brass meridian over 42° 5', the given degrees
•of latitude; turn the lower end round till the graduated edge
falls upon St. Mary; and under the graduated edge of the
quadrant, on the card, you will find E. by N. # E. nearly, or
7+ points from the north, which is the bearing required.
Or, the bearing may be found from tables calculated for
that purpose in the following manner: the meridional parts
answering to 42° 5', is 2788, and those answering to 360 59'
is 2391; hence, the meridional difference of latitude is 397;
and the difference of longitude is 44°54', or 2694': but one-
ºtenth of the meridional difference of latitude and the differ-
ence of longitude are found to agree nearly to a course of
7+ points, the same as before. See Tables I. and III. Bow-
DITEH's JNew Jämerican Practical JNavigator.
Or, if the two places are but a small distance
from each other, then the angle of position between
them will be their bearing nearly.
it is proper to observe that the angle of position between
any two places, as found in the foregoing problem, may be
called their bearing in a geographical sense; and the bearing
obtained in a rhumb line, as is the case with mariners, may
be denominated their bearing in a nautical sense.
3. Which way must a ship steer from Lizard
Point, the S. promontory of England, to the island
of Madeira 2 -
Jìnswer. S. S. W. -
4. What is the bearing between Bristol, a city in
£ngland, and St. Michael, an island in the Atlan-
tic, and the largest of the Azores 2
5. Required the bearing between New-York
and any of the following places: St. John’s, New-
foundland; Boston; Cape Hatteras; Charleston;
Savannah; Havanna; Tampico; Kingston; Ber-
6*
:66 GRAMIMAR OF ASTRONOMY.
mudas; Cape Verd, on the Westerm coast of Afri-
ca; Teneriffe ; the island of Madeira; and Havre
de Grace, one of the most important sea-ports of
France, at the mouth of the Seine.
: PROBLEM xvii. .
To find how many miles make a degree of longitude in any
given parallel of latitude. -
Rºº. Lay the quadrant of altitude over any
two places in the given latitude, which differ in
longitude 15°; the number of degrees intercepted
between them, multiplied by 4, will give the length
of a degree in geographical miles. - -
Now, any number of geographical miles may be reduced
into American miles by multiplying by 69%, and dividing by
60; or by multiplying by 1.152; for 60 : 69; : : 1 : 1.152
nearly. . . -
EXAMPLE.S.
1. How many geographical and American miles
make a degree in the latitude of Philadelphia 2
.ſhswer. Thelatitude of Philadelphia is 390 57 or nearly
400; and the distance between two places, or two meridians,
in that latitude (which differ in longitude 15°) is 11} degrees.
Now, 11% degrees multiplied by 4, produces 46 geographical
miles for the length of a degree of longitude in the latitude
of Philadelphia; and iſ 46 he multiplied by 1.152, the pro-
duct will be 52.992, or 53 American miles nearly.
2. How many geographical and American miles
make a degree in the parallels of latitude in which
the following places are situated : Laccadive Is-
lands, lying off the west coast of India; Potosi ;
Cairo, the metropolis of Egypt; Pekin; Prague,
the capital of Bohemia; Petersburg; Senjen, an
island on the coast of Norway; and the northern
part of Spitzbergen, or East Greenland.
:OR THE TERRESTRIAL GLOBE. 67
"The above rule is derived from this principle, that the
inumber of degrees contained between any two meridians,
reckoned on the equator, is to the number of degrees con-
tained between the same meridians, oh any parallel of lati-
tude, as the number of geographical miles containéd in one
degree of the equator, is to the number of geographical-con-
tained in one degree on the given parallel of latitude. Thus,
if 12 be the distance in degrees between two places having
the same latitude, but which differ in longitude 15 degrees;
159 : 120 :: 60 miles: 8 miles; or, which amounts to the
same thing, 1 : 12: ; 4:48: hence, the reason of multiply-
ing the distance in degrees by 4, is evident. '.' "
If instead of 150 we take 5, or a less number of degrees,
thélength of a degree in any párallel of latitude, would be
found more correctly. But since the quadránt of altitude
will measure no arc truly buil that of a great circle; it follows
that the preceeding rule is not mathematically true, though
sufficiently correct for all practical purposes. -
When greater exactness is required, we must have re-
course to calculation, or the following table, constructed for
that purpose:– '.
§
68 GRAMMAR OF ASTRONOMY.
A TABLE,
Showing how many geographical and flimerican mile?
2nake a degree of longitude in every degree of latitude.

Deg, Geo. Am. Deg. Geo.TAm.T.Deg. Geo. Am.
|Lat. Mºls. Mºls. Lat. M'ls. Mºls. Lat: Mºls. M'ls.
* | *m-w
*- : * ~ *-*-
1 |59.99.69.10| 81 |51.4359.24|| 61 29.0933.51
3 ºil 33 ºil tº gº
3 |59.92.69.02|33 |50.3257.96 63 27.2431.38
4 |59.8568.94 || 34 |49.7457.30|| 64 (26.3030.29
5 |59.77|68.85| 35 |49.1556,62|| 65 |25.3629.21
6 59.67/68.73| 36 48.5455.91||66 24.40.28.10
7 59,5568.60|| 37 |47.9255.20 | 67 ||23.45|27.00
8 |59.4268.45|| 38 |47.28.54.46|| 68 ||22.48|25.89
9 |59.2668.26|| 39 46.6353.71| 69 |21.5024.76||
10 |59.09.68.07|| 40 |45.9652.94|| 70 |20.5223.63
11 |58.8967.84|| 41 |45.2852.16|| 71 |19.53|22.49
12 |58.6967.61|| 42 |44.5951.36|| 72 |18.54|21.35
13 |58.4667.34|| 43 |43.88.50.54|| 73 || 7.54|90.20
1& 58,2267.06|| 44 |43.16|49.72|| 74 16.54|19.05
1, 57.9566.85| 45 42.43148.87| 75 |15.53|17.89
16, 57.6766.43|| 46 |41.68|48.01| 76 |14.52|16.72
17 57.3866.10|| 47 |40.92.47.13| 7 ||3:50.15.55
18 |57.0665.73| 48 |40.1546.25||78 |12.48|14.87
19 |56.73|65.35|| 49 (39.3645.34|| 79 11.4513.19
20 |56.3864.94|| 50 38.5744.43|| 80 10.42|12.00|
21 |56.0164.5%|| 5 || |37.7643.49|| 81 9.38||0.80
22 |55.6364.08|| 52 |36.94|42.55|| 82 | S.35| 9.61
23 |55.2363.62|| 53 (36.11}{1.59|| 83 || 7.31|| 8.42
24 |54.8163.15|| 54 |35.27|40.63| 84 6.27 7.22
; :4::::::::::: ; 34.41.3%;"| 8 || 3:3: 39,
26 |53.9362.12|| 56 |33 5538.64|| S6 || 4.18 4.81
27 |53.4661.58||57 |32.6837.64|87 || 3.14 3.61
28 |52.9761.02 58 31.7936.62|| 88 2.09| 2.40
29 |52.4860.45| 59 |30.90'35.59|| 89 | 1.05] 1.20
30 (51.96}59.85 | 60 |30.0034.56|| 90 0.00 0.00
-->
"The above table is thus calculated:— -
JMultiply the cosine of the latitude by 60, and you will find
£he length of one degree on that latitude in geographical
miles; then the geographical miles being multiplied by 1.15%
will give the flmerican miles.
of THE TERRESTRIAL, GLOBE. '69
for instance, to find how many geographical and Ameri.
can miles make one degree in the º: 84. In the
first place, the cosine of 84 degrees, taken from a table of
matural sines and cosines, is .104528 to radius unity; now
.104528 multiplied by 60, gives 6.27168, the number of
geographical miles in orie degree on that parallel of latitude;
but 6.27, which is the number in the table, will answer our
present purpose. Again, 6.27 multiplied by 1.152 will give
7.22304, the number of American in one degree on the same
parallel of latitude; three decimāl places are rejected, and
only 7.22 inserted in the table. . . . . ‘. . '
The reason of the preceding calculation is evident from
this principle; that the circumferences of circles are to each
other as their radii; and that the radius of any parallel of
latitude is equal to the cosine of that latitude; hence, if the
radius of the equator be taken equal to unity, it follows that
unity, or 1, is to cosine of any latitude, so is 60 geographical
miles, the length of a degree on the equator, to the number
of geographical in one degree of longitude on that parallel
of latitude; and, consequently, the cosine of any latitude
multiplied by 60, will give the length of one degree of longi-
tude in that parallel of latitude.
The intelligent student, who is curious to make the calcu-
lation of the preceding table, will find a correct table of
natural sines and cosines in my edition of Gibson’s Sur-
veying. &J -
PROBLEM XVII] .
To find at what rate per hour the inhabitants of any given
place are carried, from west to east, by the revolution
of the earlh on its aris. ! ,
RULE. Find how many miles make a degree of
longitude in the latitude of the given place, (by the
preceding Prob. or the annexed table,) which mul-
tiply by 15 for the answer.
* The reason of this rule is obvious, for if m be the number
of miles contained in a degree, we have 24 hours : 3600 mul-
ſtiplied by m :: 1 h. : the answer; or, which amounts to the
same thing, 1 : 15 × m :: 1: the answer; therefore, the num-
ber of geographical, or American miles in a degree of
longitude in any given latitude, multiplied by 15, will pro-
duce the answer in geographical, or American miles.
*/O GRAMMAR OF ASTRONOMY
The above rule is on a supposition that the earth revolves
on its axis, from west to east, in 24 hours'; but it has been
already observed, (Chap. VII. Art. 6,) that the earth makes
one complete revolution on its axis in 23 hours, 56 minutes,
4.1 seconds; hence, where greater accuracy is required,
we must multiply the number of geographical miles by
15,041 for the answer. . . . . . s.
ExAMPLEs. - . . .
1. At what rate per hour are the inhabitants of
Pekin carried from west to east by the revolution of
the earth on its axis 2. . . . . .
Answer. The latitude of Pekin is 409, in which parallel
a degree of longitude is equal to 46 geographical, or 53
American miles. (See Ex. 1. Prob. XVII.) Now, 46 mul-
tiplied by 15, produces 690, and 53 multiplied by 15 produces
795; hence, the inhabitants of Pekin are carried 690 geo-
graphical, or 795 American miles per hour. º
By the table. In latitude 400 a degree of longitude is
.. to 45.96 geographical miles, and 52.94 American miles.
ow, 45.96 multiplied by 15, produces 689.4; and 52.94
multiplied by 15 will give 794.1 : Hence, the inhabitants in
this parallel are carried 689.4 geographical, or 794.1 Ame-
rican miles per hour, by the earth's revolution on its axis;
which result is more correct than the former. And, if we
multiply 45.96 by 15.041, and also 52.94 by 15.041, the an-
swer will be ſound still more correctly. -
2. At what rate per hour are the inhabitants of
the following places carried, from west to east, by
the revolution of the earth on its axis: Truxillo, a
town in Peru; Sofala, a town in Africa, and capi-
tal of a country of the same name ; Lahore, a city
of Asia, and the capital of a province of the same
name, several times the capital of Hindoostan and
the residence of the great Moguls; Kiev, a city in
European Russia, situated on the right bank of the
Dnieper; and Christiana, the most beautiful city in
.Norway, situated in a bay or gulf, about 25 miles
from the sea.
of THE TERRESTRIAL GloBE. 7].
PROBLEM XIX.
The hour of the day at any particular place being given,
to }: what hour it is in any other place.
RULE. Bring the place at which the time is
given to the brass meridian, and set the index of
the hour circle to the given hour at that place: then,
turn the globe till that place for which the time is
required be brought to the meridian, and the index
will show the hour at that place. . . . .
If the place where the houris sought lie to the east of that
wherein the time is given, turn the globe westward; but if
it lie to the west, the globe must be turned eastward.
Or, bring the given place to the meridian, and set
the index of the hour circle to 12 ; turn the globe
(as before), till the other place comes to the meri-
dian, and the hours passed over by the index will
be the difference of time between the two places.
If the place where the hour is sou ght, lie to the east of that
wherein the hour is given; the difference of time must be
added to the given time; but if to the west, subtract the diſ-
ſerence of time: Thus, a place 15 degrees to the eastward
of another; has the sun on its meridian an hour earlier than
the latter place; therefore, when it is 12 o'clock in the former
place it is but 11 o’clock in the latter; and 12 o'clock in the
latter place corresponds to 1 o'clock in the former, &c.
Or, without the hour circle, find the difference of
longitude between the two places, (by Prob. VI.)
and convert it into time by allowing 15 degrees to
an hour, or 4 minutes of time to one degree. The
difference of longitude in time, will be the differ-
ence of time between the two places, with which
proceed as in the last rule. ~
To convert degrees, minutes, and seconds into time, at the
*ate of 360 degrees for 24 hours, and the contrary,
f
72. GRAMMAR or ASTRONOMY.
Say as 8600: 24h. or as 15°: 1h. : : any number of de-
grees, &c.: the time required. . . . . . .
The converse of this rule will give the degrees. Hence,
degrees of longitude may be converted into time by multi-
plying by 4, observing that minutes or miles of longitude.
multiplied by 4, produce seconds of time, and degrees of
longitude, when multiplied by 4, correspond to minutes of
time: and, on the contrary, minutes of time divided by 4, will
give degrees of longitude: if there be a remainder after di-
viding by 4, multiply it by 60, and divide the product by 4, or,
which amounts to the same thing, multiply the remainder by
15, the quotient in the former case, or the product in the
latter, will be minutes of a degree, or miles of longitude.
. . . . t EXAMPLES.
1. When it is 9 o'clock in the morning at New-
York, what hour is it at Dieppe, a sea-port of
France, in the English Channel ?
By the first method. Bring New-York to the meridian,
and set the index of the hour circle to 9 o'clock; then, by
turning the globe westward till Dieppe comes to the meri-
dian, the index will point to 2 o’clock nearly, which is the
hour at that place; hence, as Dieppe lies to the east of New-
York, when it is mine in the morning at the latter place, it
is two in the afternoon at the former. #
By the second method. Bring New-York to the meridian.
and set the index to 12 o'clock, then, by turning the globe,
as before, till Dieppe be brought to the meridian, the hours
passed over by the index will be five, which is the difference
of time between both places. And, because Dieppe lies to
the east of New-York, this difference of time must be added
to the given time; that is, 5 hours added to 9 hours will give
14 hours; consequently, it is 2 hours past noon, or 2 o’clock
in the aſternoon at Dieppe. { :
By the third method. The difference of longitude between
both places is found (by Prob. VI.) to be 750 5'. Now 75
degrees, divided by 15, will produce 5, and 5' multiplied by 4
will give 20; hence, the difference of time corresponding to
the difference of longitude, is equal to 5 hours, 20 seconds,
with which proceed as in the last method, and you will find
the time at Dieppe to be 2 hours and 20 seconds past 12
o'clock, when it is nine in the morning at New-York, which
is nearly the same as before,
OF THE TERRESTRIAL GLOBE.
; 3.
*
2. What o'clock is it at Bencoolen, a sea-port
on the south-west coast of Sumatra, when it is six
o'clock in the afternoon at Cashmere, a city of Asia,
and capital of a province of the same name, famous
for its manufacture of delicate and unrivalled
shawls 2 -
Jìnswer. 7 hours, 54 minutes, 12 seconds in the aſter-
}\OOI). -
3. When it is six o'clock in the morning at Co-
lumbia, the seat of government of South Carolina,
what o'clock is it at Palos, a sea-port in Spain, from
which port Christopher Columbus sailed, on his first
voyage for the discovery of the New World, in the
year 1492 2 - • -
4. When it is moon at Palos, what o’clock is it in
the Guanahami, or San Salvadore, one of the Baha-
ma Islands, and the first land discovered by Colum-
bus, on Friday October the 12th of the same year
that he sailed from Palos ? -
5. When it is noon at Washington city, what
o'clock is it at the following places: St. John, in
New-Brunswick; the Azores, or Western Islands ;
Madeira; Oporto, a city and sea-port in Portugal;
Waterford, a city and sea-port in Ireland; Ports.
mouth in England; Palermo, a large and beautiful
eity of Sicily, and capital of the island; Corinth, a
town in the Morea, near the isthmus of the same
Iname, and anciently one of the most flourishing ,
cities of Greece; Medina, a city of Arabia, cele-
brated as containing the tomb of Mahomet; Baş.
Sora, a city of Asia in the government of Bagdad;
and Namkin, a large city of China, not equalled
perhaps by any in the world for the ºxfont ºf
ground enelosed within its walls
7'4. GRAMMAR of ASTRONOMY.
PROBLEM XX.
The hour of the day at any particular place being giveſ,
to find all places on the globe where it is then noon, or
any other given hour. - s e
RULE. Bring the given place to the brazen me-
ridian, and set the index to the given hour in that
place ; turn the globe till the index points to the
other proposed hour, and all the places that are
then under the meridian, are those required.
If the hour at the given place be earlier than that at those
places sought, the globe must be turned westward, but iſ
later, turn it eastward. - -
Or, bring the given place to the brazen meridian,
and set the index of the hour circle to 12 ; them,
as the difference of time between the given and re-
quired places is always known by the problem, if
the hour at the required places be earlier than the
hour at the given place, turn the globe eastward
till the index has passed over as many hours as are
equal to the given difference of time; but if the
hour at the required places be later than the hour
at the given place, turn the globe westward, till the
index has passed over as many hours as are equal
to the given difference of time; and, in each case,
all the places required will be found under the
brazen meridian.
Or, without the hour circle, convert the difference
of time between the given place and the required
places into the corresponding degrees of longi-
tude, as in the last problem ; then, the difference
ºf longitude in degrees being thus determined, if
the hour at the required places be earlier than the
flour at the given place, the places sought lie so
many degrees to the westward of the given place
of THE TERRESTRIAL, GLOBE. 75.
as are equal to the difference of longitude; but, if
the hour at the required places be later than the
hour at the given place, the places sought lie so
many degrees to the eastward of the given place as
are equal to the difference of longitude.
. . . . . ExAMPLEs.
1. When it is nine o’clock in the morning at
Philadelphia, where is it three in the aſternoon at
that time 2. w
|By the first method. Bring Philadelphia to the meridian,
and set the index to 9 o'clock; now, because the hour at the
places sought is later than the hour at the given place, turn
the globe westward, till the index points to 3 o'clock; and all
the required places will be then under the meridian; as
Dresden nearly, Prague, Naples, Malta, an island in the
Mediterranean near Sicily, and a part of the following coun-
tries in Africa; mamely, Tripoli, Fezzan, Soudan or Nigri-
tia, Loango, Congo, Angola, Benguela, &c. . . .
By the second method. Bring Philadelphia to the meridian,
and set the index to 12; then, as the hour at the required
places is later than the hour at Philadelphia, turn the globe
, westward till the index passes over six hours, which is the
given difference of time, and all those places sought will be
under the meridian, as before. -
By the third method. The given difference of time, which
is six hours, being converted into degrees of longitude, as in
the last problem, corresponds to 90 degrees. Now, as the
hour at the required places is later than the hour at Philadel-
phia, by reckoning 90 degrees, the difference of longitude,
eastward on the equator from the meridian of Philadelphia,
we shall find that all the places in 149.51', or nearly 15 de-
grees east longitude, are those places required.
2. When it is noon at New-York, what inhabi-
tants of the earth are those that have the same
hour ; also those that are at breakfast, suppose nine
o'clock in the morning; rising at four ; are at Sup-
per, suppose ten in the afternoon; tea at seven ;
dinner at three ; and that have midmight all at the
same time 2 - -
‘76 GRAMINIAR of ASTRONOMY.
Answer. It is noon in a part of Canada, the eastern párt
of the Isle of Cuba, the Republic of Colombia, Peru, &c.;
the Beaver Indians, Blackfoot Indians, Snake Indians, &c.
are at breakfast; the Kamtschadales, the inhabitants of New .
Caledonia, who are supposed to be cannibals, &c. are rising;
the inhabitants of that part of Russia south of the sea of Obe,
those of the eastern part of Tartary, those of Little Tibet,
of Delhi, &c., are at supper; in Petersburg, Kiow, Alexan-
dria, &c. the inhabitants are attea; in the Azores, or West-
ern Islands, they are at dinner; and it is midnight in a part
of China, Tonkin, Cambodia, the eastern part of Sumatra,
3. When it is mid-day at London, where is it
11, 10, 9, 8, 7, 6, 5, 4, 3, 2, and 1 o'clock in the
morning 2 Also, midnight, 11, 10, 9, 8, 7, 6, 5, 4,
3, 2, and 1 o’clock in the afternoon. . .
PROBLEM XXI.
The day of the month being given, to find the sun's place
in the ecliptic, or his longitudes, and his declination:
RULE. Look for the given day in the circle of
months on the horizon, and corresponding to it in
the circle of signs, are the sign and degree which
the sun is in that day. Find the same sign and de-
gree in the ecliptic, on the surface of the globe;
bring the degree of the ecliptic thus found to the
brazen meridian ; and the degree of the meridian
which is over the sun’s place, is the declimation re-
quired. - * .
The declination of the sun is either north or south, accord-
ing as he is in the northern or southern hemisphere: Chap.
iI. Art. 9. º - .
Or, by the flnalemma. Bring the analemma to the
brazen meridian, and the degree on the meridian,
exactly above the day of the month, is the sun’s
declination; turn the globe until the point of the
ecliptic, corresponding to the given day, passes
of THE TERRESTRIAL, GLOBE. *77
under this degree of the sun's declination, and that
point will be the sun's place in the ecliptic, or his
longitude. . . . . . . . . .
If the sun’s declination be north, and increasing, the sun’s
place will be between Aries and Cancer; but if the declina-
iion be decreasing, his place will be between Cancer and Li-
bra: If the Sun's declination be south, and increasing, the
stan’s place will be between Libra and Capricorn; but if it
be decreasing, his placé will be between Capricorn an |
Aries. . . . . . . . . . - -
The sun's longitude and declimation are given in the second
page of every month, in the Nautical Almanac, for every
day in that month. .
'The analemmaon Wilson’s terrestrial globe somewhat re-
sembles the figure 8: It is drawn on a vacant part of the .
globe, usually in the Pacific Ocean, between the two tropics:
and is divided into months and days of the month, corres-
ponding to the sum’s declination for every day in the year.
The analemma, properly so called, is an orthographic
#yrojection of the sphere on the plane of the meridian, and is
useful for showing, by inspection, the time of the slin’s
rising and setting, the length of days and nights, &c.

EXAMPLES.
1. What is the sun's longitude and declimation on
the 15th of April? t -
Jìnswer. 25}o in Y, declination 10 N. nearly.
2. What is the sun's longitude and declination
on the 21st of June 2 . -
Answer. In the beginning of gº, declination 230 23 N.
3. Required the sun's place and his declination
on the following days: March 20, April 19, May
21, June 21, July 23, August 23, September 23,
October 23, November 22, December 22, January
19, and February 19. -
4. Required the Sun's longitude and declination
for the first day of each month. '
7& GRAMMIAR of ASFRONOMY.
PROBLEMI XXII.
The month and day of the month being given, to find
those places to which the sun will be vertical, or in the
zenith, on that day. . . . . . . . . . . .
RULE. Find the sun's declination for the given
day, (Prob. XXI) and mark it on the brazen meri-
dian; then turn the globe completely round on its
axis from west to east, and all those places which
pass under the observed degree of the meridian,
will have the sun verticăl on that day. . . . . .
The reason of this rule is evident, for the declination of a
heavenly body being similar to the latitude of a place on the
globé; (Art. 5, Chap. 6,) therefore the sun, on that day,
must pass over the parallel of latitude passing through those
Places. - *
I As the greatest declination the sun can have, is 23°28';
hence, it follows, that those places must be situated in the
torrid zone. . . . . . - º:
It may also be further remarked, that the inhabitants of
those places are ascii or shadowless, when the sun is on
their meridian, on that day. -
EXAMPLES.
1. Find all those places on the earth to which
the sun will be vertical on the 4th of July ; on
which day, in the year 1776, the British colonies
assumed the name of “The United States of Ame-
rica,” and declared themselves free and independent.
Jłnswer. The declination of the sun on the 4th of July
is 22° 55' nearly; therefore the sun will be nearly vertical to
Mayaguana, one of the Bahama islands; Havanna; St. Louis
de Potosi, a city of Mexico, and capital of an intendency of
the same name; Cape St. Lucas, the southern extremity of
łalifornia; the Sandwich Islands, in the North Pacific
*}cean ; Formosa, an island in the Chinese Sea; Monchaboo,
a town in the Birman empire, 52 miles north of Ava; Cal-
ºffta; tambay, a town in Goojerak, at the top of the gulf
of THE TERRESTRIAL GLOBE. tº 9
of the same name; the desert from Mecca to Omer; the
great deserts of Nubia; Sahaara, &c. in Africa.
2. Find all those places where the sum is vertical
on the 20th of March, 21st of June, 23d of Sep-
tember, and 22d of December. . . .
3. Find all those places of the earth where the
inhabitants have no shadow, when the sum is on
their meridian, on the following days : 19th of
April, 21st of May, 23d of July, 23d of August,
23d of October, 22d of November, 19th of Janu-
ary, and 19th of February. .
PROBLEM XXIII.
Ji place being given in the torrid zone, to find those two
days of the year on which the sun will be vertical at that
* place. - -.
RULE. Bring the given place to the brazen me-
ridian, and mark its latitude ; turn the globe on its
axis, and observe what two points of the ecliptic
pass under that latitude; seek those points of the
ecliptic in the circle of signs, on the horizon, and
exactly corresponding to them, in the circle of
months, you will find the days required. -
Or, by the ſlnalemma. Find the latitude of the
given place, and mark it on the brazen meridian ;
them bring the analemma to the meridian, upon
which, exactly under the latitude, will be found the
two days required. - - -
EXAMPLES.
1. On what two days of the year will the sun be
vertical to Lima 2
.dnswer. On the 16th of February, and on the 34th of
Qctobey. - : -
SO GRAMMAR OF ASTRONOMY.
2. On what two days of the year will the sun be
vertical at Mauritius or the Isle of France in the
Indian Ocean 2 “. . ..
3. On what two days of the year will the sun be
ºvertical at Candy, capital of the kingdom of the
same name; in the island of Ceylon . . . . . .
4. On what two days of the year will the sun be
vertical at the following places: Quito, Madras,
Batavia, Siam, Bencoolen, Mexico, Port Royal in
Jamaică, St. Helena, and St, Salvador, a city of
JBrazil at the entrance of All Saints' Bay ?
PROBLEM XXIV .
The day of the month and the hour of the day at any place
being given, to find where the sun is vertical at that
instant. sº • & -
RULE. Find the sun's declination (by Prob.
XXI) and mark it on the brazen meridian ; bring
the given place to the meridian, and set the index
of the hour circle to twelve ; then, if the given time
be before noon, turn the globe westward as many
hours as it wants of noon: but if the given time be
past moon, turn the globe eastward as many hours
as the time is past noon; and the place exactly
under the degree of the sun’s declination will be
that sought. &
EXAMPLES.
1. When it is half past 7 o'clock in the morning
at New-York, on the 4th of February, where is the
sum vertical ?
Jlnswer. Here the given time is four hours and thirty
minutes before noon; hence, the globe must be turned west-
ward till the index has passed over four hours and thirty
OF THE TERRESTRIAL GLOBE. 81
minutes, and under the sun's declination, on the brazen me-
ridian, you will find St. Helena, the place required.
2. When it is twenty-three minutes past five
o'clock, in the afternoon at London, on the 10th of
April, where is the sun vertical ? . . . .
Jłnswer. The sun’s declination on the 10th of April is 8
degrees north; bring London to the meridian and set the in-
‘dex to 12; then, because the given time is past noon, turn
the globe eastward till the index has passed over five hours. .
and twenty-three minutes; then, under the sun’s declination
you will find Quibo, a small island on the outer part of the .
bay of Panama; which is the place required.
Here, if the hour circle be not divided into parts less than
a quarter of an hour, which is usually the case, the odd mi-
nutes may be converted into degrees; then turn the globe so
many degrees farther, and you will find the place required."
For instance, in the above example, turn the globe eastward
till the index has passed over five hours and a quarter; then
by turning it two degrees farther to the west, (answering to
eight minutes of time,) the solution will be found exactly as
above. . . . . “. . . . . . . • * *
3. When it is forty minutes past six o'clock in
the morning at London, on the 25th of April,
where is the sun vertical? . . . . . . .
4. When it is twenty minutes past five o’clock in
the afternoon at Philadelphia, on the 18th of May,
where is the sun vertical ?] . .
© a tº tº * * ſº
5. When it is eight o’clock in the morning at Al-
bany, on the 30th of April, where is the sun, at that
time vertical ? . . . -
6. When it is midnight at Havanna, on the 1st
of August, where is the sun vertical ?
82 GRAMMAR of ASTRONOMY.
PROBLEM xxv. -
The day of the month being given, to rectify the terrestrial
globe to the sun's declination. ' -
... Rui E. Find the sun's declination (by Prob.
XXI.)then elevate the north or south pole accord-
ing as the declination is north or south, as many
degrees above the horizon as are equal to this de-
clination; then the sun will be vertical to that de-
gree of the brazen meridian which corresponds
with its declination; and the wooden horizon will
be the boundary between light and darkness on the
given day. " . . . . . . .
That circle which is the boundary between light
and darkness, usually called the terminator, changes
its position according as the sun's place varies.
As only that half of the earth is enlightened which is
turned towards the sun, the boundary between light and
darkness must be a great circle dividing the globe into two
equal parts. Hence, if the globe be rectified according to
the sun’s declination, it is evident that the sun will be in the
elevated pole of the wooden horizon ; consequently, that
hemisphere above the horizon will be illuminated; and that
hemisphere below the horizon, will be in darkness, or wholly
deprived of the solar light. Here the effects of refraction,
&c. are not considered. . . . . . . . . -
It follows, therefore, that the wooden horizon itself will be
the terminator, or the circle terminating light and darkness.
ExAMPLEs.
1. How do you rectify the globe to the sun's
declimation on the 23d of September 2 -
..?nswer. I find, (by Prob. XXI) that the sun's declination
on the given day is nothing, or which amounts to the same
thing, the sun, on the 23d of September, enters the sign Li-
bra : therefore, the two poles of the globe must be placed in
the horizon; then the globe will be rectified to the sun’s de-
ei:::::ſion for that day. Now. by hringing the equinoctial
of THE TERRESTRIAL GLoBE. 83
point Libra to the meridian, and setting the index of the hour
circle to 12, while the globe remains in this position, sup-
posing the sun to stand at a considerable distance from it,
and also vértically to that degree of the meridian corres-
ponding to his declination, which in this instance is 0; the .
solstitial colure will coincide with the terminator; all those
places under the brazen meridian will have noon; all those
above the wooden horizon will be enlightened from pole to
pole, and all those places below the wooden horizon will be
in the dark, hemisphere. . . . . . . . . .
2. How do you rectify the globe to the sun's de-
clination for the 22d of November 2 * *
Jłnswer. The declination of the sun on the 22d of No-
vember is found, (by Prob. xxi.) to the 20 degrees nearly,
and the sun's place in the ecliptic is in the first point of Sa-
gittarius; therefore, the south pole must be elevated 20 de-
grees above the horizon; and the globe will be rectified to
the sun's declination for that day. ..
Now, by bringing the beginning of Sagittarius to the me-
ridian, and setting the index of the hour circle to 12; while
the globe is in this position; all places above the wooden
horizon are illuminated; all those below the horizon are in
darkness; the South pole and the regions about it are there-
fore enlightened; and the north pole and its surrounding
regions are wholly deprived of the solar rays. ***
3. How do you rectify the globe to the sun's de-
clination on the 4th of July 7–Name the circum-
Stances. . . . . -
4. How do you rectify the globe to the sun’s de-
climation for the 20th of August 2—Name the cir-
cumstances. . . . . . . * •
5. How do you rectify the globe to the sun’s de
clination for the 19th of February 2—Name the
circumstances. '.
6. Rectify the globe to the sun’s declination on
the 25th of December 2—Name the circumstances.
84 GRAMMAR of ASTRONOMY.
- . PROBLEM xxvi, -
To illustrate by the terrestrial globe the different lengths
of the days and nights, and the vicissitudes of the
seasons. . . . . - .*
RULE. Rectify the globe for every degree of
the sun's declination, (by the last Prob.) from the
equinoctial point Aries, or any other point of the
ecliptic, till the sun returns to the same point again;
then the different arcs of the parallels of latitude,
which are above the horizon, corresponding to each
degree of elevation, will show the length of the day
in each respective latitude ; and the arcs of the
same parallels, which are below the horizon, will
show the length of the night: Hence, when the
arcs, which are above the horizon, are greater than
the arcs of the same parallels, which are below it,
the days are longer than the nights in those lati-
tudes; but if the arcs, above the horizon, are less
than those arcs of the same parallels, which are be-
low it, the mights are longer than the days.
It likewise follows that in those places where the
parallels are entirely above the horizon, there is.
constant day, and where the entire parallels are be-
low the horizon, there is constant night.
Vicissitudes of the seasons. When the Sun’s de-
climation is north and increasing, it is Spring in the
northern hemisphere, and Autumn in the southern ;
but when the declimation is north and decreasing,
it is Summer in the northern hemisphere, and Win-
ter in the southern. Again, when the sun’s decli-
nation is south and increasing, it is Autumn in the
northern hemisphere, and Spring in the southern ;
but when the declination is south and decreasing,
it is Winter to the inhabitants of the northern hemis-
phere, and Summer to those of the southern. It
of THE TERRESTRIAL GLOBE. 85 |
is only in the two temperate zones, as has already
been observed, that the succession of the four.sea-
sons are regular and perceptible. w .
These phenomena depend upon the most simple and evi-
dent principles, which may be illustrated in the following
manner:— . . - . . . -
In the first place, then, it is to be observed, that the alter-
mate succession of day and might is occasioned merely by the
uniform rotation of the earth on its axis. For, as any meri-
dian will, by the diurnal motion of the earth, revolve from
the sun to the sun again in twenty-four hours, (See Chap.
VII. Art. 3.) and only one half of the earth can be illuminated
at a time, it is evident that any particular place will some-
times be turned towards the sun, and sometimes from it, and
being constantly subject to these various positions, will en-
joy a regular succession of light and darkness: as long as
the place continues in the enlightened hemisphere it will be
day, and when, by the diurnal rotation of the earth, it is car-
ried into the dark hemisphere, it will be night. -
The motion of the earth on its axis, as has already been
observed, is from west to east; and this occasions an appa-
rent motion of the celestial bodies in a contrary direction.
The sun, for instance, seems to make his daily progress
through the heavens from the east towards the west; but
this is an optical delusion, arising from the opposite motion
of the earth: for a spectator being placed in any part of the
dark hemisphere, will, by the rotation of the earth on its
axis, be brought gradually into the enlightened one ; and as
the sun first appears to him in the east, it will seem to as-
cend higher and higher towards the west, in proportion as
the spectator moves in a contrary direction towards the east:
so that whether the earth turns on its axis in twenty-four
hours, or whether the sun and all the other celestial bodies,
move round the earth in that time, the appearānces will be
exactly the same. We shall illustrate, by the following
examples, the comparative length of days and nights, and
the vicissitudes of the seasons. .
EXAMPLES.
1. It is required to show at one view the length
of the day and might, in all places upon the earth
on the 20th of March, or at the time of the Vernal
§
ºf 86 GRAMINIAI3. OR AS'I'lèONOMY.
Equinow ; and also to illustrate how the succession;
of day and night is really, caused by the diurnal
motion of the earth, the Sun standing still. . . .
The two poles of the globe must be placed in the horizon;
for, at this time, the sun has no declination; bring the sun’s
place in the ecliptic, or the equinoctial point Aries, to the
brazen meridian, and set the hour index to twelve o’clock:
the terminator will then coincide both with the horizon and
solstitial colure, and will therefore divide each of the small
circles, which are drawn parallel to the equator, into two
equal parts. And as the uniform rotation of the earth upon
its axis must occasion every place to describe equal parts of
one of these parallel circles in equal times, the days and
nights must, of course, be equal all over the globe from pole
to pole. Now, while the globe is in this position, it will be
moon to the inhabitants of London and to all places under the
same meridian ; the Sun (supposing it to stand still at a vast
distance, yertically over that part of the brazen meridian
marked 0,) will appear setting to all those inhabitants along
the eastern edge of the horizon; those places along the west-
ern edge will have the sun rising; and all places below the
horizon will have night. If, from this position, the globe
be now turned gradually on its axis towards the east, the sun
will appear to move towards the west; and, as the different
places successively enter the dark hemisphere; the sun will
appear to be setting in the west. Continue the motion of the
globe eastward till London, or the meridian passing through
the equinoctial point Aries, comes to the eastern edge of the
horizon, the sun will appear setting to the inhabitants under
that meridian; and those places to which the sun appeared
rising, in the former position of the globe, will now have
moon. The motion of the globe being continued till London,
or the meridian passing through it, comes to the western edge
of the horizon; the moment it emerges from the horizon, the
sun will appear to be rising in the east. If the motion of the
globe be still continued eastward, the sun, to the inhabitants
of London, and those under the same meridian, will appear
to rise higher and higher, and to move towards the west:
when London comes to the brazen meridian, the sun will
again be on the meridian of that place. During this revolu-
tion of the earth on its axis, every place on its surface has
been twelve hours in the dark hemisphere, and twelve hours
in the enlightened hemisphere, as may be readily seen by ob-
serving the number of hours passed over by the index of the
- of THE TERRESTRIAL GLOBE. S7.
hour circle; and, consequently, the days and nights are equal
all over the world. * , . ‘. . .
It is evident, from a slight consideration of the subject,
that if the axis of the earth was perpendicular to the plane
of its orbit, or, which amounts to the same thing, if the plane.
of the earth's orbit coincided with the plane of the equator,
the days would, at all times, be equal to the nights all over
the world, except at the poles; where the sun would neither
rise nor set, but remain continually in the horizon; then we
would not have the beautiful diversity of seasons. Spring,
summer, autumn, and winter, lead us insensibly through
the varied circle of the year; and are no less pleasing to the
mind, than necessary towards bringing to maturity the ya-
rious productions of the earth. Whether the sun flames in
the solstice, or pours his mild effulgence from the equator,
we eqāally rejoice in his presence, and bless that Omniscient -
. Being who gave him his appointed course, and prescribed
the bounds which he can never pass. . . . * ,
2. It is required to show the comparative length
of the days and nights in all places on, the earth on
the 21st of June, or at the time of the Summer Sol-
stice; and also to illustrate how the regular succes-
'sion of day and might, and the vicissitudes of the
seasons, are really caused by the diurnal and annual
motions of the earth, the sun standing still. -
Observations show us that the axis of the earth is inclined
to the plane of its orbit, or to the ecliptic, in an angle of
66C 32 : so that, according as the earth moves in its -orbit
from Libratowards Capricorn, the sun will appear to advance
in the ecliptic, from Ariestowards Cancer; if, from the position
of the globe in the foregoing example, the north pole be
therefore elevated gradually, according to the progressive
alterations made in the sun's declination, by his apparent an-
nual motion in the ecliptic, it is evident that all the circles
parallel to the equator will be divided by the terminator or .
horizºn, intº two unequal parts, having a greater or less por-
tion of their circumferences in the enlightened than in the
dark hemisphere, according to their respective situations on
the giobe, and the place of the earth in its orbit. So that
those places situated in the northern hemisphere will have
their days longer than their nights; and on the contrary,
ihose places which lie in the southern hemisphere, will have
88 $
. GRAMMAR OF ASTRONOMY. .
their mights longer than their days; whilst at the equator,
the days and nights will be equal to each other. It likewise
follows, that constant day begins at those places round the
north pole, where the entire of the parallels of latitude are
gradually elevating above the horizon; and on the contrary,
constant night begins at those places round the south pole,
where those parallels are depressed in the same manner.
For instance, to show the comparative lengths of the days
and nights, &c. on the 16th of April, rectify the globe to the
sun's declination on that day, which is 10 degrees north (by
Prob. XXV.,) and bring the sun’s place in the ecliptic to
the meridian. Now, while the globe remains in this position,
all those places under the brazen meridian will have noon;
to all those at the eastern edge of the horizon, the sun will
be setting; and the sun will be rising to all those at the
western edge of the horizon; the parallels of latitude are
now divided by the terminator, into two unequal parts; the
greater portion of those parallels in the northern hemisphere
are above the horizon; and the greater portion of those
parallels in the southern are below the horizon, or in the
dark hemisphere. tº . . . .
If the . be now turned gradually on its axis, from west
to east, till it makes one complete revolution; it is evident, as
every place will describe equal parts of one of the parallels.
of latitude in equal times, that all those places in the north-
ern hemisphere will have their days longer than their mights,
whilst those in the southern will have their nights longer
than their days; the days and nights at the equator being
equal to each other, the same as before. It likewise follows,
that all those places between the 80th parallel of latitude and
the north pole, are in the enlightened hemisphère, or have
constant day, the beginning of constant daylight being at
this parallel, since the lower part of it just touches the hori-
zon. From this parallel to the equator, and from thence to
the 80th parallel of south latitude, the days gradually shorten;
the upper part of this circle just touches the horizon; there-
fore all places between the 80th parallel of latitude and the
south pole, are in the dark hemisphere, or have constant
night, the beginning of constant night being at this parallel.
In the same manner we may reason with respect to any other
degree of the sun's declination till he has advanced to the
tropic of Cancer. -
It may not be improper to observe, that that
half of the globe which is above the horizon, is
OF THE TERRESTRIAL GLOBE. " .. 89
called the enlightened or illuminated hemisphere; and
that half below the horizon, the dark hemisphere ;
because the horizon is the terminator of light and
darkness, when the globo is rectified to the sun’s
declimation. It may likewise be remarked, that the
arcs of the parallels of latitude, which are above
the horizon, are called diurnal arcs ; and those
arcs, which are below the horizon, are called moc-
durnal arcs. . . . . . . . . .
For the Summer Solstice.—The Summer Solstice to the
inhabitants of north latitude, happens of the 21st of June,
when the sun enters Cancer, at which time his declination is
230 28' north. Rectify the globe to this declination, and
over that degree of the brazen meridian under which the
sign Cancer in the ecliptic stands, let the sun be supposed
to be fixed at a considerable distance from the globe.
While the globe remains in this position, it will be seen
that the equator is exactly divided into two equal parts;
consequently, the days and nights at the equator are equal
to each other, the same &s before. From the equator north-
ward, as far as the arctic circle, the diurnal arcs will exceed
the nocturnal arcs; that is, more than one half of any df the
Yarallels of latitude will be above the horizon, and of course.
i. than one half will be below, so that the days are longer
than the mights. All the parallels of latitude within the
arctic circle will be wholly above the horizon ; and, conse-
quently, those inhabitants will have no night. From the
equator southward, as far as the antarctic circle, the nocturnal:
arcs will exceed the diurnal arcs, and consequently less
than one-half will be above the horizon; so that the nights
will be longer than the days: . The entire of the parallels
within the antarctic circle will be below the horizon, and
therefore the inhabitants, if any, will have constant night.
From a little attention to the parallels of latitude, while the
globe remains in this position, it will easily be seen that the
arcs of those paralleſs which are above the horizon, north of
the equator, are exactly of the same length as those below
the horizon south of the equator; consequently, when the in-
habitants of north latitude have the longest days, those in
south latitude have the longest nights; and when the inha-
bitants who are situated south of the equator have the short-
est days, those who live north of the equator have the shortest
90 * GRAMMAR OF ASTItoNOMY.
nights. And, in fact, to conclude with these observations, it
holds universally true, that whatever be the length of the day
in north latitude, the night will be equally long in the same
latitude south; also, that the length of the night in north
latitude, is equal to the length of the day in the same lati-
tude south; and that at the equator the days and nights are
always equal. * . . -
Thus we see that the length of the day and night depends on
the position of the terminator, with regard to the aa is of the
earth; and therefore, we see the reason why the days lengthen
and shorten from the equator to the polar circles; why there
is sometimes no day or night during many revolutions of the
earth on its axis, within the polar circles; why there is but
one day and one night in the whole year at the poles; and
why the days are continually equal to the nights at the
equator, which is always equally cut by the terminator.
The changes in the position of the terminator are occa-
sioned by the inclination of the eqrth's aris to the plane qf the
ecliptic, or orbit in which it moves; because through the
whole of its annual course, the 'awis of the earth remains paral-
lel to itself, or is always directed to nearly the same fiaſed
point in the heavens. Hence, as the sun will appear to move
through the northern signs of the ecliptic, whilst the earth is
describing the southern signs, the north pole will be turned
towards the sun during that time; and as the presence of the
sun’s rays produces a proportionable degree of heat, it is
evident that our summer half of the year, will be the inter-
val of time which elapses from the vernal to the autumnal
equinox; or, which amounts to the same thing, the time
which elapses from the Vernal equinox to the Summer sol-
stice is called the Spring season of the year, by the inhabi-
tants of the northern hemisphere; and the interval of time
from the Summer solstice to the Autumnial equinox, is called
the Summer season. •. - . . . . .
Again, as the sun will appear to move through the southern
signs of the ecliptic whilst the earth is moving through the
northern signs, the southpole will be turned towards the sum
during that time; and as the absence of the sun’s rays in the
long nights will produce a greater degree of cold than can be
compensated by the return of heat in the short days, it is also.
evident that our winter half of the year' is the time that
elapses from the Autumnal to the Wernal equinox; or,
which amounts to the same thing, the time which elapses
from the Autumnal equinox to the Winter solstice, is called
Autumn by the inhabitants of the northern hemisphere; and
9F THE TERRESTRIAL GLOBE. - 9 |
the time from this solstice to the Wernal equinox is called
the Winter season of the year.
In like manner it may be shown that the inhabitants of the
southern hemisphere have the same vicissitudes of seasons,
but at different times of the year; that is, when we have
Spring they have Autumn: our Summer is their Winter;
our Autumn their Spring; and our Winter their Summer.
.These observations being properly attended to, it will be
easy to account for all the inequalities in the length of days
and nights, and the change of seasons which arise from them.
3. It is required to show, at one view, the length
of the day and night in all places upon the earth
on the 23d of September, or at the time of the flu-
tumnal equinoa: ; and also, to illustrate how the suc-
cession of day and night is really caused by the
diurnal motion of the earth, the sun standing still.
4. It is required to º the comparative length
of the days and nights in all places on the earth,
on the 22d of December, or at the time of the
Winter solstice; and also, to illustrate how the regu-
lar succession of day and night, and the vicissi-
tudes of the seasons, are really caused by the diur-
Yial and annual motions of the earth, the sun stand-
ing still. . . . . . -
PROBLEM xxvii.
To rectify the globe for a given latitude, and for the sun's
. place on a given day.
RULE. Elevate the north or south pole, accord-
ing as the latitude is north or south, so many de-
grees above the horizon as are equal to the latitude;
Screw the quadrant of altitude over the given de-
gree of latitude on the brazen meridian ; then bring
the sun's place in the ecliptic to the meridian, and
Set the index of the hour circle to twelve.
92 'GRAMMAR OF ASTRONOMY.
it is proper to observe, that the globe may also be placed
so that it may represent the natural position of the earth, by
means of a meridian line, or by a mariner's compass, which
is usually attached to the globe, taking care to allow for the
variation, if necessary: For instance, if the variation of the
compass, in any particular place, is found by observation to
be N.W. or 22 degrees towards the west of the true north
point of the horizon; the globe must be placed so that the
north point of the magnetic needle shall point N. W.; then
the elevated pole of the globe will point to the elevated pole
of the world; and the globe will correspondin every respect
with the situation of the earth itself. The poles, meridians,
parallel circles, tropics, and all the circles on the globe, will
correspond with the same imaginary circles in the heavens;
and each point, kingdom, and state, will be turned towards
the real one which it represents. • . *.
It may likewise be remarked that, in this problem, and in
all others where the pole is ſº. to any given latitude, . .
the earth is supposed to be ſkēd, and the sun to move round
it from east to west. t s • * , *
# . . * EXAMPLEs. . *
1. it is required to rectify the globe for the iati-
tude of New-York, and for the sun’s place on the
21st of June. . . . . • * .
Jìnswer. The latitude of New-York is ſound (by Prob.
I.) to be 40°42' north; therefore, the north pole must be
elevated as many degrees.above the horizon as are equal to
that latitude; the quadrant of altitude being screwed over the
same degree of latitude on the brazen meridian; then bring
the beginning of Cancer, which is the sun's place on the 21st
of June, to the meridian, and set the hour index to twelve.
‘Now, iſ there be a mariner's compass attached to the globe,
let the globe be placed so that the north point of the magnetic
needle shall point 40 (which is found by observation to be
nearly the variation of the compass at present in or near this
city.) to the west of the north point of the horizon; then the
meridian of New-York will be placed due north and south,
as on the real globe of the earth; and the north pole of the
globe will point exactly to the north pole in the heavens.
The first discovery of the variation of the magnetic needle,
or, as it is properly called, its declination from the pole, is
attributed by some writers to Sebastian Cabot. a Venetian.
•of THE TERRESTRIAL GLöLE. . 93
who was employed in the service of King Henry VII. about
the year 1500; but Ferdinand, the son of Columbus, in his
life written in Spanish, and printed in Italian at Venice in
1571, asserts that his father observed it on the 14th of Sep-
tember, 1492. It now appears, however, that this variation
or declimation of the needle was known even some centuries
earlier, though it does not appear that the pse of the needle :
itself in navigation was then known; for it seems there is .
in the library of the university of Leyden, a small manu-
script tract on the magnet, in Latin, written by one Peter
Adsiger, bearing date the 8th of August, 1269: in which the
declination of the needle is particularly mentioned. See
Dr. Hutton's Philosophical and JMathematical Dictionary.
2. On the 20th of May it is required to rectify
the globe for the latitude of London, the sun’s
place on that day; and also to place the globe due
north and south, the variation of the needle, as
found by observation, being 24% degrees west.
* * proBLE'ſ XXVIII.
To illustrate by the glob, the comparative length of the
days and nights in any particular place, at all times of
the year. . . . . . . .
RULE. ...Rectify the globe for the latitude of the
place; (by Prob. XXVII.)bring every degree of
the sun's place in the ecliptic to the brazen meri-
dian from the equinoctial point Aries fill the sun re-
turns to the same point again ; and imagine circles
to be drawn through the corresponding degrees of
declination; then those parallels of declimation will
nearly represent the sun’s diurnal paths for every
day in the year. The arcs of those parallels, which
are above, the horizon, are the diurnal arcs; and
the arcs, which are below the horizon, are the noc-
turnal arcs. Consequently, while the diurnal arcs
are greater than the nocturnal arcs, the days are
longer than the nights; while the diurnal arcs are
Jess than the nocturnal arcs, the nights are longer
94 GRAMMAR OF ASTRONOMY. .
than the days; and when the diurnal and nocturnal
arcs are equal, the days must be equal to the mights.

In this problem, and in all others, where the pole is ele-
Wated to the latitude of a given place, the earth is supposed
tº be fixed, and the sun.to move round it from east to west.
When the given place is brought to the brazen meridian,
the wooden horizons the true rational horizon of that place,
but it does not separate the enlightened part of the globe
from the dark part, as in problem XXVI: - q +
EXAMPLES.
1. Required to place the globe in the position of
a right sphere; and illustrate the circumstances at-
tending that situation. - . . s -
...The inhabitants of the equator are situated in a right
sphere, the poles of the gldhe being in their horizon; for hav-
ing no latitude, the poles are not elevated above it, and the
Sun's apparent diurnal motion will be in circles, parallel to
the equator and also at right angles to the horizon: conse-
quently, the inhabitants of the exuator will have equal days
and nights at all times of the yea) because the circle of di-
urnal revolution is always divided into two equal parts by
the horizon. During one half of the year, an inhabitant at
the equator will sée the sun due north at noon, and during
the other half it will be due south at the same time.
To illustrate these facts, put marks upon the beginning of
each sign in the ecliptic; bring each mark Suecessively, be-
ginning with the first point of Aries, to the eastern edge of
the horizonand, set the index of the hour circle to twelve;
then if each of those marks be brought successively to the
western edge of the horizon, we shall find in all cases that
the sun will be twelve hours above, and consequently as
, many hours below the horizon.
The ecliptic being drawn on the terrestrial globe, young
students are often led to imagine that the apparent diurnal
motion of the sun round the earth is performed in the same
oblique manner. In order to see clearly the ſallacy of this
principle, we must suppose the ecliptic to be transferred to
the heavens, where it properly points out the sun's apparent
annual path among the fixed stars. . The sun's diurnal path
is either in the equinoctial, as at the time of the equinoxes,

of The TERRESTRIAL GLOBE, 95
or in lines nearly parallel to the equinoctial: this may be
correctly illustrated by fastening one end of a thread upon
the equinoctial point Aries, and winding it round the globe
towards the tropic of Cancer, by turning the globe from east
to west, so that one turn of the spiral line thus described may
be at the same distance from another as the sun alters his
declination, in one day, in all those places over which it
passes, till you arrive at Cancer; thus you will have a cor-
rect view of the Sun's apparent diurnal path from the vernal
equinox to the summer solstice; for, after a diurnal revo-
lution the sun-does not come to the same point of the paral-
lel whence it departed, but, according as it approaches to,
or recedes from the tropic, is a little north or south of that
Joint. t * , - 3.
} A spiral line is similar to the threads of an external screw.
It may likewise be shown that a spiral line described on
the globe, in a similar manner, from the solstitial point Can-
cer, to the solstitial point Capricorn, will represent the appa-
rent paths described by the sun round the earth every day,
in passing from one tropic to another. . But, as the inclina-
tion of those threads to one another are but small, especially
near the tropics, we may suppose each diurnal path to be.
one of the parallel circles drawn, or supposed to be drawn
upon the globe, as pointed out in the above rule.
The intelligent student is referred to Wallace on the
Globes, (Prob. 25, page 98,) where he will find some useful
and important observations upon this subject.
2. Required to place the globe in the position of
a parallel sphere, and illustrate the circumstances
attending that situation. . . . .
This position of the earth represents that of the poles.
'The latitude being 90 degrees, the north or south pole must
therefore be elevated 900; then half the ecliptic will be
above and half below the horizon; the equator will coincide
with the horizon; and the sun's apparent diurnal motion
will consequently be in circles parallel to it; hence, if there
were any inhabitant of the dreary polar regions, he would
see the sun perform entire revolutions every twenty-four
hours for six months above his horizon; and for the other
six months that luminary would be lost to his view. -
To illustrate this, let the north pole, for instanee, be ele-
wated 90 degrees above the horizon; then, it is evident that
96 . GRAMMAR OF ASTRONOMY.
the sun will shine constantly on that pole from the time that
luminary enters the equinoctial point Aries, till it arrives at
the equinoctial point }. consequently there will be con-
stant daylight at the north pole during the time the sun is
describing the northern signs. When the sun just enters
Libra, he will appear to glide along the edge of the horizon,
after which he will entirely disappear until he arrives again at
Aries or the vernal equinox; consequently there will be con-
stant night at the north pole during the time that the sun is
describing the southern signs of the ecliptic. If the south
pole be elevated, the same circumstances will take place, but
at contrary times of the year; that is, during the time of con-
stant daylight at the north pole, there will be constant night
at the south pole; and on the contrary, while there is con-
stant night at the north pole, there will be constant daylight
at the south pole. Hence, the length of the civil day at the
north pole, reckoning from the time of the vernal to the au-
tumnal equinox, consists of 187 solar days, or days of 24
hours each; and the length of the civil day at the south pole,
reckoning from the autumnal to the vermal equinox, consists
of 178 days of 24 hours each. Consequently, the length of
the night at the south pole is 187 days of 24 hours each; and
the length of the night at the north pole is 178 days. &
Here we have not considered the effects of refraction,
twilight, &c. which supplies, in a great measure, the absence
of the sun in these inclement regions. For instance, though
the inhabitants of the north pole, if any, will lose sight of
the sun a short time after the autumnal equinox, yet the twi-
light will continue for nearly two months; for the sun will
not be 18 degrees below the horizon till he enters the 20th
degree of Scorpio, as may be seen by the globe.
After the sum has descended 18 degrees below the horizon,
all the stars in the northern hemisphere will become visible,
and appear to have a diurnal revolution round the earth from
east to west, as the sun appeared to have when he was above
the horizon. As soon as the sun returns again to the same
parallel of declination, which will be about the 28th of
January, or when he enters the 9th degree of Aquarius, twi-
light begins at the north pole; so that, dark night will only
continue at that pole from the 12th of November to the 28th
of January; and the stars will not be visible there but dur-
ing that time. t - -
Even the inhabitants of the north polar regions have the
moon constantly above their horizon during fourteen revo-
butions of the earth on its axis, and at every full moon which
of THE TERRESTRIAL GLOBE. 97
happens from the 23d of September to the 20th of March, the
moon is in some of the northern signs, and consequently,
visible at the north pole; for the sun being below the hori-
zon at that time, the moon must be above the horizon, be-
cause she is always in that sign which is diametrically op-
posite to the sun at the time of ſull moon. -
When the sun is at his greatest depression below the
horizon, being then in Capricorn, the moon is at her first
quarter in Aries: ſull in Cancer: and at her third quarter
in Libra: and as the beginning of Aries is the rising point
of the ecliptic, Cancer the highest, and, Libra the setting
point, the moon rises at her first quarter in Aries, is most
elevated above the horizon and full in Cancer, and sets at
the beginning of Libra in her third quarter; having been
visible for fourteen revolutions of the earth on its axis;
that is, during the moon’s passage from Aries to Libra. Thus
the north pole is supplied one half of the winter time with
constant moonlight in the sun’s absence; and the inhabi-
tants of the polar regions only lose sight of the moon from
her third to her first quarter, while she gives but little light,
and can be of little or no service to them. This subject shall
be more fully considered in a subsequent part of the work.
3. It is required to illustrate the circumstances
of an obliquº sphere; and also to show at one view
the comparative length of the days and nights in
New-York, at all times of the year. -
All the inhabitants of the earth, except those who have a
right or parallel sphere, are situated in an oblique sphere;
because the rational horizon of all parts of the earth, ex-
cept those upon the equator or at the poles, cuts the equator
obliquely. ' ' . .
Hence, in order to illustrate the circumstances of an ob-
lique sphere, the globe must be rectified for every latitude
from the equator to the poles. For instance, if the north
pole be gradually elevated from the position of a right sphere,
and if circles corresponding to every degree of the Sun’s
place in the eliptic, or spiral lines representing the sun's di-
urnal paths, be described on the globe; we shall find that the
diurnal arcs in the northern hemisphere will continually in-
crease, while the diurnal arcs in the southern hemisphere
will continually decrease in the same proportion; all the di-
urnal arcs of the northern parallels are therefore equal to all
9
98 GRAMMAR OF ASTRONOMYı. .
the nocturnal arcs of the corresponding parallels, south: and
if the south pole be gradually elevated in like manner, we
shall find that the diurnal arcs in, the southern hemisphere
will continually increase, while those in the northern diminish
in the same proportion, &c. Consequently, every place on
the surface of the earth equally enjoys the benefit of the sun,
in respect of time, the length of the days at one season of the
year being exactly equal to that of the nights at the opposite.
Here we do not consider the effect of refraction, twilight,
&c. nor the difference of time in which the sun is passing
through the northern and southern signs, being several days
longer in the former than in the latter, as appears evident
from the foregoing example. -
From the preceding considerations, it is also plain that, in
all places of the earth, except at the poles, the days and
mights are each twelve hours long at the time of the equi-
noxes; in all places situated on the equator, the days and
nights are always equal; in all places between the equator
and the poles, the days are never equal to the nights, except
when the sun is in the equinoctial points, Aries and Libra;
and the nearer any place is to the equator, the less is the
difference between the days and nights, and the more re-
mote, the greater. Several other circumstances attending
the situation of an oblique sphere may probably be better
illustrated by particular examples. -
Thus, to show at one view the comparative length of the
days and nights in New-York, at all times of the year; let
the north pole be elevated 40° 42'; then the wooden horizon
will be the true horizon of New-York; and, if the artificial
globe be placed due north and south, (by Prob. XXVII.) it
will have exactly the same position, with respect to its axis,
as the real globe has in the heavens. *
Now, by comparing the diurnal arcs with each other, it
will be seen, that the diurnal arcs will increase as you ad-
vance from the equator towards the tropic of Cancer; but
as you approach the tropic of Capricorn, the diurnal arcs
will decrease: Also, the ſormer diurnal arcs will be greater
than their corresponding nocturnal arcs, and the latter less;
the diurnal and nocturnal arcs being equal at the equator.
Consequently, when the sum is in the equinoctial the days
and mights are equal; as he advances towards the tropic of
Cancer, the days increase and the nights decrease; when he
comes to that tropic, the days are the longest, and the night;
the shortest. As the sun approaches the equator, the length
UF THE TERRESTRIAL GLOBE. 99
of the days diminishes, and that of the nightincreases; and
when he comes to the equator, the days and nights will again
be equal. Then, as he advances towards the tropic of Ca-
pricorn, the days diminish, and the nights increase, till he
arrives at that tropic, when the days will be the shortest
and the nights the longest; and then, as he approaches the
equator, the days will increase and the nights decrease; and
when at the equator, it will again be equal day and night.
It may not be improper to observe that, though we elevate
and depress the poles of the artificial globe, in the solution
of several problems, yet we are not to imagine that the earth's
axis moves northward and southward just as the pole is ele-
wated or depressed: for the earth’s axis has no such motion,
because the axis of the earth always remains parallel to
itself during its annual motion round the sun. It has, how-
ever, a kind of libratory motion, called its mutation, which
cannot be represented by elevating or depressing the poles.
In travelling from the equator northward, our horizon va-
lies; thus, when we are on the equator, the northern point
of our horizon is exactly opposite the north pole in the
beavens, or, which amounts to the same thing, the north
pole of the earth-coincides with the north point of the hori-
zon; when we have travelled to ten degrees north latitude,
the north point of our horizon is ten degrees below the
pole, and so on : now, the wooden horizon on the terres-
trial globe is immovable, otherwise it ought to be elevated
or depressed and not the pole; but whether we elevate the
pole ten degrees above the horizon, or depress the north
point of the horizon ten degrees below the pole, the ap-
pearance will be exactly the same.
4. It is required to show at one view the com-
parative length of the days and nights, in London,
at all times of the year. -
5. It is required to show at one view the com-
parative length of the days and nights at Quito, at
all times of the year. - -
6. It is required to show at one view the com-
parative length of the days and nights at the tro-
pic of Capricorn, at all times of the year; and al-
so to illustrate the circumstances attending the
position of the sphere in that situation.
100 , GRAMMAR OF ASTRONOMY.
7. It is required to show at one view the com-
parative length of the days and mights at Spitzber-
gen, in 80 degrees of north latitude, at all times of
the year; and also to illustrate the circumstances
attending the position of the sphere at that place.
/
PROBLEM XXIX.
The day of the month being given, to find the time of the
sun’s rising and setting, and the length of the day and
might at any given place within the torrid and tem-
perate zones. . . .
RULE I. Rectify the globe to the sun’s decli-
nation, (by Prob. XXV.) bring the given place to
the brazen meridian, and set the index of the hour
circle to twelve ; turn the globe eastward till the
given place comes to the eastern part of the hori-
zon, and the index will show the time of the sun’s
Setting ; which, taken from twelve, will give the
time of the sum’s rising ; because the sun rises as
many hours before twelve as it sets after twelve.
Double the time of sun setting gives the length of
the day; and double the time of rising gives the
length of the night. -
Or, the globe being rectified to the sun’s decli-
flation, as before, bring the given place to the west-
ern part of the horizon, and set the index of the
hour circle to twelve ; then, turn the globe east-
ward on its axis till the given place comes to the
eastern part of the horizon, and the number of
hours passed over by the index will be the length
of the day; and, consequently, by subtracting the
length of the day from twenty-four, we will have
the length of the night. *
The reason of this rule will appear evident from the con-
siderations in Prob. XXVI. For, when the globe is rectified
to the Sun's declination, the sun is supposed to be fixed, and
OF THE TERRESTRIAL GLoBE, 103.
the earth to revolve on its axis; consequently, when the
given place comes to the western edge of the horizon, the
sum is rising; when the place comes to the meridian, it is
noon; and when it will come to the eastern part of the ho-
rizon, the 'sun will be setting. See the problem above re-
ferred to, where the demonstration of this rule is fully given.
RULE II. Rectify the globe for the given la-
titude, and sun’s place in the ecliptic ; (by Prob.
XXVII) then, bring the Sun's place to the western
part of the horizon, and the index will show the
time of sun rising ; hence the time of sun setting,
and the length of the day and night is found as in
the above rule. *
– Or, by the ſºnalemma. Rectify the globe for
the latitude of the given place (by Prob. XXVII);
bring the middle of the analemma to the meridian,
. set the index of the hour circle to twelve ; turn
the globe westward till the day of the month on the
analemma comes to the western part of the hori-
zon, and the number of hours passed over by the
index, will be the time of the sun’s setting; which
being given, the rest is easily found as before.
Or, the globe being rectified for the latitude of
the given place; bring the sun’s place in the eclip-
tic to the eastern edge of the horizon, and set the
index of the hour circle to twelve; then turn-the
globe westward on its axis till the sum’s place comes
to the western edge of the horizon, and the number
of hours passed over by the index, will be the
length of the day. And the length of the day taken
from twenty-four hours, will give the length of the
might. Also, half the length of the night gives the
time of sun rising; and half the length of the day,
will give the time of sun setting -
* . ~. 9%
102 GRAMIMAR OF ASTRONOMY.
For the reason of this rule, the student is referred to Prob-
lem XXVI:I where the different methods pointed out in this
rule are fully considered.
By either of the above rules, the length of the longest
days at all places within the torrid and temperate zones may
be readily ſound; for the longest days at all places in north
latitude is on the 21st of June, or when the Sun enters Can-
cer; and the longest at all places in South latitude is on the
22d of December, or when the sun enters the sign Capricorn.
EXAMPLES.
1. What time does the sun rise and set at New-
York, on the 1st of October, and what is the length.
of the day and night 2 t b
Jánswer. The sun rises at 13 minutes past 6, and sets
at 47 minutes past 5; consequently the length of the day is
12 hours 26 minutes, and the length of the night 11 hours
34 minutes.
The learner will readily perceive that if the time at which
the sun rises be given; the time at which it sets, together
with the length of the day and night, may be ſound without
a globe; if the length of the day be given, the length of the
night, and the time the sun rises and sets, may be ſound;
if the length of the might be given, the length of the day,
and the time the sun rises and sets are easily known.
2. What time does the sun rise and set at Lom-
don on the 1st of June, and what is the length of
the day and night?
Answer. The sun sets at 8 minutes past 8, and rises at
52 minutes past three; and the length of the day is 16 hours
16 minutes, and the length of the night 7 hours 44 minutes.
3. Required the length of the longest day and
shortest might at New-York.
Jlmswer. On the 21st of June, the sun sets at 28 minutes
i. 7, and rises at 32 minutes past 4; consequently the
ength of the longest day is 14 hours 56 minutes, and the
length of the shortest night 9 hours 4 minutes. -
4. At what time does the sun rise and set at
the following places, on the respective days men-
of THE TERRESTRIAL GI.OBE. 103
tioned, and what is the length of the day and
might ! . *
Thiladelphia, 17th of May; London, 20th of
April; Dublin, 4th of July; Pekin, 20th of Au-
gust; Washington City, 9th of June ; Cape Horn,
8th of October; Petersburg, 22d of December ;
Baltimore, 1st of March; Quebec, 1st of January :
Botany Bay, 1st of February. - : -
5. Required the length of the longest day and
shortest night at the following places:
Limerick Leipsic Bencoolers
Lima Lyons Berlin
Leghorn Lexington Canton
Lisbon Lubec Cape of Good Hope.
6. Required the length of the shortest night and
longest day at the following places: Archangel,
Paris, St. Helena, Alexandria in Egypt, Mexico,
Cork, Boston, Buenos Ayres, and New-Orleans.
7. How much longer is the 21st of June at
Moscow than at Potosi in Peru ?
8. How much longer is the 21st of December at
Rio Janeiro than at Montreal? -
PROBLEM XXX.
The length of the day at any place, not in the frigid
comes, being given, to find the sun's declination and the
day of the month.
RULE I. Bring the given place to the meridian,
and set the index to twelve ; turn the globe east-
ward till the index has passed over as many hours
as are equal to half the length of the day; keep
the globe from revolving on its axis, and elevate
or depress one of the poles till the given place ex-
actly coincidst ºwith the eastern part of the hori-
104 GRAMMAR of ASTRONOMY
zon; and the distance of the elevated pole from the
Horizon will be the sun’s declination.
Mark this declimation on the meridian ; turn the
globe on its axis, and the two points of the ecliptic,
passing under the Sun's declination, correspond to
the days required, which may be found in the cir-
cle of months on the horizon. Or, having found
the sun's declination as before, bring the analemma
to the brazen meridian, and the days of the months,
corresponding to the declimation, will be those re-
quired. - t
The globe may be turned eastward or westward ; but it
is more convenient to turn it eastward, because the brazen
meridian is graduated on the east side, and as the student
should generally stand on that side in performing his prob- .
lems. - -
RULE II. Rectify the globe for the latitude of
the place; (by Prob. XXVII.) bring the meridian
passing through Cancer to coincide with the brazen
meridian, and set the index of the hour circle to
twelve ; turn the globe eastward till the index has
passed over as many hours as are equal to half the
length of the day; and the point of the meridian,
cut by the eastern part of the horizon, is the sun’s
tleclination, with º proceed as before.
Or, by the ſºnalemma. Having rectified the
globe for the latitude of the place; bring the meri-
dian passing through the middle of the analemma
to the brazen meridian, and set the index of the
hour circle to twelve ; turn the globe eastward till
the index has passed over as many hours as are
equal to half the length of the day; then, the two
days, on the analemma, corresponding to the point
of the meridian, which is cut by the horizon, will be
the days required, And, if that point he brought
of THE TERRESTRIAL GLOBE. 105
to the brazen meridian, the Sun’s declination will
|be exactly over it.
Any meridian' will answer the purpose as well as that
passing through Cancer; but if a meridian, which is not
graduated, be used, it would be necessary to bring the point
cut by the horizon to the brazen meridian, in order to find
the sun’s declination. -
EXAMPLES.
1. What two days of the year are each fourteen
hours long at New-York, and what is the sun's
declination ? - .
Jìnswer. The 7th of May, and the 6th of August, the
sun’s declination is 16° 48' north. .
2. What two days of the year are each sixteen
hours long at London, and what is the Sun's de-
clination 2 - *
3. On what day of the year does the sun rise at
four o’clock at Petersburgh in Russia, and what is
the sun’s declimation ? .**
4. On what two days of the year does the sun
set at five o’clock at New-York, and what is the
sun’s declination ? *.
5. What two days of the year are each sixteen
hours and a half long at Belfast, a town of exten-
sive commerce, and the principal sea-port in the
Inorth of Ireland 2 * . . .
PROBLEM xxxi.
To find those places, not in the frigid zones, at which the
longest day is of any given length, less than twenty-
four hours. 3.
RULE. Bring the first point of Cancer or Ca-
pricorn to the brazen meridian, according as the
106 GlèAMIMAR OF ASTRONOMY.
place is in north or south latitude, and set the in-
dex of the hour circle to twelve; turn the globe
westward on its axis till the index has passed
over half the length of the day; elevate or de-
press the pole till the sun’s place comes to the
western edge of the horizon; then the elevation of
the pole will show the latitude of those places.
This problem will answer for any day in the year, as well
as the longest day, by bringing the sun’s place for the given
da ł. to the brazen meridian, and then proceeding as above.
It is also proper to observe, that this problem may be per-
formed by the analemma; but as the method is nearly
similar to that given in the above rule, the intelligent stu-
dent can Readily supply it.
EXAPMLES.
1. In what degree of north latitude, and at
what places is the length of the longest day 16;
hours ? - . -
Jłnswer. In latitude 529, and all places situated on or
near that parallel of latitude, have the same length of day.
2. In what degree of latitude, and at what places
is the length of the longest day 15 hours ?
Jìnswer. In latitude 419 nearly, and all places situated
on or near that parallel of latitude, have the same length of
day; but, as it is not expressed in what hemisphere the re-
quired places are situated, this parallel of latitude may be
419 north or south. -
3. There is a town in Norway where the longest
day is twenty hours; what is the mame of that
town 2 -
4. In what latitude south is the longest day 16
hours ?
5. In what latitude north is the longest day 19
bours ? { - .
or THE TERRESTRIAL GloBE. 107.
PROBLEM XXXII.
The day of the month being given at any place, within
the torrid or temperate zones, to find what other day
of the year is of the same length. ,
RULE. Find the sun’s place in the ecliptic for
the given day, (by Prob. XX.) bring it to the bra-
zen meridian, and observe the degree over it; turn
the globe on its axis till some other point of the
ecliptic falls under the same degree of the meri.
dian ; then, corresponding to this point of the
ecliptic on the horizon, you will find the day of the
month required, - * -
Or, by the ſlnalemma. Look for the given day of the
month on the analemma, and adjoining to it you will find the
required day of the month,
Or, without a globe. Any two days of the year which are
of the same length will be an equal number of days from
the longest or shortest day. Hence, whatever number of
days the given day is before the longest or shortest day,
just so many days will the required day be after the longest
or shortest day, and the contrary, -
EXAMPLES,
1. What day of the year is of the same length ---
as the 25th of April? -
Answer. The 18th of August,
2. If the sun rise at half past five o'clock in the
morning at New-York on the 12th of April, on
what other day of the year will he rise at the same
hour 2 - -
3. What day of the year is of the same length
as the 4th of July 2 -
108. - GRAMMIAT OF ASTRONOMY.
PROBLEM XXXIII. -
To find the beginning, end, and duration of constant dayſ
and constant night, at any given place in the north fri-
gid zone. * : t - -
RULE. Bring the given place to that part of
the brazen meridian which is graduated from the
poles towards the equator, and observe its distance
from the north pole ; count the same number of
degrees from the equator on the meridian north
and south, and mark the place where each reckon-
ing ends; bring the first quadrant of the ecliptic,
or that from Aries to Cancer, to the meridian, and
that point of it which comes under the mark, on
the north side of the equator, will be the sun’s
place when constant day commences, and the day
corresponding to it found in the circle of months
on the horizon, will be the first day on which the
sun will constantly shine without setting. Turn
the globe on its axis till some point in the second
quadrant comes under the same mark, and the cor-
responding day found on the horizon, will be the
last day on which the sun will constantly shine
without setting. The number of days of twenty-
four hours each between those two, will be the
length of the longest day at the given place.
By bringing the third and fourth quadrants of
the ecliptic to the mark on the meridian, south of
the equator, and proceeding as before, you will
find the beginning and end of constant might, and
also its duration. *-
Or, by the flnalemma. Find the distance of the
given place from the north pole, and mark it on
the meridian, as before ; bring the analemma to
the meridian, and the two days which stand under
the mark on the north side of the equator, will be
the beginning and end of constant day; and those
of THE TERRESTRIA). GEOBE. t()9;
two days under the mark, south of the equator,
will be the beginning and end of constant night;
from which the rest is given, as in the above
method. . . . . . . . . .
The reason of this rule will appear evident from Prob.
XXVI.for when the sun's declination is north, and equal to
the distance of a place from the north pole, constant day be-
gins and ends at that place; but when the sun's declination.
is south, and equal to the complement of the latitude, or what
it wº.3 of 90 degrees, constant night begins and ends there.
... it is proper to observe, that iſ the place be in the south.
frigid zone, tº: jºints of the third and fourth quadrants of
the ecliptic will show the beginning and end of constant day;
the points of the first and second quádrants will show the
beginning and end of constant night; and, consequently,
the length of the longest day and longest night at the given
place may be readily ſound by proceeding as above.
- EXAMPLES. w
1. What is the fength of the longest day and
longest night, in the north-east part of Spitzber-
gen, under the parallel of 80 degrees; and ori
what day do they begin and end ?.
ºnsver. The given place is ten degrees from the north
pole, this being marked on the meridian, north and south of
the equator, the ſour points of the ecliptic that pass under
ji will correspond to the 14th of April, 27th of August, 19th,
ºf October, and 22d of February. Consequently, constant
day begins on the 14th of April, and ends on the 27th of
August; and the length/of the longest day is therefore 133.
days of 24 hours each; that is, the sun shines constantly
without setting during 183 solar days. Constant night com-
mences on the 19th of October, and ends on the 22d of
February; and the length of the longest night is thereföre
126 days of twenty-four hours each, or the sun is absent.
without rising during 126 solar days. Here there is a
difference of 7 days between the longest day and longest
night, owing to the unequal motion of the earth in its orbit,
or the apparent unequal motion of the sum in the ecliptic.
2. What is the length of the longest day and
longest night at the North Cape, in the island of
#
10
I. I.0 &RAMMIAIt of ASTRONOMY.
Maggeroe, in latitude 74°11′ north; and on what
day do they begin and end? . . . . .
flnswer. The longest day begins on the 15th of May, and
ends on the 29th of July. "The longest night begins on the
16th of November, and ends on the 26th of January : con-
sequently, the length of the longest day is 75 solar days, and,
the length of the longest night is 71 solar days; and their
difference is 4 days. This is what can readily be proved
by consulting the Nautical Almanac; for the days corres-
ponding to the sun's declination, when it is 180 49' north
and south, are those above given. * * ,
3. What is the length of the longest day, and
longest night at the south pole; and on what days
do they begin and end ? . . . .
4. What is the length of the longest day and
longest night in Sabine island, in the Polar Sea,
in latitude 75° 32' north; and on what days do they
begin and end ? , " ‘. . . . t;
5. What is the length of the longest day,and
longest night at the Arctic Circle; and on what
day do they begin and end ? * g
#
PROBLEM XXXIV,
To find the number of days that the sun will rise and set
alternately every twenty-four hours, at any given place
in the north frigid zone. ' §
RULE. Find the length of the longest day and
longest night at the given places, (by Prob.
XXXIV.) add these together, and subtract their
sum from 365 days, the length of the year; the
remainder will show the number of days on which
the sun will rise and set alternately every twenty-
four hours. - . . . . *
Or, find the beginning and end of the longest
day, and also the beginning and end of the longest
night at the given place; (by Prob. XXXIV.).
then, the number of days between the end of the
of THE TERRESTRIA!, GLOBE. Hºli.
longest day and the beginning of the longest might,
added to the number of days from the end, of the
longest night to the beginning of the longest day,
will give those days on which the sum will rise and
set alternately every twenty-four hours.
EXAMPLEs.
1. How many days of the year does the sun is:
and set at the North Cape, in the island of Mag-
geroe, in latitude 74°11′ north 2 -
Jlmswer. The length of the longest day is 75 days; the
length of the longest night is 71; (sée Ex. 2, Prob. XXXIII.)
and their sum is equal to 146 days; which subtracted from
365, leaves 219 days, the whole time of the Sun's rising and
setting alternately every 24 hours. -
Or, by the second method, the sun will rise and set alter
nately from the 26th of January to the 15th of May, which
is 109 days from the end of the longest night to the begin-
ning of the longest day; and also from the 29th of July to
the 16th of November, which is 110 days from the end of
the longest day to the beginning of the longest night; so
that 109 added to 110, gives 219 days, as above. . . . . .
It may be observed that on the 26th of January the sun
will just touch the horizon, and again descend below it;
the next it will advance a little above the horizon, &c.; so
that, the days will be continually increasing:till the sun ar-
rives at the equator, when the day and night will be ex-
actly equal; then according as the sun advances from the
equator towards the tropic of Capricorn, the days will still
continue increasing, till the 15th of May, at which time the
day will be exactly 24 hours; or the sun will just touch the
horizon without setting, and constant day will begin at that
time. We may reason, in a similar manner, with regard to
those days on which the sun rises and sets from the 29th of
July to the 16th of November; but during that time; the
mights will continually increase from the end of...constant
day to the beginning of constant night.
2. How many days of the year does the sunrise
and set at Spitzbergen, in the latitude of 80 de-
grees north 2 * , , ,
#12 GfèAMMAR OF ASTRONOMY
3. How many days of the year does the sun
dise and set at the northern extremity of Nova
Zembla, in latitude 76 north 2
... PROBLEM XXXV.
To find in what degree of north lalilude, on any day ber
#ween the 20th of JMarch and the 21st of June, or in
what degree of soulli latitude, on any day between the
23d of September and 22d December, the sun begins to
shine constantly without setting; and also in whal lati-
tude in the opposite hemisphere he beging to be totally
..absent. . . . . . . . . .
RULE I. Finál the Sun's declination for the
given day, (by Prob. XXI.) and coant, the same
number of degrees towards the equator, from the
north or south pole, according as the declination
is north or south, and mark the place on the meri-
dian where the reckoning ends; turn the globe on
its axis, and all places passing under this mark are
those in which the sun begins to shine constantly
without setting at that time : the same number of
degrees from the contrary pole will point out the
parallel of latitude in which he begins to be totally
absent, or where constant night begins.
RULE H. Rectify the globe to the sun's decli-
nation for the given day; (by Prob. XXV.) then
the parallel of latitude that touches the horizon
near the elevated pole, will be that on which the ,
suri is beginning to shine constantly; and the par-
allel in the opposite hemisphere just touching the
‘horizon near the depressed pole, will be that from
which the sun begins to be totally absent.
For the reason of these rules the student is referred to
Problems XXVI and XXVIII where they are clearly illus-
ſtrated. Both methods are the same in effect; but the latter
seems to be more natural, and the former more convenient,
OF THE TERRESTRIAL GloBE. 113
- ! -
- EXAMPLEs.
}
l
1. In what latitude north does the sum begin to
sline without setting, on the 10th of April; and in
what latitude south does he begin to be totally
absent? - | - -
ſ -
Answer. The sun's declination is'80 north; therefore,
he begins to shine constantly in latitude 820 north, and to
be totally absent in latitude $20 south.
2. In what latitude north; and at what places,
does the still begin to shine constantly without set.
ting on the 1st of June ; and in what latitude south
does he begin to be totally absent? . t
3. What inhabitants of the earth are Periscians,
or those who have their shadows directed to every
point of the compass on the 20th of May 2.
l’É.O BLEM XXXVI.
&ny number of days not eaceeding 187 north, or 178 in
south latilude, being given, to find the parallel of lati.
lude in which the sun does not set during that time.
RULE. Count half the number of days from
the 21st of June, or the 22d of December, accord-
ing as the place is in north or South latitude, east-
ward or westward on the horizon, and find the
sun’s declination corresponding to the day on which
the reckoning ends; (by Prob. XXI.) them, the
same number of degrees reckoned from the north
or south pole, according as the declimation is north
or south, on the meridian towards the equator, will
give the latitude required. .
. The parallel of latitude, in which the sun does not rise
during any number of days not exceeding 178 in north, or
187 in south latitude may be found in a similar manner.
- 10* x -
*,
# 14. GRAMMIAR OF ASTRONOMY.
ExAMPLE8.
. 1. In what degree of north latitude, and at what
places, does the sun continue above the horizon
during 76 days of 24 hours each 2 -
...Answer. Half the number of days, being 38, which,
reckoned towards the east from the 21st of June, will an-
swer to the 14th of May; on which day the Sun's declina-
tion is 18O 37 north. Consequently the latitude is 71°23'
morth; and the places sought are the North Cape in Lap-
land, the southern part of Nova Zembla, Olenska, a town in
Russia, Icy Cape on the north-west coast of America in the
Frozen Sea, a part of Greenland, &c. - . . .
2. In what degree of north latitude is the long-
est day 134 days of 24 hours each 2 -
3. Tn what degree of south latitude is the long-
est night 140 days of twenty-four hours each 2
4. In what degree of north latitude does the sun
continue below the horizon without rising, during
100 days of twenty-four hours each 2 -
PROBLEM xxxvii. -
To find in what geographical climate any given place on
the globe is situated.
RULE I. If the place be not in the frigid zones,
find the length of the longest day at that place, (by
Prob. XXIX.) from which subtract twelve hours;
then, if the remainder be less than half an hour,
the place is in the first climate; if more than half
an hour and less than one hour, the place is in the
second climate; and so on. And, if the difference
between the longest day and twelve hours be an
exact number of half hours, the remainder will
show the climate, at the end of which the given
place is situated. - f
2. But, if the place be in the frigid zones, find
the length of the longest day at that place, (by
Prob. XXXIII.) and if that be less than 30 days, the
* OF T1:IE TERRESTRIAL GLOBE. 1 15
place is in the twenty-fifth climate, or the first with-
in the polar circle ; if more than thirty and less
than sixty, it is in the twenty-sixth climate, or the
second within the polar circle; if more than sixty
and less than ninety, it is in the twenty-seventh cli-
mate, or the third within the polar circle, and so on.
There are twenty-four climates between the equator and
each polar circle, and six climates between each polar circle
and its pole, making in all 60 climates, into which the sur-
face of the earth is divided: for, at the equator the length
of the day is always 12 hours, at each polar circle the length
of the longest day is 24 hours, and at the poles the length
of the day is six months; therefore, the difference between
the length of the day at the equator and the longest day at
each polar circle, is 24 half hours; and the difference be-
tween the length of the longest day at each polar circle,
and the day at its pole is six months nearly. See the de-
finition of climate, Chap. VI. Art. 12.
The climates between the polar circles and the poles were
unknown to the ancient geographers; they reckoned onl
seven climates north of the equator. The middle of the first
northern climate they made to pass through Meroe, a city of
Ethiopia, built by Cambyses, on an island in the Nile, nearly
under the tropic of Cancer; the second through Syene, a city
of Thebais in Upper Egypt, near the Cataracts of the Nile;
the third through Alexandria; the fourth through Rhodes:
the fifth through Róme or the Hellespont; the sixth through
the mouth of the Borysthenes or Dnieper; and the seventh
through the Riphoean mountains, supposed to be situated
near the mouth of the Tanais or Don river. The southern
part of the earth being in a great measure unknown, the
climates received their names from the northern ones, and
not from particular towns or places. Thus, the climate
which was supposed to be at the same distance from the
equator southward, as Meroe was northward, was called
Antidianereos, or the opposite climate to Mereo, and so on.
, ExAMPLEs.
1. In what geographical climate is New-York,
and what other remarkable places are situated in
the same climate 2
116 GRAMMAR OF AS'ſ RON.O.M. Y. /
Jłnswer. The longest day at New-York is 14 hours 56
minutes, from which subtract 12 hours, and the remainder
is 2 hours 56 minutes, or 3 hours nearly; hence, New-York
is nearly at the end of the sixth climate nortn of the equator.
And, as the breadth of this climate extends from latitude
36O 31' to 410 24 north, all those places within these two
parallels are in the same geographical climate: that is to
say, Philadelphia, Baltimore, Richmond, Washington City,
Lexington, Cincinnati, St. Louis, &c. in the United States;
a part of Niphon, a great part of Corea, Pekin, Bukaria,
Samarcand, Smyrna, &c. in Asia; Constantinople, the
Archipelago islands, ancient Greece, the island of Sicily,
the southern part of Italy, Sardinia, Minorca, Madrid,
Lisbon, &c. in Europe; and the Azores or Western Isles,
in the Atlantic Ocean. . . . - t
2. In what geographical climate is the North
Cape in the island of Maggeroe, latitude 719 11.
north 2 . . . -
Jānswer. The length of the longest day is 75 solar days,
or days of 24 hours each; which is equal to 2 months and
15 days: hence the place is in the third climate within the
polar circle, or the 27th climate, reckoning from the equator.
And as the breadth of this climate extends from 69C 33' to
73° 5', (see the tables of climates annexed to the following
problem) the places contained within these two parallels aré
in the same geographical climate; that is, the southern
part of Nova Zembla, the northern part of Siberia, the
northern part of Russian America, Baffin's Bay, &c.
3. In what geographical climate is Cape Horn,
latitude. 55° 58' south 2 - . -
4. In what geographical climate is London, and
what other remarkable places are situated in the
same climate 2
5. In what geographical climate is Truxillo, a
city of Peru, built by Pizarro, in the year 1535;
and what other places are situated in the same
climate 2 * : - . . . .
{
of THE TERRESTRIAL GLOBE. 117
| 2
PROBLEM XXXVIII.
to find the breadths of the several geograp
whical climates,
from the equator to the poles. * , ,
RULE. I. For the climates from the equator to the
polar circles. Elevate the north pole 23° 28′ above
the horizon, bring the solstitial point Cancer to the
"brazen meridian, set the index of the hour circle
to twelve ; turn the globe eastward on its axis till
the index has passed over a quarter of an hour, and
the point of the meridian passing through Libra,
which is cut by the horizon, will show the end of
the first climate; continue the motion of the globe
eastward till the index has passed over another
quarter of an hour, and the point of the same
meridian, which is cut by the horizon, will show
the end of the second climate; proceed in this
manner till the meridian passing through Libra
will no longer cut the horizon, and you will find
the latitudes where each climate ends, from the
equator to the polar circles; the difference of
which will give the breadth of each climate.
2. To find the climates from the polar circles to the
poles. Find the latitude in the north frigid zone,
- in which the longest days are one, two, three,
four, five, and six months, respectively, (by Prob.
3XXVI.) and you will have the latitudes where
reach climate ends; the difference of which will
give the breadth of each climate from the arctic to
the north pole. * ,
When the breadth of the several climates between the
equator and the north pole are found, the several climates
from the equator to the south pole are also given; because
'the climates south of the equator are of the same breadth
as their corresponding climates north of the equator.
I 18 GRAMMAR OF ASTRONOMY.
EXAMPLES.
1. What is the beginning, end, and breadth of
the 6th climate north of the equator; and what
remarkable places are situated within it?
Jłnswer. The beginning of the 6th climate is 36° 31',
the end 410 24'; therefore, their difference 4o 53', is the
breadth required; and all places situated within this space,
are in the same geographical climate. (See Ex. 1, of the
preceding Problem.)" - . .
2. What is the beginning, end, and breadth of
the 27th climate north of the equator; and what
places are situated within it 2 ,
Jłnswer. The beginning of the 27th climate is 699 33,
the end 78° 5'; hence, its breadth is 30 32', and all places
situated within this space are in the same geographical cli-
mate. (See Ex. 2, of the preceding Problem.)
3. What is the breadth of the 9th climate north
of the equator, and what remarkable places are
situated within it 2 w
4. What is the breadth of thre 3d climate south
of the equator, and what remarkable places 3.1°C
situated within it 2 , , ,
5. What is the beginning, end, and breadth of
the 29th geographical climate 2. º
of THE TERRESTRIAL GLoBE. 119
t
I. Climates between the Equator and the Polar Circles.

; ; , Ends Where Breadths twº Ends Where Breadths
~ l; the Sº . . t1u
ºf in lati- ngest of the 3 |ºn lati. longest of the
à |tudes.|'''éº"|Climates.|| 5 |tudes.|º"|Climates.
: |day is. 2: day is.
O * Q || 4
I. 8° 34'12; h.| 8° 34' | XIII.59° 59'184 h. 1° 32'
II./16 44; 13 8 10 || XIV.]61 18|19 1 19
III.24 12||13; 7 28 || XV |52 26|19% 1. 8
IV.]30 48|14 6 36 || XVI.[63 22|20 || 56
V.36 41|14; 5 43 || XVII.[64 10.20% 48
VI.[4] 24/15 4 53 || XVIII.34 50|21 || 40
VII.]45 32.15% || 4 || 8 || XIX.]65 22:21; , , 32
VIII.]49 2 | 6 3 30, XX.165 48|22 26
IX.]51 59|16% 2 57 XX||66 522# 17
. X.54 3017 2 31 | XXII./66 2:23 I6
XI.[56 38|17; 2 8 || XXIII.]66 29|234 8
XII.58 27|18 1 49 || XXIV.[66 3224 3
II. Climates between the Polar Circles and the Poles.
à wher: § Where!Bdths
* Ends the Breadths *: Ends the of the
.5 in lati-longest of the .5 in lati-longest Cli-
5 tudes.|day is.|Climates.| 5 |tudes, day is. mates
XXV. 67° 18′ 1 mo, 46 XXVIII.l77° 40'4 mo. 4° 35'
XXVI. 69 33 2 2° 15 XXIX.182 595 5 19
XXVII. 73 5. 3 3 32 | XXX. |90 6 7_l

These tables may be constructed by the globes, according
to the methods pointed out in the preceding rule, but not
with that exactness given above.
The first table is thus calculated : v
As tangent of the sun's greatest declination 23O 23',
Is to radius or sine of 90 degrees; -
. So is sine of the sun's ascensional difference,
To the tangent of the latitude.
For instance, to find the end of the second climate; halſ
an hour or 30 minutes, the time which the sun rises before
6, converted into degrees, (by Prob. XIX.) will give the
ascensional difference equal to 70 30': then,
!
As tangent of 23° 28′ - - - - 9.63761
Is to radius - - - -- -' - - . 10.00000
So is sine 7o 30' - - - - - , , 9.11570
tºns
To tangent latitude 16944 a.47800
120 GRAMIMAR OF ASTRONOMY.:
The above proportion is founded upon this principle: that
the latitude where any climate ends between the equator
and polar circles, and the ascensional difference on the
longest day in that latitude, form a right angled spherical,
triangle; and the angle opposite to the latitude is equal.
to the complement of the sun’s greatest declination, or 669
32. Consequently, there is given in a right angled spheri-
cal triangle, one side and an angle, to find the side opposite
to the given angle. Hence, by Napier's rules, radius multi-
plied by sign of the ascensional difference, is equal to tangem!
of the sun’s greatest declination multiplied by tangent of the
latitude: . . . . . . . . . . . .
The second table is thus constructed: -
As the declination of the sun is always equal to the com-
plement of the latitude, or what it wants of 90°, when the
longest day begins or ends within the polar circles; and as
the sun’s declination is also equally distant from the solsti-
tial point Cancer, in which the sun is on the 21st of June.
Hence, count half the number of days which the sun shines
constantly without setting, from the 21st of June, both be-
fore and after it; find the sun's declination answering to
those two days in the Nautical Almanac, in a table of the
sun's declination, and add the two declinations together;
then half, their sum subtracted from 909, will give the
Hatitude. - - r
*
PROBLEM XXXIX. . . ,
To find the beginning, end, and duralion of twilight at
any given place, on a given day.
RULE I. Rectify the globe to the sun’s declina-
tion for the given day, (by, Prob. XXV.) and
screw the quadrant of altitude in the zenith; bring
the given place to the meridian, and set the index
of the hour circle to twelve ; turn the globe east-
ward till the given place comes to the horizon;
and the hours passed over by the index will show
the time of the sun's setting, or the beginning of
evening twilight; continue the motion of the globe
eastward, till the given place coincides with 18°
on the quadrant of altitude below the horizon, and
the time passed over by the index, from sun-set
or THE TERRESTREAL GLoBE. 12]
ting, will show the duration of evening twilight.
The morning twilight is nearly of the same length,
and found in the same manner. . . . . . . . ..” . . .
When the greatest depression of the sun is less than 18
degrees below the horizon, the twilight will continue during
the whole night, of which amounts to the same thing, there
will be no total darkness at the given place, during several
revolutions of the earth on its axis; as shall be clearly illus-
trated in the next problem. . . . . . . . . . . . . . . . .
It may not be improper to observe, that the length of the
day, is usually reckoned from the beginning of morning
twilight to the end of evening twilight; and, consequently,
that the continuation, oſ-total darkness, properly called the
length of the night, is counted from the end of evening twi-
light to the beginning of morning twilight...".
RULE II. Rectify the globe for the given latitude,
sun's place, &c. (by Prob. XXVII) turn the globe
westward on its axis till the sun's place comes to the
western edge of the horizon, and the hours passed
over by the index will show the time of the sun’s
setting, or the beginning of evening twilight; con-
tinue the motion of the globe westward till the sufi's
place coincides with 18° on the quadrant of alti- .
tude below the horizon; the time passed over by
the index of the hour circle, after sun setting, will
be the duration of evening twilight; and the index
will point out the time of its ending. " . . . .
The duration of twilight varies at different seasons at the
same place, according as the sun’s apparent path is more or
less oblique to the horizon; it also differs at the same time
at different latitudes, according as the atmosphere is more
or less elevated; and the variation in the same place even
during one day, is so sensible, that the evening twilight is
found to continue longer than the morning twilight, owing
to the expansion of the atmosphere during the day, and con-
sequently to its greater height. . . . " !
... " - * - 11
122 GRAMMAR OF ASTRONOMY.
EXAMPLEs.
1. Required the beginning, end, and duration of
morning, and evening twilight at London, on the
19th of April. . \ . -
Jłnswer. The sun sets, at two minutes past seven, and
evening twilight ends at nineteen minutes past nine; conse-
quently, morning twilight begins at 2 hours 41 minutes, ends
at 4 hours 58 minutes; the duration of evening twilight is
2 hours 17 minutes, and the duration of morning twilight is
the same, or nearly the same. . . . . .
2. What is the duration of twilight at New-
York on the 23d of September 2 what time does
dark might begin, and what time does day break in
the morning 2 . . . . * -
3. Required the beginning, end, and duration of
morning and evening twilight at Washington city,
on the 21st of March.
4. Required the beginning, end, and duration of
morning and evening twilight, at the following
places, on the 20th of May : Philadelphia, New-
Orleans, Lima, Havanna, and Gibraltar.
problew XL.
To find the beginning, end, and duration of constant .
t twilight at any given place on the globe. . .
RULE, Add 18 degrees to the latitude of the
given place; the sum subtracted from 90, will give
the sun's decliniation, when constant twilight com-
mences, and also when it ends; observe what two
points of the ecliptic correspond to this declination,
then, that point in which the sun's declimation is in-
creasing, will show on the horizon, the beginning
of constant twilight; and that point in which the
declination is decreasing, will show the end of
Constant twilight, at the given place.
OF THE TERRESTRIAL GLOBE. 123
When the declination of the sun is 180 south, and de-
creasing, constant twilight commences at the north pole;
but when the declination is 18° south, and increasing, con-
stant twilight ends, or total darkness, properly called might,
commences at that pole. When the declination of the sun
is 18° north, constant twilight commences, &c. at the south
pole, in a similar manner. . . . . . . . . . . . . ;
It is proper to observe, that, after adding 18 to the given
latitude, and substracting the sum from 90, if the remainder
exceed 23° 28, there can be no constant twilight at the given
place. Hence, there can be no constant twilight, between
48° 32', north or south latitude, and the equator. * *
. . . . . . . . . EXAMPLEs. . . . . . .
1. When do the inhabitants of London begin to.
have constant twilight, when does it end, and
what is its duration ?
Jhuswer. The latitude of London is 510 31', to this add
18°, and the sum will be 690 31', which sum subtracted .
from 90, gives 20°29', the sun's declination, when constant
twilight begins, and also when it ends. - 3.
Now, the two days of the year corresponding to 200 29'
north declination, are easily found to be the 22d of May and
the 21st of July; so that constant twilight commences on the .
22d of May, and it ends on the 21st of July. Hence, the
duration of constant twilight is nearly two months; or, which
is the same thing, there will be no total darkness at Lon-
don, from the 22d of May to the 21st of July. . . . -
All other places that are situated in the latitude of Lon-
don, will have constant twilight during the same time.
2. What is the duration of twilight at the north
pole, and what is the duration of dark night there 2
Jłi-swer. The day on which the sun’s declination is 189
south and decreasing, is on the 28th of January; and the day
on which the declination is the same and increasing, is on
the 14th of November. Consequently, constant twilight
commences on the 14th of November, and ends on the 28th
of January; so that the evening twilight continues from the
23d of September, (the time of the autumnal equinox) to the
14th of November, (the beginning of dark might) being 52
days; and the morning twilight continues from the 28th of
January to the 20th of March, (the time of the vernal
124 GRAMMAR of ASTRONOMY.
equinox) being 51, and sometimes 52 days. Hence, the
duration of total darkness at the north pole, is about 75
days; and even during that period, the moon and the aurora
borealis, shine with uncommon splendour.
8. Can twilight ever continue from sun-set to
sun-rise at New-York at any time of the year !
4. What is, the duration of constant twilight at
the North Cape in Lapland; and how long does
dark night continue there? . . . . . . . . . . s’ s
* * 4. -
5. When does constant twilight begin at Peters-
burg in Russia, when does it end, and how long
does it continue there 2 " . . . " . . .
is s & - ..'. . ** * - . . . . .
PROBLEM -x LI. . . . . . "
*
* +. i
: ' . .. - º s - . . . * * ' s . . . . . .
To find the sun’s meridian altitude on any given day, at
. . . . &ny given place. . . . . . . . . . . .
RULE I. Rectify the globe to the sun's declina-
tion for the given day; (by Prob. XXV) bring
the given place to the brazen meridian; and the
number of degrees contained on the meridian be- .
tween the given place and the nearest point of the
horizon, will be the meridian altitude requiréd.
RULE II. Rectify the globe for the given lati-
tude; bring the sun's place in the ecliptic to the
meridian ; and the number of degrees contained
on the meridian between the sun’s place and the
horizon, will be the meridian altitude required.
Or; find the latitude of fle given place, and also the de-
elination of the sun on the given day; then, if they are of
the same name, (that is, both north or both south,) the com-
plement of the latitude, (or what it wants of 900) added to
the declination, will be the meridian altitude required; but,
if one be north and the other south, the difference between
the complement of the latitude and the sun's declination.
will be the meridian altitude. . -
$
OF THE TERRESTRIAL GLOBE. 125
f
*...,
ExAMPLEs. . . .
1. What is the sun’s meridian altitude at New-
*
York on the 21st of June 2 . . . . . . . . .
flaswer. 72°46'20". This is the greatest altitude at
New-York. . . . . . . . . . . .
2. What is the sun's meridian altitude at Quito
on the 20th of March 2 .
... 3. What is the sun's meridian altitude, at New-
York on the 22d of Becember 2 . . . . . . .
4. What is the difference between the greatest
and least meridian altitude of the sun at Washing-
-ton city ? . . . . . . . . . & -
- 5. What is the sun's meridian altitude at Peters-
burg in Russia, on the 22d of December 2
&
ef
PROBLEM IXLII.
Given the sun's meridian altitude, gnd the day.of the
'month, to find the latitude of the place of observation: .
RULE. Bring the sun’s place in the ecliptic to
the brazen meridian ; then count as many degrees
frpm the sun's place on the meridian, as is equal to
the given altitude, reckoning towards, the south
point of the horizon, if the sum was south when
the altitude was taken, or towards the north, if the
sun was to the fiorth of the observer, and mark
the degree where the reckoning ends; elevate or
depress the pole till this mark coincides with the
horizon, and the number of degrees the elevated
pole is above the horizon, will be the latitude re-
quired.
Or, by calculation. Subtract the sun's altitude from 90
degrees, and the remainder is the zenith distance. . If the
sun be south when his altitude is taken, call the zenith dis-
tance north; but, if north, call it south; find the sun's de-
clination in the Nautical Almanac, or in a table of the Sun's
1 I
| 36 GRAMMAR OF ASTRONOMY.
declination; and observe whether it be north or south; then,
if the zenith distance and declination have the same name, .
thèir sum is the latitude; but if they have contrary names,
their difference is the latitude, and it is always of the same
name with the greater of the two quantities. ''
EXAMPLEs. - f .
1. On the 1st of August 1825; I observed the
sun's meridian altitude to be 20°25' 19, and it was
south of me at that time; required the latitude of
the place. . . . . . . . . . . . . . . . . . .
Answer, 87 degrees 38 minutes 22 seconds. º y -
!'
f
º
Or, by calculation. . . . . . .
90o . . . . . . . ſº
20025' 19" S, sun's altitude at noon.
18 3 41 N. sun's declinationist of August
,
696 34: 41° N. the zenith distance. ' . . . . . .
& , 1825...
870:38 22" N. the latitude sought. - -
2. On the 21st of June, 1825, the sun's meridian
altitude was observed to be 66° 20' north of the
observer; what was the latitude of the place of ob-
servation? * 4. . . ' ' . .
3. On the 21st of June, 1825, I 'observed the
sun's meridian altitude to be 72°45'20", and it was
south of me at that time; required the latitude of .
the place. .
4. On the 14th of July, 1825, the sun’s meridian
altitude was observed to be 509 30 29° north of the
observer; what was the latitude of the place of ob-
servation ? . . A
. . . PROBLEM XLIII. ,
2. - y
t
sk * - . -
To find the sun's azimuth and his altitude at any given .
place, the day and hour being given.
RULE. Rectify the globe for the latitude of
the given place, and for the sun's place on the
|
of THE TERRESTRIAL GLOBE. 127
given day; (by Prob. XXVII.) then, if the given
time be before moon, turn the globe eastward as
many hours as it wants of noon; but if the given
place be past noon, turn the globe westward as ma-
my hours as it is past noon; bring the graduated .
edge of the quadrant of altitude to coincide with the
sun's place; then the mtimber of degrees on the
horizon, réckoned from the north or South point
thereof to the graduated edge of the quadrant, will
show the azimuth ; and the number of degrees on
the quadrant, counting ſtom the horizon to the
sun's place, will be the altitude, . . . . . .
This problem may be also resolved. by the analemma;
but as the method is méarly similar to that above given, it
can be readily supplied by the intelligent student.
It may not be improper to observe that, at all places in the
torrid zone, whenever the declination of the sun exceeds the
latitude of the place, and both are of the same, the sum will
appear twice in the forenoon, and twice in the aſternoon, on
the same point of the compass; and consequently, its azi-
*
smuth will be the same at two different hours.
{ - - f
{
EXAMPLES. -
§
1.What is the sun’s altitude, and his azimuth
from the north, on the 10th of May, at New-York,
at 9 o'clock in the morning 2 .
Answer. The altitude is 459 30'. and the azimuth 1070
30' from the north. *g
2. What is the sun's azimuth and altitude at
Antigua, on the 21st of June, at half past six in the
morning, and at half past ten ?, .
Answer. The sun’s azimuth is 690 from the north, at
both those hours; the altitude at half-past six, is 129 near-
ly; and the altitude at half-past ten, is 679 nearly. These
altitudes are found by the globe, and therefore are not so
accurate as if they had been ſound by calculation:
3. What is the sun's azimuth and altitude at
| 28 \ GRAMMAR OF Ast RONOMY. . . .
the morning? . . . . . . . . . -
4. What is the sun’s azimuth and altitude at
Barbadoes, on the 20th of May, at six o'clock in the
morning; and at what other hour in the forenoon
º
has the sun the same azimuth?
* PROBLEM XLIV. .
*
To find the Sun's amplitude at any given place, on a given.
. . . . . . . . . . . day."
RULE. Rectify the glo
New-York on the 20th of May at seven o'clockin
be for the latitude of the -
given place; bring the sun's place in the ecliptic to
the east part of the horizon, and the degree cut on
the horizon, reckoſing from the east, will be the
sun’s amplitude at rising ; bring the sun's place to
the western part of the horizon, by turning the
globe on its axis, and the degree cut on the horizon,
reckoning from the west point of it, will be the
sun's amplitude at setting. . . . .
This problem may be also resolved by the analemma.
For a table of the sun's amplitude, corresponding to every
degree of the sun's declination, and also to every degree of
latitude from the equator to the polar circles, the student is
referred to Bowditch's JVew ſlimerican Practical JNavigator.
ExAMPLEs. . .
f

1. What is the sun's amplitude at Philadelphia .
on the 21st of June 2,
19 to the north of the west. “ . . f . ,
2. On what point of the compass does the sun
rise and set at New-Orleans on the 20th of April?
3. On what point of the compass does the sun
rise and set at Boston on the 4th of July 2
4. What is the sun’s amplitude at Charleston, in
South Carolina, on the 22d of December 2
Answer. 81919 to the north of the east, nearly; and,319 -
of the TERRestrial. globe. 129
PROBLEM xlv. ...
Given the sun’s amplitude and the day. of the month, to
find the latitude of the place of observation. . .
RULE. Bring the sun's place in the ecliptic to
the eastern or western part of the horizon, accord-
ing as the eastern or western amplitude is given;
then elevate or depress the pole till the sun's place
coincides with the given amplitude on the horizon,
and the elevation of the pole will show the latitude.
- - ExAMPLEs. : -
1. The sum’s amplitude was observed to be 390
48 from the east towards the north, on the 21st of
June; required the latitude of the place of observa-
tion. . .
Answer 510 32 north. - .
2. The sun's amplitude was observed to be 150
30 from the east towards the north, at the same
time his declination was 15° 30'; required the lati-
tude. . . . . . . . . . .
3. When the sun's declination was 2° north, his
rising amplitude was 4° north of the east; required
the latitude. :
PROBLEM XLVI
When it is midnight at any place in the torrid or tempe-
rate zones, to find the sun's altitude at any place (on
the same meridian) in the north frigid zone, where the
sun does not descend below the horizon.
RULE. Rectify the globe to the sun’s declina-
tion for the given day, (by Prob. XXV.;) bring
the place in the frigid zone to that part of the bra-
Zen meridian which is numbered from the north
pole towards the equator, and the number of de-
130 GRAMMAR OF AstroNOMY.
grees between it and the horizon, will be the sun’s
altitude. . . . . . .
Or, rectify the globe for the latitude of the place
in the frigid zone; bring the sun's place in the
ecliptić to the brazen meridian, and set the index
of the hour circle to twelve ; turn the globe on its
axis till the index points to the other twelve ; and
the number of degrees between the sun’s place and
the horizon, counted on the meridian towards that
part of the horizon marked north, will be the sun’s
altitude.
- EXAMPLEs. *
1. What is the sun’s altitude at the North Cape
in Lapland, when it is midnight at Alexandria in
Egypt, on the 21st of June 2
Jłnswer. 5 degrees. *
2. When it is midnight to the inhabitants of the
island of Sicily on the 22d of May, what is the sun’s
altitude at the north of Spitzbergen, in latitude 80
degrees north 2 . . . -
3. What is the sun’s altitude at the north ol.
Baffin’s Bay, when it is midnight at Buenos Ayres,
on the 28th of May 2 -
ProBLEM XLVII. +
The day of the month being given, to find the sun's right
ascension, oblique ascension, oblique descension, ascen-
sional difference, and time of rising and setting at any
given place. - *
RULE. Rectify the globe for the given latitude ;
bring the sun’s place in the ecliptic to the brazen
meridian, and the degree on the equator cut by the
graduated edge of the meridian, reckoning from the
point Aries eastward, will be the sun's right ascen-
of THE TERRESTRIAL GLOBE. 13]
Sion. Then, bring the sun’s place to the eastern
part of the horizon; the degree of the equator cut
by the horizon, reckoning from the point Aries as
before, will be the sun’s oblique ascension; and the
difference between the sun’s right ascension and
oblique ascension, is the ascensional difference.
The oblique descension is found in a similar manner, by
bringing the sun's place to the western part of the horizon,
and reckoning from the point Aries eastward as before; and
the difference between the sun's right ascension and oblique
descension, is also the ascensional difference. -
If the ascensional difference in degrees be converted into,
time, (see Prob. XIX.) - then, if the sun's declination and
the latitude of the place be both of the same name, (that is,
both north or both south,) the sun rises before six, or sets.
aſter six, an interval of time equal to the ascensional differ-
ence; but, if the sun’s declination and the latitude be of
contrary names, (that is, the one north and the other south)
the sun rises after six, or sets after six. . . . . . .
EXAMPLEs.
1. Required the sun’s right ascension, oblique
ascension, oblique descension, ascensional differ-
ence, &c. at New-York, on the 21st of June. .
JAnswer. The sum’s right ascension is 90 degrees, oblique.
ascension 68 degrees; therefore, the ascensional difference
is 220, which being converted into time, corresponds to 1
hour 28 minutes. Hence, the time of the sun’s rising is 4
hours 32 'minutes; and the sun sets at 28 minutes past
seven. The oblique descension is 68 degrees, the same as .
the oblique ascension. Y -
2. Required the sun's right ascension, oblique
ascension, and oblique descension at St. Louis, on
the 22d of December. What is the ascensional
difference, and at what time does the sun rise and
set 2 , - - {
3. Required the sun's right ascension, oblique
132 GRAMMAR or ASTRONOMY.
\
ascension, and oblique descension at Washington
City, on the 20th of March. 'What is the ascen-
sional difference, and at what time does the sun
rise and set ! . . . . . . . . . " " ' ',
PROBLEM xlviii.
. The day and hour at any place being given, to find all
those places of the earth where the sun is rising, those
... places where the sun is setting, those places that have
noon, that particular place where the sun is vertical,
those places that have morning twilight, those places
that have evening twilight, and those places that have
midnight.
RULE. Rectify the globe to the sun's declimation
for the given day; bring the given place to the
brazen meridian, and set the index of the hour
circle to twelve; then, if the given time be before
moon, turn the globe westward as many hours as it
wants of moon; but, if the given time be past moon,
turn the globe eastward as many hours as the time
is past noon ; keep the globe, in this position; then
all places along the western part of the horizon
have the sun rising; those places along the eastern
part have the Sun setting; those under that part of .
the meridian, which is above the horizon, have
noon; that particular place which stands under the
sun's declination on the meridian has the sun ºver-
tical; all places below the western part of the
horizon, within eighteen degrees, have morning
twilight; those places which are below the eastern
part of the horizon, within eighteen degrees of it,
have evening twilight; all places under that part of
the meridian, which is below the horizon, have mid-
night; all places above the horizon have day, and
those below it have night. -
The reason of this rule is very evident from what has been
explained in the foregoing problems. .
{}}F THIE 'TERRESTRIAI, GLOBE,. . T38
A.
EXAMPLES.
1. When it is ſorty minutes past four o’clock in
the morning at Philadelphia, on the 5th of Febru-
ary, find all the places of the earth where the sun
is rising, setting, &c. * -
Jłnswer. 'The declimation of the sun will be ſound to be
15° 54 south; therefore, elevate the south pole 15° 54';
then bring Philadelphia ſo the incridian, and set the index
of the hour circle to twelve; turn the globe westward till
the index has passed over 7 hours 20 minutes, what the
given time wants of moon.
Ret the globe be fixed in this position; then, the sum is
rising at the northern part of Labrador, or near Hudson’s
Straits ; Upper Canada; States of Ohio, Kentucky, Ten-
messee, and Alabama; and that part of Mexico, situated
between the bays of Campeachy and Honduras. Setting at
Russian Lapland, &c.; Tartary; the eastern part of
Cabulistan; a part of Hindoostan; the eastern part of the
island of Ceylon, &c.
JNoon at Falmouth in England; Cadiz; Fez; Ivory
Coast, &c.
Vertical at St. Helena. -
JMorning twilight at the north-western part of Hudson's
Iłay; Missouri Territory; the internal provinces of Mex-
ico, &c. - ,
Evening twilight at the western coast of New-Holland;
Batavia; Sumatra; Malacca; Birman Empire, &c.
Day in all Europe, Africa, and all that part of Asia, com-
prehended between Ceylon and Little Tibet, &c. towards
the east ; in all South America; the whole of the West
indies, Florida, Georgia, North and South Carolina, Vir-
ginia, District of Columbia, Maryland, Delaware, Pennsyl-
vania, New-Jersey, New-York, &c. - \
JNight in all that part of North America, comprehended
between the eastern part of Cuba and Hudson's Straits, &c.
towards the west; in all that part of Asia, comprehended
between the island of Ceylon and the sea of Obe, towards
the east. -
2. When it is fifty-two minutes past four o’clock
in the morning at London, on the 1st of March,
12
734 GRAMMAR OF ASTRONOMY."
find all places of the earth where the sun is rising,
setting, &c. - - -
3. When it is seven o’clock in the morning at
Washington city, on the 17th of February, where is
the Sun rising, setting, &c. g -
Questions to exercise the learner in the foregoing
- problems.
The questions referring to the rules are in italics, in
order that the student may distinguish them from those
questions which refer to the examples:
I. On what circles of the terrestrial globe are the
latitude and longitude of places counted 2 *
2. Required the latitude and longitude of Bom-
bay, city and island, on the west coast of Hiu-
doostan, and capital of all the British possessions
on that side of the peninsula. l
3. How do we find all the places that have the same
latitude as any given place 2 - . -
4. Which places have the same latitude as Berne,
the capital of a cantom of the same name in Swit–
zerland 2 § - * * *
5. How do we find all the places that have the same
longitude as any given place 2 -
6. Which places have the same longitude as
Hanover, a city of Germany, and capital of the
kingdom of the same name 2
7. How do we find what place is situated in a parti-
cular latitude and longitude 2 A
8. What place in the Austrian dominions is in
480°12' north latitude, and 16°12' east longitude 2
9. How do we find the difference of latitude between
two places, situated either on the same, or on contrary
sides of the equator 2
}
OF THE TERRESTRIAL GLOBE. £35
30. What is the difference of latitude between
Cape Ortegalin Spain, and New Madrid, a town in
Missouri, on the Mississippi, 70 miles below the
mouth of the Ohio 2 --
14. What is the difference of latitude between
Boston and Buenos Ayres 2 -
12. How do we find the difference in longitude be-
tween two places, when both have either east or west
longitude, also, when one has east and the other west
longitude 2 . . .
13. What is the difference in longitude between
Augusta, a city in the state of Georgia, and the
mouth of Columbia river ? -
14. What is the difference in longitude between
Raleigh, the capital of North Carolina; and Flo-
rence, the capital of the grand Duchy of Tuscany,
and one of the finest cities of Italy, or perhaps in
Europe 2 - ...'
15. How do we find the shortest distance between
any two places on the globe 2
16. What is the nearest distance between Da-
mascus, a city of Syria, in Asiatic Turkey; and
Mocha, an extensive city of Yemen, in Arabia, and
the principal port on the Red Sea?
17. How do we find all those places that are at the
same distance from a particular place as any other
given place 2 -
18. Required all those places that are at the
same distance from London as Milan, the capital of
. Austrian Italy.
19. How do we find that place on the globe, the
latitude of which is given, and its distance from a
particular place 2 -
20. A place in latitude 50° N., and situated in
cast longitude, is 2700 geographical miles from
Medina, a town in Africa, and capital of the
136 - GRAMMAR OF ASTRONOMY.
kingdom of Woolly, situated a few miles north of
the Gambia, about 400 miles from its mouth : re-
quired the place. . --
21. How do we find that place, the longitude of
which is given, and its dislânce from a particular
place 2 *.
22. A celebrated island in the Mediterranean,
and in ſongitude 27° 32' E., is 51.14 English miles
from New-York; what is that island called 2
23. How do you illustrate the circumstances of the
antaeci, 2 - v. - .
24. Which are the antoeci of the inhabitants of
Porto Rico, an island in the West Indies, belonging
to Spain 2 - -
25. How do you illustrate the circumstances of the
perioci 2 - . -
26. Which are the perioeci of the inhabitants of
Barbadoes, one of the Caribbees, and the most
eastern of the West India islands 2
- 27. How do you illustrate the different circumstances
arising to the inhabitants who are antipodes to each
other ? . . . *
28. Which inhabitants of the earth are the anti-
podes of Paraíba, the capital of a province of the
same name, in Brazil 2 . -
29. How do we find the anteci, periaci, and anti-
podes of any particular place 2
30. Required the antoeci, periocci, and antipodes
of Bencoolen. g - -
31. How do you find the angle of position between
places on the horizon of the globe 2
32. What is the angle of position between New-
York and St. Antonio, the most northerly of the
Cape de Verd Islands 2 t
33. How do we find the bearings of places to each
other ? name the different methods.
of TiE TERRESTRIAL GLOBE. 13.7
34. What is the bearing between Friendly
Islands and Navigation Islands, both in the south
Pacific Ocean 2
35. How do you find the number of miles contained
in a degree of longitude on any given parallel of lali-
tude 2
36. How many geographical and American miles
make a degree of longitude in the latitude of Que-
bec 2 . . . . . .
37. How do you find at what rate per hour the in-
habitants of any given place are carried from west to
east, by the earth’s rotation on its awis.
38. At what rate per hour are the inhabitants of
Cayenne, capital of French Guiana, carried from
west to east by the revolution of the earth on its
39. How do we find by the globe, the hour of the
day at different places at the same instant &
40. When it is six o'clock in the morning at
Lima, what o'clock is it at the following places:
Pernambuco, capital of the province of the same
name in Brazil; Sierra Leone in Africa; Dublin,
Madrid, London, Palermo, Mocha a city in Arabia,
and Canton in China Ż
4!. How do you find those places where it is noon,
or any other given hour, when the hour til any particu-
lar place is given & . . . . .
42. What places have noon, when it is seven
o’clock in the morning at Philadelphia 2 '.
43. How do you find the stºn's place in the ecliptic,
and his declination, on a given day 2 g -
44. What is the sun’s longitude and'his declina-
tion, on the 23d of September 2
45. How do we find what latitude the sun will be
vertical to, on a given day? . . . . . .
.. . . . . . 12%
A 38 Gl{AMIM) Aſt OF ASTR ()NOM. Y.
46. Find all those places of the earth to which
the sun will be vertical on the 20th of May.
47. How do you find those two days of the year on
which the sun will be vertical to any given place in the
torrid zone 2
48. On what two days of the year will the sun
be vertical to Bayamo, a town on the south coast
of Cuba? . -
49. How do you find where the sun is vertical, the
day and hour at any pºrticular place being given 2
50. On what two days of the year is the sun
vertical at St. Christopher’s island, in the West
Andies 2 '.
51. How do you rectify the globe to the sun’s de-
ciination, on a given day 2
52. Rectify the globe to the Sun's declimation on
the 1st of November. Napie the circumstances.
53. How do you illusiriite by the globe, the variety
in the length of the days and nights, Gºwd the change
of seasons 2 . . . . . . .
54. Required to show the comparative length of
the day and night in all places on the earth, on the
4th of July; and also, to illustrate how the regular
succession of day and wight, and the change of
seasons, are really caused by the diurnal and annual
motions of the earth. . . :
55. How do you rectify the globe for the latilude
ºf a given place, end for the sun's place ºn a given
day ? . . . . .
56. It is required to vectify the globe for the la-
titude of Washington City, and for the sun’s place
on the 21st of Junº. - ‘. . . .
57. How do you illustrate by the globe, the com-
parative length of the days and nights, in any particu-
lar place, at all times of the year 2
or Tji I, TERRESTRIAi, GLOBE. 139
58. It is required to show at one view the com-
parative length of the days and nights, at the tropic
of Cancer, at all times of the year. Name the cir-
cumstances. &
59. How do you find the rising and selling of the
sun, and the length of the day &nd night at any place
in he lorrid or temperate zones 2 . . "
60. What time does the sun rise and set at Mos-
cow on the 22d of December 2 -
61. IIow do you find the sun's declination and day
of the month, the length of the day, at any particular
place being given & . -
62. On what two days of the year does the Sun
rise at 4 o’clock at Archangel 2 - - •
63. How do you find those places in the torrid or
temperate zones, whom the longest day is of any given
length, less than twenty-four hours?' \
64. In what latitude north is the longest day 16%
hours ? Name the most remarkable places. r
65. Given the day of the month, at any particular
place, not in the frigid zones, how do you find what
other day is of the same length 2
66. What day of the year is of the same length
as the 20th of March 2 . .
67. How do you find the beginning, end, and dura-
tion ºf constitºt day wild constant night at any place in
!he frigid zones 2
68. What is the length of the longest day and
longest night at the mouth of the Lena, a river in
Asiatic Russia, which rises in the mountains north-
west of lake Baikal, and ſalls into the Frozen Ocean
in latitude 73 north, after a course of nearly 2000
miles 2 -
69. How do you find the number of days that the
Sun will rise and set allernalely every twenty-four
hours, at any place in the north or south frigid zones &
340 GRAMMAR of AstroNoMx.
70. How many days of the year does the sun
Rise and set alternately every twenty-four hours, at
Sabine island, in the Polar Sea 2 . . "
71. How do you find in what degree of north lali-
tude, on any day between the 20th of JMarch and 21st
of June, the suit begins to shine constantly without set-
ting, and also in what latitude in the opposite hemis-
phere he begins to be totally absent 2
72. In what latitude north does the Sun begin to
shine constantly without setting, and also in what
latitude south does he begin to be totally absent, on
the 25th of May 2
73. Given any number of days not exceeding 187
north, or 178 in south lalitude, how do you find the
parallel of latitude in which the sun does not set during
that time 2 -
74. In what degree of latitude north does the sun
continue above the horizon during 120 days of
twenty-four hours each 2 *
75. How do you find in what geographical climalſ.
any given place is situated 2 .
76. In what climate is Havana 2
77. How do you find the breadths of the several cli-
Amales, from the equalor to the poles 2
78. What is the beginning, cud, and breadth of
the eleventh north climate ; and what remarkable
places are situated within it 2
79. How do you find the beginning, end, and dura-
tion of morning and evening twilight, al a given place,
on a given day ?
80. What is the duration of twilight at the tropic
of Capricorn, on the 21st of June 2 .
81. How do you find the beginning, end, and dura.
tion of constant livilight at any place between the forty-
minlh degree of north or south latitude, and the north
or south pole 2
or TIE TERRESTRIAL GLOBE. 14}.
82. What is the duration of constant twilight at
Archangel ? - .
83. Having given the place and day of the month,
how do you find the sun's meridian allilude 2
84. What is the sun’s meridian altitude at the
north polar circle, on the 22d of December 2
85 The sun's meridian altitude and day of the
month being given, how do you find the lalitude of the
place of observalion ?
86. On the 20th of November, 1825, the sun’s
meridian altitude was observed to be 409 south of
the observer, what was the latitude of the place 2
87. How do you find the sun’s azimuth and his alti-
tude al any given place, the day and hour being given?
88. What is the sum’s altitude, and his azimuth
from the north, at New-Orleans, on the 21st of
June, at 9 o'clock in the morning 2 .
89. How do you find the sun’s amplitude, at a
given place, the day and hour being given 2, .
90. On what point of the compass does the sun
rise and set at Albany, on the 20th of March 2
91. The sun’s amplitude and day ºf the month be-
ing given, how do you find the lalitude of the place of
observation? - -- -
92. The sun’s amplitude was observed to be 329
from the east towards the north, on the 21st of
June ; required the latitude of the place of observa-
tion. -
93. How do you find the altitude of the sun at any
place in the frigid zones, when it is midnight at a parti-
cular place in the lorrid or temperate zones 2
94. What is the sun’s altitude at Sabine Island,
when it is midnight at Bejapoor, a city in Hin-
doostan, on the 21st of June 2
95. How do you find the sun’s right ascension, &c.
the day of the month at any place being given 2 -
#42 GRAMMAR of ASTRONOMY.
96. Required the sun's right ascension, &c. at
Paris, on the 22d of December 2
97. The day and hour at any place being given, to
find all those places of the earth where the sun is rising,
setting, noon, vertical, &c. -
98. When it is eight o’clock in the afternoon at
Rome, on the 25th of March, where is the sun
rising, setting, noon, vertical, &c.? -
BOOK II.
OF THE CELESTIAL GLOBE.
*º-º-º-º:
CHAPTER I.
Definitions and terms belonging to the celestial globe.
1. The celestial globe, as has already been ob-
served, is an artificial representation of the heavens,
having all the stars of the first and second magni-
tude, and the most noted of the rest that are visible,
truly represented on it, according to their proper
angular distances in the concave surface of the
heavens. \ . • * 3.
2. The rotation of this globe upon its axis from
east to west, represents the apparent diurnal motion
of the concave surface of the celestial sphere, on an
axis passing through the poles of the world, com-
pleting its revolution in 23 hours, 56 minutes, and
4 seconds nearly, and carrying along with it the sun,
moon, and stars. The axis of the celestial sphere,
is usually called the aris of the heavens.
This hypothesis illustrates and represents the apparent
diurnal motion of the several celestial objects in parallel cir-
cles, with an equable motion, each completing its circular
path, in the same time. That the motion of each star is:
equable, and that they describe parallel circles on the con-
cave surface, we reduce from observation and the computa-
tion of spherical trigonometry.—See Dr. Brinkley's flstro-
70my. -
3. The wooden horizon circumscribing the ce-
lestial globe, is divided exactly into the same
144 Glt AMI}\l A iſ. Of' AS'I'RON ONI. Y.
concentric circles, as the wooden horizon of the
terrestrial globe. See Book I. Chap. IV.
The horizon of the celestial globe must be considered as
continued to pass through the centre, where the eye is sup-
posed situate viewing the hemisphere above the horizon, and
the axis of the globe is to be placed at the same elevation.
as the axis of the concave surface of the spectator. In this .
way all the circles of the celestial sphere will be easily
understood. Any consideration of the form or figure of the z
earth is entirely ſoreign to a knowledge of the circles of the
sphere. They were originally invented without any reſer-
ence to it. And in fact, the prºgress in astrongmy was
from the celestial circles to terrestrial, and not the contrary.
*.
4. That imaginary great circle in the heavens,
which the sun describes in his apparent diurnal re-
volution at the time of the equinoxes, or when the
days and nights are equal all over the world, is
called the equinoctial, ahd sometimes the celestial
equator. -
"The circle in which the plane of the equinoctial cuts the
surface of the earth, is usually called the equator or terres-
trial equator, which has been already defined, (Art. 5,
page 8.) g
It is however proper to observe, that in treatises on as-
tronomy and the globes, the terms equinoctial and equator
are used indifferently for each other.
5. A great circle passing through the poles of
the world and through the zenith of a place, is
called the celestial meridian of that place. The
celestial meridians are also called circles of declina-
tion. (See Art. 5, page 21.)
The circle in which the plane of the celestial meridian
intersects the surface of the earth, is called the terrestrial
meridian. Those terms are used indifferently for each
other. (See Art. 10, page 9.) • * ...~"
There are no meridians drawn on the celestial globe; but
they are supplied by the brazen meridian, which is gradua-
ted in the same manner as the brazen meridian belonging
to the terrestrial globe. (Art, 12, page 10.)
OF THE CELESTIAL Gſ, OBE; 145
6. The ecliptic, colures, equinoctial and solstitial
points, are situated on the celestial globe just as on
the terrestrial ; and therefore, it is unnecessary to
take any farther notice of them here, as they have
already been sufficiently defined in the first book.
It is also proper to observe that the tropics, polar circles,
and parallels of declination, on the celestial sphere, corres-
pond to the tropics, polar circles, and parallels of latitude on
the terrestrial globe.
7. The poles of the ecliptic are situated on the
celestial globe, at the distance of 23° 28′ from the
poles of the equinoctial.
For the pole of any great circle on the surface of the
sphere, is 90 degrees distant from every part of its circum-
ference, and the angle which the ecliptic makes with the
equinoctial is equal to 28° 28′; consequently, the north pole
of the ecliptic must be 23° 28′ distant from the north pole
of the equinoctial, and the south poles must likewise be
similarly situated.
8. Secondaries to the ecliptic are called circles
of celestial latilude, or circles of latilude; because
the arc of the secondary, intercepted between any
celestial object, and the ecliptic is called its latitude,
north or south; according as the object is on the
north or south side of the ecliptic. -
Every point on the surface of the celestial sphere is sup-
posed to have a circle of celestial latitude passing through
it, though, to prevent confusion, there are, in general, only
twelve drawn on most of the celestial globes, the rest being
supplied by the quadrant of altitude.
9. The longitude of a heavenly body is an arc
of the ecliptic intercepted, in the order of the
signs, between the equinoctial point Aries, and a
circle of celestial latitude passing through the
body.
13
146 GRAMMAR OF ASTRONOMY.
Hence, the latitudes and longitudes of the heavenly
bodies are ascertained by secondaries to the ecliptic, and
the latitudes and longitudes of places upon the earth, are
found by secondaries to the equator. •
10. The right ascension of a heavenly body is
an arc of the equinoctial intercepted, reckoning in
the order of the signs, between the vernal equi-
noctial point and a circle of declimation passing
through the body. And the arc of the circle of
declination intercepted between the celestial object
and the equinoctial, is called the declination of the
object. -
The definitions contained in this article agree exactly with
those which are given in Art. 5, page 21, and Art. 12,
page 36. .
In the practice of astronomy, the most general and con-
venient method of ascertaining the position of any celestial
object on the concave surface, is to determine its position
with respect to the equinoctial, or celestial equator, and the
vernal equinoctial point, that is, to determine its declimation
and right ascension. The position of a celestial object,
with respect to the equinoctial, being ascertained, it is very
often necessary to determine its position with respect to the
ecliptic, that is, to determine its latitude and longitude. See
the ſoregoing two articles. - -
11. Diurnal arc is the arc described by the sum,
moon, or stars, from their rising to their setting.
The sun’s semidiurnal arc is the arc described in
half the length of the day. .
12. Nocturnal are is the arc described by the
sum, moon, or stars, from their setting to their
rising. -
13. That parallel of declination, in an oblique
sphere, which is as many degrees distant from the
elevated pole of the heavens, as the place itself is
distant in degrees from the equator, is called the
circle of perpetual apparition; because all the
stars included within this circles are continually
() F '''}{E C ſº LESTIAL GI,0BJP. 147
above the horizon of the place, and consequently
The VC1' 30t.
14. The circle of perpetual occultation is another
parallel of declination, opposite the former, and at
a like distance from the depressed pole of the
heavens. All the stars contained within this circle,
never appear above our horizon, and consequently
never rise.
All the stars contained between these two circles, do
alternately rise and set at certain moments of the diurnal
rotation. -
QUESTIONS. .
How are the stars represented on the celestial
globe 2 - ,”
What docs the rotation of this globe on its axis
from east to west represent; and what is the axis
of the celestial sphere called ! * .
How is the wooden horizon of the celestial globe
divided ? - * '
What is the equinoctial or celestial equator?
What are the celestial meridians, and what are
they usually called 2
At what distance in degrees is the north pole of
the ecliptic from the north pole of the equinoc-
tial 2 “, . . . . .
What are the circles of celestial latitude, and
what is the latitude of a heavenly body ?
What is the longitude of a heavenly body ?
What is the right ascension and declination of a
heavenly body ?
What are the diurnal and nocturnal arcs &
What is the circle of perpetual apparition?
What is the circle of perpetual occulation ?
i48 GRAMMAR of ASTRONOMY.
CHAPTER II.
of the fired stars—division of the stars into constel.
lations, &c.
1. Those celestial bodies, which have always
been observed to keep the same relative distances
with regard to each other, are called fived stars,
or simply stars. . . .
From continued observations on, the heavens, in clear
nights, we shall soon see that the fixed, stars constitute by
far the greater number of the celestial bodies. It will like-
wise follow that they do not appear to have any proper mo-
tion of their own; but that the several apparent motions of
the fixed stars are really caused by the diurnal motion of the
earth, the precession of the equinoxes, properly called the
Yecession of the equinoctial points, the aberration of light,
&c. For, the apparent diurnal motion of all the heavenly
bodies from east to west, is caused by the real motion of the
earth on its axis, in a contrary direction; and the recession
of the equinoctial points, will cause the fixed stars to have
an apparent motion backwards from west to east, in cir-
cles parallel to the ecliptic, at the rate of 50" nearly in a
year: in consequence of this motion, the longitude of the
stars will be always increasing; their latitude remaining
the same, because it is ſound by observation, that the equi-
noctial moves on the ecliptic, contrary to the order of the
signs, while the ecliptic keeps nearly the same position in
the heavens. The mutation of the earth's axis, the aber-
ration of light, &c., cause some small change in the places
of the stars. There are other changes in the apparent
magnitude, lustre, &c. of the fixed stars, which shall be
considered in a subsequent part of this work. -
2. Those celestial bodies that are constantly
changing their places, as well with regard to the
fixed stars as to one another, are called planets, or
wandering stars. g
or THE CELESTIAL GLOBE. 149
A planet may be known from a fixed star, by the steadi-
ness of its light; for a fixed star appears to emit a twinkling
łight, but a planet gives a mild steady light. The planets,
besides their apparent diurnal motions, have apparent mo-
tions that at first seem not easily brought under any general
laws. Sometimes they appear to move in the same direc-
tion in the heavens as the sun and moon; at other times in
a contrary direction; and sometimes they appear nearly
stationary, or fixed in the same point of the heavens.
There are ten planets, whose names are, Mercury,
Venus, Mars, Ceres, Pallas, Juno, Vesta, Jupiter, Saturn,
and Uranus. Five of these planets have been observed
from the remotest antiquity; the other five, lately dis-
covered, are only visible by the assistance of telescopes.
The motions, magnitudes, distances, &c. of the planets,
shall be fully considered in the next book.
3. The fixed stars are divided into orders or
classes, according to thcir apparent magnitudes.
Those stars which appear largest, are called stars
of the first magnitude ; the next to them in lustre,
stars of the second magnitude ; and so on to the
siath, which are the smallest that are visible to the
naked eye. All those stars which cannot be seen
without the aid of a telescope, are distinguished by
the name of telescopic Stars. - •
The stars of each class are not all of the same apparent
magnitude; there being considerable difference in this re-
spect; and those of the first magnitude appear almost all
different in lustre and size. There are also others of inter-
mediate magnitudes, which astronomers cannot refer to one
class in preference to another, and therefore they place them
between the two. For instance, in M. Laland's catalogue of
600 principal stars visible at Paris, and which contains none
less than of the fifth magnitude, there are no fewer than 126
stars of intermediate magnitudes. So that instead of six
magnitudes, we may say that there are almost as many or-
ders of stars as there are stars; such considerable varieties
being observable in their magnitude, colour, brightness, &c.
Whether these Varieties of appearance are owing to a diver-
sity in their real magnitude, or from their different distan-
ces, is impossible to determine; but it is highly probable that
both of these causes contribut: to produce those effects:
13: -
i50 &RAMMAR OF ASTRONOMY.
4. The number of stars visible to the naked
eye in both hemispheres, is not more than 2000 ;
but to whatever part of the heavens a telescope is
directed, multitudes of stars appear, which were
before invisible. The number of stars. that can
be seen by the naked eye in the whole visible
hemisphere, is not more than 1000.
The reason why they appear so innumerable on casting
the eye quickly to the heavens in clear winter nights, arises
from our sight being deceived by their twinkling, and from
our viewing them confusedly, and not reducing them to-any
order. Different astronomers have given catalogues of the
fixed stars, disposed according to some order, in their several
constellations; with the right ascension, declination, longi-
tude, latitude, &c. of each; and from the accuracy of their
observations, there is scarcely a star to be seen in the hea-
vens, whose place is not better known than that of most
towns upon the earth. , #
Hipparchus, who first undertook to make a catalogue of
the fixed stars, from his own observations, and those of the
ancients that preceded him, inserted in his catalogue only
1022 stars, annexing to each of them the latitude and longi-
tude which they had at that time. - -
Ptolemy added four to this number; and others were
afterwards discovered by different astronomers who applied
themselves to this subject. ... -
Tycho Brahe determined the places of 777 stars, for the
end of the year 1600; Kepler from the observations of
Tycho, afterwards increased this number to 1000, in the
Rhudolphine tables. Dr. Halley made a catalogue of 350-
stars not visible above the horizon of London. . .
De la Caille, at the Cape of Good Hope, in the year
1751 and 1752, made accurate observations of about 10,000
stars, near the South pole; the catalogue of which was pub-
lished in the Memóirs of the French Academy of Sciences,
for the year 1752. Bayer and John Hevelius, also pub-
lished catalogues of the stars, and Flamstead, in his His-
toria Caelestis, published a most complete catalogue of
more than 3000 stars, observed by himself.
In 1782, M. Bode, of Berlin, published a very extensive
catalogue of 5058 of the fixed stars, collected from the obser-
vations of Flamstead, Bradley, Hevelius, Mayer, La Caille,
OF THE CELESTIAL GLOBE. T 51
Messier, Monnier, D'Arquier, and several other astronomers,
all rectified to the beginning of 1780; and accompanied
with a celestial atlas of the constellations, engraved in a
most delicate and beautiful manner. •
M. Laland has published a new catalogue of more than
12,000 stars. Almost all of which has not been before ob-
served. - -
But the most surprising list that has ever been formed
of the fixed stars, is the catalogue by M. F. Laland, in
which are determined the places of 50,000 stars from the
pole to 2 or 3 degress below the tropic of cépricorn. . .
The telescope opens an extensive field to the contempla-
tive mind. By its aid we are enabled to discover myriads
of stars which before were invisible to the unassisted eye;
as we increase the power of the instrument, more and more
stars are brought into view, so that their numbers may be
considered infinite. Many of the stars that appear single to
the naked eye, are by the telescope ſound to be double,
treble, &c.; or to consist of several stars very near each
other; of these, several have been observed by Cassini,
Hooke, Long, Maskelyne, Hornsby, Pigott, Mayer, &c.;
but Dr. Herschel has been by far the most successful in
observations of this kind. He has already formed a cata-
logue containing 269 double stars, 227 of which have not
been noticed by any other person. Among these there are
also some stars that are treble, quadruple, and multiple.
5. The ancient' poets, referring the rising and
setting of the stars to that of the sun, make three
kinds of rising and setting; namely, cosmical,
achronical, and heliacal. § -
These are called the poetical rising and setting of the stars,
because they are mostly taken notice of by the ancient
poets; formerly they served to distinguish particular seasons
of the year; but they are now chiefly useful in comparing
and understanding passages in the ancient writers.
6. The cosmical rising and setting of a star, is,
when the star rises with the sun, or sets when the
Sun rises. . . .
7. The achronical rising and setting of a star, is,
when the star sets with the sun, or rises when the
sun sets. • -
i -
152 GRAMIMAR OF ASTRONObi Y.
8. The heliacal rising and setting of a star, is,
when the star first becomes visible in the morning,
after having been so near the sun as: to be hidden
by the splendour of his rays; or when the star
becomes invisible in the evening on account of its
nearness to the sun. - • .
9. An imaginary zone or belt in the heavens,
which extends about 8 degrees on each side of the
ecliptic, is usually called the zodiac. . .
The zodiac includes the paths of all the planets among
the fixed stars, except Ceres and Pallas, which have been
discovered since the year 1800. . . . . . . . z
The zodiac appears to be very ancient, and to have passed
from the ancient Hindoos, successively westward, through
Persia, Arabia, Assyria, Egypt, &c. to Europe; as speci-
mens of the same kind of zodiac have been found in all
those countries with only some variation in the figures of
some of thc constellations; accompanied also with appro-
priate emblematical figures of the sun and moon, with those
of the planets in their order. -
10. In order to distinguish the fixed stars from
each other, the ancients classed them under the
outlines of certain imaginary figures of men, birds,
fishes, &c. called constellations or asterisms. Those
stars which were not included in the ancient con-
stellations, were called unformed stars; but on the
modern celestial globes, the constellations are made
to include all the unformed stars. y
The constellations are called after the names of those
figures under which they are represented. See the tables at
the end of this chapter. In what age of the world this ar-
rangement of the stars into constellations took place, is not
known; but it was certainly antecedent to any authentic
record; so that whether the shepherd or the sage was em-
ployed in their formation, cannot now be ascertained. Boötes
and the Bear are spoken of both by Homer and Hesiod;
Arcturus, Orion, and the Pleiades, are mentioned in the book
of Job; the writer of the book of Amos has also mentioned
Orion and the seven stars; and there is scarcely any ancient
OF THE CELESTIAL, GLOBE, 153
author in which the names of the most remarkable ones are
not to be found. But to trace the origin of this invention,
and to show why one animal had the honour of being ad-
vanced to the heavens in preference to another, is no easy
task. . . M. Fréret, the Abbe la Pluche, and several other
writers of considerable eminence, have ransacked all the
legends of fabulous history for the illustration of this sub-
ject; but, except in a few obvious instances, no consistent
and satisfactory account has as yet been given. , t
11. Besides the names of the constellations, the
ancients gave particular names to some single
stars or small collections of stars; thus the cluster
of Small stars in the neck of Taurus was called
the Pleiades; five stars in his face, the Hyades ;
a bright star in the breast of Leo, the Lion’s Heart;
and a large star between the knees of Boötes,
Jłrcturus, &c. ... . ** *
12. In order that the memory may not be
burthened with a multiplicity of names, astrono-
mers mark the stars of every constellation, by the
letters of the Greek and Roman alphabets; de-
moting the first or principal star by a, the next in
order by 8, the third in order by y, and so on;
when the Greek alphabet is finished, the letters of
the Roman alphabet a, b, c, &c. are applied to
the remaining stars in the same manner; and when
the number of stars in a constellation exceeds the
letters of both alphabets, the ordinal numbers 1, 2,
3, &c., are used to denote the rest in the same
regular succession; so that by this means the
stars can be spoken of with as much ease as if each
had a separate name. •
The method of denoting the stars in every constellation by
the Greek and Roman alphabets, was the invention of John
Bayer, a German lawyer and astronomer, who first intro-
duced it about the year 1603, in his charts of the constella-
tions; this useful method of describing the stars has been
adopted by all succeeding astronomers, who have farther
154 GRAMMAR OF ASTRONOMY.
enlarged it, by adding the numbers 1, 2, 3, &c. to the other"
stars discovered since his time, when any constellation con-
tains more than can be marked by the two alphabets. By
means of these marks the stars of the heavens may, with as
great facility, be distinguished and reſerred to, as the several
places of the earth are by means of geographical tables.
Astronomers, in speaking of any star in the constellation,
denote it by saying it is marked by Bayer, c., 8, or Y, &c.
As the Greek letters so frequently occur in catalogues of
the stars and on the celestial globes, the Greek alphabet is
here introduced for the use of those who are unacquainted
with the letters. The capitals are however sclélom used in
denoting the stars.
THE GREEK ALPHABET.
C. Alpha -
A a ’
B (3 & . . Beta b
Iº y Gamma §.
A ô Delta d
E. e. Epsilon e short
Z 3 & Zeta Z
H 71. Eta ‘e long
G) § 6 Theta th
I ! . Iota i
RC 2. Kappa k
A. X Lambda |
IM M. . Mu m
N V Nu - D.
£, # X - X,
O O Omicron o short
II a ºr Pi ...” p
P g p Rho I'
X . 0 g Sigma s
T + 7 Tau t
ºf v - Upsilon u
it (p Phi ph
X x Chi . ch
Y . . Psi ps
Q (a) Omega o long
OF THE CELESTIAL GLOBE, 155
12. The MILKY WAY, Via Lactea, or Galaxy,
is a broad path, or track, encompassing the whole
heavens, and also distinguishable by its white ap-
pearance, whence it obtains the name.
Astronomers have ſound, by the help of telescopes, that
this track in the heavens consists of an immense multitude
of stars, seemingly very close together, whose mingled light
gives this appearance of whiteness; by Milton beautifully
described as a path “powdered with stars.” - s”
13. JWebulous is a term applied to those stars
which show only a dim hazy light, like little specks
or clouds; they are smaller than those of the 6th
magnitude, and therefore seldom visible to the ma-
ked eye. -
The milky way may be considered as one great nebula,
which Dr. Herschel has found to consist of a continued as-
semblage of Nebulae, or vast clusters of small stars.
14. Astronomers have divided the constellations
into three classes, called the northern, the Southern,
and the zodaical. The northern constellations are
37 in number, the southern 47, and the zodaical
12; making in the whole 96. The number of the
ancient constellations was only 48.
The following tables contain the names of all the constel-
lations, and the principal stars in each, with their magnitudes
marked 1, 2, 3, &c. By adding together the number of stars
in the first column of the tables, the total will be ſound to be
3457; of this number there are only 19 of the first magni-
tude, and 422 cannot be seen at London. The figures on the
left hand of the tables show the number of stars in each con-
stellation, from Flamstead's catalogue; R. denotes right as-
cension; D declination of the middle of the several constel-
lations, for the ready finding them on the celestial globe.
The modern constellations are distinguished from the
ancient by an asterisk or star (*). .#
156
GRAMMAR OF ASTRONOMY.
JNames of the constellations, and of the principal stars
66.
141.
85.
83.
95.
110.
51
66. Andromeda, Mirach 2, Almaach 2, 15
71. Aquila, the Eagle, with Antinúus, Altair
g or Atair 1, 295
25. Asterion et Chara,” vel Canes Wenatici,
$ the Greyhound, - 200.
66. Auriga, the Charioteer or Wagoner, Ca-
s pella 1, . . . . . 75
54. Boötes, Arcturus 1, Mirach 3, g 212
58. Camelopardalus,” the Camelopard, 68
59. Caput Medusae, the Head of JMedusa, and
f Perseus, - . 44
55. Cassiopeia, the Lady in her Chair, Sche-
; dar 3, - 12
85. Cepheus, Alderamin 3, ' " 338
– Cerberus,” the Three-headed Dog, and
'Virgo, the Virgin, Spica Virginis, 1
- § 5 © 5 e Sºo f = 2
. Libra, the Balance, Zubernick Meli 2, 226
44. *
69.
51.
108.
113.
in each, with their magnitudes.
I. ConstELLATIONS IN THE ZODIAC.
- ‘, - R.
Aries, the Ram, Arietis 2, . . . . 30
Taurus, the Bull, Aldebaran 1, the Plei- *
ades, the Hyades, 65
Gemini, the Twins, Castor 1, Pollux 2, 111
Cancer, the Crab, Acubene 4, - 128
Leo, the Lion, Regulus or Cor Leonis 1,
Deneb 2, -
Wendemiatrix 2, .
Scorpio, the º Antares 1, 244
Sagittarius, the flrcher, . . . . 285
Capricornus, the Goat, : 310
Aquarius, the Water-bearer; Scheat 3, 335
Pisces, the Fishes, s 5
150
D
22 N.
1
5.
N
1:
i
i
II. THE NoFTHERN ConstELLATIONs."
35 N.
8 N.
40 N.
45 N.
20 N.

70 N.
40 N.
60 N.
65 N.
22 N
Hercules, ‘. . . - 271
43. Coma Berenices, Berenice's Hair, 185
3. Cor Caroli,” Charles’s Heart, 191
26 N
39 N
OF THE CELESTIAL GLOBE.
l
5
7
. . . . . * R. D
21. Corona Borealis, the JNorthern Crown, .
Alphacca 2, . - 235 30 N.
81. Cygnus, the Swan, Deneb Adige 1, .308 42 N.
18. Delphinus, the Dolphin, 308 15 N.
80. Draco, the Dragon, Rastaben 2, . . 270 66 N,
0. Equulus, the Little Horse, . . . .316 -5 N.
113. Hercules, vide Cerberus, Res Algethi 3, 245 22 N.
16. Lacerta,” the Lizard, 336 43.N.
53. Leo Minor,” the Little Lion, 150 35.N.
44. Lynx,” the Lyna, 111° 50 N.
22. Lyra, the Harp, Vega or Wega I, 283.38 N.
11. Mons Moenalus, the JMountain JMaenalus, 225 5 N.
6: Musca,” the Fly, ... . 40 27 N.
89. Pegasus, the Flying Horse, Markab 2, . e
Scheat 2, , - . -- . 340 14 N.
—. Perseus, vide Caput Medusae, Algenib 2,
Algol 2, - 46 49 N.
18. Sagitta, the Arrow, 295 18 N.
8. Scutum Sobieski,” Sobieski’s Shield, 275 10 S.
64. Serpens, the Serpent, - : 235 10 N.
74. Serpentarius, the Serpent Bearer, Ras
Alhagus 2, ſº 260 13 N. '
7. Taurus Poniatowski,” the Bull of Ponia-
towski, t 275 7 N.
11. Triangulum, the Triangle, - - 27 32 N.

5. Triangulum Minus, the Little Triangle, 31 29 N.
87. Ursa Major, the Great Bear, Dubhe 1,
Alioth 2, Benetnach 2, . -
* * 153 60 N.
24. Ursa Minor, the Little Bear, Polar Star,
* or Alrukabah 2, . 235 75 N.
37. Vulpecula et Anser,” the Foa and Goose, 300 25 N.
10...Tarandus," the Reindeer, w 30 75 N.
To the preceding list of northern constellations, modern
astronomers have also added Le Messier, Taurus Regalis;
Frederick's Ehre, Frederick’s Glory; and Tubus Herschelii
Major, Herschel’s Great Telescope. . .
14
158
GRAMMAR OI! ASTRONOMY.
11.
9.
64.
3.
31.
f4.
35.
'97.
10:-
4.
10.
12.
31.
6.
7.
S.
84.
14.
13.
12.
60.
10.
19.
19.
24.
3.
| 0.
31.
30.
4.
12.
43.
19.
78.
14.
13.
III. SouTHERN ConstellATIONs.
Apus vel Avis Indica," the Bird of Pe.
radise, &
Ara, the Jältar, . e * *
Argo Navis, the Ship ſlºgo, Canopus 1,
Sº,
of Brandenburgh,” •
Canis Major, the Great Dog, Sirius 1,
Canis. Minor, the Little Dog, Procyon 1,
Centaurus, the Centaur,
Cetus, the Whale, Mencar 2, .
Chamaeleon,” the Chanieleon, . . . .
Circinus,” the Compasses,
Columba Noachi,” JNoah's Dove,
Corona Australis, the Southern Crown,
Corvus, the Crow, Algorab 3, *
Crater, the Cup or Goblet, Alkes 3,
Crux,” the Cross, .
Doroda, or Xiphias,” the Sword Fish,
Equuleus Pictorius," the Painter's Easel,
lºridanus, the River Po, Achernar 1, .
Formax Chemica,” the Furnace,
Grus,” the Crame, -
Horologium,” the Clock, -
Hydra, the Water Serpent, Cor Hydra 1,
Hydius,” the Waley Snake, • ‘
Indus,” the Indian,
Lepus, the Hare,
lupus, the Wolf,
Machina Pneumatica,” the flir Pump,
Microscopium,” the JMicroscope,
Moneceros,” the Unicorm,
Mons Mensae,” the Table JMountain,
Brandenburgium Sceptrum, the Sceptre
Musca Australis, vel apis,” the Southern
|Fly or Bee,
Norma vel Quadra Euclidis,” Euclid's.
Square, * *
Octans Hadleianus,” Hadley’s Octant,
Officina Sculptoria,” the jº. Shop,
Orion, Betelguez 1, Rigel 1,
Pavo," the Peacock,
Phoenix, *
ellatrix 2,
25%
255
115.
67
105
| 10
200
25
I75
222
S5
278
185
168
183
75
S4
60
42
330
40
139
, 28
315
S0
230
150
315
110
76
75 S.
55 S
50 S .
15
20 S.
5
50
19
7S S.
64
35
40 S.
15
15
60
69.
55
10 S.
30
45
60
S
6S
55
18
45
39
35
00
72
68 S.
45 S.
S0 S.
98 S.
00. S.
68 S,
50 S.
of THE CELESTIAL GLoBE. 159
... ' - D.
24. Piscis Notius, vel Australis, the Southern
Fish, Fomalhaut 1. . 335 30 S
8. Piscis Wolans," the Flying Fish. . . . . 127. 68 S
16. Praxiteles, vel cela Sculptoria,” the En-
graver's Tools. * * • 68 40 S.
4. Pyxis Nautica,” the JMariner's Compass. 130, 30 S.
10. Reticulus Rhomboidalis,” the Rhomboidal . -
JNet. * , we - 6%. 62 S.
12. Robur Caroli,” Charles’s Oak. 159 50 S.
41. Sextans,” the Sea:tant. ... 145 00 S
9. Telescopium,” the Telescope. . . . 278 50 S
9. Touchan,” the filmérican ãº. 359 66 S.
5. Triângulum Australis,” the Southern Tri-.
angle. . . " g . . 238 .65 S
—Xiphias,” Wide Dorado. • * , . 75' 62 S.
Modern astronomers have also added to the preceding list
of southern constellations, Solitaire, an Indian. Bird; the
Georgian Psaltery or Harp; . Tubus Herschelii Minor,
Herschel's Less Telescope;. JMontgolfier’s Balloon; the Press
of Guttenberg; the Cat, &c. . . . . . • *
QUESTIONs.

What are fixed stars 2 tº g
What are planets, and how are they distinguish-
ed from the fixed stars 2 tº
. How are the fixed stars classed, and what are
telescopic stars 2 &
How many stars are supposed to be visible to
the naked eye at one time ! -
What is the poetical rising and setting of the
stars called 2 . " g - *
What is the zodiac 2 . - *
What is a constellation, and what are the un-
formed stars 2 . . .
How are particular stars distinguished 2 .
How are the stars of each constellation distin-
guished 2 .. - • . .
What is the milky way, and what is a nebulous
star 2. . . .
160 GRAMMAR of ASTRONOMY.
Into how many classes are the constellations
divided ? Name the zodaical constellations. Name
the morthern and southern constellations.
CHAPTER III. .
Of the zodaical constellations, and fables relative to
. . . . them. . . . . .
~ - a
1. If the twelve zodaical constellations, there
are five stars of the first mágnitude, called ſilde-
barán, Castor, Regulus, Spica Virginis, and flntares; ,
and five remarkable stars of the second magiii-
ſtude, called ſlrietis, Pollua, Deneb, Windemiatſia,
and Zuberich JMeli. Thé Pléiades and the Hyades
are also in these constellations.
The constellations in the zodiac, which now seem so
whimsical and uncouth, were not however the offspring of
unsystematic fancy; they appear to...have been intended to
relate to the motion of the sun, or to signify the state of the
earth at the different seasons of the year; the figures of
these constellations are supposed by astronomers to be
£gyptian or Chaldean hieroglyphics, intended to represent
Some remarkable occurrence, in each month. Among these
figures there are some that have, as it were, a common re-
lation to every portion of the globe, while others seem to.
relate to circumstances or events merely local. Thus, ºries .
is said to signify that the lambs begin to follow the sheep
about the time of the vernal equinox, when the sun enters
this sign; and that the cows bring forth, their young about
the time, he approaches the second, constellation, Taurus. .
The third sign, now called Gemini, was originally two kids,
and signified the time of the goats bringing forth their
young, which äre usually two at a time, while the former
(the sheep and the cow,) commonly produce only one.
The fourth sign, Cancer, an animal that goes sideways
OF THE CELESTIAL GLOBE. 16]
and backwards, was placed at the northern tropic, or that
point of the ecliptic where the sun begins to return back
again from the north to the southward. The fifth sign, Leo,
as being a furious animal, was thought to denote the heat
and ſury of the burning sun after he had left Cancer, and
entered the next sign Leo. The sixth sign, Virgo, received
the sun at the time of the ripening of corn, and the ap-
proach of harvest; which was aptly expressed by one of
the female reapers, with an ear of corn in her hand.
The next sign, Dibrü, evidently denotes the equality of
days and mights, which takes place at that season; and
Scorpio, the next sign in order, the time of gathering in the
fruits of the earth, which being generally an unhealthy sea-
son, is represented by this venomous animal, extending his
long claws, threatening the mischief which is to follow.
The fall of the leaf was the season of the ancient hunt-
ing; and for this reason the constellation Sagittarius repre-
sents a huntsman with his arrows and his club ; the
weapons of destruction employed by huntsmen at that time.
The reason of the goat being chosen to mark the farthest
south point of the ecliptic, is obvious enough, for when the .
sun has attained his extreme limit in that direction, he be-
gins to return, and mounts again to the northward, which is
very well represented by the goat, an animal which is al-
ways found climbing and ascending some mountain as it
browses. As the winter has always been considered a wet
and uncomfortable season, this was expressed by Jīquarius,
the figure of a man pouring out water from an urn.
. The last of the zodaical constellations was Pisces, a
couple of Fishes tied together, which had been caught,
which signified that the severe season was over, and though
the flocks did not yield their store, yet the seas and rivers
were open, and fish might be caught in abundance.
2. Although these signs might have served to
distinguish the seasons of the year when they were
first formed, or employed for that purpose, yet
this is not altogether the case at the present day.
For owing to the retrograde motion of the equi-
noctial points, the constellations of the zodiae
have now so far changed their positions, as to be
found more than a sign advanced.
- - 1.4%
162 GRAMMAR of ASTRONOMY.
The constellation Aries, for example, is now three or
four degrees within the sign Taurus, or the first point of
Aries, which used to coincide with the vernal equinoctial
point, is now about thirty-four degrees farther advanced;
however, the first point of the sign Aries still continues to
be reckoned from the equinoctial point. The signs of the
zodiac must therefore now be distinguished from the con-
stellations, the signs merely being ideal, and serving only
to designate the course of the sun in the ecliptic, while the
constellations continue to signify a group or cluster of stars
designated by a particular name.
3. ARIES : Arietis, a star of the 2nd magnitude,
8 of the 3d, and two stars of the 4th, are the prin-
*
cipal stars which form this constellation.
Jłries is thought by some to be the ram with the golden
fleece, that carried Phryxus and Helle through the air on his
back, when they fled from their father Athamus, who was
going to immolate them, at the instigation of their step-
mother ſno. Helle, in this ačrial passage, fell into the
Hellespont, where she was drowned. .
Phryxus continued his flight, and arrived safe at Colchis,
an ancient country of Asia, east of the Black Sea, now Min-
grelia, Guriel, and a part of Georgia; where he sacrificed
the ram to Mars, the god of war. The fable of the flight
of Phryxus from Boeotia to Colchis, on a ram, has been ex-
plained by some, who observe, that the ship in which he
embarked was called by that name, or carried on her prow
the figure of that animal, which ensign may probably be
called the golden ram. ” -
The fleece of gold is explained by the immense treasures
which he carried from Thebes. He was afterwards murder-
ed by his father-in-law AEtis, which gave rise to a celebrated
expedition which was achieved under Jason and many of
the princes of Greece, and which had for its object the re-
covery of the golden fleece, and the punishment of the king
of Colchis for his cruelty to the son of Athamus. -

4. TAURUs : Aldabaran, a star of the first mag-
nitude, the Pleiades, and the Hyades, are in this
constellation. Seven remarkable stars in the
neck of Taurus, are called the Pleiades; there are
now only six of these stars visible to the snaked
OF THE CELESTIAL GLOBE. 163
eye, the largest of which is of the 3d magnitude,
and called Lucido Pleiadum. Five stars in the
face of Taurus are called the Hyades. t -
Taurus is supposed by some to be the animal under the
figure of which. Jupiter carried away Europa, the daughter
of Agenor, king of Phenicia, to the island of Crete. As it
was the custom of the ancients to have images on their
ships, both at the head and stern, the first of which was
called the sign, from which the ship was named, and the
other was that of the tutelar deity to whose care the ship
was committed; it is supposed by some that this circum-
stance gave rise to the ſable, that Europa was carried away
by Jupiter under the figure of Taurus. Some supposed that
Europa lived about 1552 years before the Christian era. See
the history of Europa in Lempriere's Classical Dictionary.
5. GEMINI : In this constellation are two re-
markable stars called Castor and Polluſc, the for-
mer is of the first, and the latter of the second
magnitude. f -
Castor and Pollux were the sons of Jupiter by Leda, the
wife of Tyndarus, king of Laconia. They embarked with
Jason to go in quest of the golden fleece, and both behaved
with superior courage. During the Argonautic expedition,
in a violent storm, a flame of fire was seen to play around
the head of each of them, and immediately the tempest
ceased; from this occurrence their power to protect sailors
has been credited; and the two fires, which are very com-
mon in storms; have since been called Castor and Pollux.
These brothers cleared the Hellespont, and the adjacent
seas, of pirates; on which account they have always been.
deemed the friends of navigation. The appearance of these
stars together was, according to many ancientwriters, thought
favourable to mariners; and therefore for a good omen, they
had them carved or painted on the head of the ship, and gave
it a name from thence. The Alexandrian vessel in which
Paul sailed from Melita or Malta, to Syracuse in Sicily, had
for its sign, and consequently its name, Castor and Pollux.
6. CANcen: There are no stars of the first three
magnitudes in this constellation, and therefore it is
less remarkable than any other in the zodiac.
164 GRAMMAR OF ASTRONOMY.
This is supposed to be the sea-crab which Juno sent to
bite the foot of Hercules, while he ſought the serpent
Hydra, in the lake of Lerna, which was situated near Argos
in the Peloponnesus. This new enemy was soon dispatch-
ed; and Juno,.unable to succeed in her attempts to lessen
the fame of Hercules, placed the crab, among the constella-
tions. *
LEo : Regulus of the 1st, and 8 or Denebola
of the 2nd magnitude, are the principal stars in this
constellation. There are also several remarkable
stars of the 3d magnitude in Leo.
Leo is supposed to be the famous lion killed by Hercules
on mount Citheron, which preyed on the flocks of Amphi-
tryon, his supposed father, and which laid waste the adjacent
country. Others suppose it to be the Nemaan lion which
was sent by Juno against Hercules; being slain by this hero,
the goddess placed the animal among the constellations.
8. WIRGo : Spica Virginis of the 1st, and Vin-
demiatria of the 3d magnitude, are the principal
stars in this constellation. - &
This constellation is supposed to take its rise from the
Virgin Astraea, the goddess of justice. She lived upon the
earth, as the poets mention, during the golden age ; but the
wickedness and impiety of mankind drove her to heaven in
the brazen and iron ages, and she was placed among the
constellations under the name of Virgo. She is represented
as a virgin, with a stern but majestic countenance, holding a
pair of scales in one hand, and a sword in the other. Some,
however, maintain that Erigone was changed, into the
constellation Virgo. Her father Icarius, an Athenian,
perished by the hands of some shepherds, whom he had
intoxicated with wine. When Erigone heard of her father’s
death, she hung herself, and was afterwards changed into
ro
the constellation Virgo.
9. LIBRA : cº, or Zubemelchamali of the 2nd
magnitude, is the principal star in this constella-
tion.
Libra is supposed to be the balance of Astraca, with which
that goddess is always painted; hence this constellation is
of THE CELESTIAL GLOBE. 165
called by Virgil, “Astraa's balance.” others suppose that
Jupiter made Themis the goddess of love and justice, and
placed her balance among the constellations. -
10. Scorpio : Antares of the 1st, and 8 of the
2nd magnitude, are the principal stars in this con-
stellation. . . . . . . . . . . . .
This is supposed to be the Scorpion which stung to death .
the boasting hunter Orion; on account of which, Jupiter
placed the Scorpion among the constellations. . •
According to Ovid, this serpent was produced by the earth,
to punish Orion for his vanity in boasting that there was not
on earth any animal which he could not conquer.
11. Sagittarius: There are no stars of the
1st or 2nd magnitude in this constellation,
It is supposed that Sagittarius took its name from Ghiron,
the famous Centaur, who had changed himself into a horse,
to elude the jealous inquiries of his wife Rhea. . . . .
Chiron was famous for his knowledge of music, medicine,
and shooting. He taught mankind the use of plants and
medicinal herbs; and instructed in all the polite arts the
greatest heroes of his age. He taught Æsculapius physic;
Apollo music; Hercules astronomy; and was tutor to Achil-
les. Being accidentally wounded by Hercules with a
poisoned arrow, and the wound being incurable, and the
cause of excruciating pains, Chiron begged of Jupiter to
deprive him of immortality. His prayers were propitious,
and he was therefore placed by that god among the con-
stellations of the zodiac; under the name of Sagittarius, the
Archer. Some, however, assert that. Crocus, a famous
hunter, (not the youth mentioned by Ovid, who, for love of
the nymph Smilax, was changed into a flower,) was, at the
request of the Muses, metamorphosed into this sign.
12. CAPRICORNUs: In this, constellation, there
are no stars of the first or second magnitude; nor
any remarkable star of the third. . . . .
Capricornus is supposed to be Pan, the god of shepherds,
of huntsmen, and of all the inhabitants of the country, who,
166. GRAMMAR. Ol' ASTRONOMY
fleeing from the giant Tiphon into the river Nile, transform-
ed himself into a sea-goat, upon which account Jupiter pla–
ced him among the constellations. Others suppose this con-
stellation to be the goat'Amalthea, which fed Jupiter with
her milk. . . . . . . . ."
. . . 18. AQUARIUs; Scheat of the third magnitude,
is the principal star in this constellation. .
Aquarius is supposed to be the famous Ganymede, a
beautiful youth of Phrygia, son of Tros, king of Troy.
He was taken up to heaven by Jupiter, under the figure of
an eagle, as he was tending his father's flock on Mount Ida;
and he became the cup-bearer of the gods, in place of
Hebe, the goddess of youth, who had been dismissed from
this office by Jupiter, because she ſell down a little disor-
derly as:she was pouring nectar at a grand festival.
14. Pisces: ‘In this constellation there is only
one star of the 3d, and none of the 1st or 2nd mag-
nitude. . . . . . . . . . . . . .
These are said to be the fishes into which Venus and her
son Cupid transformed themselves, to avoid the fury of Ty-
phon-when he assailed heaven. There are various other
opinions relating to this constellation, , See Francoeur's
Uranographia, or Traite Elementaire D'Astronomie.
QUESTIONS.
How many stars, of the first magnitude are there
in the zodaical constellations, and whāt are they
called 2 . . . . . . . . . . . . . . . . .
What effect has the recession of the equinoctial
points, upon the constellations of the zodiac 2 Name
the circumstances. ' ' ' . . . . . . .
Of what magnitude are the principal stars in
Aries, and what are they called 2 . . . .
"Of what magnitude are the principal stars in
W
Taurus, and what are they called?
OF THE CELESTIAL, GLOBE. 167
Of what magnitude are thé principal stars in Ge-
mini, and what are they called 2 .
Of what magnitude is the most remarkable star
in Cancer, and what is its name 2 . . *
Of what magnitude are the principal stars in
Leo, and what are they called 2 -
Of what magnitude are the principal stars in
Virgo, and what are they called 2
What is the most remarkable star in Libra
called 2 . . . . . * ,
Of what magnitude are the principal stars in
Scorpio, and what are they called 2
Are there any remarkable stars in Sagittarius 2
Of what magnitude is the principal star in Aqua-
rius, and what is it called ! t - . .
Of what magnitude is the principal star in
Pisces 2 * * -
!
* Nº || ||
***
CHAPTER III.
Of the northern constellalions, and fables relative to
them. -
1. In the northern constellations, which are
thirty-seven in number, there are six remarkable.
stars of the first, twelve of the second, and three
of the third magnitude. g
The names of the northern constellations and of the
most remarkable stars in each, are given in the second table
of the preceding Chapter. The student should commit
those namies to memory. &
168 GRAMMAR of ASTRONOMY.
2. ANDromeda: JMirach and filmaach both or
the second magnitude, are the principal stars in
this constellation.
Andromeda is represented on the celestial globe by the
figure of a woman almost maked, having her arms extended,
and chained by the wrist of her right arm to a rock. She
was the daughter of Cepheus, king of Æthiopia, who in or—
der to preserve his kingdom, was obliged to tie her naked
to a rock, near Joppa, now Jaffa, in Syria, to be devoured
by a sea monster; but she was rescued by Perseus, in his
return from the conquest of the Gorgons, who turned the
monster into a rock by showing it the head of Medusa.
She was made a constellation after her death, by Minerva.
The fable of Andromeda and the sea monster has been ex-
plained by supposing that she was courted by the captain
of a ship, who attempted to carry her away, but was pre-
vented by the interposition of another more successful rival.
3. Perseus: Algenib and Algol, both of the
2nd magnitude, are the principal stars in this con-
stellation. -
Perseus is represented on the globe with a sword in his
right hand, the head of Medusa in his left, and wings at his
ankles. Perseus was the son of Jupiter and Danāe, the
daughter of Acrisius. He was no sooner born, than he was
thrown into the sea with his mother Danie; but being
driven upon the coast of the island of Seriphos, one of the
Cyclades, they were found by a fisherman called Dictys,
and carried to Polydectes, the king of the place. They
were treated with great humanity, and Perseus was in-
trusted to the care of the priests of Minerva’s temple.
At a sumptuous entertainment given by Polydectes to his
friends, and to which Perseus was invited, he promised to.
bring that monarch the head of Medusa, the only one of the
Gorgons who was subject to immortality. To equip him for
this arduous task, Pluto lent him his helmet, which had the
wonderful power of making its bearer invisible; Minerva
the goddess of wisdom, ſurnished him with her buckler, which
was as resplendent as glass; and he received from Mercury
wings and the telaria, with a short dagger made of diamonds.
According to some, it was from Vulcan he received the
OF THE CELESTIAL GILOBE, 169
telaria, or Herpe, which was in form like a scythe. Thus
equipped, he cut off the head of Medusa, and from the blood
which dropped from it in his passage through the air, sprung
innumerable serpents which have ever since invested the
sandy deserts of Lybia. . . . - ~ *
Diodorus and others explain the fable of the Gorgons, by
supposing that they were a warlike race of women near
Amazon, whom Perseus, with the help of a large army, to-
tally destroyed.' ' t \ g
The Abbe Bannier is of opinion that the Gorgons dwelt
in that part of Lydia which was afterwards called Cyrenai-
ca. He makes their father Phorcys to have been a rich and
powerful prince, and engaged in a lucrative commerce.
Perseus, he supposes, made himself master of a part of his
fleet, and some of his riches, &c., See Lemprier’s Classical
Dictionary, Anthon's Ed. -

4. AURIGA : Capella, a very remarkable star of
the first magnitude, and 8 of the 2d, are the princi-
pal stars in this constellation. - -
Auriga is represented on the celestial globe, by the figure
of a man in a kneeling or sitting posture, with a goat and
ber kids in his left hand, and a bridle in his right. w
The Greeks give various accounts of this constellation;
some suppose it to be Erichthonius, the fourth king of Athens,
and son of Vulcan and Minerva; he was very deformed,
and his legs resembled the tails of serpents; he is said to
have invented chariots, and the manner of harnessing horses
to draw them. Others say that Auriga is Mirtilus, a son of
Mercury and Phoetusa; who was charioteer to OEnomaus,
king of Pisa in Elis, and so experienced in riding and the
management of horses, that he rendered those of CEnomaus
the swiftest in all Greece. But as neither of those fables
seems to account for the goat and her kids, it has been sup-
posed that they refer to Amalthoea, daughter of Melissus,
king of Crete, who, in conjunction with her sister Melissa,
fed Jupiter with goat’s milk. C.
5. URSA MAJoR : In the Great Bear, there are
seven very conspicuous stars, four of which, o, 8, 7.
and 6, form a trapezium, in the body; and the other
three, s, 3 and n, make a curve line in the tail of that
15
170 GRAMMAR OF ASTRONOMY.
animal, of which the first two are the continuation of
the diagonal 86 of the trapezium. These seven stars,
according to FRANCOEUR, are all of the second
magnitude, (except 6, which is of the third;) but,
according to some other writers, & named Dubhe
is of the first; a fllioth, & JMizar, n Benetnach, 8,
and y, are of the second; and 6 of the third mag-
nitude. -
Ursa JMajor is said to be Calisto or Helice, who was
daughter of Lycaon, king of Arcadia, and one of Diana’s
attendants. Jupiter seduced her under the shape of Diana;
and Juno in revenge changed her into a she bear; but the
god, fearful of her being hurt by the huntsmen, made her a
constellation of heaven. Ursa Major is well known to the
country people at this day, by the title of the plough, which
it resembles; it is also called in some places Charles's wain,
because the ancients represented this constellation under the
form of a waggon drawn by a team of horses.
6. URSA Minor : In this constellation there are
also seven stars, forming a figure like those of the
Great Bear, but both the figure arid the stars are
considerably less. The figure of the Lesser Bear
is also situated in a contrary position, with respect
to that of the Great Bear. The principal star in
Ursa Minor is called Alruccabah, or the pole star;
which is situated in the tip of the tail.
Ursa Minor is said to be Arcas, the son of Jupiter and
Calisto. He nearly killed his mother, whom Juno had chang-
ed into a bear. He reigned in Pelasgia, which from him was
called Arcadia, and taught his subjects agriculture. After
his death, Jupiter made him a constellation with his mother.
Some consider Arcas the same as Böotes. * *.
7. Bootes: Arcturus, one of the brightest stars
of the first magnitude, and JMirach of the third, are
the principal stars in this constellation.
OF THE CELESTIAL GLOBE. 171
Bootés Is Supposed to be Arcas, a son of Jupiter and Ca-
listo, (see Ursa Major and Ursa Minor.) Bootes is repre-
sented as a man in a walking posture, grasping in his left
hand a club, and having his right hand extended upwards,
holding the cords of the two dogs Asterion and Chara, which
seem to be barking at the Great Bear; hence, he is some-
times called the bear-driver, and the office assigned him is
to drive the two bears round the north pole. -
8. DRAco : There are four stars of the second
magnitude in this constellation, the most remark-
able of which, called Rastaben, is situated in the
tail, nearly in a line, between y of the Little, and
f
Mizar of the Great Bear.
The Greeks give various accounts of this constellation;
by some it is represented as the watchful dragon which
guarded the golden apples in the garden of Hesperides, near
Mount Atlas in Africa, and was slain by Hercules, being his
eleventh labour. Juno, who presented those apples to Ju-
piter on the day of their nuptials, took Draco up to heaven,
and made a constellation of it as a reward for its faithful ser-
vices. Those, who attempt to explain mythology, observe
that the Hesperides were three sisters, who had an im-
mense number of flocks; and that an ambiguous Greek word
which signifies an apple, and a sheep, gave rise to the golden
apples of these gardens. . It is also asserted that Draco was
their shepherd. . . . . . - :
9. CEPHEUs : The principal star in this constel-
lation is Alderamin of the third magnitude.
Cepheus was a king of Ethiopia, and the father of Andro-
meda. He was one of the Argonauts who went with Jason.
to Colchis to fetch the golden fleece. -
10. Cassiopeia: Schedar of the third magnitude
is the principal star in this constellation. . . .
Cassiopeia, or the Lady in her Chair, was the wife of Ce-
pheus, and the mother of Andromeda. She boasted that she
was fairer than the Nereides. Neptune, at the request of
those despised nymphs, to punish her insolence, sent a huge
sea monster to ravage Ethiopia, the country where she re-
sided; and the wrath of the god could only be appeased by
172 GRAMMAR OF ASTRONOMY.
exposing Andromeda, whom Cassiopeia tenderly loved, to
the fury of the beast. (See ſindromeda and Perseus.)
11. HERCULES: Ras Algethi of the third mag-
nitude is the principal star in this constellation.
Hercules is represented on the celestial globe with a club
in his right hand, the three headed dog, Cerberus, in his left,
and the skin of the Nemacan lion thrown over his shoulders.
This Hercules, generally called the Theban, was the son of
Jupiter and Alcmena, and reckoned the most famous hero
of antiquity. He was a scholar of Chirom, and accompanied
Jason in the Argonautic expedition. - |
12. CERBERUs : There are no remarkable stars
In this constellation. sº s
... Cerberus was a dog belonging to Pluto, the god of the in-
fernäl regions; this dog had fifty heads according to Hesiod,
and three according to other mythologists: he was stationed,
at the entrance of the infernal regions, as a watchful keeper,
to prevent the living from entering, and the dead from es-
caping from their confinement. The last and most danger-
ous exploit of Hercules, was to drag Cerberus from the in-
fernal, regions, and bring him before Euristheus, king of
Argos. * º . . . . -
13. LyFA: Lyra or Wega, of the first, and 8 a
quadruple star of the third magnitude, are the prin-
cipal stars in this constellation. . . . . .
Lyra, the harp, was at first a tortoise, afterwards a lyre,
because the strings of the lyre were originally fixed to the
shell of the tortoise; it is asserted that this is the lyre which
Apollo or Mercury gave to Orpheus, and with which he de-
scended the infernal regions in search of his wife Euridice.
He played upon it with such a masterly hand, that even the
most rapid rivers ceased to flow; the savage beasts of the
forests forgot their ferocity; the mountains came to listen to
his song, and all nature seemed animated. Orpheus, after
death, received divine honours; the Muses gave an honour-
able burial to his remains, and his Lyre became one of the
constellations. " * . -
14. PEGASUs : JMarkab and Scheat both of the
second, and Algenib of the third magnitude, are the
principal stars in this constellation.
(JF THE CELESTIAL GLOBE. 173
Pegasus was a winged horse, sprung from the blood of
Medusa, after Perseus had cut off her head. Pegasus fixed
his residence, according to Ovid, on Mount Helicon in
Boetia, where, by striking the earth with his foot, he pro-
duced a ſountain, called Hippocrane. He became the
favourite of the Muses, and being afterwards tamed by
Neptune or Minerva, he was given to Bellerophon to con-
quer the Chimaera, a hideous monster that continually vo-
mited flames, which had three heads, that of a lion, a goat,
and a dragon. * º -
This fabulous tradition is explained by the recollection
that there was a burning mountain in Lycia, called Chi-
maera, whose top was the resort of lions, on, account of its
desolate wilderness; the middle, which was fruitful, was co-
vered with goats; and at the bottom, the marshy ground,
abounded with serpents; and that Bellerophon was the first
who made his habitation on it. Pegasus was placed among
the constellations by Jupiter. -
15. CYGNUs: Deneb ſldige of the first, Alberto
of the second, and two stars that sometimes are in-
visible, at other times of the third magnitude, are
the most remarkable stars in this constellation.
Cygnus is fabled by the Greeks to be the swan, under the
form of which Jupiter deceived Leda, or Nemesis, the wiſe
of Tyndarus, king of Laconia. Leda was the mother of
Pollux and Helena, the most beautiful woman of the age,
and who was the cause of the Trojan war, and also of Castor
and Clytemnestra. The former two were deemed the offspring
of Jupiter, and the others claimed Tyndarus as their father.
16. CoRoNA BoreALls: Alphacea of the second
magnitude, is the principal star in this constellation.
Corona Borealis is said to be the crown of seven beautiful
stars given by Bacchus, the son of Jupiter, to Ariadne, the
daughter of Minos, second king of Crete. Bacchus is said
to have married Ariadne, after she was basely deserted by
Theseus, king of Athens, and after her death, the crown that
Bacchus had given her, was made a constellation.
17. TRIANGULUM : This constellation is formed
by three stars of the fourth magnitude, situated be-
tween the feet of Andromeda and Aries. *
1.5%
174 GRAMMAR OF ASTRONOMY.
Triangulum, or the northern triangle, was placed in the
heavens in honour of the most fertile part of Egypt, being
called the delta of the Nile, from its resemblance to the
Greek letter of that name A. The Nile, anciently called
CEgyptus, flows through the middle of Egypt, in a northerly
direction, and when it comes to the town of Cercassorum,
it divides itself into several streams, and falls into the Me-
diterranean by seven channels or mouths'; and the island
which these several streams form, is called delta.
The invention of geometry is usually ascribed to the
Egyptians, and it is asserted that the annual inundations of
the Nile, which swept away the bounds and landmarks of
estates, gave occasion to it, by obliging the Egyptians to
consider the figure and quantity-belonging to the several
proprietors. Thiangulum JMinus was made by Hevelius,
out of the unformed stars between the Triangulum Borealis
- } *
and the Head of Aries.
18. AQUILA, with ANTINous: Altair or ſitair,
of the first magnitude, is the principal star in this
constellation. +
Jīquila is supposed to be Merops, a king of the island of
Cos, one of the Cyclades; who, according to Ovid, was
changed into an eagle and placed among the constellations.
Jłntinous, was a youth of Bythinia, in Asia Minor, a great
favourite of the emperor Adrian, who erected a temple to
his memory, and placed him among the constellations. An-
tinous is generally reckoned a part of the constellation
Aquila. - *
19. As TERIon Et CHARA : Cor Caroli a double
star of the third magnitude, is the principal star in
this constellation. -
.#sterion et Chara are the two greyhounds held in a string
by Bootes; they were composed by Hevelius out of the un-
formed stars of the ancient catalogues.
Cor Caroli, Charles’s Heart, is considered by some astro-
nomers to be an extra-constellated star of the second magni-
tude, between Coma Berenices and Ursa Major; and others
make it a constellation consisting of three stars. Cor Caroli
was so called in honour of Charles the First, by Sir Charles
Scarborough, physician to king Charles the Second. -
‘OF THE CELESTIAL GI, OBE. 175
20. CoMA BERENicEs: This constellation was
composed by Hevelius, out of the unformed stars
between the Lion’s tail and Bootes.
Berenice was the wiſe of Evergetes, a surname signifying
benefactor; when he went on a dangerous expedition, she
vowed to dedicate her hair to the goddess Venus if he return-
ed. in safety. Sometime after the victorious return of Ever-
getes, the locks, which were in the temple of Venus, disap-
peared; and Conon, an astronomer, publicly reported that
Jupiter had carried them away and made them a constella-
tion. + * *
21. SERPENTARIUs: Ras Alhagus of the second
magnitude, is the most remarkable star in this con-
stellation. r --
Serpentarius, also called Ophiuchus, and anciently OEscu-
lapius, was represented with a large beard, and holding in
his hand a staff, round which was wreathed a serpent; his
other hand was supported on the head of a serpent, CEscu-
lapius was physician to the Argonauts, and considered so
skilled in the medicinal power of plants, that he was called
the inventor as well as the god of medicine. Serpents were
more particularly sacred to him, not only as the ancient phy-
sicians used them in their prescriptions, but because they
were the symbols of prudence and foresight, so necessary
in the medical profession. ,
Serpens is also called serpens Ophiuchi, being grasped by.
the hands of Ophiuchus. . . . . . . . .
22. DELPHINUs: In this, constellation there are
five stars of the third magnitude, but none of the
first or second. 3. *:
The Dolphin was placed among the constellations by Nep-
tune, because, by means of a dolphin, Amphitrite became
his wife, though she had made a vow of perpetual celibacy.
23. CAPUT MEDUsie: Mons MENAEU's: Equu-
LUs : SAGITTA: There are no remarkable stars in
these constellations, except ºfflgol in the Head of
Medusa, which has already been observed in Per-
Seus, (Art. 3.) * *
§ 76 GRAMIMAR OF ASTRON ONLY.
The JMountain JMaenalus in Arcadia was sacred to the god
Pan, and frequented by shepherds: it received its name from
Maenalus, a son of Lycaon, king of Arcadia. It was made
a constellation and placed by Hevelius under the feet of
Böotes. . . . * * ~ * r
The Little Horse, sometimes called equisectia, the horse's
head, is supposed to be the brother of Pegasus. º *
The Arrow is supposed, by the Greeks, to be one of the
arrows of Hercules, with which he killed the eagle or vul
ture that perpetually gnawed the liver of Promotheus, who
was tied to a rock on Mount Caucasus, by order of Jupiter.
24. Camelopardalus, Lacerta, Leo JMinor, Lyna,
JMusca, Scutum Sobieski, Taurus, Poniatowski, Vul-
pelcula et Anser, and Tarandus, are all new con-
stellations, made out of the unformed stars of the
ancient catalogues. . . . .
The Camelopard was formed by Hevelius out of the un-
formed stars, between Auriga and the north pole. . . .
The Lizard was formed by Hevelius out of the unformed
stars, between the Flying Horse and the Head of Cepheus.
The Lesser Lion was composed by Hevelius out of the un-
formed stars between the Great Bear and Leo. - -
The Fly has been formed out of the stars between Aries
and the head of Medusa. ..
Sobieski’s Shield was made out of the unformed stars be-
tween the Archer and the tail of Serpentarius. This con-
stellation was called Sobieski’s Shield by Hevelius, in ho-
nour of John Sobieski, king of Poland,
The Bull of Poniatowski was so called in honour of Count
Poniatowski, a Polish officer of great merit, who saved the
life of Charles XII. king of Sweden, at the battle of Pul
towa, a town in Russia, and capital of the government of the
Saſſle. - - - - . , -
The For and Goose was made by Hevelius out of the un-
formed stars between the Flagle and the Swan. John Heve-
lius, a celebrated astronomer, and burgomaster at Dantzick,
was born in that city, in 1611. His wife, was also well
skilled in astronomy, and made a part of the observations
that were published by her husband.
The Rein Deer was made out of the unformed stars be.
tween Cassiopeia and the north pole. - -
JF THE CELESTIAL GI, OBE. . 177
... QUESTIONS.
In the thirty-seven northern constellations, name
the most remarkable stars of the first three magni-
tudes. - - 4. .
Of what magnitude are the most remarkable
stars in Andromeda, and what are they called 2
Name the principal stars in Perseus.
Name the most remarkable star in Auriga, the
Charioteer. -
How many conspicuous stars are there, in the
Great Bear 2 - • .
How many in the Îlesser Bear, and what is the
principal star called , “ . • * .
Which are the principal stars in Bootes ?
Of what magnitude are the most remarkable
stars in the Dragon, and what is the principal star
called 2 º
What is the principal star in Cepheus called 2-
Which is the principal star in Cassiopeia 2 .
Of what magnitude is the principal star in Her-
cules 2 - . .
Are there any remarkable stars in Cerberus?
Name the most remarkable star in the Harp.
Name the principal star in the Northern Crown.
Of what magnitude are those three stars which
form the Triangle 2
Name the principal star in the Eagle.
Name the principal stars in the Greyhounds.
Where is Berenice's Hair situated 2 -
Name the principal star in Serpentarius. - .
Of what magnitude are the principal stars in the
Dolphin 2 f . . . .
Are there any remarkable stars in the Head of
Medusa, the Mountain Maenalus, &c. 2 , * ,
sº
178 (3RAMIMAR OF ASTRONOMY.
Name some of the principal new constellations,
that have been composed out of the unformed stars,
in the northern hemisphere.
CHAPTER IV.
of the southern constellations, and fables relative to
- them. -
1. The Southern Constellations are 47 in num-
ber, besides afew new constellations that have lately
been added by Lemonnier, Bode, and other mo-
dern astronomers. * *
Besides the constellations in the Zodiac, the catalogue of
Ptolemy, (which is the first or earliest on record,) enume-
rates 15 constellations to the south of the equinoctial; but
these included only the visible part of the southern hemis-
phere, or such as came under the notice of the ancient as-
tronomers. The number of constellations, however, in-
creased as the knowledge of the stars became more exten-
sive ; and, at the same time, more stars were introduced,
into each constellation, as their positions became known.
For the names of the southern constellations, and of the
most remarkable stars in each, the student is referred to
Table III. Chapter II.
2. CETUs.: JMenkar of the 2d, Baten Kailos of
the 3d, and JMira, which is sometimes of the 2d and
at other times invisible, are the most remarkable
stars in this constellation. - -
Cetus, the Whale, is represented by the Greek poets as
the sea-monster which Neptune, brother to Juno, sent to
devour Andromeda, and which, as we have before stated,
was killed by Perseus,
JF THE CELESTIAL GLOBE. 179
3. ERIDANUs : Achernar, a star of the first mag-
nitude, which is not visible at the city of New-York,
is the principal star in this constellation. -
Eridanus, the river Po, called by Virgil the king of rivers,
was placed in the heavens for receiving Phaeton, whom Ju-
piter struck with thunder-bolts, when the earth was threaten-
ed with a general conflagration, through the ignorance of
Phaeton, who had presumed to be able to guide the chariot
of the Sun. According to those who explain this poetical
fable, Phaeton was a Ligurian prince, who studied astronomy,
and in whose age the neighbourhood of the Po was visited
with uncommon heats. He is generally acknowledged to
be the son of Phoebus and Clymene, one of the Oceanides.
The river Po is sometimes called Orion’s river.
4. OR1ON: Rigel and Betelguez, both of the first
magnitude, are the most remarkable stars in this
constellation. Bellatria and the three stars in
Orion’s belt, are also very conspicuous stars of the
second magnitude. So that Orion is composed of
a greater number of bright stars than any other
constellation in the heavens. - s -
Orion is represented on the celestial globe by the figure of
a man, with a sword in his belt, a club in his right hand,
and the skin of a lion in his left; he is said by some authors
to be the son of Neptume and Euryale, a famous huntress.
Orion was a celebrated hunter, superior to the rest of man-
kind, by his strength and uncommon stature; and he even
boasted that there was not any animal on the earth which he
could not conquer. Others say, that Jupiter, Neptune, and
Mercury, as they travelled over Boetia, met with great hospi-
tality from Hyrieus, a peasant of the country, who was ig-
norant of their dignity and character. When Hyrieus had
discovered that they were gods, he welcomed them by the
voluntary sacrifice of an ox. Pleased with his piety, the
gods promised to grant him whatever he required, and the
old man, who had lately lost his wife, and to whom he made
a promise never to marry again, desired them that, as he was
childless, they would give him a son without obliging him to
break his promise. The gods consented, and Orion was pro-
duced from the hide of an ox. Some authors, who explain
this fable, say that Orion was a great astronomer and a dis-
180 GRAMMAR OF ASTRONOMY.
ciple of Atlas. Others assert that the ſable respecting Orion
was a copy of the story of Abraham entertaining the three
angels, who came and foretold him the birth of a son, though
his wife was superannuated. (See Lemprier's Classical Dic-
tionary.) -> ' ' . . .
5. CANIs MAJoR: Sirius, usually called the Dog
Star, of the first magnitude, is the most remarkable
star not only in this constellation, but in the hea-
vens, being the largest and brightest, and therefore
considered the nearest to us or all the fixed stars.
There are also several other conspicuous stars
in this constellation. According to Francºur, the
stars marked 8, y, 6, 8, and n, are all of the Second
magnitude. - ; *.
Canis JMajor, the Great Dog, according to the Greek ſa-
bles was one of Orion's hounds. The Egyptians, who care-
fully watched the rising of this constellation, and by it judged
of the swelling of the Nile, called the bright star Sirius, the
centinel and watch of the year; and, according to their hie-
roglyphical manner of writing, represented it under the
figure of a dog. The Egyptians called the Nile Siris, and
hence, according to some mythologists, is derived the name
of their deity Osiris. The Abbe Bannier is of opinion that
Osiris is the same with Misraim, the son of Ham, who peo-
pled Egypt some time after the deluge, and who after his
death was deified; and he is called by the ancients the son
of Jupiter, because he was the son of Ham or Hammon,
whom he himself had acknowledged as a god.
6. CANIS MINor : Procyon of the first magni-
tude is the principal star in this constellation.
Canis JMinor, the Little Dog, according to the Greek ſa-
bles, is one of Orion’s hounds; but the Egyptians were most
probably the inventors of this constellation, and as it rises be-
fore the dog star, which, at a particular season was so much
dreaded, it is properly represented as a little watchful crea-
ture, giving notice of the other's approach; hence, the Latins
have called it Anti-canis, the star before the dog.
POPULAR ILLUSTRATION OF THE CONSTELLATION
CANIS MAJOR.
- - - -
-
- -
- -
- - -
- - -
-
-
-
-
- -
-
-
|
-
-
-
- -
º
º
-
º
º -
-
-
-- -
-
-
-
- - -
-
-
-


OF THE CELESTIAL, GLOBE. 18i
7. Hydra: Alphard or Cor Hydra, of the first
magnitude, is the principal star in this constellation.
Some authors assert that Cor Hydra is a triple star
of the second magnitude. -
Hydra is the water serpent which, according to poetic fa-
ble, infested the lake Lerna in Peloponnesus. This monster
had a great number of heads, and as soon as one was cut
off another grew in its stead: it was killed by Hercules.
The general opinion is, that this Hydra was only a multitude
of serpents which infested the marshes of Lerna.
8. ARGo NAvis : Canopus, of the first magni-
tude, is the principal star in this constellation.
Jłrgo JNavis, the ship Argo, is supposed to be the famous
ship which carried Jason and his companions to Colchis,
when they resolved to recover the golden fleece. The de-
rivation of the word Argo has been often disputed. Some
derive it from Argos, the person who first proposed the ex-
pedition, and who built the ship. Others maintain that it
was built at Argos, whence its name. Cicero calls it Argo,
because it carried Grecians, commonly called Argives.
9. PiscIs NotiUs: Fomalhaut, of the first mag-
nitude, is the principal star in this constellation.
Piscis JNotius, vel Australis, the Southern Fish, is sup-
posed by the Greeks to be Venus, who transformed herself
into a fish to escape from the terrible giant Typhon.
10. CENTAURUs : In this constellation there are
several bright stars. The two stars, marked a and
8, of the first magnitude, are the most remarkable,
but they are never visible at New-York. -
The Centauri were a people of Thessali, half men and
half horses. The Thessalians were celebrated for their skill
in taming horses, and their appearance on horseback was so
uncommon a sight to the neighbouring states, that at a dis-
tance they imagined the man and horse to be one animal.
When the Spaniards landed in America, and appeared on
horseback, the Mexicans had the same ideas. Centaurus,
the Centaur, is by some supposed to represent Chiron, the
Centaur; but as Sagittarius is likewise a Centaur, others
have contended that Chiron is represented by the constella
tion Sagittarius.
16
182 GRAMIMAR OF ASTRONOMY,
11. CRUx: There are four remarkable stars in
this constellation, forming a cross, by which mari-
ners, sailing in the southern hemisphere, readily
find the situation of the Antarctic pole, by means of
the stars a of the first, and y of the second magni-
tude, which nearly point in this direction.
Crua, the Cross, is a new constellation, and formed by
Royer, no doubt, in honour of that instrument on which the
Son of God redeemed mankind. The venerable Bede, in-
stead of the profane names and figures of the twelve zodai-
cal constellations, substituted those of the twelve apostles,
which example was followed by Schiller, who completed the
reformation, and gave scripture mames to all the constella-
tions in the heavens, in a work entitled Coelum Stellatum
Christianum, the Christian Starry Heaven, published in
1627. But the more judicious among astronomers never ap-
proved of these innovations, as they only tend to introduce
confusion into the science. The old constellations are there-
fore still retained, because better could not be substituted in
their place; and because they keep up the greater corres-
pondence and uniformity between the old astronomy and the
IneV.
12. Corvus : JAlgorab, of the third magnitude, is
the most remarkable star in this constellation.
Corvus, the Crow, was, according to the Greek fables,
made a constellation by Apollo. This god, being jealous of
Coronis, the daughter of Phlegyas and mother of Æsculapius,
sent a crow to watch her behaviour. The bird, perched on
a tree, perceived her criminal partiality to Ischys, the Thes-
salian, and acquainted Apollo with her conduct.
13. Crater, ſtra, Lupus, Lepus, and Corona flus-
tralis. See the table of the southern constellations
in Chap. II. - -

Crater, the Cup, according to the mythologists, is the cup
or pitcher of Aquarius. Alkes, of the third magnitude, is
the principal star in this constellation.
Jira, the Jältar, is supposed by some to be the altar on
which the gods swore, before their combats with the giants;
others assert that it was Apollo’s altar at Delphos. Three
stars of the third magnitude, under the tail of the Scorpion,
3re the principal stars which form this constellation,
OF THE CELESTIAL GLOBE. 1S3
Lupus, the Wolf, is supposed to be Lycaon, king of Ar-
eadia, celebrated for his cruelties. He was changed into a
wolf by Jupiter, because he offered human victims on the
altars of the god Pan. This constellation is composed of
several small stars towards the south-east of Antares in the
Scorpion. * -
Lepus, the Hare, is composed of four stars of the third
magnitude, near Rigel in Orion. The Hare, according to
the Greek ſables, was placed near Orion, as being one of
the animals which he hunted. ;
Corona flustralis, the Southern Crown, is composed of
three small stars below the constellation Sagittarius.
14. The Bird of Paradise, the Compasses, the
Chameleon, JNoah’s Dove, the Furnace, the Crane,
the Clock, the Water Snake, the Indian, the ſlir
Pump, the JMicroscope, the Table JMountain, the
Southern Fly or Bee, Euclid's Square, Hadley’s
Octant, the Sculptor’s Shop, the Phenia, the South-
ern Fish, the Flying Fish, the Engraver’s Tools,
the JMariner’s Compass, the Rhomboidal JN'et,
Charles’s Oak, the Seatant, the Telescope, the flme-
rican Goose, and the Southern Triangle, are all new
constellations, which were made by Bayer, Royer,
Hevelius, Dr. Halley, &c. out of the unformed
stars, and those stars in the Southern hemisphere
that were invisible to the ancient astronomers on
account of never appearing above their horizon.
As a great number of these constellations are never visible
at New-York, nor in any part of the United States, it is un-
necessary to take any farther notice of them here. They
may be readily found on the celestial globe, by means of the
table of southern constellations in Chap. II.
QUESTIONS
How many constellations are there between the
Zodiac and the south pole 2
Name the most remarkable stars in Cetus
Name the most remarkable star in Eridanus
J 84 * GRAMMIAR OF ASTRONOMY.
Name the most remarkable stars in Orion.
What is the brightest star in the heavens called,
and of what constellation is it the most remarkable
star 2 • , -
Of what constellation is Procyon the principal
star 2 & - -
What is the most remarkable star in Hydra
called 2
Name the principal star in Argo Navis.
Name the most remarkable star in the Southern
Fish. r t
Of what magnitude are the principal stars in the
Centaur 2 * - t
Of what magnitude are the principal stars in the
Cross 2
Name the principal star in the Crow !
Name the principal stars in the Cup, the Altar,
the Wolf, and the Hare.
Name the new southern constellations.
m
CHAPTER. vi.
On the position of the constellations, and principal
stars in the heavens.
1. In order to describe the position of the con-
stellations and principal stars that are visible in the
heavens, we shall first give a description of Ursa
Major, and then proceed to trace out the others, by
means of this constellation.
roPULAR illustra ATION OF THE CONSTELLATION:
URSA MAJOR.
H
E.
H

of THE CELESTIAL GLOBE. iš5
2. The Great Bear mever goes below the horizon
of places of considerable northern latitude; and,
therefore, it will have all possible situations in turn-
ing round the north pole. This is also one of the
most remarkable constellations in the northern he-
misphere, because it is composed of seven very con-
spicuous stars, which have already been described
in Art. 5. Chap. III. The two stars 8 and Dubhe,
in the body of the Great Bear, are called the guards,
or pointers, because an imaginary straight line pass-
ing through them, points to the north pole. And
the two stars 8 and y, in the body of Ursa Minor,
are sometimes called the guards, or pointers, of the
Little Bear. - .
3. Nearly in the direction of the pointers of the
Great Bear, and about five times the apparent dis-
tance between them, reckoning from Dubhe, is Al-
ruccabah, or the pole-star, in the tail of the con-
stellation Ursa Minor. -
4. Animaginary line passing from Dubhe through
7 in the opposite angle of the trapezium, which
forms the body of the Great Bear, will nearly in-
tersect Cor Caroli, an extra-constellated star of the
second magnitude in the neck of Chara, whose dis-
tance from the latter star is nearly double the dis-
tance between the former two. e
5. A straight line from Alioth, passing through
Cor Caroli, produced a little farther than the dis-
tance between them, will reach Windemiatrix, the
farthest northern star in the constellation Virgo.
Between Cor Caroli and Virgo is the constellation
Coma Berenices, or Berenice's Hair, so named
from its resemblance to hair. -
6. A straight line from Benetmach, in the tail of
the Great Bear, passing through Cor Caroli, and
extending downwards or towards the horizon about
16*
186 GRAMMAR OF ASTRONOMY.
double the distance between these two stars, will
reach Denebola, a star of the second magnitude,
in the tail of the constellation Leo ; and about 25
degrees to the west of Denebola, and about 3 de-
grees lower is Regulus, a star of the first magnitude,
in the heart of the Lion, and almost in the plane of
the ecliptic. - -
7. To the eastward of Denebola, at the distance
of about 35 degrees, is Arcturus, a remarkable star
of the first magnitude in the constellation Bootes.
Under Bootes is the constellation Virgo, in which
there is the very bright star, Spica Virginis, which
forms with Denebola in Leo and Arcturus in Bootes,
a very large equilateral triangle. -
8. A little to the south-west of Spica Virginis,
is the constellation Corvus, the stars of which form
a long trapezium, but none of them exceeds the
third magnitude. Algorab, the principal star, is
about 18 degrees from Spica Virginis. -
9. A line from Windemiatrix in Virgo, through
Arcturus in Bootes, will intersect Alphacca, a star
of the second magnitude, in the constellation Co-
roma Borealis, or the Northern Crown; the dis-
tance between Alphacca and Arcturus being nearly
equal to that between the latter and Windemiatrix.
This constellation is very conspicuous, the stars in
it being arranged in a circular form, somewhat re-
sembling a crown. A line passing from Regulus
through Spica Virginis, and extending an equal
distance beyond the latter, will reach Antares, or
Cor Scorpio, a star of the first magnitude in the
Scorpion’s heart. Between Scorpio and Virgo is
the constellation Libra, containing a number of
small stars; and to the south of Scorpio is the
constellation Lupus, which also contains a number
of THE CELESTIAL GLOBE. 187
of stars; but none of them exceeds the third or
fourth magnitude. * . -
10. Nearly in the line produced from Arcturus,
through the Northern Crown, and about twice the
distance between them, and beyond Alphacca, is
Vega, one of the brightest stars in the heavens, in
the constellation Lyra. In the line adjoining this
star and the guards of Ursa Minor, and about 15
degrees distant from the former, is Rastaben, a star
of the second magnitude in the constellation Dra-
co; and in the opposite direction from Vega, a
little to the east of the line, and about 34 degrees
distant, is Altair, a star of the first magnitude in the
Eagle. The stars Altair, Lyra, and Deneb, a star
of the second magnitude in the constellation Cyg-
nus, form nearly a right angled triangle, the right
angle being at Lyra. -
11. About 14 degrees north-east of Altair, is a
rhomboidal figure, formed by four stars in the con-
stellation Delphinus; and about 35 or 36 degrees
east of this figure, is the constellation Pegasus, in
which we will observe the bright star Scheat. About
13 degrees south of that is Markab, a star of the
second magnitude; 16 degrees to the east of Mar-
kab is Algenib, another star of the second magni-
tude, in the same constellation; and nearly 14
degrees east of Scheat is a star of the third magni-
tude, in the head of Andromeda. These four
stars form a square, usually called the square of
Pegasus.
12. A line from Scheat through Markab, at the
distance of 45 degrees from the latter, will nearly
intersect Fomalhaut in the Southern Fish, and
about 10 degrees south of the former, is the con-
stellation Pisces. To the west of the line joining
188 GRAMMAR OF ASTRONOMY.
the last two mentioned constellations, is Aquarius,
one of the zodaical constellations. -
13. A line from Deneb in the Swan, passing
through Markab, and distant from it about 41 de-
grees, will point out the second brightest star in
the constellation Cetus: and a line from the rhom-
boid already mentioned, in the Dolphin, through
Markab, at the distance of nearly 60 degrees from
this last star, will intersect Menkar, a star of the
second magnitude in the jaw of Cetus. About 37
degrees north of Menkar is Algol, the second star
in the constellation Perseus, which is one of those
stars that vary in brightness.
14. At the distance of about 27 degrees from
the star in the head of Andromeda, and a little to
the south of the line, joining it and Markab, is
Almaach, a star of the second magnitude in the
Southern foot of Andromeda: and about half way
between it and Markab, is Mirach, a star of the
second magnitude in the girdle of that constella-
tion. A little to the north of the same line, at the
distance of about 42 degrees, is Algenib, a star of
the second magnitude in the constellation Perseus.
The three stars Almaach, Algol, and Algenib,
form nearly a right angled triangle, Algol being at
the right angle. g
15. Between Mirach and Menkar, about 17 de-
grees from the former, is & Arietis, a tolerably bright
star of the second magnitude in the constellation
Aries, between which, and Almaach are the two
Triangles, and about 10 degrees south-east of the
Triangles is the small constellation Musca. To the
north-east of Menkar, about 26 degrees, and as
many south-east of Musca, is Aldebaran, a star of
the first magnitude, of a red colour, in the con-
Stellation Taurus. This star, with several other
of THE CELESTIAL GLoBE. - 189
small ones, called the Hyades, forms a triangle.
Between this triangle and Musca, is that well
known cluster of stars, the Pleiades, or seven stars,
situated in the neck of Taurus. A line from Al-
debaran through Algol, will intersect Schedar, a
star of the third magnitude in the constellation
Cassiopeia. This constellation will easily be known,
being composed of five or six stars of nearly the
same magnitude, and being always on the opposite
side of the pole, with respect to the star Alioth in
Ursa Major. r
16. About 22 degrees south-east from Aldeba-
ran, are three stars of the second magnitude in a
straight line, which form the belt of Orion. Be-
low the belt are a few stars that compose the sword
of Orion, in a beautiful nebulae. Above these
are two bright stars, distant from each other about
74 degrees; the farthest west one is Bellatrix,
and ºthe other Betelgueze; and about as far dis.
tant on the other side of the belt is Rigel, a star of
the first magnitude; all of them are in Orion,
one of the most beautiful constellations in the
heavens.
17. About half way from Rigel and the north
pole is Capella, a star of the first magnitude in the
constellation Auriga. In a line from Menkar
through Rigel, at the distance of 23; degrees from
the latter, is Sirius, the brightest star in the hea-
vens, in the mouth of Canis Major. A line from
Aldebaran, through the middle of Orion’s belt, and
about as far below it as Aldebaran is above it,
will also point out this remarkable star. About
5 degrees west from Sirius is a star between the
second and third magnitudes, and about eleven de-
grees farther south than Sirius there are three
others in a straight line, all of the third magni-
} 90 GRAMMAR OF ASTRONOMY.
tude, and in the same constellation. About 26
degrees to the east of Betelgueze, and the same
distance north-east from Sirius, is Procyon, a star
of the first magnitude, in the back of Canis Minor.
18. In a line with Rigel and the middle star in
the belt of Orion, about 44 degrees from the latter,
is Castor, a star of the first magnitude in the con-
stellation Gemini, and about 4% degrees south-east
of Castor is Pollux, a star of the second magnitude
in the same constellation. Pollux may also be
known by observing, that it is about 45 degrees dis-
tant from Aldebaran in the line produced, passing
through it from Menkar.
19. About half way between Procyon and Re-
gulus is Acubene, a star of the fourth magnitude, in
Cancer. -
20. A line from Alioth through Regulus being
produced about 23 degrees, will intersect Alpha-
red, a star of the second magnitude in the constel-
lation Hydra ; and a line from Procyon through
Alphared, produced about 24% degrees beyond
Alphared, will intersect Alkes in the Cup. This
constellation may also be known by being on the
meridian nearly at the same time with the pointers
in the Great Bear. -
21. Directly south of Arcturus, and about 80
degrees distant, is 0, a star of the first magnitude,
in the Centaur; and about 5 degrees nearly east
of a, is 8, a star of the first magnitude in the same
constellation. About 12 degrees nearly east from
£3 in the Centaur, is a in the Cross, a star of the first
magnitude, and one of the most remarkable in all
the southern constellations. A line passing through
y, a star of the first magnitude in the Cross, and &
in the same constellation, will point out the south
role, about 28 degrees distant from the latter star.
OF THE CELESTIAL GILOBE. 19 i
As the constellations and stars now described comprise the
greater number of those that can be seen, in any part of the
United States, it is unnecessary to take any notice of the
others. Those who are possessed of a celestial globe, will in
a few evenings, acquire a knowledge of the principal stars
that may be above the horizon at that season; but the fore-
going directions will be found to answer the same purpose,
without the assistance either of a globe or a map of the
heavens. The use of the celestial globe in the solution of
problems, relative to the stars, &c. shall be fully illustrated
in the next chapter.
22. The Milky Way can be traced among the
constellations, from Argo Navis, between Camis Ma-
jor and Monoceros, then separating Taurus and Ge-
mini, afterwards passing through Auriga, Perseus,
Cassiopeia, Cepheus, Cygnus, Taurus Ponio-
towski, Scutum Sobieski, Sagittarius, Ara, Crux
and Roper Caroli, then revisiting Argo Navis.
The breadth of the Milky Way appears to be very un-
equal. In a few places it does not exceed five degrees, but,
in several constellations, it is extended from ten to sixteen.
In its course it runs nearly 12 degrees in a divided clustering
stream, of which the two branches between Serpentarius and
Antinous are expanded over more than 22 degrees". That
the sun is within its plane, may be seen by an obséver in
the latitude of about 60 degrees; for, when at 100 degrees of
right ascension, the Milky Way is in the east; it will at the
same time be in the west at 180 degrees; while, in its meri-
dional situation, it will pass through Cassiopeia in the
zenith, and through the constellation of the Cross in the
madir. -
QUESTIONS.
By means of what constellation do you describe
the position of the constellations and principal stars
in the heavens !
Which is the most conspicuous constellation in
the northern hemisphere 2
How do you point out Alruccabah, or the north
pole star 2
192 & GRAMIMAR OF ASTRONOMY.
How do you point out Cor Caroli, in the neck of
Chara?
How do you point out Windemiatrix 2
How do you point out Denebola in the Lion's
tail, and Regulus in his heart 2
How do you point out Arcturus in Böotes, and
Spica Virginis in the hand of Virgo 2
How do you point out Alphacca in the Northern
Crown 2
How do you point out Algorab in the Crow, and
Antares in the heart of the Scorpion ?
How do you point out Vega or Lyra in the
Harp, Rastaben in the Dragon, and Altair in the
Eagle 2 - , -
Name the figure which is formed by Altair, Lyra,
and Deneb in the Swan. •
How do you point out the rhomboidal figure in
the Dolphin, Scheat in Pegasus, and the star in the
head of Andromeda 2 *
How do you point out Fomalhaut, in th
Southern Fish 2 -
How do you point out Menkar in Cetus, and Al-
gol in Perseus 2 ---. -
How do you point out Almaach in the foot of
Andromeda 2 -
Describe the figure that is formed by Almaach,
Algol, and Algenib. \
Where is a Arietis situated, and how many de-
grees from Mirach 2
How do you point out Aldebaran 2
How do you point out Schedar in Cassiopeia 2
How do you point out the principal stars in
Orion ? .
How do you point out Sirius, the brightest star
in the heavens !
How do you point out Procyon in Canis Minor?
of THE CELESTIAL GLOBE. 193
How do you point out Castor and Pollux, both in
Gemini ? -
How do you point out Alphared in the Hydra,
and Alkes in the Cup 2 *
How do you point out the principal stars in the
Centaur 2 . . . . . . . *
How do you trace the Milky Way among the
constellations 2 Y - . . .
*
CHAPTER VII.
Jlstronomical problems performed by the celestial globe.
PROBLEM I. . . . . yº
| - - - - - j
To find the right ascension and declination of the sun, or any
ſited slar.
RULE. Bring the sun’s place in the ecliptic, or
the star, to that part of the brazen meridian which
is numbered from the equinoctial towards the poles;
then the degree that is over the sun’s place, or the
star, is the declination; and the degree of the equi-
noctial cut by the meridian, reckoning from the
vernal equinoctial point (or the sign, Y) eastward,
is the right ascension. . . - ".
Whenever the sun's place, or any fixed star, is brought
to the brazen meridian, the graduated edge, which is nun-
bered from the equinoctial towards the poles, is always to
be understood, unless the contrary be expressed.
Or: Place both the poles in the horizon, bring
the sun’s place, or the star, to the eastern part of
the horizon, then the degree cut on the horizon,
counting from the east, northward or southward,
* 17 t
194 GRAMMAR OF ASTRONOMY.
will be the declimation, north or south; and the de-
gree on the equinoctial, reckoning from the sign
Aries eastward, will be the right ascension.
The right ascensions and declinations of the moon and
planets must be found from the Nautical Almanac, or as-
tronomical tables calculated for that purpose: for the moon
and planets cannot be represented on the celestial globe,
because they are continually changing their places among
the fixed stars.
EXAMPLES.
Required the right ascension and declination of
Antares in the Scorpion’s heart.
Jánswer. Right Ascension 2440 41', and declimation 260
2 nearly. W * ex
2. Required the right ascensions and declimations
of the following stars:–
a, Alruccabah in the Little Bear,
, Jłrietis in Aries,
a, Arcturus in Bootes,
a, Aldebaran in Taurus,
a, Capella in Auriga,
a, Ras fllgethi in Hercules,
3, Rigel in Orion,
£8, JAlgol in Perseus,
8, Pollua in the Twins,
8, Denebola in Leo,
8, Scheat in Pegasus,
8, Zubelg in Libra.
(l,
of THE CELESTIAL GLoBE. 195
TABLE. -
Right flscensions and Declinations of 43 Principal
Stars, adapted to the beginning of the Year 1825.
- - w * l 7 + ‘. . . .

's I - º e 'c. - - ig t - • ū ſº tº
É 'Names and iºnions of the a Ascensionſ:# Declination|}}}
st; e 㺠in Time..[5° - B.º.
, -º 3 : . •g F -
Q_ s 2. – I- * |
i . H. M. S. S. o ' ". . . ")
|ºinor . . . Poºj; ; ; ; ;| #|; N 13
a |Aries - - - Jºrietis ( ; 2 | 1, 57, 24 34 22, 38, 4. 17
a Taurus - - aligº,' I | 4, §§ſ 3.4 ſ, , 4 SH-3.
g|Auriga - - - - Capella | 1 || 5, 3, 50 || 44|43, 48, 9 NH 5
3 Qion. - - - Rigel || 1 || 5, 16, 10 ſ 29 3, #33 & à.
#|}}." . . . . g.º...! #| #########|f
- * ČE6/97.826 *
a Canis Major - - . *::::: 1 5. 37, 33 || 3 & 15, 28'53 S|—|- 4
a Gemini - , -, - Castor || 1 || 7, 23. 28 38|| 32, 15, 42 NH-7|
g ganis Minor- - Procyon | 1 || 7, 30, i. 32 || 5, 39, 55 NH 9
& Gemini - - - Poiluz | 2 || 7, 34, 39 3 7 || 28, 26, 20 NH 8
#. . . . . .”;| |}}} | #|####T};
* - * - - 2 C. - W *
* Bººs - " - " - arāś| | |f|, # 37|26. 5.39 NHLig
& Ursa Minor - Kochab | 3 || 14, 51, 16 ' – 3 74, 53, 29 N'- 15
Q. jºrio - - - Antares | 1 #. ; 42 | 3.7 ; 3% 3. § º ;
a Lyra * Vega || | | 18, 30, 59 || 2.0 [ -
a |Andromeda - " - Alpherit: 2 23, 55. 22 30 . #. 44 N #:
a |Piscis Aust - Fomalhaut | 1 |22, 47, 58] 33 30, 32, 50 S (-19|
4|ºus - - - gºal | 3 |##| || 3 || || || NH-1}
#|º . . . *|| ||###| ||*:::::NLL }
l * *~ (12.7" l' 3.0 -
a Cygnus - - Denebºiligel i |36, §5, § 3 j|43,333i NH-13.
a Cepheus - Jälderamin, 3 |21, 14, 24 || 14 ||61; 50, 36 N]+15
(3 §epheus - - - , , - ' || 3 |21, 25, 19 || 0 8ſ. 69, 47, §§ +1.
a Bridanus Acheruar || 1 || 1, 31, 10 || 22 |58,..., 39 SH 19
g|Argo Navis Canopus | | | 6, 20, 4 || 1:3}{2, 3}}] §H-3
|#;" . . . i.i.al | #####|"#####
* W T. * : * º,617°t * ...!!º º -
a Ursa Major - #. I 1ö. ; 51 38 63; Ai. 38 NW– 19
Q. $ºorealis .Alphacca || 2 || 15, 27, 18 l'?.5 27, 18, ; N —- 12
tl |. Hercules Ras Algeth: | 3 || 17, 6, 40 | 3: 14, J5, 54 NJ— 4
a |Serpentarius, Ras Aliague 2 iž. ; 49' 2.8 ić, ; N - :
d “erpens - - - - - - 2 ( 15, 35, 39 , 2.9 6, 59, – 12
a | Libra - zubanesch || 3 ||iſ fi. Úji:33| 15, ii., §§|+15
, 8 Perseus - - - - Algol Var). 2,56, 50) 3.8 40, 16, 29 NH-14
a (Setus -* - JMenkar || 2 |S.2, 53,08 | 3 l ', 3, 23, 56 NH-15
ſt Centaurus * - " " - 1 14, 28, #| 44 60, 7, 21 Sl—H·16
a Crux - - , , , , , || 1 | 12, 16, 57 #|: 7, 49 SH 17
{{..., " . . . *;| 3 || $º! ####|NH|2|
*ga S - S 6??? * - • , , ‘vºr; I & -
* [Ursa Major - Bº. 2 || 13; 40. 38 24, 50, iſ. 24 N – 18
3 |Ursa Major - - T. l.2 10, 51, 14 '37 57, 19.06 N1–19


As the right ascension of any fixed star is measured by the
portion of time elapsed between the passages or transits of
the vernal equinoctial point, and the star over the meridian;
the right ascension in time, being therefore multiplied by 15,
gives the right ascension in degrees, &c. See pages 71 and 72.
*.
196 GRAMMAR OF ASTRONOMIY.
PROBLEM II.
The right ascension and declination of the sun, a fired
star, the moon, or a planet, being given, to find its
place Un the globe. *\.
RULE. Bring the given degree of right ascension
to the brazen meridian ; then, under the given de-
clination, on the meridian, you will find the star, or
place of the planet required. * ,
{ ExAMPLEs.
1. What star has 99° 22' of right ascension, and
160 29 nearly, south declination ?
(JAnswer. Sirius, the brightest star in the heavens, and
therefore supposed by some astronomers to be the nearest
to the earth. .*
2. What stars have the following right ascensions
and declinations ! $ *
** RIGHT ASCENSIONS. T
In time. ‘. In degrees.
13h. 40m. 88s. 2050 9' 30"
13, 16 00 199 0 00
0 4 ! N. 14 * - 1 *- ~3 30
5 6 10 76 32 30
22 47 58 341 59 30
9, 59 - 5 149 46 15
DECLINATIONs.
500 11’ , 24” N.
10 14 45 S.
14 || 2 | 40, N.
8 24 38 S.
30 32 50 s.
, 12 48. 57 N.
3. On the 1st of September, 1825, the moon's
right ascension was 19°20'14", and her declination
12° 35' 4" north; find her place on the globe at
y
that time.
. OF THE CELESTIAL GILOBE. 197
4. On the 1st of November, 1825, the declina-
tion of Venus was 1° 43' south, and her right ascen-
sion 1880 15'; find her place on the globe at that
time. , * - --
5. On the 25th of July, 1 825, the declination of
Jupiter was 17° 15', and his right ascension 137°
15; find his place on the globe at that time.
|
PROBLEM III. . . . .
) , ' ' ' ' ', -
To find the latitude and longitude of any given fived star.
RULE. Elevate the north or south pole 66% de-
grees above the horizon, according as the given star
is on the north or south side of the ecliptic'; bring
the elevated pole of the ecliptic to the brazen méri-
dian, and screw the quadrant of altitude upon the .
meridian over this pole; keep the globe from re-
volving on its axis; and move the quadrant till its
graduated edge, comes over the given star; then
the degree on the quadrant over the given star is its
latitude; and the sign and degree on the ecliptic,
reckoning from the vernal equinoctial point to the
quadrant, is its longitude." . . . . .
The latitudes and longitudes of the planets'must be found
from the Nautical Almanac, or astronomical tables calcula-
ted for that purpose. Or their right ascension and declina-
tion being given, (see the preceding tables,) their latitudes
and longitudes may be found by spherical trigonometry.
#
Place the upper end of the quadrant of altitutié
on the north or south pole of the ecliptic, according
as the given star is on the north, or south side of
the ecliptic, and move the other end till the sta
comes to the graduated edge of the quadrant; then
the number of degrees between the ecliptic and the
star, will be the latitude; and the number of der
grees on the ecliptic, reckoning from the equinoc-
tial point Aries, will be the longitude. .
". 17* , r O
198 GRAMMAR of ASTRONOMY.
- EXAMPLEs. . . .
1. Required the latitude and longitude of & Re-
gulus in Leo. . . . . . .
Answer. Latitude 00'27' 40”; longitude 4 signs 270 23:
44" or 27023'44" in the sign Leo. ? &
S. 2. Required the latitudes and longitudes of the
following stars:- ' ' . . . . . . . . . . . . .
3 & Aldebaram in Taurus, - || cº, Algemiš in Perseus,
8, Pollua, in Gemini, * , ), Algénib in Pegasus,
o, Acubcne in Cancer, , 8, Albiero in Cygnus.
- . . .TABLE. . . . .
Longitudes and Latitudes of 30 principal Fiaſed Stars, jor
. . . . . the beginning of the year 1825. . .
3 ,” * * '-. , sº I - • tº § -
§ {Names and Situations off; | Longitude. . . . Latitude.
§ the Stars. |}| ". . . . . §§
O . . . . . |S| |s; ‘S,
a |Aries...........Arietis 2|| 1: 5°12' 55"|50"2"| 9°57'39"N
g Gemini.......s. Pollux 2 || 20 47.58 |49.5 || 6 40 17 N
a |Aquila ...........Altair 1 || 9 29, 18 24 50.8 29 1845 Ní
a |Pegasus..........JMarkab 2 | 11 21, 2 59 || 50.1 | 19 24 45 N.
y-Pegasus........Algenib|2| 0 6 42 58 |50. 1: 12:35 43 N
a |Scorpio.........Antarés 1 | 8, 7 19 5 |50.1 . . 4.32 43 S
a Taurus.. ... Aldebaran 1 || 2 7 20 34 50.2 5 28,42 S
a Pisces Ast... Fomalhaut| 1 || 11 1 23 45 |50.6|21 6 41 S.
la Leo. . . . . . . ‘.... Regulus ; ; 427 23 44 |49. 9 0.27 40 NF
a Virgo.............Spical | 6’21 23 54 |50.1 || 2 2 21, S
a Gemini.......: Castor 1 || 317 43. 13, 50.2|10 5 2.N
|a Bôotes ........Arcturus 1 || 6’21:47 42 50.5|3053 59 N
a Cygnus...; . . . . . Deneb| 1 || 11 2 55 23 |49.5|59 54 56 N
a |Ophiuchus. R. Alhague 2 8 1959 34 |50.2|3552 24 N
a Lyra. . . . . . . . ..... bega| 1 || 9 12 51, 28 |49. 9 ||61 44, 24.N
a Corona Bor... Alphaccal 2 7 9 49 17 |50.5 || 0 21 27 N.
|a Canis Major.....Sirius 1 || 311 40 44 || 50.2| 2. 2 57 N
a Qanis Minor...Procyon 1 || 323 22.59 |50. 1 || 15 57 45 s
a Cancer........4 cubene 4 || 4 12 11 41 || 50.2 || 5 5-37 S
a |Auriga. . . . . . . . Capella 1 || 2 19 24 36 50.2122 52 14 N
a |Qrion.......Belelgueze|1|-226, 1831 || 50.2 | 16, 3 2 S
|3, Taurus.................|2| 220 747 |50.2 || 5 22 28 N
(3 |Capricornus........., |3| 10 1 36 .3|50.2| 4 36 30 N
9 |Scorpio...............|2| 728 40, 49 || 50,2| 5 27 47 S
* Pleiades........Lucido. 3 | 127-3236. 50. I 4, 2 5 N
9 |Hydra.........Alphard| 1 || 424 50 40 |50.0|22 23 37 S
|8 |Virgo........ ..........| 3 || 5 24 40 5 50.2i O 41' 32 N
a Andromeda. . . . . . . . ..., |2|| 0 11 52 16 || 50.0 25 41 8 N |
& Leo . . . . . . . . . Denebola| 2 || 5 19 11 42 || 50.3 | 12 17 10 N
a Libra. . . . . . . Zubenesch] 2 || 7 12 30 15 50.2} 0 21 30 N


OF THE CELESTIAL GLOBE. 199
PROBLEM IV.
The latitude and longitude of the moon, a star, or a
planet being given, to find its place on the globe.,
RULE. Place the division of the quadrant of al-
titude marked 0, on the given longitude in the eclip-
tic, and the upper end on the pole of the ecliptic;
then, under the given latitude, on the graduated
edge of the quadrant, you will find the star, or place
of the moon or planet. . . . . . .
Or, elevate the north or south pole 664 degrees
above the horizon, according as the given latitude
is north or south ; bring the elevated pole of the
ecliptic to the brazen meridian, screw the quadrant
of altitude upon the meridian over this pole; and ex-
tend the quadrant over the given longitude in the
ecliptic; then, under the given latitude, on the
graduated edge of the quadrant, you will find the
star, or place of the moon or planet. * *
º \.
> ExAMPLEs.
... 1. What star has two signs 14° 23' of longitude,
nearly ; and whose latitude is 319 8ſ 42° south 2
*
-
h
ſlnswer. Rigel, a star of the first magnitude, in Orion.
2. On the 14th of September, 1825, at midnight,
the moon’s longitude was 8 signs 3° 35'13", and her
latitude 0° 50' 33" south, find her place on the
globe. . . . . ." - . . .
Answer. The moon was nearly north of Antares, in the
Scorpion’s heart, and about 40 distant from it.
It is proper to observe that the moon and planet's places
are here given for the meridian of Greenwich observatory.
200 GRAMMAR OF ASTRONOMIY
3. What stars have the following longitudes and
latitudes 2 . . . . . .
!,
Longitudes. Latitudes.
8s. 199, 59' 34" . . , 350 32 24”.N l
8 - 7 19 .5, " .. 4 32' 43 S.
2 26 18 31 . . 16 3 2 S.
3 11 40 44 . . . . . 2 2, 57 N.
9 12 51 28 61 44 ° 24 N.
4. On the 1st of November, 1825, the longitudes
and latitudes of the planets were as follows; re-
º *
quired their places on the globe. . " . .
- Longitudes. . . . . Latitudes.
3 Mercury 7s. 89: 59" | 09 16' N .
Q Venus: , ; 6 8, 9 1 40 N.
3 Marš. 5 - 17 50 || 1 28 N.
ll." Jupiter 5 9. 27 || || 0 , 57 N.
h: Saturn'. 2, 21 15 . . . . 21 36 N.
"Hi Uranus. 9 × 16 33 || 0 , 27. S.
- PROBLEM v. . . . .
The day and hour, and the latitude of a place being given,
- to find what stars are rising, setting, culminating, &c.
Definition. A star is said to culminate, when it. passes -
the meridian. , , , . . ; * . A. F.
RULE. Elevate the pole to the latitude of the
place, find the sun's place in the ecliptic, bring it to
the brazen meridian, and set, the index of the hour
circle to 12; then, if the time be in the forenocn,
turn the globe eastward on its axis till the index has.
passed over as many hours as the time wants of
noon ; but, if the time be in the aſternoon, turn the
globe westward as before ; then, all the stars at the
eastern edge of the horizon will be rising, those at
the western part will be setting, those under the
meridian above the horizon will be culminating; all
*
Of THE CELESTIAL GLOBE. 201
those above the horizon will be visible, and those
below it will be invisible at the given time and place.
If the globe be turned on its axis from east to west,
those stars which do not go below the horizon never
set at the given place; and those which do not
come above the horizon, never rise ; or, if the given
latitude be subtracted from 90 degrees, and circles
be described on the globe, parallel to the equinoc-
tial, at a distance from it equal to the degrees in the
remainder, they will be the circles of perpetual ap-
parition and occultation. . . . . . . . . . . . . .
It is proper to observe, that the globe may also be placed
so as to represent the natural position of the heavens, at the
given time and place, by means of a meridian line, or by a
mariner's compass, which is usually attached to the globe,
taking care to allow ſor the variation iſ necessary. Hence,
if the celestial globe be taken into the open air, on a clear
star-light night, where the view on the surrounding horizon
is uninterrupted by different objects; for instance, on the
top of a house that has a flat roof; and, if the globe be
rectified at the given time and place; by the above rule, and
also placed due-north and south according to this observa-
tion. Then, the globe being fixed in this position, every.
star on the globe will correspond to the same star in the
heavens; so that if the flat end of a pencil be placed on any
star on the globe, the other end will point to that particular
star in the heavéns; all those stars whose declinations are
equal to the given latitude, will be vertical successively at
the given place; and in fact, by this means the constellations
and remarkable stars, that come above our horizon, may be
easily known. . . . . . . . . . . . &
EXAMPLEs. . . . \,
1. At 9 o'clock in the evening at St. Augustine,
in East Florida, on the 17th of December, what
stars are rising, setting, culminating, &c. 2 .
, Answer. Benetnach in the tail of the Great Bear, Cor
Caroli in the neck of Chara, and Denebola in the Lion's
tail are rising; Capella and Rigel are culminating; Deneb
in the Swan, is setting; Alioth, Mizar, and Dubhe, in the
202 t;RAMMAR OF ASTRONOMY.
Great Bear; Castor and Pollux in Gemini; Sirius and Pro-
cyon ; Betelgueze and Bellatrix, in Orion; Algol and Alge-
nib, in Perseus; Alderamin in Cepheus;, Baten Kaitos in
the Whale; Mirach, Almaach, and Alpherast, in Androme-
da; Algenib, Scheat, and Markab, in Pegasus; &c. are all
visible, if it be a clear star-light night.
2. At 9.o’clock in the evening at New-York, on
the 26th of December, what stars are rising, set-
ting, culminating, &c. : :".. , * ~
Jłnswer. Regulus in Leo, is rising; Algemib in Perseus,
is culminating; Vega in Lyra, is setting; and the principal
stars above the horizon, are Sirius in Canis Major, Procyon
in Canis Minor, Betelgueze, Rigel, and Bellatrix, in Orion,
Aldebaran in Taurus, Castor and Pollux in Gemini, Capella
in Auriga, o, Arietis, Alpherast in the head, Mirach in the .
Girdle, and Almaach in the southern foot of Andromeda,
Markab, Scheat; and Algenib in the Flying Horse, Aldera-
min in Cephelis, Deneb in the Swan, Ménkar and Mira in
the Whale, &c. . . . , - -
About 12 o'clock, Arcturus'in Böotes, will be rising; De-
mebola in the Lion's tail will be above the horizon, &c. So
that the greater number of the most brilliant stars in the,
heavens, will be visible at New-York during the night of
the 26th of December, if it be a clear star-light might.
3. At 10. o'clock in the evening at New-York, on
the 16th of November, what stars are rising, Setting,
culminating, &c. 2 ~ . . ." - . . . . .
4. At 9 o'clock in the evening at Charleston in
South Carolina, on the 20th of January, what stars
are rising, setting, culminating, &c. 2 . . . .
5. At 4 o’clock in the morning at Washington
city, on the 20th of February, what stars are rising,
setting, culminating, &c. : : ... ?" *
6. At fi o’clock in the evening, on the 22d of
November, what stars are rising, setting, culmina-
ting, &c. at the following places:—Boston, Phila-
delphia, Baltimore, Savannah, New-Orleans, Pitts-
burg, St. Louis, Havana, Rio Janeiro, St. Salva-
{
OF THE CELESTIAL GLOBE. 203
dore, Lima, Buenos Ayres, Quito, Mexico, and
* Y. -- - \
Quebec. . . . . . . *
PROBLEM v1.
To find the distances of the stars from each other in
. . . . . degrees. . . . . . . . . . . . .
** • ‘V . - - - f • * *
RULE. Laythe quadrant of altitude over any two
stars, so that the division marked 0 may be on one
of the stars; the degrees on the quadrant between
that and the other star, will show their distance, or
the angle which these stars subtend, as seen by a
spectator on the earth. . . . .
t
\, * **
ExAMPLEs. - -
** p to - ".. \, : . .*. * * - g
1. What is the distance in degrees between Ca-
pella in Auriga, and Aldebaran in Taurus 2 ... .
Answer, 31 degrees.
2. Required the distance in degrees between
Castor in Gemini, and Procyon in Canis Minor.
3. What is the distance in degrees between Vega.
in Lyra, and Altair in the Eagle 2 . . . .
4. What is the distänge in degrees between Sirius
in Canis Major, and Rigel in Orion ? . . . . . .
5. What is the distance in degrees between the
autumnal equinoctial point, and each of 'the follow-
ing stars: Arcturus, §. Virginis, Denebola, Re-
gulus, Antares, Algórab, 6 in the Great Bear, Pro-
cyon, and Sirius 2 ; : -
PROBLEM VII. . . .
To rectify the celestial globe for the latitude of a given.
place, aud for the sun's place in the eclipticon a given
day. 2 . . . . . . . . .
RULE. Elevate, the north or south pole of the
< \
204 GRAMMAR OF ASTRONOMY.
celestial globe, according as the given latitude is
north or south, so many degrees above the horizon
as are equal to the latitude; then bring the sun’s
place in the ecliptic on the given day to the brazen
meridian, and set the index of the hour circle to 12.
If the latitude of the place be not given, find the latitude
on the terrestrial globe, with which progeed as above. Then
will the celestial globe represent the position of all the fixed
stars and imaginary circles of the heavens, in respect to a
spectator at the given place at 12 o'clock at noon on the
given day: for the horizon of the celestial globe represents
the rational horizon of the spectator, the zenith on the celes-
tial globe will correspond to his zenith in the heavens, and
the spectator is supposed to be situated in the centre of the
celestial sphere, and viewing the stars in the concave surface.
To avoid repetition, I shall not explain the manner of
rectifying the celestial globe with every problem, but merely
say, rectify the celestial globe; except in problems, where
all-are not required, and then the circumstances which are
to be observed in rectifying, the globe, shall be expressed.
, - , EXAMPLES.
~ }
1. Rectify the celestial globe for the latitude of
New-York, and for the sun’s place in the ecliptic,
on the 22d of November.
Answer. The latitude of New-York is 40° 49' north, and
the sun’s place in the ecliptic is in the beginning of Sagit-
tarius; therefore, elevate the north pole of, the celestial
globe 400 42 above the horizon, bring the beginning of Sa-
gittarius to the brazen meridian, and Sct the index of the
hour circle to 12. , - . *
2. Rectify the celestial globe for the latitude of
the following places, and for the sun’s place in the
ecliptic on the 20th of April: Philadelphia, Cin-
cinnati, Java, Bombay, Cantom, Pekin, Alexandria
in Egypt, and Bagdad in Asia Minor.
"THE CELESTIA3, GLOBE. 205
w PROBLEM VIII.
To find at what hour any star, or planet, will rise, culmi-
nate, and set, the latitude of the place and day of the
month being given. - s
RULE. Rectify the celestial globe by the last
problem ; then if the star, or planet's place, be be-
low the horizon, turn the globe westward till it
comes to the eastern part of the horizon, and the
hours passed over by the index of the hour circle
will show the time from noon when it rises; and, by
continuing the motion of the globe westward till the
star, or planet’s place comes to the meridian, and
to the western part of the horizon successively, the
hours passed over by the index will show the time
of its culminating and setting. -
If the star, or planet's place, be above the horizon and
east of the meridian, find the time of culminating, setting,
and rising, in a similar manner; but if the star, or planet's
place be west of the meridian, find the time of setting,
rising, and culminating, by turning the globe on its axis.
The latitude and longitude, or the right ascension and de-
climation of the planet, must be found from the Nautical
Almanac, or from astronomical tables calculated for that
purpose; and its place on the celestial globe mus' be de-
termined by Prob. IV. or II. 2
., EXAMPLEs.
I. At what time will Arcturus rise, culminate,
and set at New-York, on the 1st of January 2
Answer. It will rise at 12 o'clock at night, comu ) the
Faeridian at a quarter past 7 in the morning, and set & half
gast 2 o’clock in the aſternoon.
2. On the 25th of December, 1825, the longi-
tude of Venus was 8 signs, 15 degrees, 26 minutes,
and her latitude 38' north ; at what time, did she
rise, come to the meridian, and set at Greenwich
observatory, and was she a morning or an evening
Stål 2 - * -
|S
206 GRAMIMAR OF ASTRONOMIY.
.ſlnswer. She will set at a quarter past 2 o'clock in the
afternoon, rise at a quarter past 6 in the morning, and come
to the meridian at three quarters past 10 in the morning.
Here Venus was a morning star, because she rose before
the sun. * * -
3. At what time does Sirius rise, culminate and
set at Philadelphia, on the 31st of January 2 &
4. At what time does Aldebaran rise, culminate,
and set at St. Louis, on the 10th of March 2
5. On the 25th of December, 1825, the longi-
tude of Jupiter was 5 signs, 14° 25', and his latitude
19 11’ north; at what time did he rise, come to the
meridian, and set at Greenwich, and was he a
morning or an evening star 2
6. At what time does Rigel in Orion, rise, cul-
minate, and set at the following places, on the 20th
of November : London, Paris, Petersburg in Rus-
sia, Washington city, Baltimore, Pensacola, and
New-Orleans ? . .
- PKoBLEM Ix. w
To find the amplitude of any star, its oblique ascension
and descension, and its diurnal arc, for any giveſ,
place. 4 - - -
RULE. Elevate the pole to the latitude of the
place, and bring the given star to the eastern edge
of the horizon; then the number of degrees between
the star and the east point of the horizon, will be its
rising amplitude ; and the degree of the equinoctial
cut by the horizon, will be the oblique ascension :
keep the globe in this position, and set the index of
the hour circle to 12; then, turn the globe west-
ward till the given star comes to the western part of
the horizon; the number of degrees between the
8tar and the west point of the horizon will show the
setting amplitude ; the degree of the equinoctial,
cut by the horizon, will be the oblique descension ;
of THE CELESTIAL GLOBE. 207
and the number of hours passed over by the index
will be the star's diurnal arc, or time of continuance
above the horizon.
When the given star, in turning the globe from east to
west, comes to the brazen meridian, the degree of the equi-
noctial corresponding with the graduated edge of the meri-
dian, will be the star's right ascension; and the difference
between the right and oblique ascension, will be the ascen-
sional difference. - * ,
's 8 EXAMPLEs. I
1. Required the rising and setting amplitude of
Sirius, its oblique ascension, oblique descension,
and diurnal arc, at New-York. -
Answer. The rising amplitude is 21 degrees to the south
of the east; oblique ascension 1130; setting amplitude 218
to the south of the west; oblique ascension 850; and diur-
mal arc, or time of continuance above the horizon, 10 hours
} • e i tº e -
15 minutes. The right ascension is 999; and the ascen-
sional difference is therefore 14 degrees. . . . . . .
2. Required the rising and setting amplitude of
Aldebaran, its oblique ascension and descension,
and diurnal arc, or time of continuance above the
horizon, at the following places: Washington city,
London, Dublin, Copenhagen, Paris, Constanti-
nople, Alexandria in Egypt, Syracuse, Gondar in
Abyssinia, and Rome in İtaly. -
3. Required the rising and setting amplitude of
Rigel, its oblique ascension, oblique descension,
and diurnal arc, at the following places: Montreal,
Boston, New-York, Philadelphia, Baltimore, Rich-
mond, Charleston, Pensacola, Havana, Lima, and
Buenos Ayres. t
- PROBLEM x. . . . .
The latitude of a place being given, to find the time of
the year al which any known star rises or sets achromi-
cally. - - - * . . . . 3.
RULE, Elevate the pole to the latitude of the
208 GRAMMAR OF ASTRONOMY.
place, bring the given star to the eastern part of
the horizon, and observe what degree of the ecliptic
is intersected by the western part of the horizon;
the day of the month answering to that degree, will
show the time when the star rises achronically, or
at sunset, and, consequently, when it begins to be
visible in the evening. Turn the globe westward till
the star comes to the western part of the horizon,
and observe the degree of the ecliptic that is setting
with it; the day of the month corresponding to that
degree will show the time when the star sets achro-
nically, or when it ceases to appear in the evening.
Hence, it is plain, that during those months of the year
which intervene between the achronical rising and setting of
a star, the star will be seen above the horizon, at the given
place, in the evening. . . . . -
EXAMPLES. ~
1. At what time does Arcturus rise achronically
at AScra in Boeotia, where Hesiod, a celebrated
poet, lived; the latitude of Ascra, according to
Ptolemy, being 37° 45′ north 2 ,, . . . .
Answer. When Arcturus is at the eastern part of the ho-
rizon, the 12th degree of the sign Aries will be at the wes-
tern part, which answers to the 1st of April, the time when
Arcturus rises achronically; and it will set achronically on
the 30th of November. Hence, Arcturus now rises achroni-
cally in latitude 37° 45' north, about -100 days after the
winter solstice. Hesiod, in his Opera et Dies, lib. ii. verse
185, says, . . , , ... • -
When from the solstice sixty wintry days " .
Their turns have finished, mark, with glittering rays, .
From ocean's sacred flood, Arcturus rise,
Then first to gild the dusky evening skies. r
Here is a difference of 40 days in the achronical rising of
this star (supposing Hesiod to be correct) between the time
of Hesiod and the present time; and as the apparent mean
motion of the sun in the ecliptic is 59'8.2" in a day, 40 days
will answer to 39° 25' 21"; and consequently, the winter
solstice in the time of Hesiod was in 9025' 21" of Aquit...
of THE CELESTIAL- GLOBE. 209
i
Now, since the recession of the equinoctial points is 50.1
seconds in a year, we shall have 50.1": 1 year: : 390 25
21": 2832 years nearly, since the time of Hesiod; so that
(the places of the stars on the globe being adapted to the
year 1825) he lived 1007 years before Christ by this mode
of reckoning. Homer, who is supposed to be contemporary
with Hesiod, flourished 968 years before the Christian era,
according to Paterculus, or 884 according to Herodotus.
The Arundelian Marbles fix his era 907 years before Christ,
and make him also contemporary with Hesiod. See Lem-
prier's Classical Dictionary. . . * . ... •
2. At what time of the year does Regulus rise
achronically at New-York; and at what time of the
year does it set achronically 2
3. At what time of the year does Sirius rise or
set achronically at Alexandria in Egypt, in 31° 13'
north latitude 2 . . . .
4. At what time does Aldebaran rise or set
achronically at Athens, in latitude 37° 58' north 2
5. At what time does Rigel rise or set achromi-
cally at Cape Horn, in latitude 55° 58' south 2
J
• * - PROBLEM XI. ,
The latitude of a place being given, to find the time of the
year at which any known star rises or sets cosmically.
RULE. Elevate the pole to the latitude of the
place, bring the given star to the eastern part of the
horizon, then the day of the month, corresponding
to the degree of the ecliptic, which is cut by the
eastern part of the horizon, will show when the star
rises cosmically. Turn the globe westward on its
axis till the star comes to the western part of the
horizon, and the day of the month answering to the
degree of the ecliptic, which is 'cut by the eastern
part of the horizon, will show when, the star sets
cosmically or at sun-setting. . . )
‘. . ExAMPLEs. . . . . . .
1. At what time of the year do the Pleiades set
18* -
210 . GRAMMAR OF ASTRONOMY.
cosmically at Miletus in Ionia, the birth-place of
Thales; and at what time of the year do they rise
cosmically, the latitude of Miletus, according to
Ptolemy, being 37° north 2 .. - -
Answer. The Pleiades rise with the sun on the 11th of
May, and they set at the time of sun rising on the 21st of
November. . . . . . . .
Pliny (Nat. Hist. lib. xviii, chap. 25), says, that Thales
determined the cosmical setting of the Pleiades to be 25
days after the autumnal equinox. . Supposing this observa-
tion to be made at Miletus, there will be a difference of 34
days in the cosmical setting of the Pleiades since the time
of Thales; and, as a day answers to about 59' 8.2" of the
ecliptic, hence 1d: 59'8.2":: 34d.: 33930'38", consequently,
in the time of Thales, the autumnal equinoctial colure passed
through 30 30 38" of Scorpio; and 50.1": 1 year: : 30 30'
38" : 2408 years since the time of Thales; so that Thales
lived (2408–1825) 583 years before the birth of Christ.
According, to Sir Isaac Newton's Chronology, Thales
flourished 596 years before the Christian era. . . .
Thales was born about 640 years before Christ, and was, ,
according to Laertius and several other-writers, the father
of the Greek philosophy, being the first that made any re
searches into natural knowledge and mathematics. In geo-
metry he was a considerable inventor, particularly in that
part concerning triangles; and all writers agree, that he was
the first even in Egypt, who measured the height of the
Pyramids by the shadow. His knowledge and improve-
ments in astronomy were very considerable. He divided the
celestial sphere into five zones. He observed the apparent
diameter of the sun, which he made equal to half a degree;
and formed the constellation of the Little Bear. He also
observed the mature of eclipses, and cakeulated them ex-
actly; one in particular, memorably recorded by Herodotus,
as it happened on a day of battle between the Medes and
Lydians, which, Laertius says, he had foretold to the
Ionians. Plutarch not only confirms his general knowledge
of eclipses, but his doctrine was, that an eclipse of the sun
is occasioned by the intervention of the moon, and that an
eclipse of the moon is caused by the intervention of the earth.
Thales died at the Olympic games, at above 90 vears of age.
f
OF THE CELESTIAL GLOBE. 21 i
2. At what time of the year does Vega in Lyra,
rise with the sun at New-York ; and at what time
of the year will Vega set when the sun rises 2
3. At what time of the year will Antares, in the
heart of Scorpio, set and rise cosmically, at Wash-
ington City; and also at what time does Antares
set when the sun rises 2 . . , ~,
PROBLEM XII. . . .
To find the time, of the year when any given star rises or
sets heliacally at any given place. . . . .
RULE. Rectify the globe to the latitude of the
given place, and screw the quadrant of altitude up-
on the brazen meridian over that latitude ; bring
the given star to the eastern part of the horizon, and
move the quadrant till it intersects the ecliptic, 12 .
degrees below the horizon, if the star be of the first
magnitude; 13 degrees, if the star be of the second; .
14 degrees, if the star be of the third, &c. : the
point of the ecliptic, cut by the quadrant, will show
the day of the month, on the horizon, when the star
rises heliacally. Bring the given star to the wes-
tern, part of the horizon, and move the quadrant
till it intersects the ecliptic below the western edge
of the horizon, in a similar manner as before ; the
point of the ecliptic, cut by the quadrant, will show
the day of the month, on the horizon, when the star
set heliacally at the given place.
The heliacal rising and setting of the stars will vary ac-
cording to their different degrees of magnitude and brillian-
cy, for it is evident that the brighter a star is when above
the horizon, the less the sun will be depressed below the .
horizon when the star first becomes visible. . . According to
Ptolemy, stars of the first magnitude are seen rising and
setting when the sun is 12 degrees below the horizon; stars
of the second require the sun’s depression to be 13 degrees;
stars of the third, 14 degrées; and so on. reckoning-one de-
gree for each magnitude. -*. * -
212 GRAMMAR of ASTRONOMY
EXAMPLES.
1. At what time of the year does Sirius, or the
Dog Star, rise heliacally at Alexandria in Egypt;
and at what time does it set heliacally at the same
place 2. y * .
Jìnswer. The latitude of Alexandria is 31° 18' north; the
12th degree of the quadrant, below the horizon, will inter-
sect the 12th of the sign, Leo, when Sirius is at the eastern
horizon; and in like manner it is found, that the 12th degree
of the quadrant, below the horizon, will intersect the 2d de-
gree of the sign Gemini. Hence, Sirius rises heliacally at
Alexandria, on the 4th of August, and sets heliacally at the
same place, on the 23d of May. - º
The ancients reckoned the beginning of the dog days from
the heliacal rising of Sirius, and their continuance to be
about forty days. Hesiod informs us, that the hottest season
(or the dog days) ended about fifty days aſter the summer
solstice. It has been shown in the note of Ex. I. Prob. X.
that the winter solstice, in the time of Hesiod, was in about
9° 25' 21" of Aquarius, and consequently, the summer sol-
stice was in 99 25' 21" of Leo. Now it appears, from the
above example, that Sirius rises heliacally at Alexandria,
when the sun is in the 12th degree of the sign Leo ; and, as
59, 8.2" (or a degree nearly) answer to a day, Sirius rose
heliacally, in the time of Hesiod, about four days after the
summer solstice; and if the dog days continued forty days,
they end about 44 days after the summer solstice. -
The dog days, in our almanacs, begin on the 3d of July,
which is 12 days after the summer solstice, and end on the
11th of August, which is 51 days after the summer solstice;
and their continuance is 39 days. Hence, it is plain, that
the dog days of the moderns have no reference whatever to
the rising of Sirius, for this starrises heliacally at New-York
on the 12th of August, and, as well as the rest of the stars,
varies in its rising and setting according to the variation of
the latitudes of places; and, therefore, the heliacal rising of
Sirius coull have no influence whatever on the temperature
of the atmosphere." However, as the Dog Star rose heliacal-
ly at the commencement of the hottest season in Egypt,
Greece, &c. in the infancy of astronomy, and at a time when
astrology referred almost every thing to the influence of the
of THE CELESTIAL GLOBE. 213
stars, it was natural for the inhabitants of those countries to
imagine that the heat, &c. was the effect of this star's in-
fluence: - . . . . *-
The dog days are now, very properly, altered, and made
not to depend on the variable rising of any particular star,
but on the summer solstice. .* - . . . . • ,
2. At what time of the year does 8 Tauri, or the
bright star in the Bull's horn, of the second magni-
tude, rise and set heliacally at Rome'? . . .
3. At what time of the year does Arcturus rise.
heliacally at New-York, and at what time does it
set heliacally 2 . . . . . *
4. At what time does Sirius rise and set heliacally
at the following places: Cairo in Egypt, in latitude
30° 2' north ; Jerusalem, London, New-Orleans,
Quito, and St. Helena 2 " .
. . . PROBLEM XIII.
The latitude of a place and day of the month being given,
to find all those stars that rise and set achronically,
cosmically, and heliacally. -
*
#
RULE. Rectify the globe for the given latitude;
then, . s
1. For the achronical rising and setting ; bring the
sum’s place, in the ecliptic to the western part of the
horizon, and all the stars along the eastern edge of
the horizon will rise achronically, while those along
the western edge will set achronically.
2. For the cosmical rising and setting ; bring the
sun’s place in the ecliptic to the eastern part of the
horizon, and all the stars along that part of the
horizon will rise cosmically, while those along the
western part will set cosmically. . . . .
3. For the heliacal rising and setting ; screw the
quadrant of altitude on the meridian, over the
given degree of latitude, turn the globe eastward
214 GRAIMIMAR OF ASTRONOMY.
on its axis till the sun’s place cuts the quadrant
twelve degrees below the horizon, then all stars of
the first magnitude, along the eastern part of the
horizon, will rise heliacally; and, by continuing
the motion of the globe eastward till the sun’s place
intersects the quadrant in 13, 14, 15, &c. degrees
below the horizon, you will find all the stars of the
2d, 3d, 4th, &c. magnitude. By turning the globe
eastward on its axis, in a similar manner, and bring-
ing the quadrant to the western part of the horizon,
you will find all the stars that set heliacally.
The principal use of this and the last three problems, (of
which it is the reverse) is to illustrate several passages in the
ancient writers, as Hesiod, Virgil, Ovid, Pliny, &c. The
knowledge of these poetical risings and settings was held in
great esteem among the ancients, and was very useful to
them in adjusting the time set apart for their religious and
civil duties, and for marking the seasons proper for their
several parts of husbandry; for the knowledge which the
ancients had of the motions of the heavenly bodies was not
sufficient to adjust the true length of the year; and, as the
returns of the seasons depend upon the approach of the sun
to the tropical and equinoctial points, so they made use of
these risings and settings to determine the commencement
of the different seasons, the time of the overflowing of the
Nile, &c. The knowledge which the moderns have ac-
quired of the motions of the heavenly bodies, renders such
observations as the ancients attended to in a great measure
useless, and, instead of watching the rising and setting of
particular stars for any remarkable season, they can consult
an almanac for every purpose of husbandry.
`, EXAMPLES.
1. What stars rise and set achronically at Dron-
theim in Norway, latitude 63° 26' north, on the
18th of May 2 - ‘. ---
Answer. Altair in the Eagle, the head of the Dolphin, &c.
rise achronically; and Aldebaran, Betelgueze, &c. set
achronically. *
OF THE CELESTIAL GLOBE. n 215
2. What stars rise and set achronically at Peters-
burg in Virginia, latitude 37° 15' north, on the 20th
of November 2 - . . -
3. What stars rise and set achronically, cosmi-
cally, and heliacally, at New-York, on the 1st of
January 2 . . . . . . . . . . .
4. What stars rise and set achronically, cosmi-
cally, and heliacally, at Lexington in Kentucky, la-
titude 38°6'.north, on the 1st of March 2
5. What stars of the 1st magnitude set heliacally
at London, on the 5th of May 2 4
PROBLEM xiv.
The latitude of a place and day of the month being given,
to find the meridian altitude of any star or planet.
RULE. Rectify the globe for the latitude of the
given place ; them, • , . . . .
For a Star. Bring the given star to the brazen
meridian ; the degrees on the meridian, contained
between the star and the next point of the horizon,
will be the altitude required. - .
When the meridian altitude of a star is required, it is not
necessary to attend to the day of the month, since the meri-
dian altitude of the stars on the globe are invariably in the
same latitude. - -
For the JMoon or a Planet. Find the longitude and
latitude, or the right ascension and declination of
the planet, for the given day, and mark its place on
the globe, (by Prob. II. ;) bring the planet's place
to the brazen meridian, and the number of degrees,
on the meridian, between that place and the horizon,
will be the altitude required. -
The longitude and latitude, or the right ascension and de-
clination of the moon or a planet, must be found by means
of the Nautical Almanac. -
216 GRAMMAR OF ASTRONOMY.
! -- EXAMPLES. - «
1. What is the meridian altitude of Aldebaran at
Philadelphia 7 º y
2. What is the meridian altitude of Arcturus at
Richmond? * •- -
3. What is the meridian altitude of the following
stars, at Washington City: Vega, Sirius, Arcturus,
Pollux, Castor, Regulus, Procyon, Denebola, Çor
Caroli, and Cor Scorpio 2 . . . . - -
4. On the 25th of February, 1825, the right as-
cension of Venus was 20° 15', and declination 10°
9' north; what was her meridian altitude at Green-
wich, at that time !
. PROBLEM XV.
The meridian altitude of a known star being given, to
find the latitude of the place of observation.
RULE. Bring the given star to the brazen meri-
dian ; count the number of degrees in the given al-
titude, on the meridian, from the star, towards the
south point of the horizon, if the place of observa-
tion be in north latitude, or towards the north if in
south latitude, and mark where the reckoning ends;
then, elevate or depress the pole till this mark
coincides with that part of the horizon towards
which the altitude was reckoned ; and the eleva-
tion of the pole above, the horizon will show the
latitude. ſ
- ExAMPLEs.
1. In what degree of north latitude is the meri-
dian altitude of Spica Virginis 20 degrees 2
Answer. 60 degrees north.
2. In what degree of south latitude is the meri
dian altitude of Vega in Lyra 50 degrees 2
OF THE CELESTIAL GLOBE. 217
3. In what degree of north latitude is the meri-
dian altitude of Regulus, 28 degrees 2 l
PROBLEM XVI.
Given the latitude of a place, day of the month, and the
altitude of a star, to find the hour of the night, and
the star's azimuth. . . . . . . . .
RuLE. Rectify the celestial globe, (by Prob.
VII.) screw the quadrant of altitude upon the bra- .
zen meridian over the given latitude ; bring the
lower end of the quadrant to that side of the meri-
dian on which the star was situated when observ-
ed, and turn the globe westward till the centre of
the star cuts the given altitude on the quadrant;
then the hours which the index has passed over,
will show the time from noon when the star, has the
given latitude; and the quadrant will intersect the
horizon'in the required azimuth, . . . . . .
EXAMPLES.
1. At New-York, on the 20th, of August, the
star Alpherast, in the head of Andromeda, was
observed to be 19, degrees above the horizon, and
east of the meridian ; required the hour of the night
and the star's azimuth. . . . * ,
Answer. The celestial globe being rectified, and turned
westward till the star cuts 190 of the quadrant of the meri-
dian, the index will have passed over 8 hours; consequent-
ly, the star has 199 of altitude east of the meridian, at 8
o'clock in the evening. Its azimuths will be 680 ſrom the
north towards the east. ‘. . . . .
2. On the 21st of December, the altitude of
Sirius, when west of the meridian at London, was
observed to be 8° above the horizon; what hour
was it, and what was the star's azimuth 2
19 * -
218 GRAMMAR ol. ASTRONOMY.
PROBLEM XVII.
Given the latitude of a place, the day of the month, and
azimuth of a star, to find the hour of the night and the
star's altitude. - &
RULE. Rectify the celestial globe, (by Prob.
VII.) screw the quadrant of altitude upon the bra-
zen meridian, over the given latitude; bring the
lower end of the quadrant to coincide with the
given azimuth on the horizon, ând hold it in that
position; then, turn the globe westward, till the
given star comes to the graduated edge of the
quadrant; the hours passed over by the index will
be the time from noon, and the degrees on the
quadrant, reckoning from the horizon to the star,
will be the altitude. -- , -
. . . ExAMPLEs. - .
1. On the 20th of August, the azimuth of Alphe-
rast in the head of Andromeda, was observed to
be 68 degrees from the north towards the east ;
required the hour of the night, and the star's al-
titude. . . . . . - -
Answer... By turning the globe westward on its axis, till
the given star coincides with the quadrant, the index will
have passed over 8 hours; therefore, the time will be 8
o'clock in the evening, the altitude is ſound to be 19 degrees.
2. At London, on the 18th of December, the
azimuth of Denebola was observed to be 624 de-
grees from the south, towards the west; required
the hour of the night and the star's altitude.
3. On the 20th of November, the azimuth of
Aldebaran, was 78 degrees from the south towards
the east; required its altitude at Philadelphia and
the hour of the night. . . .
4. On the 10th of May, the azimuth of Arcturus
was 85° from the north towards the east; required
OF THE CELESTIAL GLOBE. 219
its altitude at Havana, in the island of Cuba, and
also the hour of the right. . . t *
# - PROBLEM XVIII. -
The day of the month and hour when any star rises or
sets being given, to find the latitude of the place of
observation. . *
RULE. Bring the sun's place in the ecliptic to
the brazen meridian, and set the index of the hour
circle to 12; then, iſ the given, time be in the fore-
moon, turn the globe eastward till the index has
passed over as many hours as the time wańts of
noon; but, if the given time be in the afternoon,
turn the globe westward till the index has passed
over as many hours as the time is past noon; the
globe being kept in this position, elevate or depress
the pole till the centre of the given star coincides'
with the horizon; then, the elevation of the polé
will show the latitude. . . . . . . . .
| EXAMPLES. - - -
1. In what latitude does Rigel rise at half past
six o'clock in the evening, on the 10th of De-
cember 2 - • . . -
- Jìnswer. In latitude 41° north, nearly. -
2. In what latitude does Mirach in Bootes, rise
at half past 12 o'clock at night, on the 10th of
December 2 . . .
3. In what latitude does Betelgueze in Orion,
rise at 10 o’clock at night, on the 21st of January 2
- ProBLEM xix. •
Two stars being given, the one on the meridian, and the
other at the east or west part of the horizon, to find
the latitude of the place. - -
RULE. Bring the star which was observed to
be on the meridian, to the brazen meridian; keep
erº,
220 GRAMMAR OF ASTRONOMY.
the globe from turning on its axis, and elevate or
depress the pole till the other star comes to the
eastern or western part of the horizon; then the
degrees from the elevated pole, will be the latitude ,
required. . . . . -
. . . EXAMPLEs. f
-1. When Vega in Lyra was on the meridian, &
Arieties was rising; required the latitude.
Jìnswer. 400 42 north, which is the latitude of New
York. . . . . :
2. When the two pointers of the Great Bear,
marked a and 8, were on the meridian, Vega in
Lyra was observed to be rising; required the lati-
tude of the place of observation.
3. In what latitude are: Sirius, and 8 in Canis
Major rising, when Algenib in Perseus, is on the
meridian 2 -
PROBLEM xx.
The latitude of a place, the day of the month, and two
stars, that have the same azimuth, being given, to find
the hour of the night. . . . -
RULE. Rectify the celestial globe, (by Prob.
VII.) screw the quadrant of altitude upon the
"brazen meridian over the given degree of latitude;
turn the globe on its axis from east to west, till the
two given stars coincide with the graduated edge
of the quadrant; then, the hours passed over by
the index, will show the time from noon; and the
common azimuth of the two stars will be found on
the horizon. f *
- .. EXAMPLEs. .*
1: On the 21st of November, what is the hour
at New-York when Capella and Castor have the
same azimuth, and what is the azimuth 2
of THE CELESTIAL Globe. 22}
Answer. At 9 o'clock in the evening, and the azimuth
will be 610 from the north towards the east.
2. At what hour, at London, on the 1st of May,
will Altair in the Eagle, and Vega in the Harp,
have the same azimuth, and what will that azimuth
be 2 * .* ... . . .
3. On the 21st of December, what is the hour
at Dublin when Algenib in Perseus, and 8 in the
Bull’s horn, have the same azimuth, and what is
that azimuth 2 . . .
• ‘ ‘PROBLEM XXI.
The latitude of a place, the day of the month, and two
stars, that have the same altitude, being given, to find
the hour of the night. . . . . . . . . . . -
RULE. Rectify the celestial globe, (by Prob.
VII.) and screw the quadrant of altitude upon the
brazen meridian over the given latitude; then,
turn the globe on its axis till the two given stars
coincide with the graduated edge of the quadrant,
and the hours passed over by the index will be the
time from noon when the two stars have the same
altitude. . . . . . .
... '
f
EXAMPLES.
1. At what hour at New-York, on the 20th of
April, will y in the Dragon, and o. in the Serpent,
have each 359 of altitude 2 * ~ * * * ,
Answer. At half past 10 o’clock in the evening. . .
2. At what hour at London, on the 2nd of Sep-
tember, will Markab in Pegasus, Alpherast in the
head of Andromeda, have each 30 degrees of al-
titude 2 - .
-- 19:
222 GRAMMAR or ASTRONoMY.
PROBLEM XXII.
The altitudes of two stars having the same azimuth, and
that azimuth being given, to find the latitude of the
place. * * g , , k
RULE. Place the graduated edge of the quad-
rant of altitude over the two given stars, so that
each star may be exactly under its given altitude
on the quadrant; hold the quadrant in this posi-
tion, and elevate' or depress the pole till the divi-
sion marked 0, in the lower end of the quadrant,
coincides with the given azimuth on the horizon;
then, the elevation of the pole will be the latitude
required. - . . -
~
*. * ! EXAMPLEs. 4
1. The altitude of Castor was observed to be
53° nearly, and that of Regulus. 13 degrees; their
common azimuth at the same time was 83° from
the north towards the east; required the latitude
of the place of observation.
flnswer. 41 degrees north, nearly. - {
2. The altitude of Arcturus was observed to be
40°, and that of Cor Caroli 68 degrees; their
common azimuth at the same time was 71° from
the south towards the east; required the latitude
of the place of observation. *
3. The altitude of Dubhe was observed to be
40°, and that of y in the back of the Great Bear
29#9; their common azimuthat the same time was
30° from the north towards the east; required the
latitude of the place of observation. *
PROBLEM xxIII.
To find on what day of the year any known star passes
the meridian of any given place, at any given hour.
RULE. Bring the given star to the meridian,
and set the index to 12; then, if the given time be
of THE CELESTIAL GLOBE. 223
in the forenoon, turn the globé westward till the
index has passed over as many hours as the time
wants of floon; but if the given time be past moon,
turn the globe eastward till the index has passed
over as many hours as the time is past noon; ob-
servé that degree of the ecliptic which is intersected
by the graduated edge of the brazen meridian ; and
the day of the month corresponding to this degree
of the ecliptic will be the time required.
If the given star comes to the meridian at noon; the sun's
place will be ſound under the brazen meridian, without
turning the globe; but if the given star comes to the meri-
dian at midnight, the globe may be turned either eastward
or westward till the index has passed over 12 hours.
EXAMPLEs.
1. On what day of the month does Procyon
come to the meridian of New-York, at 3 o'clock
in the morning 2 ,-/ , - , .
Answer. About the 1st of December. . . .
2. On what day of the year does Denebola come
to the meridian of Dublin, at 9 o'clock at night?
3. On what day of the year does Sirius come to
the meridian of New-Orleans, at 8 o’clock in the
evening 2 -
i PROBLEM xxiv.
The altitudes of two known stars being given, to find the
latitude of the place. . . . . . .
RULE. Subtract each star's altitude from 90
degrees; take successively.the extent of the num-
ber of degrees, contained in each of the remain-
ders, from the equinoctial with a pair of com-
passes; then, with the extent of compasses thus
extended, place one foot successively in the centre
of each star, and describe arcs on the globe with a
224 GRAMMAR OF ASTRONOMY
black lead pencil, fixed in the other-leg of the com-
passes; these arcs will intersect each other in the
zenith ; the zenith or point of intersection, being
them brought to the brazen meridian, will show the
latitude required. . . . . . . . . . . . *
. . . EXAMPLEs. . .
1. The altitude of Markab in Pegasus was 30°,
and that of Altair in the Eagle 659; required the
latitudes, supposing it north. . . . . . . . . .
Jhiswer. 29 degrees north. º • . W.
2. At sea in north latitude, the altitude of Ca-
pella was observed to be 30°, and that of Aldeba-
ran 350; what was the latitude of the place of
observation ?
. . . PROBLEM XXV. ~ :
The latitude of a place and day of the month being given,
to find how long Venus rises before the sun when she is
a morning star, and how long she sets after the Sun
, when she is an evening star. . . . .
RULE. Elevate the pole so many degrees above
the horizon as are equal to the given latitude; find
, the longitude and latitude of Venus in the Nauti-
cal Almanac, or any good ephemeris, and mark.
her place on the globe; and bring the sun’s place
in the ecliptic to the meridian ; then, if the place
of Venus be to the right hand of the meridian,
she is an evening star; if to the left hand, she is
a morning star. . . . . , . . . . .
When Venus is an evening star. Bring the sun’s
place to the western edge of the horizon, and set
the index of the hour circle to 12; turn the globe
westward on its axis till Venus coincides with the
western part of the horizon; and the hours passed
or THE CELESTIAL GLOBE. 225
over by the index, will show
after the sun. . . . . . . . º . .
When Venus is a morning star. Bring the sun’s
place to the eastern part of the horizon, and set
the index of the hour circle to 12; turn the globe
eastward on its axis till Weſſus comes to the eastern
part of the horizon; and the hours passed over by
the index, will show how long Venus rises, before
the sun. * * . . . . . . .
how long Venus sets
3
It may not be improperto observe, that the same rule will
answer to show when any of the planets rises before the
sun, or sets after him; and how long. . . g .
* .. J * •. 3 , - \ z.
EXAMPLEs. * .
1. On the 1st of March, 1825, the longitude of
Venus was 0 sign, 26° 44', or 26° 44' in the sign
Aries, latitude 1950' north; was she a morning.
or an evening star at that time ! If a morning star, J
how long did she rise before the sun at New-York;
if an evening star, how long did she shine after the
sun set 2. . . . . . . . . . . . . . . . . . .
Answer. Venus. was an evening star, and set 2 hours 45.
minutes after the sun. ... . . . . . . . . . .
2. On the 19th of November, 1825, Jupiter's
longitude will be 5 signs. 119 56', or 11° 56' in the
sign Virgo; will Jupiter be a morning or an evening
star 2 If a morning star, how long will he rise be-
fore the sun at Madrid; if an evening star, how
long will he shine after sun-set ! . . . . . . . . . .
3. On the 25th of April, the longitude of We- . .
mus was 2 signs, 6 degrees, 26 minutes, latitude 5°
30' north ; was she a morning or an evening star 2
If a morning star, how long did she rise before
the sun; if an evening star, how long will she
shine after sun-set 2 . . . . .
226. GRAMMAR OF ASTRONOMY.
- QUESTIONs. -
- - f - - * * * > A *
For the examination of the student in the preceding
. . . problems. -
. The questions referring to the rules are in italies, in
order that the student may distinguish them from those
questions which refer to the examples. . - g
1. How do you find the right ascension and declina-
tion of a fixed star 2 . . . . . . . . . . . . .
2. What is the right ascension and declination.
of Dubhe in the back of the Great Bear? . . . .
3. The right ascension and declination of a star,
or planet, being given, how do you find its place on the
globe 2 . . . . . . . . . . . . . . . .
4. What star has 9594" of right ascension, and
52° 36' 11" south declination ? " . . . . . . . . . . .
5. How do you find the longitude and latitude of a
star or planet 2 . . . . . . . . . . . . . . . . . . .
... 6...Required the longitude and latitude of Acu-
bene in Cancer. . . . . . . . . . . .
7. The iongitude and latitude of a star being given,
how do you find its place on the celestial globe? *
8. What star has 8s. 79 19 of longitude, and
4o 32'43"of south latitude 2 . . . . . . . . .
9. The hour of the day and the latitude of a place
being given, how do you find what stars are rising,
culminating, setting, &c. 2 . . . * f. ' ' . . . .
10.- At 9 o'clock in the evening at St. Helena,
on the 20th of June, required those stars that are
rising, culminating, setting, &c. . . . . . . . . .
11. How do you find the distance between any two
known stars in degrees 2 y a . *-*
12. Required the distance. in degrees between
Alphacca and Dubhe. ' - - * ,
13. How do you rectify the globefor the latitude
of a given place, and for the Sun's place in the ecliptic
on a given day ? * ... • #
of THE CELESTIAL, GLOBE. 227
14. Rectify the celestial globe for the latitude
of Lima, and for the sun’s place on the 21st of
June. . . . . . . . . . . -
15. The latilude of a place and day of the month
being given, how do you find the time of the year when
a known star will rise, culminate, and set 2 . . . . . .
16. At what time will Canopus rise, culminate,
and set at Buenos Ayres 2 . . . . . . . . .
17. How do you find the amplitude, oblique ascen-
sion, &c. of a known star, for any given placé 2 ,
18. Required the rising and setting amplitude
of Antares, its oblique ascension and descension,
its diurnal arc, at the Cape of Good Hope. ... .
19. The latitude of a place being given, how do
you find the time of the year at which any known
star rises or sets achronically 2 . . . . . . . . . .
20. At what time of the year does Bellatrix rise
achronically at Quito in Peru, and when does it
set achronically . . . . . . . . . . .
21. The latitude of a place, being given, how do
you find the time of the year at which any known star
rises or sets cosmieally 2 . . . . . . . . . . . .
22. At what time of the year does. Alphard, in
the heart of the Scorpion, rise cosmically at Cape . .
Horn; and at what time of the year does it set
cosmically 2 . . . . . . . . .
23. How do you find the time of the year at which
any known star rises and sets heliağally, at any given
place 2 . . . . . . . . . . . . . . . . . .
24. At what time of the year does Procyon
rise at Canton, and at what time of the year does.
*
- - - *
it set heliacally 2' . . . . . . . . . . .
25. The day of the month being given, how do you
find those stars that rise and set achronically, cosmi-
cally, and heliacally 2 -- *- *
228 GRAMMAR or ASTRONOMY.
26. What stars rise and set achronically, cos-
mically, and heliacally, at Alexandria in Egypt,
on the 21st of March 2, -
27. How do you find the meridian altitude of any
star or planet, the latitude of a place and day of the
month being given? . . . . . . . . . . . . . .
28. What is the meridian altitude of Regulus at
Moscow in Russia 2 . . . . . . . .
29, The meridian allitude of a known star being
given, how do you find the latitude of the place of
observation?... . . . . . . . . . . . . . . . .
30. In what degree of north'latitude is the me-
ridian altitude of Regulus 66 degrees 2 . . . ."
31. The latitude of a place, day of the month, and
altitude of a know star, being given; how do you find
the hour of the nighi, and star's azimuth?, , . . . .
32. At London on the 28th of December, the
star Dénebola, in the Lion’s tail, was observed to
be 40 degrees of altitude; what hour was it, and
what was,the star's azimuth 2 . . . . . . . .
* 33. The latitude of a star, day of the month, and
azimuth of a star, being given, how do you find the
hour of the night and the star's altitude 2 . . . .
34. On the 10th of September, the azimuth of .
the star marked s, in the Dolphin, was 20 degrees
from the south towards the éast; required its alti-
tude at London and the hour of the night: . .
35. The day of the month and hour when any
known star rises, and sets, being given, how do you find
the latitude of the place 2 « » .
36. In what latitude does Regulus rise at 10
o'clock at night, on the 23.3% of January 2
37. Two stars being given, the one on the meri-
dian, and the other at the east or nest part of the
horizon, how do you find the latitude of the place 2
g
of THE CELESTIAL GLoBE. 229
38. When Arcturus in Bootes was on the meri-
dian, Altair in the Eagle was rising ; required the
latitude. . . .
39. The latitude of a place, day of the month, and
two stars that have the same azimuth, being given, how
do you find the hour of the night 2 . . .
40. On the 20th of February, what is the hour
at Edinburgh when Capella and the Pleiades have
the same azimuth, and what is the azimuth? . -
41. The latitude of a place, the day of the month,
and two stars that have the same altitude, being given
how do you find the hour of the night 2 &
42. At what hour at Dublin, on the 15th of May,
will Benetnach in the Great Bear's tail, and y, in
the shoulder of Bootes, have each 56 degrees of
altitude 2 . . . . . . * *
43. The altitudes of two stars having the same
azimuth, and that azimuth being given, how do you
find the place of observation? . . . . . . . -
44. The altitude of Vega in the Harp, was ob-
served to be 709, and that of Ras Algethi in the
head of Hercules, 39% degrees; their common
azimuth at the same time was 60° from the south
towards the west; required the latitude of the
place of observation. -
45. The hour of the day being given, how do you
find on what day of the year any known star will pass
the meridian of a given place 2 -
46. On what day of the month, and in whât
month, does Aldebaran come to the meridian of
Philadelphia, at 5 o'clock in the morning at Lon-
don? - f *
47. The altitudes of two known stars being given,
how do you find the latitude of the place of observa-
tion ? - -
- 20
Y
230 GIRAM1MAR, UF ASTRONOMY.
48. In north latitude the altitude of Procyon
was observed to be 50 degrees, and that of Betel-
gueze in Orion, at the same time, was 58 degrees;
required the latitude of the place of observation.
49. The latitude of a place and day of the month
being given, how do you find how long Venus rises
before the sun when she is a morning star, and how
long she sets after the sun when she is an evening star 2
50. On the 1st of September, 1825, the longi-
tude of Venus was 3 signs, 25° 59', and latitude
1° 16' south; was she a morning or an evening
star? If a morning star, how long did she rise
before the Sun at London; if an evening star, how
long did she shine after sun-set 2 --
BOOK III.
of THE SOLAR systEM, AND THE FIRMA-
MENT OF THE FIXED STARS.
CHAPTER I. . . . .
Of the bodies which compose the solar system. . .
1. The Sol AR System consists of the Sun G) in
the centre; and of eleven primary planets, which,
taken in the order of their proximity to that lumi-
nary, are Mercury & , Venus Q, the Earth (B,
Mars 3, Juno 3, Westa ji, Ceres J, Pallas 3.
* - $ e" 2
Jupiter 1, Saturn H, and Uranus or Herschel iſ
These are called primary planets, because they perform
revolutions round the sun in their respective periodic times.
The four planets, Juno, Vesta, Ceres, and Pallas, are
sometimes called minor planets or asteroids.
2. It also contains eighteen other small planets,
that revolve round several of the primary ones, and
on that account are called secondary planels or sq-
tellites ; besides a considerable but indeterminate
mumber of comets.
The Moon is therefore, considered as one of these
secondary planets, or satellites, because she performs her
revolutions round the Earth ; the rest are, the four satellites
or moons of Jupiter, the seven, satellites of Saturn, and sic
belonging to the planet Uranus or Herschel. All the
planets, both primary and secondary, are opaque bodies,
which borrow their light from the Sun. *
The solar or planetary system, is usually confined to nar-
row bounds; the stars, on account of their immense distance,
and the little relation they seem to bear to us, being ac-
counted no part of it. - w,
3. The primary planets all revolve eastward,
or in the order of the signs of the zodiac, round
the Sun as a centre, in elliptic orbits, or paths
232 GRAMMAR of ASTRONOMY.
which are nearly circular. All these orbits, ex
cept that of the Earth, lie in planes different from
that of the ecliptic, and the angle which the plane
of any makes with that of the ecliptic, is called the
inclination of that orbit. -
4. JMercury, the nearest planet to the sun re-
volves round that luminary in about 88 days, at the
mean distance of 37 millions of miles, -
For the exact duration of the sidereal revolutions of the
planet, the student is referred to the table towards the end
of this chapter. V. -
The period of time which a planet employs during its side-
real revolution, or in passing from any fixed startill its return-
ing to the same again, is the length of that planet's year.
5. Venus revolves round the sun in about 225
days, at the mean distance of 69 millions of miles.
6. The Earth revolves round the sun in about 365;
days, at the mean distance of 95 millions of miles.
7. JMars completes his revolution in about 687
days, at the mean distance of 145 millions of miles.
8. Vesta completes a revolution in about 1335
days, at the mean distance of 225 millions of miles.
9. Juno, in 1591 days, at the mean distance of
253 millions of miles. . . . |
10. Ceres, in 16814 days, at the mean distance
of 262; millions of miles. . .
11. Pallas, in 1682 days, at the mean distance
of 263 millions of miles. . -
12. Jupiter, in about 4333 days, at the mean dis-
tance of 494 millions of miles. . .
13. Saturn, in about 10,759 days, at the mean
distance of 906 millions of miles. . . .
14. Uranus or Herschel, in about 30,689 days,
at the mean distance of 1822 millions of miles.
. . The two planets, Mercury and Venus, are called inferior
planets, because their orbits are included in that of the Earth,
and because they perform their revolutions in less than a year,
GF THE SOLAR SYSTEM. 233
The eight planets, Mars, Juno, Westa, Ceres, Pallas,
Jupiter, Saturn, and Uranus, require a longer period than
a year to complete their revolutions round the Sun; and as
their orbits include that of the Earth, they are called supe-
rior planets. º º
15. The JMoon, the Satellites of Jupiter, Saturn,
and Uranus, describe orbits round their respective
primaries, similar to those which the planets des-
cribe round the sun.
16. The motions of the Comets are very com-
plicated; their orbits, instead of being nearly cir-
cular, like those of the planets, are very eccentric.
Sometimes a comet approaches so near the sun as
to be hid in his rays; at other times, it recedes
from that luminary so far as to be carried beyond
the planetary system, and does not return for seve-
ral hundred years. \
The comets are opaque bodies, which borrow their light
from the sun; they are principally distinguished from the
planets by their tails, or some hairy or nebulous appearance,
and their always disappearing after having been visible only
for a few months. )
TABLE.
Of the sidereal revolutions of the primary planets.
Days. Years. Days. Hours. JMin. Sec.
Mercury S7.96926 || 0 87 23 15 44
Venus 224.70082 || 0 224 16 49 11
The Earth 365.256384 1 O 6 9 || ||
Mars 686.979579 || 1 321 23 30 36
Westa 1335 205 || 3 240 4 55 12
Juno 1590.99792 || 4 130 23 57 0
Ceres 1681.53888 || 4 221 12 56 0
Pallas 1681.7125 || 4 221 17 1 0
Jupiter 4332.60207 || 11 317 14 27 0
Saturn 10758.97.014 || 29 173 23 17 0
Uranus 30688.7 125 | 84 28 17 § 0
The year in this table contains only 365 days of mean
solar time.
Q0*
234 GRAMMAR OF ASTRONOMY.
QUESTIONS.
How many primary planets are there in the so-
lar system 2
How many secondary planets are there 2
How do the primary planets perform their revo-
lutions round the Sun ? 7.
In what time does Mercury revolve round the
Sun ? *
In what time does Venus revolve round the Sun,
and how far is she at her mean distance from that
luminary?
In what time does the Earth perform its revo-
lution round the Sun, &c. 2
In what time does Mars complete his revolu-
tion, &c.
In what time does Westa complete a revolu-
tion, &c. 2 -
In what time does Juno complete her revolu-
tion, &c. 2
In what time does Ceres complete her revolu-
tion, &c. 2
In what time does Pallas complete a revolu-
tion, &c. 2 -
In what time does Jupiter complete his revolu-
tion, &c. 2
In what time does Saturn perform his revolu-
tion, &c. 2.
In what time does Uranus perform his revolu-
tion, &c. 2
How do the secondary planets perform their re-
volutions 2
Name the circumstances respecting the motions,
&c. of the Comets.
Before we conclude this chapter, it may not be improper
to make some observations on the solar system; and also to
OF THE SOLAR SYSTEM, 235
describe the different systems which have been invented,
in order to explain the natural appearances of the heavenly
motions. &
Obs. 1. The most celebrated systems of the world are
the Ptolemaic, the Copernican or Pythagorean, and the
Tychonic. t
2. The Ptolemaic System, so called ſrom the celebrated
Ptolemy, an Egyptian philosopher, who flourished at Alex-
andria about 130 years after the Christian era. . . . e
In this system; he supposed with the vulgar, who measure
everything by their own conceptions, that the earth was fixed
immoveably in the centre of the universe; and that the Moon,
Mercury, W. the Sun, Mars, Jupiter, and Saturn, re-
volve round it in the order of distances in which they are
mentioned. Above these he placed the firmament of the
fixed stars, the crystaline orbs, the primum mobile, and last
of all, the coelum empyrium, or heaven of heavens. All these
vast orbs were supposed to move round the earth once in
twenty-four hours, and also in certain stated or periodical
times, agreeably to their annual changes and appearances.
Every star was supposed to be fixed in a solid transparent
sphere, like crystal ; and, to account for their different mo–
tions, he was obliged to conceive a number of circles called
eccentrics and epicycles, which crossed and intersected each
other in various directions. And if any new motion was
discovered, a new heaven of crystal was formed to account
for it. So that, as Fontenelle observes, heavens of crystal
cost him nothing, and he multiplied them without end, to
answer every purpose. /
Although this system was supported by many of the old
philosophers, and, indeed, almost all astronomers, for nearly
1400 years; yet it has long since been rejected by the most
eminent mathematicians and philosophers.
It is now well known that the planets, Mercury and Vc-
nus, do not include the earth in their orbits; because, if the
earth were the centre of motion, they would be sometimes
in opposition to the sun, which is never known to be the
case. Besides, the comets moving through the heavens in
all manner of directions, must inſallibly have met with con-
{inual obstructions, and would, long ere this, have broken
these crystal spheres to pieces, and rendered them totally
unfit for the purposes for which they were designed.
3. The Copernican, or Solar System, which is now univer-
Sally adopted by all mathematicians and astronomers, is not
only the true, but also the oldest system in the world. It was
236 t; RAMMAR OF ASTRONOMY.
first of all, as far as we know, introduced into Greece and
Italy, about 500 years before Christ, by Pythagoras; from
whom it was called the Pythagorean system. But, from the
accounts of his disciples and followers, it is evident, that it
was not the result of his own observations, but that he had
received hints of it from some more enlightened nations,
who had made greater advances in the science of astronomy.
\
It is most probable, indeed, that the doctrine was trans-
planted by him from the east, in which part of the world he
spent two and twenty years, and scrupled not to comply
with all the customs peculiar to the eastern nations, in order
to obtain free access to their priests and magi, to whom al-
most all knowledge of the arts and sciences was then con-
fined. And as he was a man of extraordinary qualities,
and had an insatiable thirst for knowledge, so he seems to
be the most successfül of any of the ancients in making
himself acquainted with their philosophies.
The Pythagorean system had, in a great measure, been
lost during several ages; but Copernicus, a bold and
original genius, retrieved it about the year 1500; from whom
it took the name of the Copernican System.
Copernicus having adopted the Pythagorean or true sys-
tem of the universe, published it to the world with new and
demonstrative arguments in its favour, in his work entitled
De Revolutionibus Orbium Caelestium, first printed at Nu-
remberg in 1543, a little previous to his death, which took
place in the same year, at the age of seventy. In this trea-
tise he restored the ancient Pythagorean system, and deduced
the appearances of the celestial motions from it in the most
satisfactory manner. Every age since has produced new
arguments in its favour; and notwithstanding the opposition
it met with from the prejudices of sense against the earth’s
motion, the authority of Aristotle in the schools, &c.; the
truth of the ancient Pythagorean system, by applying ma-
thematical reasoning to mechanical experiments, was
established by Sir Isaac JNewton; and upon this foundation
he raised the superstructure of that philosophy, which,
whilst all other systems sink into ruins, and little more than
their inventors’ names are remembered, will remain for ever
firm and unshaken; for being once demonstrated to be true,
it must eternally remain to be so, as nothing can alter it but
the utter subversion of the laws of nature, and the constitu-
tion of things.
In the ancient Pythagorean system, which was revived by
OF THE SOLAR SYSTEMI. 237
Copernicus, clearly demonstrated by Newton, and which is
now adopted by all astronomers and mathematicians, as the
true system of the universe; the sun is placed in the centre,
about which the planets revolve, from west to east, in the
following order of distances; Mercury, Venus, the Earth,
Mars, Jupiter, Saturn, and Uranus; beyond which, at an
imnaense distance, are placed the fixed stars. The Moon
revolves round the earth; and the earth revolves about its
own axis. The other secondary planets move round their
respective primaries from west to east at different dis-
tances, and in different periodical times.
4. Although the Copernican System was received by
most men of science then living, yet there were some who
would never assent to it. The motion of the earth was so
contrary to what they were always accustomed to hear on
the subject, and, as they thought, to appearances, they could
never agree to support such doctrine. Among those who
opposed the system of Copernicus, was Tycho. Brahe, a
Danish nobleman, who was born in 1546, and who devoted
the whole of his life to the study of astronomy. As Tycho
could not entirely adopt the Ptolemaic system, being con-
vinced that the earth is not the centre about which the
planets revolve, and out of respect for some passages of
Scripture, which seemed to contradict the doctrine of the
Pythagorean system, which Copernicus had lately revived;
he invented a new system, which was a kind of mean between
the Ptolemaic and Copernican. In the Tychomic System,
the Earth is placed in the centre of the orbits of the Sun
and Moon; but the Sun is supposed to be the centre of the
orbits of the five primary planets then known.
In this new system of Tycho, there is some ingenuity,
though but little conformity to truth and observation. For
having rejected the diurnal rotation of the earth on its axis,
he was obliged to retain the most absurd part of the Ptole:
maic hypothesis, by supposing that the whole universe; to its
farthest visible limits, was carried by the primum mobile
about the axis of the earth continually every day. But in
this, however, he was abandoned by some of his followers,
who chose rather, to save this immense labour to the spheres,
by ascribing a diurnal motion to the earth; on which account
they were distinguished by the name of Semi-Tychonics.
5. Besides these different systems, there is also another,
called the System of Des Cartes, which, on account of its
being the celebrated system of vortices, may not be impro-
perly taken notice of here.
238, GRAMMAR OF ASTRONOMY.
In this system of Des Cartes, the Sun is supposed to be
placed in the centre of a vast whirlpool of subtle matter,
which extends to the utmost limits of the system, and the
planets, being plunged into such parts of this vortex as are
equal in density with themselyes, are continually dragged
along with, and carried round their several orbits by its con
stant circulation. Those planets which have satellites are
'likewise the centres of other smaller whirlpools which swim
in the great one; and the bodies that are placed in them, are
driven round their primaries, in the same manner as those
primaries are driven round the sun. Now as the sun turns
on his axis the same way that the planets move round him,
and the planets also turn round their axis the same way as
their satellites move round them; it was imagined, that if
the whole planetary region was filled with a fluid matter,
like that before mentioned, the sun and planets, by a constant
and rapid motion on their axis, would communicate a circu-
lar motion to every part of this medium, and by that means
drag along the bodies that swim in it, and give them the
g
g
same circumvolution. *
This, in a few words, is the celebrated system of vortices,
and the world of Des Cartes. The fabric, it must be con-
fessed, is raised with great art and ingemuity, and is evi-
dently the produce of a lively fancy and a fertile imagina-
tion. But then it can be considered only as a philosophical
romance, which amuses without instructing us, and serves
principally to show that the most shining abilities are fre-
Quently misemployeri; and will always be found inadequate
to the arduous task of forming a complete system of nature,
which is not to be expected even from the labour of ages.
Besides various objections which may be brought against
Des Cartes’ system, it has been demonstrated by Newton
and others, that let the nature of these vortices be what it
may, yet the circulations, in such a fluid, would never agree
with the known laws of their motion, established by later
astronomers, from repeated observations. But, admitting
for a moment that this system of whirlpools was compati-
ble with the phenomena of nature, and the laws of me-
chanics, still their cause would be but little better; for no
such whirlpools have ever yet been shown to exist. It is
not sufficient that a hypothesis accounts for the phenomena;
but it must be shown that it is founded in fact, and sanc
tioned both by reason and experience.
OF THE SOLAR SYSTEM. 239
C#APTER II.
Explanation of astronomical terms, &c.
1. The orbit of a planet or comet is the imagi-
nary path or track, in which it performs its revo-
lution round the Sun. The orbits of all the pri-
mary planets are elliptical or oval, with the Sun
situated in one of the foci ; as at S. This is usually
called Kepler’s first law. t
If in two points F, S, taken in a plane, are fixed the ends
of a thread, the length of which is greater than the distance
between these points; and if the point of a pen or pencº
applied to the thread, and held so as to keep it uniformly
tense, is moved round, till it returns to the place from
whence the motion began; the point of the pen or pencil,
as it moves round, describes upon the plane a curve line,
which is usually called the ellipse. The figure bounded by
the curve line is, properly speaking, the ellipse or oval,
though the term ellipse is more commonly used to imply
the boundary of that figure.”

240 GRAMMAR OF ASTRONOMY.
The points F and S, where the ends of the thread were
fixed, are called the foci of the ellipse. The point C, which
bisects the straight line between the foci, is named the centre
of the ellipse. The line A B is called the transverse or greater
awis, and Q H the conjugate or lesser aſcis ; and the dis-
tance between one of the foci as S, and the centre C, is
called the eccentricity of the ellipse. It is evident, that the
less the eccentricity is, the nearer will the figure of the
ellipse approach to that of a circle.
2. Jiphelion is that point in the orbit of a planet
which is farthest from the Sun, sometimes called
the higher apsis.
3. Perihelion is that point in the orbit of a
planet which is nearest to the Sun, sometimes called
the lower apsis. -
4. Apogee is that point of the earth's orbit
which is farthest from the Sun, or that point of the
Moom’s orbit which is farthest from the Earth.
5. Perigee is that point of the Earth's orbit
which is nearest to the Sun, or that point of the
Moon’s orbit which is nearest to the earth.
The terms Aphelion and Perihelion are also applied to
the Earth’s orbit. * *
6. Apsis of an orbit is either its aphelion or pe-
rihelion apogee or perigee ; and the straight line
which joins the apsides, is called the line of the ap-
sides. -
7. The distance of the Sun from the centre of
a planet’s orbit, is called the eccentricity of the orbit.
8. A straight line drawn from the centre of the
Sun to the centre of any of the primary planets, is
called the radius vector of that planet.
A straight line joining the centres of the Earth and Moon,
is called the radius vector of the Moon.
9. As the orbits of the planets are elliptical, having
the Sun in one of the foci ; their motions round
RELATIVE SIZES OF THE PLANEPs.
|-
-
|-
----
-
----
|-
|-
|-
|-
-
|||||||||||||

of THE SOLAR systEM. 24l
that body are not equable, being greatest in the
perihelion, and least in aphelion. The motion of
a planet in every point of its orbit is, however, re-
gulated by an immutable law, which is this ; that
the radius vector of a planet describes equal elliptic
areas in equal times. This is usually called Kepler’s
second law. . . . . . . . -
10. It was also discovered by Kepler, and has
been fully confirmed by " astronomers and ma-
thematicians since his time, that the square of the
time in which any planet revolves round the Sun, is to
the square of the time in which another planet does the
same, as the cube of the mean distance of the former
from the Sun, is to the cube of the mean distance of
the latter. This is usually called Kepler’s third law.
Hence, if the distance of the Earth, or of any planet, from
the Sun, and the periodical revolutions of all the planets be
once ascertained ; the cubes of the mean distances of the
several planets from the sun may be readily found by direct
proportion. +. - -
11. The true anomaly of a planet is its angular
distance at any time from its aphelion, or apogee.
12. The mean anomaly is its angular distance
from its aphelion, or apogee, if it had moved uni-
formly with its mean angular velocity. . . . .
In the tables of the Sun, Moon, and planets, the epochs,
have been hitherto given for the apogee'; but as they must
be taken for the perigee of comets, De la Caille proposed
that, for the sake of uniformity, the same should be adopted
for all the bodies in the planetary system. . . .
13. The difference between the mean anomaly
and true anomaly, is called the equation of the centre.
14. The mean place of a body is the place where
that body (not moving with an uniform angular
velocity about the central body) would have been
if the angular velocity had been uniform. Its true
- Q t -
,-e M.
242 GRAMMAR OF ASTRONOMY.
place is the place where the body actually is at
any time. - -
Illustrations of the above articles. .
1. Let APQBH, (see fig., page 239,) be the elliptical
orbit of a planet, S the Sun in one of the foci; the planet in
revolving round that luminary in the direction of the letters
APRQ, &c. cannot be always at the same distance from the
focus S, but will be farthest from it at the extremity A of the
greater axis, and nearest to it when in B. The point A is
named the higher apsis, or the aphelion ; and the point B
the lower apsis, or perihelion; these two points vary, and
their motion in a century is called the secular motion. The
distance between the centre C and the sun, or focus S, is
the eccentricily of the orbit. The greater axis AB is the
line of the apsides. The straight line SQ, drawn from the
extremity of the lesser axis QH to the sun, is the mean
distance of the planet from the sun.
The mean distance added to the eccentricity is equal to
the aphelion distance SA. And the mean distance minus
the eccentricity is equal to the perihelion distance SB.
2. A planet does not proceed in its orbit with an equal
motion; but in such a manner that the Radius Vector de-
scribes an area proportional to the time: for instance, Sup-
pose a planet to be in A, when in a certain time it arrives
at P, the space, or area, ASPA is equal to the space, or
area, PSQP, described in the same time from P.
3. If the angular motion of the planet about the sun were
uniform, the angle described by the planet in any interval of
time, after leaving the aphelion, might be found by simple
proportion, from knowing the periodic time in which it de-
scribes 3609; but as the angular motion is slower near aphe-
lion, and faster near perihelion, to preserve the equable de-
seription of areas, the true place will be behind the mean
place in going from aphelion to perihelion; and from peri-
helion to aphelion, the true place will be before the mean
place. For instance, suppose P be the true place of a
planet at the end of a certain ti, after leaving the aphelion
A ; then, its mean place woul. . . ºn some part of the orbit
between P and B. Now, let I, be the mean place of the
planet, when P is its true place; then the angle ASR is the
mean anomaly; the angle ASP, the true anomaly ; and the
angle PSR, the difference between the mean anomaly and
the true anomaly, is the equation of the centre.
of THE solar systEM. 243
Or, if a planet is supposed to move in a circle, in the
centre of which is the sun, the portion R.O of the circle bears
the same ratio to the whole circumference, that the time
since the planet passed its aphelion does to the time of its
whole revolution; the arc RO is termed the mean anomaly.
Again, if the elliptical orbit of a planet be so divided that
the area ASP shall have the same ratio to the area of the
whole-ellipse AQBH, which the time since the planet passed
its aphelion has to its whole period, then is the angle ASP.
the measure of the planet’s distance from the aphelion, at
the time the planet is in P. This angle is also the true
anomaly; and the difference between the mean anomaly and
the true anomaly, is the equation of the centre, as before.
4. The arc AD of the circle AGBK intercepted between
the aphelion A, and the point D, determined by the perpen-
dicular DPE to the line of the apsides, drawn through the
true place P of the planet, is called the eccentric anomaly, or
of the centre. Or, the angle ACD at the centre of the circle,
is usually called the eccentric anomaly. -
5. Equations, in Astronomy, are corrections which are
applied to the mean place of a body, in order to get its true
place; and argument is also a term sometimes used to de-
note a quantity upon which another quantity or equation de-
pends; or, it is the arc, or angle, by means of which another
arc may be found, bearing some proportion to the first: thus,
the argument of the equation of the centre, is the distance of .
a planet from the aphelion or apogee, because it is upon
that the equation of the centre depends. . . . .
15. The JNodes are the two opposite points
where the orbit of a primary planet intersects the
plane of the ecliptic, or where the orbit of a secon-
dary planet cuts that of its primary. The straight
line joining these two points is called the line of the
modes. • * - , ' ' , , , * ...
Jäscending node is that point where the planet ascends
from the south to the north side of the ecliptic; and the op-
posite point where the planet descends from the north to the
south side of the ecliptic, is called the descending node.
The ascending node is denoted by the character Ö, and the
descending node by Q . The inclinations of the planes of
the orbits of all the planets, except Pallas, to the plane of
the Earth’s orbit are small, . *
, 244 GRAMMAR OF ASTICONOMY.
16. Aspect of the stars or planets, is their situa-
tion with respect to each other. There are five
aspects, viz. 3 Conjunction, when they have the
same longitude, or are in the same sign and degree;
* Seatile, when they are two signs, or a sixth part
of a circle distant; [] Quartile, when they are three
signs, or a fourth part of a circle, from each other;
A Trine, when they are four signs, or a third part
of a circle, from each other, and 8 Opposition, when
they are six signs, or half a circle, from each other.
The conjunction and opposition, particularly of
the moon, are called the Syzegies; and the quartile
aspect the Quadrature. . . . . . . . . . . . . .
Or, the five principal aspects of the planets, with their
characters and distances, are as follows:– *:::: *
f JName. Character. Distance.
Conjunction, . . . . | 6 | 09 – 6 signs.
Sextile, . . . . . . . . .* 60 -— 2 Sºis,
Quartile, , . . . . [...] "90 = 3.s.
Trine, ... . . . . . . . . A | "120 = 4.s.
Opposition, . . . . 8 180 = 6 s.
These intervals are reckoned according to the longitudes
of the planets; so that the aspects are the same, whether
the planet be in the ecliptic or out of it. - . . . .
These terms were introduced by the ancients for the pur-
poses of Astrology, but they are still retained in some cases
in astronomical works; in the former case, they are more
numerous; but it would be improper to enumerate such
foolish distinctions in the present day. * , . . .
17. An inferior planet is said to be in inferior
conjunction, when it comes between the Sun and
the Earth. In superior conjunction, the Sun is be-
tween the Earth and planet. And a superior planet
is in opposition, when the Earth is between the Sün
and planet, * . . . . . . . . . . . . . . . . * , .
*. , ****
... . . . . . ; - vº
QF THE SOLAR SYSTEMI. 245
18. The apparent motion of the planets is either
I)irect, Stationary, or Retrograde. The motion of
a planet is said to be direct when it appears to a
spectator on the earth to perform its motion from
west to east, or according to the order of the signs.
A planet is said to be stationary when, to an ob-
server on the earth, it appears to have no motion,
or, which amounts to the same thing, when it ap-
pears in the same point of the heavens for several
days. And retrograde is an apparent motion of
the planets, by which they seem to move backward
in the ecliptic, or contrary to the order of the signs.
These terms shall be more fully illustrated in a subse-
quent part of the work. ! r c -
*
19. The 12th part of the sun or moon’s apparent
diameter is called a digit. Disc is the face of the
sun or moon, such as they appear to a spectator on
the earth; for though the sun and moon be really
spherical bodies, they appear to be circular planes.
20. The geocentric place of a planet méans its
place as seen from the Earth; or it is a point in
the ecliptic, to which a planet, seen from the Earth,
is referred : and its heliocentric place as seen from
the Sun. . . 3. * -
g
Geocentric is said of a planet or its orbit, to denote its
having the Earth for its centre. The Moon alone is pro-
erly geocentric, and yet the motions of all the planets may
i. cönsidered in respect to the Earth, or as they would ap-
pear from the Earth’s centre, as geocentric; and thence called
their geocentric motions. The heliocentric motions of the
planets are their motions as seen by a spectator situated in
the Sun, which is always direct, or in the order df the signs.
21. Geocentric latitudes and longitudes of the
planets, are their latitudes and longitudes as seen
*
from the earth. . . .
21*
246 'GRAM]]VíAR OF ASTRON ONIY.
22. Heliocentric latitudes and longitudes of the
planets, are their latitudes and longitudes, as they
would appear to a spectator situated in the Sun.
23. Occultalion is the obscuration or hiding from
our sight any star or planet, by the interposition of
the body of the moon, or of some other planet,
24. Transit is the apparent passage of any planet
over the face of the sun, or over the face of another
planet. Mercury and Venus, in their transits over
the sun, appear like dark speeks.
25. Aberration is an apparent motion of the ce-
lestial bodies, occasioned by the earth’s ammual mo-
tion in its orbit, combined with the progressive mo–
tion of light. . . . . . ..' .
26. The Elongation of a planet is, its angular
distance from the sun, with respect to the earth, or
it is the angle formed by two limes drawn from the
earth, the one to the sun, and the other to the
planet. . . . . . . . t *
27. Eclipse is a privation of the light of one of
the luminaries, by the interposition of some opaque
body, either between it and the observer, or between
it and the sun. ‘. . . . - §
Tó the first class belong solar eclipses, and occultations
of the fixed stars by the moon or planets, and to the second
lunar eclipses, and of the other satellites, particularly those
of Jupiter. & * = º * y *
• W
28. Eclipse of the JMoon is a privation of the light
of the moon, occasioned by an interposition of the
earth directly between the sun and moon, and so
intercepting the Sun's rays that they cannot arrive at
the moon to illuminate ber. . . .
'Or, the obscuration of the moon may be considered as a
section of the earth's conical shadow, by the moon passing
through some part of it. - * . . .
‘OF THE SOLAR SYSTEM. 24.7
29. Eclipse of the Sun is an occulation of part of
the sun’s disc, occasioned by the interposition of the
moon between the earth and the sum. On which
account it is by some considered as an eclipse of
the earth, since the light of the sun is hid from it by
the moon, whose shadow involves a part of the
earth.
2 * ,
\
into total, partial, annular, central, &c. - ‘.
Total eclipse is that in which the whole luminary is dark-
ened. Partial eclipse is when only a part of the luminary
is eclipsed. Annular eclipse is when the whole is eclipsed,
except a'ring, or annulus, which appears round the border
or edge: this is peculiar to the sun. And a central eclipse
is that in which the centres of the two luminaries and the
earth come into the same straight line.
Eclipses are divided, with respect to the circumstances,
QUESTIONs.
What is the orbit of a planet! Of what figure are
the orbits of the planets, and in what part of the
figure is the sun placed 2 * — º .”
What is the aphelion or higher apsis of a planet's
orbit? What is the perihelion or lower apsis of a
planet's orbit?
When is the moon in apogee, and when is she in
perigee ? f , - ‘’’ s
What is the line of the apsides 2 h
What is the eccentricity of the orbit of a planet?
What is the radius vector of a planet, and by
what law is the motion of a planet in every point of
its orbit regulated 2
By what law are the periodical revolutions of the
planets, with respect to their several distances from
the sun, regulated 2 -J
What is the true anomaly of a planet, and what
is its mean anomaly 2
248 GRAMIMAR OF ASTRONOMY.
•ºrs
What do you call the equation of the centre :
What is the mean place of a planet, and what is
its true place 2 * f $. *
What are the nodes of a planet, and what do you
call the line of the nodes 2 *
What are the different aspects of the planets, and
how many are there ! , - . .
When is a planet’s motion said to be direct, sta-
tionary, and retrograde 2 -
What is a digit, and what is the disc of the sun or
~
moon? 3. l * *
What are the geocentric and heliocentricºlati-
tudes and longitudes of the planets 2 a
What is the occultation of a star or planet 2
What is the transit of a planet 2
What is the aberration of a star 2
What is the elongation of a planet 2
What is meant by an eclipse 2
What is an eclipse of the moon, and what is the
cause of it? . . • * . .
What is an eclipse of the sun, and what is the
cause of it?', ', • *
•
*
&
--- Iº
-º-º-º-º:
$ & ** * }
*
CHAPTER III.
* * of the Sun. .
The SUN is a spherical body, placed nearly in the
t” }
centre of the solar system, and the several planets
revolve about it in different periods, and at different
distances. The comets also revolve about the
Sun, but in very eccentric orbits, being sometimes
very near, and at others at an immense distance
from him. V ->
OF THE SOLAR SYSTEMr. 249
The Sun is the great source àf fight, heat, and animation
to all those bodies; and ſo the influence of which, combined
with their sidereal and diurnal revolutions, they owe the
successive alternations of suimmer and winter, day and night.
2. The Sun is the largest body yet known in the
universe; its mean, diameter being 887,000 Ameri-
can miles, or about 112 times the mean diameter of
the Earth; and its size 1,406,550 times that of the
Earth; but its mass or quantity of matter, is only
32,960 times greater, and its density about; that of
the Earth. . . . . , , , , , , , , * . . .”
A body. which weighs one pound at the surface of the
Earth, would, if removed to the surface of the Sun, weigh
-27 pounds, 14 ounces and 15 drachms, and bodies would fall
ºthere, with a velocity.oſ 334 feet 8 inches in the first second
of time." ( -., . . * :
* 3: The apparent diameter of the Sun, as seen
from the Earth, undergöes a periodical variation.
It is greatest when the Earth' is in its perihelion,
which is about December the 31st, at which time
it is 32' 35.6"; and it is least, when the Earth is in
its aphelion, which is about July the ist, at which
time it is 31' 31". Its méan apparent diameter is
therefore 32' 3.3" . . . . . . . . . .
The greatest equation of the Sun's centre is 10 55' 27.7",
which diminishes at the rate of 16.9% in a century. The
Sun's horizontal parallax, as determined by the transit of
Venus, is 8%". See the chapter on Parallax, &c. in a sub-
sequent part of this work. . . . . . . .
4. The Sun, is surrounded with an atmosphere
of great extent; its height, according to Dr. Her-
schel, is not less than 1843, nor greater than 2765
miles. . . . . . . . . . . . . . . .
This atmosphere, Dr. Herschel thinks, consists of elastic
fluids that are more or less lucid and transparent, and of
which the lucid ones ſurnish all the bodies in the solar sys-
...tem with light; and he supposes that the density of the
luminous solar clouds need not be greater than that of our
~,
250 GRAMIMAR OF ASTIRONOMY.
Aurora Borealis, to produce the effect with which we are
acquainted. ' * * ,
5. The Sun is frequently obscured by spots,
some of which have been observed so large as to
exceed the Earth five or six times in -diameter.
Sometimes, though rarely, the Sun has appeared
pure and without spots, for several years together.
. The number, position, and magnitude of the solar spots,
are very variable; they are often very numerous, and of con-
siderable extent. Some imagine they may become so
numerous as to hide the whole face of the Sun, or at least
the greater part of it; and to this they ascribe what Plutarch
mentions, viz.: that in the first year of the reign of Augus-
tus, the Sun's light was so faint and obscure, that one might
look steadily at it with the naked eye. To which Kepler
adds, that in 1547, the Sun appeared reddish, as when
viewed through a thick mist; and hence he conjectures that
the spots in the sun are a kind of dark Smoke, or clouds
ſloating on his surface.' . . . .
The solar spots, in general, consist of a dark space, or
umbra, of an irregular form ; they are almost always sur-
rounded by a penumbra, which is enclosed in a cloud of
light, more brilliant than the rest of the Sun, and in the
midst of which the spots are seen to form and disappear.
All this, according to La Place, indicates that at the surface
of this enormous fire, vivid effervescences take place, of
which our volcanoes form but a feeble representation. But
whatever be the nature of the solar spots, they have made
us acquainted with a remarkablé phenomenon, that is, the
rotation of the Sun. . e ->
Amidst all their variations we can discover regular mo–
tions, which are exactly the same as the corresponding
points of the surface of the Sun, if we suppose it to have a
motion of rotation on an axis, almost perpendicular to the
ecliptic, in the direction of its apparent, annual motion
round the earth. *
6. The continued observation of these spots
shows that the Sun revolves on its axis in 25 days,
10 hours; that its figure is not truly spherical, but
an oblate spheroid like the earth ; and that the
*
of THE solah SYSTEM. 251
solar equator is inclined 70 30 to the plane of the
ecliptic. - *
For, some of these spots have made their first appearance
near the eastern edge, from thence they have seemed gradu-
ally to pass over the Sun's disc to the opposite edge, then
disappear; and hence, after an absence of about 14 days,
they have re-appeared in their first place, and have taken
the same course over again; finishing their entire circuit in
27 days, 12 hours and 20 minutes, which is hence inferred
to be the period of the Sun's rotation round his axis; and
therefore: the periodical time to a fixed star, usually called
the sidereal revolution, is 25d. 15h. 16m.; because, in 27d.
12h. 20m. of the month of May, when the observation was
made, the Earth describes an angle about the Sun's centre of
26O 22', and therefore as the angular motion 3600–1260
22 or 386D 22': 8600: ; 27d. 12h. 20m. ; 25d. 15h. 16m.
As the solar spots appear to move on the Sun's disc, from
the eastern to the western edge, whence we, may conclude
the motion of the Sun, to which the other is owing, to be
from west to east, or in the same direction, with respect to
the order of the signs, as the diurnal rotation of the Earth.
The more correct period of the Sun's rotation is now stated
at 25d. 10h. as in the above article. ~ : -
7. The Sun, together with the planets, moves
round the common centre of gravity of the solar
system, which is nearly in the centre of the Sun.
This small motion of the Sun round the centre of gravity
is occasioned by the various attractions of the surrounding .
planets. . . . . * ~
8. Besides the two real motions of the Sun al-
ready mentioned, the Sun has also two apparent
motions; that is, the diurnal motion from east to
west, and his annual motion in the ecliptic ; but
these apparent motions arise from the real motions
of the earth on its axis, and in its orbit.
Whether the Sun and stars have any proper motion of
their own in the immensity of space, however small, is not
absolutely certain, though some very accurate observers
have intimated conjectures of this kind, and have shown
that such a general motion is not improbable. Dr. Herschel
253, . . . GRAMMAR, or ASTRONOMY.
cónceives the Sun and the planets to have a general mo-
tibm; which carries the solar system towards the constella-
tion Hercules. . . . . . . . . ' ', $
} \, ... ...As to the nature of the Sun. , , , , , , ,
*For many ages the Sun was believed to be a globe of fire,
ańd those who have maintained this hypothesis, argue in the
following manner. The Sun shines, and his rays, collected
by concave mirrors, or convex lenses, will burn, consume,
ańd melt the most solid bodies, or else convert them into
ashes or glass; therefore, as the ſorce of the solar' rays is
diminished by their divergency, in the duplicate ratio of
their distancés reciprocally taken, it is evident that their
förce and effect are the samc, when collected by a burning
lèns or mirror, as if we were at such distance ſtom the sun,
where they were equally dense. The Sun's rays, therefore,
in the neighbourhood of the Sun, produce the same effects
as might be expected from the most vehement fire; conse-
quently, the Sun is of a fiery substance. Q. . . . .
Hence it follows, that its surface is probably every where
fluid ;, that being the condition of flame. Indeed, whether
the whole body of the Sun be fluid, as some think, or solid
as others, they do not présumé to determine ; but as there
are no other marks, by which to distinguish fire from other
bodies, but light, heat, a power of burning, consuming,
melting, calcining, and vitrifying, they do not see what ob-
jection should be made to the hypothesis, that the Sun is a
globe of fire like our fires, invested with a flame; and, sup-
posing that the maculae, or spots, are formed out of the solar
exhalations, they infer that the Sun is not pure fire, but that
*
f
there are heterogeneous parts mixed with it. . .
'. But, the majority of modern astronomers, have rejected
this opinion, and several of them, have published very inge-
nious hypotheses on this, curious subject, Qne of the most
plausible and ingénious theories on this subject is given by
* Dr. Herschel; in the philosophical transactions of the Royal
**
Society. He supposes the Sun has an atmosphere resembling
that of the Earth, and that this atmosphere consists of vari-
..ous elastic fluids, some of which exhibit ashining brilliancy,
while others are merely transparent. Whenever the lumi-
'rious fluid is removed, the body of the Sun may be seen
through those that are transparent. In like mafiner, an ob-
server placed in the JMoon will see the solid body of the Earth
only in those places where thé transparent fluids of our ai.
of THE SOLAR systEM. 253
mosphere will permit him. In others, the opaque vapours
will reflect the Sun's light, without permitting his solid body
to be seen on the surface of our globe. In the same manner
he illustrates the various appearances of spots in the Sun.
Such appearances, he thinks, may be easily and satisfacto-
rily explained, if it be allowed that the real solid body of the
Sun itself is seen on these occasions, though we seldom see
more than its shining atmosphere. Dr. Herschel apprehends
that there are considerable inequalities in the surface of the
Sun, and that there may be elevations not less than 500 or
600 miles in height; that a very high country, or chain' of
mountains, may oftener become visible by the removal of .
the obstructing fluid than the lower regions, on account of
its not being so deeply covered by it. In the year 1799, he
observed a spot on the Sun large enough to be discerned by
the naked eye, for it extended more than fifty thousand miles.
He also says, that he observed a large spot in 1783, which
he followed up to the edge of the Sun's limb; that he plainly .
perceived it to be depressed below the surface of the Sun,
and that it had very broad'shelving sides. This appearance
may be explained hy a gentle and gradual removal of the
shining fluid, which permits us to see the globe of the Sun.
Dr. Herschel also says, that on the 26th of August, 1792,
he examined the Sun with several powers, from 90 to 500,
and that it evidently appeared that the black spots were the
opaque ground, or body of the sun, and that the luminous
part was an atmosphere, which being interrupted or broken,
gave a glimpse of the Sun himself. He further adds, that
with his seven feet reflector, which was in an excellent state
of perfection, he could see the spots, as on former occasions,
with the same telescope, much depressed below the surfacé
of the luminous part. - -
On the 8th of September, 1792, he made a speculum,
which he brought to a perfect figure on hone, without polish;
this had the effect of stifling a great part of the Sun's rays;
and on this account the object speculum admitted a great
aperture, which enabled him to see with more comfort and
less danger. He then discovered that the surface of the
Sun was unequal, many parts of it being elevated, and others
being depressed ; but this inequality was in the shining sur-
face only, for he thinks that the real body of the Sun is sel-
dom seen otherwise than in its black spots.
As light is a transparent fluid, it may not be impossible
that the Sun's real surface may be now and then perceived.
22 n -
254 GRAMMAR OF ASTRONOMY.
as the shape of the wick of a candle may sometimes be seen
through its flame, or the contents of a furnace in the midst
of the brightest glare of it. . But this, Dr. Herschel thinks,
can only happen where the luminous matter of the Sun is
not very accumulated. - - * . -
From these appearances Dr. Herschel draws the follow-
ing conclusions, that the Sun has a very extensive atmos-
phere, which consists of various elastic fluids, that are more
or less lucid and transparent, and that the lucid one is that
which furnishes us with light; that the generation of this
lucid ſluid on the solar atmosphere is a phenomenon similar
to the generation of clouds in our atmosphere, which are
produced by the decompósition of its constituent elastic
fluids; but, with this difference, that the continual and very
extensive decomposition of the elastic fluids of the Sun are
of a phosphoric nature, and attended with lucid appearances,
by giving out light. To the objection that such decompo-
sition, and consequent emissions of light, would exhaust the
Sun, he replies, that, in the decomposition of phosphoric
fluids, every other ingredient except light may return to the
body of the Sun; and besides, the exceeding subtilty of
light is such, that in ages of time, its emanation from the
Sun cannot very sensibly lessen the size of so great a body.
From the atmosphere, Dr. Herschel next proceeds to state
that the body of the Sun is opaque, of great solidity, and its
surface diversified with mountains and valleys; that the Sun
is nothing else but a large lucid planet, evidently the first,
or, strictly speaking, the only primary one of our system, all
others being truly-secondary to it. Its similarity to the other
globes of the solar system, with regard to its solidity, its at-
mosphere, and its diversified surface, the rotation on its axis,
and the fall of heavy bodies, lead to suppose that it is inha-
bited, like the rest of the planets, by beings, whose organs are
adapted to the peculiar circumstances of that vast globe.
Should it be objected that the heat of the Sun is unfit for a
habitable world, he answers, that heat is produced by the
Sun's rays only when they act on a calorific medium, and
that they are the cause of the production of heat by uniting
with the matter of fire. whióh is contained in the substances
that are heated. He also suggests other considerations in-
tended to invalidate the objections, but they require more
room to detail them than can be afforded in this work.
After Dr. Herschel thinks he has shown that the heat of
the Sun is not so great as to prevent it from being inhabited,
OF THE SOLAR SYSTEMI. 255 .
he then deduces from analogy a variety of arguments to
confirm the notion of the Sun being a habitable body; and
then infers, that if the Sun be capable of accommodating
inhabitants, the other stars, which are suns, may be appro-
priated to the same use; and thus, says he, we see at once
what an extensive field for animation thus opens to our view.
The reader is referred to the Philosophical Transactions for
1795, where he will find many ingenious remarks and ob-
servations relating to this subject. - * *
Dr. Wilson, late professor of astronomy, Glasgow, sup-
poses the spots of the San are depressions, or excavations,
rather than elevations, and that the dark nucleus of each
spot is the opaque body of the Sun, seen through an opening
in the luminous atmosphere with which he is surrounded.
See Wilson: Philosophical Transactions, 1744 and 1783.
Various other hypotheses have been advanced, as to the
cause of these spots, and the nature of the luminary on
which they appear. Lahire and Laland suppose them to be
eminences, or dark bodies like rocks, on the body of the Sun,
appearing at times in consequence of the flux and reflux of
the liquid igneous matter of the Sun. That part of the
opaque rock which at any time thus stands above, gives the .
appearance of the nucleus; while those parts that lie only a
little under the igneus matter appear to us as the umbra
which surrounds the dark nucleus. Some other astronomers'
consider these spots as scoria floating in the inflammable
liquid matter, of which they conceive the sun to be composed. . .
Galileo, Hevelius, and Maupertius, seem all to have enter-
tained this opinion. All these hypotheses are founded upon
a supposition that the Sun being in itself a hot and luminous
body; which opinion is contradicted by numerous and well
established facts; for instance, on the tops of mountains of
sufficient height, where clouds can seldom reach to shelter
them from the direct rays of the Sun, we find regions of
perpetual snow. Now, if the solar rays themselves con-
veyed all the heat we find on our globe, it ought to be hot-
test where their course is least interrupted, viz. on the tops
of those mountains, which we know, from observation, to be
in a constant state of congelation. The same has been ob-
served by those who have ascended in balloons'; that is, the
higher they ascend the greater degree of cold they expe-
rience : the Sun itself appears diminished both in splendour
and magnitude, and the heavens, instead of the azure or
blue, which we observe, approach more and more towards
256 . GRAVIMAR OF ASTRONOMY.
a total obscurity. These facts, to which might be added
many others, are sufficient to explode the common notion of
the Sun being a globe of fire, and to show at the same time
that those planets which are nearest to the Sun, are not ne—
cessarily the hottest, nor those the coldest that are more re- .
mote ; and hence, many of the fanciful calculations relative
to light and heat experienced by the different planets of our
-’system fall to the ground; as it is obvious, from what is
stated above, that by certain modifications of the planetary
atmospheres, the light and heat might be equalized through-
out the solar system. . . . - -
9. That luminous appearance, or faint light,
which is sometimes seen, particularly about the time
of the vernal equinox, a little before the rising or
after the setting of the Sun, is called the zodiaca;
light. - r º
It is the general opinion that this phenomenon is produced
by the reflection of the Sun's atmosphere. The fluid which
transmits the zodiacal light to us, according to LA PLACE, is
extremely rare, since the stars are visible through it; its co-
lour is white, and its apparent figure that of a cone, whose
base is applied to the Sun. The length of the zodiacal light
sometimes subtends an angle of more than 90°, but the at-
mosphere of the Sun does not extend to so great a distance,
and cannot therefore reflect this light. La Place concludes
that the true cause of the zodiacal light is still unknown.
QUESTIONS.
What is the Sun? . - s
What is the mean diameter of the Sun ?
How many times is the Sun larger than the
Earth 2 • w
What is the mean apparent diameter of the Sun,
when is it greatest, &c. 2 -
Has the Sun an atmosphere, and what is its sup-
posed height 2 -
What are the solar spots 2
In what time does the Sun revolve on its axis;
what is its true figure; and in what angle is the
solar equator inclined to the plane of the ecliptic 2
OF THE SOLAR SYSºpM. 257
Has the Sun any other real motion, besides that
on its axis 2. , - . . .
What are the apparent motions of the Sun ?
What is the cause 2 " . . . . . ..
What is the zodiacal light 2
=
CHAPTER IV -
Of the Geocentric motions of the Planets, &c.
1. The most striking circumstance in the planet-
ary motions, is the apparent irregularity of those
motions; the planets, one while appearing to move
in the same direction among the fixed stars as the
Sun and Moon; at another in opposite directions,
and sometimes appearing nearly stationary.
These irregularities are only apparent, and arise from a
combination of the motion of the Earth and motion of the
planet; the observer not being conscious of his own motion,
attributing the whole to the planet. The planets really
move, as has already been observed, according to the order
of the signs, in orbits nearly circular, and with motions near-
ly uniform, round the Sun in the centre, at different dis-
tances, and in different periodical times. The periodical
time is greater or less, according as the distance is greater
or less. Upon the hypothesis that the planets thus move,
we can ascertain, by help of observation, their distances
from the Sun, and thence compute for any time the place of
a planet, which is always found to agree with observation.
As the principal planets are always observed to be nearly
in the ecliptic, and as they revolve round the Sun in orbits
nearly circular; in order to simplify the illustration of their
geocentric motions, we may, for the present, without any
material error, consider them ās moving uniformly in cir-
cular orbits, which coincide with the plane of the ecliptic.
2. The inferior planets, Mercury and Venus, are
limited in their elongations from the Sun; the
greatest elongation of Mercury being about 28°,
and that of Venus 47°. -
. . was
25$ GRAVIMAR Ol' JīS'I'I&GN GM H.
The interval of time between two successive inſerior con-
junctions can be observed ; ſor, in inſerior conjunction, the
planet being nearest to the earth, appears largest, and may
i. observed with a good telescope, even a very short time'
before the conjunction. For our purpose here it is not ne-
cessary that the time of conjunction should be observed
with great accuracy. Let T represent the time between
two successive inſerior conjunctions; then, to a spectator
in the Sun, in the time T, the inferior planet, (moving with
a greater angular velocity) will appear to have gained four
right angles, or 360° on the Earth; and the planet and
Earth being supposed to move with uniform velocities about
the Sun, the angle gained (that is, the angle at the Sun be
tween the Earth and planet, reckoning according to the
order of the signs,) will increase uniformly. -
g-
Let TEL represent the orbit of the Earth, DPGON that
of an inſerior planet, each being supposed circular, S the
Sun in the centre, and P the place of the planet when the
Earth is at E. Then in the triangle SEP we obtain the
angle SEP the elongation by observation, and the angle PSE
by computation; for it is the angle the planet has gained on.
the Earth since the preceding inferior conjunction. There-

OF THE SOLAR SYSTEMI. 259
fore, this angle PSE: 360° : : the time ſrom inferior con-
junction: T. The two angles SEP and PSE being known,
the angle SPE is known, and hence SP relatively to SE; ſoy
sine angle SPE: sine ang. SEP: : SE: SP. Having thus"
obtained the distance of the planet from the Sun, we can, at
any time, by help of the time 'F' and the time of the prece-
ding inferior conjunction, compute the angular distance of
the planet ſrom the Earth, as seen from the Sun, and thence,
by help of the distances of the planet and Earth from the
Sun, compute the planet’s elongation from the Sun. Thus
the planet being at O, and the Earth at E, we can compute
the angle ESO ; and having the sides SE and 80, we can,
by trigonometry, compute the angle 8EO, the elongation of
the planet from the Sun. This being compared with the
observed angle, we always find them nearly agreeing, and
thereby is shown that the motions of the inferior planets,
Mercury and Venus, are explained by those planets moving
in orbits nearly circular about the Sun in the centre.
Now, in order to find the greatest elongation of the inſerior
planets, upon the supposition of circular orbits, at their
mean distances, we have this trigonometrical proportion; as
£8: SG :: radius: to sine angle SEG, because EG is a tan-
gent to the orbit of the planet at the time of its greatest elon-
gation, and the angle SGE, is therefore a right angle.
Hence, the greatest elongation of an inſerior planet is ex-
- \ • R. &
pressed by this formula; the sine of the angle SEG= 5
- \ . . " -
b being equal to the distance of the Farth from the Sun, a
the distance of the planet, and R radius or sine 909. Or, the
greatest elongation may be expressed by this formula, sine
ang. SEG=a X radius, a being the relative distance of the
planet from the Sun, that of the Earth being unity or 1. For
instance, let us take Venus: in this case, b may be taken
* 69X radius
equal to 95, and ar=69; then, sine angle SEG=--—==
* 95
0.86113–460 35'. Again, b being taken equal to 1, a will
be equal to .70526, and sine ang. SEG=radius X.70526;
therefore, the angle SEG is equal to 46° 35', the same as
before. - - • ‘
The variations in the greatest elongations of the inferior
planets, Mercury and Venus, is owing to the elliptical figure
of their orbits, and that of the Earth, which also causes a
260 6FAMMAR of ASTRoNoMy.
variation in the stationary points, and in the conjunctions.
The ancients observed the places of the fixed stars and
planets with respect to the Sun, by the assistance of the
Moon, or planet Venus. In the day time they very ſre-
quently could observe the situation of the Moon, with re-
spect to the Sun. Venus also being occasionally visible to
the naked eye in the day time, they used that planet for the
same purpose. Now we can, owing to the convenience of
our instruments, without the intervention of a third object,
obtain the angular distance of a planet from the Sun, by
observing the declinations of each, and the difference df
their right ascensions. By which we have, in the triangle
formed by the distances of each from the pole of the equator
and from each other, two sides and the included angle, to
find the third side, the angular distance of the planet from
the sun. - - -
3. The motion of an inferior planet is direct
from its stationary point, before its superior con-
junction, to its stationary/point, after the same con-
junction ; and it appears retrograding from the
st tionary point, before its inferior conjunction, to
the stationary point, after its inferior conjunction.
As the computed place of an inſerior planet always agrees
with the observed place, (see the preceding Art.) it neces-
sarily follows that the retrograde, stationary appearances,
and direct motions of the planets, Mercury and Venus, are
explained, by assigning circular motions to them, in orbits
which coincide with the plane of the ecliptic. -
In order to demonstrate the retrograde and stationary ap-
pearances in a clear manner, it will be necessary to consi-
der the effect of the motion of the spectator, arising from
the motion of the Earth, in changing the apparent place of
a distant body. The spectator not being conscious of his
own motion, attributes the motion to the body, and conceives
himself to be at rest. -
GF THE SOLAR SYSTEMI. 26.1
RN !
Illustrations. 1. Let S be the Sun, ET the space described
by the Earth in a small portion of time, which therefore
may be considered as rectilinear; the motion being from
Etowards T. -
Let W be a planet, supposed at rest, any where on the
same side of the line of direction of the Earth’s motion, as
the Sun. Draw EP parallel to TV; then, while the Earth
moves through ET, the planet supposed at rest, will appear
to a spectator, unconscious of his own motion, to have
moved by the angle VEP. which motion is direct, being the
same way as the apparent motion of the Sun. And because
the Earth appears at rest with respect to the fixed stars, the
planet will appear to have moved forward among the fixed
stars, by the angle WEP=EWT=the motion of the Earth
as seen from the planet supposed aſ rest. Thus the planet,
being on the same side of the line of direction of the Earth’s
motion as the Sun, will appear, as far as the Earth’s motion
only is concerned, to move direct. Let M be a planet any
where on the opposite side of the line of direction, then, the
planet will appear to move retrograde by the angle MER.
And therefore, as far as the motion of the Earth only is con-
cerned, a planet, when the line of direction of the Earth's

262 GRAMMAR OF ASTRONOMY.
motion is between the Sun and planet, will appear re-
trograde. & - t
2. To return to the apparent motion of the inſerior planets.
Let the Earth be at E, and draw two tangents GE and ED;
then, when the planet is at D or, G, it is at its greatest elon-
gation from the Sun S. . It is clear that the planet being in
the inferior part of its orbit between D and G, relatively to
the Earth, and the Earth being supposed at rest, the planet
will appear to move from left to right, that is, retrograde :
and in the upper part of the orbit, from right to left, that is,
direct. But the Earth not being at rest, we are to consider
the effect of its motion. In the case of an inferior planet,
the planet and the Sun are always on the same side of the
line of direction of the Earth’s motion; and therefore the
effect of the Earth's motion is always to give an apparent
direct motion to the planet. -
Hence, in the upper part of the orbit between the greatest
elongations, the planet’s motion will appear direct, both on
account of the Earth’s motion and its own motion. In the
interior part of the orbit, the planet's motion will only be
direct between the greatest elongation and the points where
the retrograde motion, arising from the planet’s motion, be
comes equal to the direct motion which arises from the
Earth's motion. At these points the planet appears sta
tionary ; and between these points through inferior con
junction, it appears retrograde. See Dr. Brinkley's Ele-
ments of J1stronomy.
3. Or, the geocentric motions of the inferior planets may
be explained in the following manner: Let S be the Sun,
(fig. 1. 258) E the Earth, DPGON the orbit of one of the
inferior planets, and AI the sphere of the fixed stars. Draw
Ed, EC, EB, and EF through the several stations a N, b0,
G and D, of the inferior planets. The positions a and N
are called conjunctions; the latter is the superior, and the
former the inferior conjunction, they being then in a line, or
the same vertical plane to the ecliptic, with the Sun. The
lines EG and ED being tangents to the orbit at G and D;
the planet, when in these points of its orbit, is at its
greatest angular distance from the Sun, called its greatest
elongation. . Now, admitting the Earth to be stationary at
E, and the planet to be moving in its orbit from d to b, and
from b to G., &c.; it is obvious that when the planet is at a
it must appear from the Earth among the fixed stars at d ;
when it is at b, it must appear at C ; when at G, it must
or THE SoLAR systEM. 263
appear at B; when at O, it will appear again at C ; and
when at N, it must appear at d ; when at D, it will appear
in the heavens at F ; and when it returns to a, it must ap-
pear again at d. In this manner will ån inſerior planet,
viewed from the Earth, seem to move backwards and ſor-
wards in the heavens, from F to B, and from B to F. The
points D and G would be the stationary points, if the Earth
was at rest; but as the Earth moves in an orbit, the sta-
tionary points will not coincide, or be at the time of the
greatest elongation, but some days after, when the planet
approaches the inferior conjunction, and before the time it
is approaching the superior conjunction. For instance,
Mercury’s greatest elongation at D, 1819, was on the 15th
April; but that planet was not stationary until the 22d of
the same month: Mercury was at its inferior conjunction at
a, on the 3d of May, stationary on the 17th, and at its
greatest elongation, on the 31st of the same month. See
Squire's Astronomy. -
4. A superior planet appears to move retrograde
from its stationary point before opposition, to its
stationary point after opposition ; and direct, from
its stationary point before conjunction, to its sta-
tionary point after conjunction, being retrograde
through opposition, and direct while passing through
conjunction: - - +.
The interval of time between two succeeding oppositions
of a superior planet to the Sun can be observed, for it is
known when a superior planet is in opposition, by observ-
ing when it is in the part of the zodiac opposite to the place
of the Sun. Let T represent the time between two suc
cessive oppositions; then viewing the planet from the Sun,
the Earth will appear to have gained an entire revolution,
or 360° on the planet, in the time T ; and the Earth and
planet being supposed to move with uniform angular velo-
cities about the Sun, the angle gained by the Earth willin-
crease uniformly. .
264 GRAMMAR 6F ASTRONOMY.
B. 9- B
Tº SA
&\/\a Zºº,8.
I 4%
|
\
Illustrations. 1. Let TEL represent the orbit of the
Earth, IDOG that of a superior planet, N the place of the
planet when the Earth is at E. Then in the triangle SNE,
we have the angle SEN by observation, and the angle NSE
by computation. For NSE is the angle at the Sun, which
the Earth has gained on the planet since the preceding oppo-
sition. This angle: 360°: : time since opposition : T. The
two angles NSE and SEN being known, the angle SNF is
known, and therefore SN relatively to SE : for sine angle
SNE: sin. angle SEN: : SE: SN. Having thus obtained
the distance of a superior planet from the Sun, we can, at
any time, by help of the time T, and time of the preceding
opposition, compute the angular distance of the Farth from
the planet, as seen from the Sun, and thence, by help of the
Sarth’s distance, and planet’s distance, from the Sun, we
can compute the planet’s elongation from the Sun. Thus,
the planet being at R and the Earth at E, we compute the
angle RSE, and knowing the sides ES and SR, we can, (by

of THE solar systEM. 265
plane trig.) compute the angle RES, the elongation of the
planet from the Sun. This being compared with the observed
angle, we always find them nearly agreeing, and thereby is
shown that the motions of the superior planets are explained
by those planets moving in orbits nearly circular about the
Sun. As the computed place nearly agrees with the observed
place, it necessarily follows that the retrograde and direct
motions, and the stations of these planets are explained, by
assigning to them these circular motions. And it is easy to
demonstrate these appearances; for it is clear that the planet
being in any part of its orbit, and the Earth being supposed
at rest at any point E, the planet will appear to move from
west to east, or direct. But the earth not being at rest, we
are to consider the effect of its motion. The Earth being at
E, draw the tangent DEG.; then, if the planet is in the upper
part of the orbit DIG, it is on the same side of the line of di-
rection of the Earth's motion, as the sun; and therefore the
effect of the Earth’s motion is to give an apparent direct mo–
tion to the planet. The Earth being at E, and the planet at
D or G, the planet is said to be in quadrature; consequently,
from quadrature to conjunction, and from conjunction to
quadrature, the planet appears to move direct, both on ac-
count of its own motion and the motion of the Earth. If the
planet is in the lower part of the orbit DOG, the effect of the
Earth’s motion is to give an apparent retrograde motion to
the planet: consequently, ſrom quadrature to opposition, and
from opposition to quadrature, the planet moves direct or re-
trograde, according as the effect of the planet's motion ex-
ceeds, or is less, than the effect of the Earth’s motion. Be-
tween quadrature and opposition their effects become equal,
and the planet appears stationary; and afterwards, through
opposition to the next station, retrograde.
2. These appearances may be also demonstrated in the
following manner: Suppose S the Sun, e the Earth, 6 TEL
the orbit of the Earth, Ibſ)06a the orbit of a superior planet,
AF an arc of the heavens at the distance of the fixed stars.
Through e and S draw the line OC, through L and a the line
LD", through T and b the line TB, and through e and b the
line nD'. Then, when the Earth is at e, and the planet at I,
it is in opposition to the Sun; but when the planet is at L, it
is in conjunction with the Sun, the latter body being in the
line or vertical plane joining the Earth and planet. As the
velocity of the Earth is greater than that of the superior
planet, let us suppose that whilst it moves from L to e, the
•oyce
~ :-)
266 GRAMMAR of ASTRONOMY.
planet describes the small arcs aſ and Ib. Hence, when the
Earth is at L, and the planet at a, it appears in the heavens
at D'; when the earth is at e, the planet at I appears in the
heavens at C; and when the Earth is at T, the planet at b,
appears in the heavens at B. So that whilst the Earth was
moving through LeT according to the order of the signs, and
the planet through alb, the latter when referred to the hea-
vens, appears, to a spectator at the Earth, to have retrogra-
ded through the arc D’CB. Suppose now, that when the
Earth is at E, the planet is at I, or in conjunction; and whilst
the Earth moves from E to n, the planet moves from I to b,
then it must have appeared to have moved in the heavens from
C to D', according to the order of the signs, or direct.
To find the angle of elongation SLD' of any superior pla-
met, when stationary, upon the supposition of circular orbits,
at the mean distances of the planets from the Sun ; we shall
have this formula; sine of supplement of the angle SLD’
(º, -
- 7. Tii, a being equal to the relative distance of the
planet from the Sun, that of the Earth being unity or 1.
For example, let us take Mars: in this case, a-1.5236925,
a 1.5236925 * … •o e
therefore, vº a DT2.201211 T=.692207–sine 430 48
17’’; so that the angle of elongation SLD' of Mars is 1360
11' 48", when he is stationary upon the above supposition.
We have supposed above that the orbits are accurately
circular, that the planes of these orbits and that of the Earth
coincide, and that the angular motions were uniform; but if
the planes of the orbits coincided, if the orbits were accu-
rately circular, and were uniformly described, the planets
would always appear in the ecliptic, and would always be
found exactly in the places which the computation on the
circular hypothesis points out; but none of these things take
place exactly. The deviation however can be explained, by
showing that the planes of the orbits of the planets, except
that of Pallas, are inclined to the plane of the Earth's orbit
at small angles, and that the orbits are not circles, but only
nearly circles, being ellipses, not differing much from circles,
as has already been observed. Every phenomenon, even
the most minute, can be deduced from such an arrangemen.,
no doubt therefore would remain of the motions of the
planets, in such orbits, round the Sun, even had we not the
evidence derived from physical astronomy. -
of THE so.AR systEM. 267
5. The apparent velocities of the planets, whe-
ther direct or retrograde, are accelerated from one
of the stationary points, to the midway between that
and the following stationary point ; from thence
they are retarded till the next station. sº
6. Their greatest direct velocity is in their con-
junction, and their greatest retrograde velocity is in
the opposition of the superior planets, and in the
lower conjunction of the inferior planets.
The greatest apparent motion of a planet when in oppo-
sition or conjunction with the Sun, is owing to the parallel
motion of the Earth and planet in these points of its orbit.
The lower conjunction of an inferior planet, is the same
as the inferior conjunction. -
7. The shorter the periodic time of an inferior
planet, the more frequent are its stations and retro-
gradations, the shorter time they continue, and the
less they are in quantity. tº
This is well known to be the case, both from observation
and calculation. For instance, in the year 1819, Mercury
was stationary no less than six times, and retrograded four
times, whilst Venus was stationary only once, and retro-
grade only once. The mean arc of Mercury’s retrograda-
tion is about 13° 30', and its mean duration about 23 days;
whilst that of Venus is about 16°12', and its mean duration
about 42 days. - -
8. The longer the periodic time of a superior
planet, the more frequent are its stations and retro-
gradations, but they are less in quantity, yet con-
tinue a longer time. - -
*
The greater the relative motion of the Earth and a supe-
rior planet is, the more frequent will a given situation of the
two bodies occur; and the less it is, the longer time it will
be before similar situations of the two bodies take place.
The mean arc of Mars, is 16°12', and its mean duration.
about 73 days; whilst the mean arc of retrogradation of Ju-
piteris only 99 54, but its mean duration is about 121 days.
268 GRAMMAR OF ASTRONOMY.
9. When the planets are in their syzygies, their
longitude, seen from the Earth is the same as their
longitude seen from the Sun, except in the löwer
conjunction of an inferior planet, when its longi-
tude seen from the Earth, differs 180 degrees from
its longitude as seen from the Sun.
Obs. 1. That the superior planets have the same longitude
as seen from the Earth and Sun, when in conjunction or oppo-
sition, will readily appear, (see fig. 3, page 264) for when
the planet is at I, and the Earth at e, in opposition, it will
have the same longitude as seen from the Earth or Sun, the
three bodies being in the same vertical plane, or right line
directed to the same part of the heavens. The like will be
the case when the Earth is at E, or the planet is in conjunc-
tion at I. -
2. When an inferior planet is in its superior conjunction
at N, (fig. 1, page 258) it will have the same longitude,
whether observed from the Sun or Earth; but when the
planet is in its inſerior conjunction at a, it will appear from
the Sun to be in the opposite part of the heavens, or 180 de-
grees from its place, as seen from the Earth, the planet be-
ing at the time between the Earth and the Sun.
'3. To find the geocentric latitude of a planet, we have the
proportion; as the sine of the difference of longitudes of the
Earth and planet ; the sin. of elongation in longitude : : to
tang. of the heliocentric latitude : the lang. of the geocentric
lalitude. - -
For example, to find the geocentric latitude of Mars, De-
cember 1st, at noon, 1819. Sun's long. 8s. 80 30' 7", hence
the Earth’s place, 2s. 80 30'7" ; heliocentric long. of planet,
3s. 4° 7', geocentric longitude, 4s. 50 29, heliocentric lati-
tude of the planet 10 20'. Then, 2s. 80 30 7" subtracted
from 3s. 4° 7', gives 25° 36'53" diff long. of Earth and pla-
net. Again, 4s. 50 29' taken from 8s. 80 30' 7", leaves 123°
1' 7", elongation in longitude. Hence, sin. 250 36' 35": sin.
123° 1' 7":: tang. 10 20': tang. 20 35' 5" the geocentric la-
titude, as required. e
4. It may not be improper to observe, that by knowing
the longitude of the Earth, its distance from the Sun, the he-
liocentric long. of the planet, and its distance from the Sun
when referred to the ecliptic, there are given two sides of a
plane triangle, and the included angle, to find the angle at
the Earth, or elongation in longitude: so that by knowing
OF THE SOLAR SYSTEM. 269
the heliocentric place of a planet, its geocentric place may
be found; and on the contrary, if its geocentric place be
known, its heliocentric may be found. $
10. The periodic times of the inferior planets can be
deduced nearly, from observing the time between two
conjunctions, their orbits being supposed circular.
Let T equal the time between two successive inferior or
superior conjunctions. E equal to the periodic time of the
Earth. Pequal to the periodic time of the planet. Then,
considering the planet’s angular motion as uniform, P: E::
4 right angles: angle described about the sun in time of
Earth’s revolution=4 right angles plus angle gained by
planeton Earth, in time of the Earth's revolution. But as the
angles gained are as the times of gaining them, therefore 4
right angles: 4 right angles-H angle gained by planet on
Earth in time of Earth’s revolution: : T : T--E. .*
TXE
Hence, P : E :: T : T-HE; therefore, P=TLE: conse-
quently knowing the time between two inferior conjunctions,
which can be readily observed, we obtain the periodic times :
of the planets Mercury and Venus.
The interval between the inferior conjunctions of Mercu-
* * 115 × 365
ry is 115 days, therefore its periodic time =–=87
davs. -. 115–H365
The interval for Venus is 584 days, and consequently its
584 × 365 -
periodic time=–=224 days.
584––365 *.
11. The periodic times also of the superior
planets can be obtained, from observing the time
between two successive oppositions. • *
Let T, E and P represent as before. Then P: E:: 4
right angles: angle described by planet in time of Earth's
revolution, equal to 4 right angles minus angle gained by
Earth or planet in time of Earth's revolution. Also 4
right angles : 4 right angles — angle gained by Earth in
time E : : T : T-E; hence P : E : : T : T-E; therefore
T-LE - 2.
* ===
- ==
T–E
33°
2? () GRAMMAR OF ASTRONOMY.
}
The interval between two oppositions of Uranus or Her-
schel is 369; days; hence the periodic time of Uranus
369.75 × 365.25 369.75 ×365.25
*= *se —=82 × 365}=82 years
Ts69.75–865.25 4.5
For Saturn, the interval is 378 days, and consequently the
378 × 365} t
—-29, X365}=29#
878–365,
years. In like manner, the periodic times of the other Su-
perior planets may be nearly determined. -
12. When an inſerior planet is near one of its
nodes at inferior conjunction, it appears a dark
spot on the Sum’s surface, and thereby is shown
that the inferior planets receive their light from the
Sun.
periodic time of Saturn =
Obs. 1. When Venus is in superior conjunction, at a con-
siderable distance ſrom its mode, it may be seen, by help of
a telescope, to exhibit an entire circular disc. Indeed all
the different appearances of the inferior planets, as seen
through a telescope, are consistent with their being opaque
bodies, illuminated by and moving about the Sun in orbits,
nearly circular. Near inſerior conjunction they appear
crescents, exhibiting the same appearances as the Moon a
few days old.
At the greatest elongation they appear like the Moon
when halved, and between the greatest elongation and supe-
rior conjunction they appear gibbous, or like the Moon be-
tween being halved and full: these appearances are usually
called the phases of the Moon or planets. g
2. These appearances are easily explained. The planet
being a spherical body, the hemisphere turned towards the
Sun is illuminated. A small part only of this hemisphere is
turned towards the Earth, when the planet is near inferior
conjunction. Halſ the enlightened hemisphere is turned to-
wards the Earth, when the planet is at its greatest elongation.
More than half, when the planet is between its greatest elon-
gation and superior conjunction. For, generally, both with
respect to inferior and superior planets, the greatest breadth
of the part of the illuminated hemisphere turned towards the
Earth, is proportional to the exterior angle at the planet,
É. by lines drawn from the planet to the Sun and
arth. .
@F THE SOLAR SYSTEM. 271
S Let PS be in the direc-
- tion of the Sun, PE in that
of the Earth, IPHLO the
IBT section of the planet in the
* --. }. of the Earth’s orbit.
raw HO perpendicular
to EP, and HIO is the
G greatest breadth of the
illuminated hemisphere,
and HI common to each, is
T the greatest breadth of the
* O 'illuminated partseen from
the Earth. The measure of this is the angle IPH=IPS+
SPH=HPG+SPH=SPG the exterior angle at the planet.
Now near inferior conjunction the exterior angle is less, than
a right angle; at the greatest elongation it is a right angle;
and afterwards greater than a right angle. Therefore the
breadth of the illuminated part is respectively less than a
quadrant, equal to a quadrant, and greater than a quadrant
3. It is easy to see that as the planets appear flat discs on
the concave surface, so their illuminated parts will be pro-
jected on the flat surface, and the greatest breadth will be
projected into its versed sine, as in figures 5, 6, 7, where IH
is projected into its versed sine AB.
Fig. 5. Fig. 6. Fig. 7.
|P
Because the projection of a circle, inclined to a surface, by
right lines, perpendicular to that surface, is an ellipse, the
inner termination of the enlightened part appears elliptical,
and the enlightened surface: surface of planet: ; Ab : AC ::
versed sine of exterior angle: diameter. ... "
4. With respect to the superior planets; the exterior an-
gle of the planet is least when the planet is in quadrature ;
for when the exterior is least the interior is greatest. Now
it is evident that SDE, (see fig. 3, page 264) when DE is a


272 GRAMMAR of ASTRONOMY.
tangent to the orbit of the Earth, is greater than when E is
at any other point, and therefore the planet being in quadra-
ture, the exterior angle is least. SDE for every superior
planet is acute, and the exterior angle obtuse, and conse-
quently its versed sine is greater than radius. Whence
more than half the disc of a superior planet is always seen,
and it appears most gibbous in quadrature. Mars then ap-
pears gibbous about s of his diameter; Jupiter only by
about ºf of his diameter, which quantity is imperceptible,
even by a telescope, because Jupiter’s disc then subtends
only an angle of 30". Accordingly all the superior planets,
except Mars, appear always with a full face.
The new planets appear so small, that it cannot be expect-
ed any gibbosity should be exhibited by them. * *
13. Mercury and Venus have the same phases
from their inferior to their superior conjunction, as
the Moon has from the new to the full; and the
same from the superior to the inferior conjunction,
as the Moon has from the full to the new.
Illustration. Let DabCON, (see fig. 1, page 258) be the
orbit of Venus, ELT that of the Earth, and S the Sun; let E.
be the place of the Earth, when Venus is at a in her inferior
conjunction with the Sun: the dark side of Venus is entire-
ly turned towards the Earth, and she quite disappears, unless
she happen to be in or near one of her nodes, when she will
appear like a black spot, as has already been observed, or
pass over the body of the Sun, and is then said to transit his
disc. In passing from inferior conjunction to quadrature,
less than half her enlightened face would be directed towards
the Earth, and Venus would appear horned; at her quadra-
ture, the part enlightened is 90 degrees; then the circle di-
viding the illuminated from the darkened hemisphere will be
projected into a straight line, and half her disc will be seen.
Between the quadrature and superior conjunction, more than
half her enlightened hemisphere would be directed towards
the Earth; for instance, if Venus were at O, and the Earth
at E, then the circle dividing the illuminated from the darker
part will be projected in an arc of an ellipse upon the disc,
when the planet will appear gibbous. Let E be the place of
the Earth, when Venus is at N in her superior conjunction
with the Sun: the illuminated part of Venus is then directed
towards the Earth, and, of course, the planet appears as a
full lucid circle, like the Moon at full. In a similar manner
of THE solar systEM. 273
the appearances in the different positions from the superior to
the inferior conjunction might be traced out; and the same
delineation and explanation will serve for the planet JMer-
Cllry.
14. The brightness of a planet depends both on
the quantity of illuminated surface and its distance.
The greater the distance is, the less the brightness;
which, the illuminated surface remaining the same,
decreases as the square of the distance increases,
so that in computing when a planetappears brightest,
both the illuminated surface and distance must be
taken into the account. Both circumstances con-
cur in making a superior planet appear brightest at
opposition. . The inferior planets are not brightest
at superior conjunction, because of their greater
distance; and near inferior conjunction, the illumi-
nated part visible to us is very small. The place of
greatest brightness then lies between inferior and
Superior conjunction. • ,
The solution of the problem when Venus appears brightest,
gives her elongation then about 40 degrees. The places of
greatest brightness are between the places of greatest elonga-
tion and inferior conjunction. This, according to Dr.
Brinkley, agrees very well with observation. When she is
near this position she occasions a strong shadow in the ab-
sence of the Sun"; and for a considerable time both before
and after she is at this elongation, she may be readily seen in
full day-light by the naked eye.
QUESTIONs. .
What is said of the planetary motions 2
What is the greatest elongation of Mercury 2
What of Venus 2 . . .
Is an inferior planet direct or retrograde whilst
passing between the Earth and Sun ? -
When is a superior planet retrograde, &c. 2
When is the direct motion of a superior planet
the greatest ? -* # & -
*º-
º º
274 GRAMMAR of ASTRONOMY.
;
When is the retrogradation of a planet the
greatest ? . - t
Is the mean arc of retrogradation of Mars greater
than that of either of the other superior planets?
Do the phases of the inferior planets undergo the
same changes as those of the Moon 2 -
When does an inſerior planet appear as a dark
spot on the surface of the Sun ?
What is the reason Venus appears so much
brighter when crescent, or between inferior and
Superior conjunctions, than when her illuminated
disc is wholly turned towards the Earth 2 .
!
sº-sº-sº-sº-sº
CHAPTER V.
Of JMercury. § r
1. JMercury, the nearest planet to the Sun, per-
forms, its sidereal revolution round that body in 87
days, 23 hours, 15 minutes, and 44 seconds, which
is the length of its year: the rotation of Mercury
on its axis from west to east, or in the same direc-
tion as the Earth’s diurnal motion, is performed in
24 hours, 5 minutes, and 28 seconds; which is the
length of its day. . . .
The interval of time which any planet employs in passing
from a fixed star, or from one of the nodes, (making allow.
ance for the secular variation of the node,) till it returns to
the same again, is called the sidereal revolution of that planet.
The time between two consecutive conjunctions, or opposi-
tions, of a body with the Sun, is called a synodic revolution
of that body. . . . - -
The sidereal revölution of a planet round the Sun is usu-
ally called the length of that planet's year; and the time it
takes to revolve on its axis, is the length of its day.
*
& 8
J
OF THE SOLAR SYSTEMI. 275
2. Mercury is a spherical body, whose diameter
is about 3130 miles; its size is, therefore, nearly
one sixteenth of that of the Earth ; and its rela-
tive mean distance from the Sun is nearly 4, that of
the Earth being considered as 10.
The magnitude or size of Mercury, according to Fran-
eteur, is .0565; its mass 1627, and its density 2.879646;
the size, mass, and density of the Earth being respectively
considered as unity, or 1. And a body weighing 1 pound
on the surface of the Earth, will weigh 1 pound 8% drachms .
on the surface of Mercury. e
Mercury is the smallest of all the principal planets, and .
moves the quickest in its orbit, its mean hourly motion being
about 109,442 miles. , Hence, it was that the Greeks gave
this planet its name after the nimble messenger of the gods,
and represented it by the figure of a youth with wings at
his head and feet; whence is derived 3, the character by
which it is commonly represented. .
3. The inclination of the orbit of this planet to
the plane of the celiptic, is the greatest of all the
planets, except the foup asleroids, being about 7°,
which is equal to its greatest heliocentric latitude :
and its orbit is also far more eccentric than that of
any of the other planets, being about ; of its mean
distance from the Sun. s - - -
The inclination of its orbit is subject to a small increase
of about 18" in a century. The greatest geocentric lati-
tude of this planet is about 40 30'. Its greatest heliocentric
latitude, in the present year, will take place on or about the
following days: January 19th, March 16th, April 19th,
June 10th, July 16th, &c. & - t
4. The extent, orangular distance, of the greatest
elongations of Mercury from the Sun, on each side,
varies from 16 degrees 42 minutes, to 28 degrees
48 minutes. -
Mercury emits a very bright white light, but it is seldom to
be seen, owing to its being so near the Sun; and when it
makes its appearance, its daily mean motion is so swift, that
*
276 GRAMMAR of ASTRONOMY.
it can be discerned only during a few successive evenings or
mornings. For when it begins to appear in the evening, it
is with difficulty distinguished in the rays of twilight: it dis-
engages itself more and more in the following days, and af.
ter arriving at about 22° 46' from the Sun, it returns towards
him again. . In this interval, the motion of Mercury, with
respect to the fixed stars, is direct; but when in returning it
comes within the distance of 18 degrees of the Sun, it seems
stationary, after which its motion appears retrograde, it con-
tinues to approach the Sun, and is again in the evening lost
in his rays. After continuing some time invisible, it is seen
again in the morning, disengaging itself from the Sun's rays
and departing from the Sun, its motion is still retrograde as
before its disapparition. Arrived at the distance of 189 it is
again stationary, then resumes its direct motion, its distance
increases to 22° 30', it then returns, and disappearing in the
morning in the light of the dawn, is soon aſter seen again in
the evening, producing the same phenomenon as before.
5. The length of this planet's entire oscillation,
or return to the same position relatively to the
Sun, varies likewise from 106 to 130 days; the
mean arch of retrogradation is about 13° 30', and
its mean duration 23 days; but there is a great
difference in their quantities in different retrogra-
dations. - - -
A long series of observations was no doubt necessary to
recognise the identity of the two stars, which were alternately
seen in the morning and in the evening to depart from and
réturn to the Sun; but as one never showed itself till the
other disappeared, it was at last suspected to be the same
planet which thus oscillated on each side of the Sun. See
La Place’s System of the World.
6. The apparent diameter of Mercury is very
variable, and its changes are evidently connected
with its relative position to the Sun and the direc-
tion of his motion. The mean apparent diameter
. º planet is about 7", and the greatest diame-
ep J. J. ". . - . . .
of THE solar systEM. 27?
The best time to see Mercury in the evening is in the
spring, at the time the planet is east of the Sun, and at the
greatest distance from that body. It will then be visible for
several minutes, and will set about one hour and fifty minutes
after the Sun. But if the planet is west of the Sun, and at
its greatest distance, it will rise about one hour and fifty mi-
nutes before that body, and will be most advantageously seen
in the morning, at the latter end of summer or beginning of
autumn. - - -
7. When Mercury is viewed at different times in
a good telescope, it presents to us phases similar to
those of the Moon, and directed in the same man-
ner towards the Sun.
This planet never appears quite full, because its enlight-
ened hemisphere is never turned directly towards the Earth,
except when it is so near the Sun, in or near its superior
conjunction, as to be either hidden by the Sun's body, or by
his beams, and therefore to us invisible. The enlightened
hemisphere of Mercury being thus always turned towards the
Sun, proves that it shines not by any light of its own; for if
it did, it would always appear round, and fully enlightened.
8. Mercury is sometimes in inferior conjunction
near one of its nodes: it then appears as a dark
and well defined spot on the disc of the Sun; and a
transit of Mercury takes place, which can only be
seen by the assistance of a telescope.
The apparent diameter of Mercury, viewed in a good
telescope, at the time of its transit, is about 11". The tran-
sits of Mercury are very frequent, arising from the propor-
tion of the periodic time of Mercury to that of the Earth,
being nearly expressed by several pairs of small whole num-
bers. If an inferior planet be observed in conjunction near
its mode, (or in a certain place in the zodiac,) it will be in
conjunction at the same node, (or place,) after the planet and
the Earth have each completed a certain number of revolu-
tions. Now it is easily computed from the periodic times of
Mercury and the Earth, that nearly -
7 periodic revolutions of the Earth are = to 29 of Mercury.
18 per.' . . . . of the Earth = 54 of Mercury.
33 per. . . . . . of the Earth = 137 of Mercury,
* ~~
278 &RAMMAR or ASTRONOMY.
Therefore transits of Mercury, at the same node, may
happen at intervals of 7, 13, 33, &c. years.
At present the ascending node of Mercury, is in 1s. 16°
nearly; and the descending node in 7s. 169. The Earth, as
seen from the Sun, is in the former longitude, in the begin-
ning of November, and the latter in the beginning of May.
Hence the transits of Mercury will happen for many ages to .
come in November and May. The first transit of Mercury
was first observed by Cassendi, in November, 1631 ; since
which time seven transits of this planet have been observed.
The last appearance of this kind was in November 5th,
1822 : the next four will take place May 5th, 1832; No-
vember 7th, 1835; in 1845, and 1848, all of which will be
visible in the United States. -
TABLE.
Showing the mean distance of JMercury from the Sun, and its
eccentricity, m miles; longitudes of the ascending node and
the perihelion, &c. r
Mean distance in miles . . . . . . . 36,668,873
Eccentricity . . . . . . . . . . . . . 7,434,424
Longitude of ascending mode at the be- f
ginning of 1801 . . . . . . . . . . 1s. 15° 57' 31"
Longitude of the perihelion at the same
time . . . . . . . . . . . . . 2 14 21 47
Greatest equation of the centre . . 0 32 40 0
Heliocentrig longitude on the 1st of Janu- •
ary, 1825 . . . . . . . . . . 0 O 23 10
Geocentric longitude at the same time 0 10 0 15
Mean hourly motion . . . . . . 0 0 0 10
The line of the apsides has a sidereal motion, according to
the order of the signs, equal to 9'44" in a century; or 10
33 44" when referred to the ecliptic.
The sidereal secular motion of the node is retrograde
about 13/2.3"; but if referred to the ecliptic, the place of the
nodes will, on account of the recession of the equinoctial
points, be direct about 42" in a year, or 19 10 27" in a
century.
On account of the proximity of Mercury to the Sun, as-
tronomers have not yet ascertained with any degree of cer-
tainty, whether the axis of this planet has any inclination to
its orbit; and therefore, whether it has any difference of sea-
Sons, is also quite uncertain,
º
º º -
- sº
- -
º
-
--
-
º
-
º
-
|-
----

of THE SOLAR SYSTEM. 279
QUESTIONS.
What is the length of Mercury's year? what is
the length of its day ? -
What is the diameter of Mercury in miles 2
What is its relative magnitude with respect to the
Earth, &c. 2 -
What is the inclination of Mercury’s orbit to the
ecliptic 2 .*
What is said of its eccentricity, &c. 2
What are the limits of the greatest elongation of
Mercury 2 -
What is the mean arc of Mercury’s retrograda-
tion, and what is the duration ?
What is the mean apparent diameter of Mercury?
When Mercury is viewed in a telescope, does he
present similar phases to those of the Moon 2
When does a transit of Mercury take place 2
*
ºmmºssºmºsº
CHAPTER WI.
Of Venus. Q
1. Venus is the next planet in order after Mer-
cury, and surpasses in brightness all the other stars
and planets, being sometimes so brilliant as to be
seen in full day and by the naked eye. This planet
revolves round the Sun in 224 days, 16 hours, 49
minutes and 11 seconds, which is the length of its
year; and the mean hourly motion in the orbit is
about 80,062 miles.
Venus is denoted by the character Q, which is supposed
to be a rude representation of a female figure, with a trailing
280 GRAMMAR OF ASTRONOMY.
or flowing robe. Venus is the only planet mentioned in the
sacred writings, or by the most ancient poets, such as Homer
and Hesiod. r
2. Venus is a spherical body, whose diameter is
about 7687 miles, and she revolves on her axis,
from west to east, in 23 hours and 21 minutes, which
is the length of her day. This planet is, therefore,
about the size of the Earth ; and its relative mean
distance from the Sun is nearly 7, that of the Earth
being considered as 10.
The magnitude or size of Venus, is .8828, its mass .9243,
and its density 1.04701 ; the size, mass, and density of the
Earth being respectively considered as unity or 1. And a
body weighing one pound on the Earth, will weigh one
pound nearly on the surface of Venus.
i
3. The inclination of the orbit of Venus, to the
plane of the ecliptic, is 3° 23' 30", and its eccentri-
city is the least of any of the planets, being about
492,000 miles. - -
The secular decrease of the inclination of the orbit to the
plane of the ecliptic is 4.6". The greatest geocentiric lati-
tude north is 3° 13', and the greatest geocentric latitude
south is 7° 55'. The greatest heliocentric latitude, which is
equal to the inclination of the orbit to the plane of the eclip-
tic, will take place in 1825, on or about the 1st of of April,
25th of July, and 13th of November.
4. The planet Venus offers the same phenomena
as Mercury, with this difference, that its phases are
much more sensible, its oscillations more extensive,
and their period more considerable. The greatest
elongations of Venus vary from 45° to 47° 42'; its
mean elongation is, therefore, 46° 21', and the mean
length of its entire oscillations, or synodic revolu-
tion, is 584 days. -
5. The retrogradations of Venus commence or
finish, when the planet, approaching the Sun in
the evening or receding from that body in the
\
() F PHE SOLAR SYSTEM. 281
morning, is distant from the Sun about 28° 48'.
The mean arc of retrogradation is about 16942,
and its mean duration 42 days. -
This planet is never seen in the eastern part of the heavens
when the Sun is in the western, but always seems to attend
that body in the evening, or to give notice of its approach in
the morning, and never receding from the Sun more than
about 47 degrees. This proves that the orbit of Venus in-
cludes that of Mercury, but is included by that of the Earth.
6. From inſerior to superior conjunction Venus
is to the westward of the Sun, and therefore rises
before the Sun, and by the splendour of her ap-
pearance, being much noticed, is called the morning
star. From superior to inferior conjunction, she
appears to the eastward of the Sun, and therefore
does not set till after the Sun, and is then called the
evening star. --
When in the former of these situations, Venus was called
by the Greeks Phosphorus, and in the latter Hesperus. The
evening and morning stars were at first supposed to be dif-
ferent, and it is said that Pythagoras was the first person
who discovered they were the same.
When Venus is an evening star, and at her greatest dis-
tance from the Sun, or what is termed her greatest eastern
elongation, she appears, when viewed with a telescope, to
have a semicircular disc, like the Moon in the last quarter,
with its convexity turned to the west. From that time
during her approach to the Sun, her splendour increases for
a whiie, though the quantity of the illuminated disc dimi-
nishes like the Moon; but her apparent diameter, when
measured by the distance of the horns, is found to be in-
creased. At the time of her greatest elongation, Venus ap-
pears to be stationary, with respect to the Sun, for some
time. After this her motion eastward becomes slower than
the Sun's, and then she approaches nearer to the Sun, as just
Nemarked. At a certain point she becomes stationary with
respect to the fixed stars, and then her motion becomes re-
trograde, or appears to be directed westward with respect to
the fixed stars. At last she approaches the Sun, so as to be
kºstin his light; but, after soº. time, she is to be seen to the
282 GRAMMAR OF ASTRONOMY. .
west of the Sun, and appears in the morning before he rises.
As she proceeds to the westward, her illuminated disc is seen
as a crescent continually increasing, at the same time that
her diameter is diminishing. When she has got 450 to the
west of the Sun, her disc is a semicircle; and as she again
approaches the Sun, it increases till she is lost in the Sun’s
rays ; her orb being almost a circle, but its diameter not
more than one-sixth of what it was at the former conjunc-
tion. The superior conjunction takes place after the western
elongation, and the inferior after the eastern elongation. At
the former of these periods, Venus is the breadth of her orbit
farther from the Earth than at the latter; for at the time of
the superior conjunction, she is on the opposite side of the
Sun to what the Earth is ; but at the time of the inſerior
conjunction, Wºnus and the Earth are on the same side of the
Sun. This planet appears to keep on the same side of the
Sun for 290 days together, although this is a longer period
than she takes to perform a complete revolution round that
body: she is therefore an evening star during 290 days, and
a morning star somewhat longer. This may appear strange
to those who are but little acquainted with astronomy; but
when it is considered that the Earth is all the while moving
round the Sun the same way, though not so fast as Venus,
the difficulty vanishes; because she must continue to appear
on the same side with the Earth, till the excess of her daily
motion above that of the Earth's motion amounts to 1799, or
nearly to half a circle; which, at the rate of 27' per day, will
be in about 290 days, as above stated.
After the superior conjunction, the orb of Venus increases
in magnitude as she approaches her greatest eastern elonga-
tion, but the enlightened part diminishes, just reversing the
order of what has already been stated to take place from the
inferior conjunction to her greatest western elongation.
The different phases or appearances of Venus, described
above, were first discovered by Galileo in 1611, which ful-
filled the prediction of Copernicus, who foretold, before the
discovery of the telescope, that the phases of the inferior
planets would be one day discovered to be similar to those
of the Moon. The accomplishment of this prediction af-
fords some of the strongest and most convincing proofs of the
truth º the Copernican system of the World, that can be ob-
tained. -
7. The apparent diameter of Venus, like Mer-
cury, is very variable; her greatest diameter being
or THE SOLAR systEM. 283
*
about 58", and her least diameter about 10". The
apparent diameter of Venus, when she is at her
mean distance from the Earth, is about 16;".
It was long doubted whether Venus be surrounded by an
atmosphere or not; but this question has been completely
settled by the very nice and -accurate observations of the
German astronomer Schroeter, who has ascertained the exis-
tence of a pale ſaint light extending along the line of the
dark hemisphere of this planet, which he supposes to be a
kind of twilight, occasioned by the Sun illuminating its at-
mosphere. From this circumstance, Schroeter has been en-
abled to ascertain the density of this atmosphere, and that it
extends to a very great height, which must prevent the Sun
from overpowering the inhabitants with his heat and splen-
dour, which are supposed to be nearly twice as great as on
the Earth’s surface. -
Dr. Herschel, after a long series of observations on this
planet, accounts of which are given in the Philosophical
Transactions for 1793, says, that the planet revolves about its
axis, but the time of its rotation is uncertain; that the posi-
tion of its axis is also very uncertain; that the planet’s at-
mosphere is very considerable; that the planet has probably
hills and inequalities on its surface, but he has not been able
to see much of them, owing perhaps to the great density of
its atmosphere: as to the mountains of Venus, no eye, he
says, which is not considerably better than his, or assisted by
much better instruments, will ever get a sight of them : and
that the apparent diameter of Venus, at the mean distance
from the Earth, is 18.8%; whence it may be inferred, that
this planet is somewhat larger than the Earth, instead of be-,
ing less as former astronomers have asserted.
8. When Venus, in her inferior conjunction, is in
or near one of her nodes, she appears in the form
of a circular black spot on the Sun’s disc, and a
transit of Venus takes place. The apparent dia-
meter at the time of this planet’s transit, according to
Dr. Brinkley and other astronomers, is about 57".
The transits of Venus are not so frequent as those of Mer-
cury; for 8 periodic revolutions of Mercury are equal nearly
to 13 of Venus; and there are no other intervening whoſe
284 \ GRAMMAR OF ASTRONOMY.
numbers till 335 periodic revolutions of the Earth, which are
equal nearly to 382 per of Venus. Hence a transit of We-
nus, at the same node, may happen after an interval of 8
years. If it does not take place aſter an interval of 8 years,
it cannot happen till after 235 years. At present the ascend-
ing node of Venus, as seen from the Sun, is in 2 signs, 149,
and the descending node in 8s. 149. The Earth, as seen
from the Sun, is in the former longitude in the beginning of
December, and in the latter in the beginning of June.
Hence the transits of Venus will happen for many ages to
come in December and June. Those of Mercury, as has al-
ready been observed, will take place in May and November.
In the years 1761 and 1769, there were transits of Venus,
being at those periods in her descending node : the next
transit at that node will happen in 2004. But a transit was
observed at the ascending node in the year 1639, by Horrox,
who had previously computed it, from having corrected the
tables of Venus by his own observations, all other astrono-
mers having been ignorant of its occurring. This transit
will again happen at the end of 235 years from that time, or
in the year 1875, and the next in 1882. -
When a transit of Venus is observed, it not only proves
that she is an opaque body, and that her orbit is included by
the Earth's, but it is of admirable use in determining what
is called the Sun’s parallax, which is of so much use in as-
tronomy, as we shall see in a subsequent chapter. Hin 1672
and 1686, Cassini, with a telescope of 34 feet, thought he saw
a satellite move round this planet, at the disiance of about
# of Venus's diameter. It had the same phases as Venus,
but without any well defined form ; and its diameter scarce-
ly exceeded # of the diameter of Venus. -
Jºſ. JMontaign, of Limoges in France, preparing for ob-
serving the transit of 1761, discovered in the preceding
month of May, a small star, about the distanée of 20' from
Venus, the diameter of it being about ; that of the planet.
Some other astronomers have asserted that they perceived
the like appearance. And indeed it must be acknowledged
that Venus may have a satellite, though it is difficult for a
spectator on the surface of the earth to see it. See Dr.
JHutton's Philosophical &nd JMalhematical Dictionary.
‘OF THE SOLAR SYS3?EIM. 285
TABLE.
Showing the distance of Venus from the Sun, her eccentri-
city, longitude of the ascending mode, &c. -
Mean distance in miles . . . . . . . 68,514,044
Eccentricity in miles fº º a e 492,000
Longitude of ascending node at the be-
ginning of 1801 . . . . . . .
Longitude of the perihelion at the same
time . . . . . . . . . . . . . 4 8 37
reatest equation of the centre . . 0 0 47, 2
Heliocentric longitude on the 1st of
January, 1825 . . . . . . . . . . . 0 15 29
Geocentric longitude at the same time 10 18 51
Mean daily motion . . . . . . 0 1 36
The line of the apsides had a sidereal motion in anteceden-
£ia, or contrary to the order of the signs, of 4' 27.8% it a
century. But in longitude this motion will appear direct at
the rate of 47.4" in a year, or about 1° 19' 2" in a hundred
years. The nodes have a direct motion in longitude of
31.4", or about 52'20" in a century.
The secular decrease of the inclination of the orbit to the
ecliptic is 4.6°. *
The inclination of the axis of this planet to the plane of its
orbit, according to some astronomers, is not known; but, ac-
cording to others (with a great degree of probability,) it is 75
degrees; therefore her tropics are only 150 from her poles; .
and her polar circles are as far distant from her equator.
When Venus is observed with a good telescope, she ex-
hibits bright and dark-spots on her disc, and the mountains on
her surface are supposed to be 10 miles in height; but, ac-
cording to some astronomers, the mountains are six times
higher than any on our globe. From the best observations
the height of the atmosphere of Venus has been calculated
to be about 50 miles. -
2s. 14C 52' 40"
t
QUESTIONS.
What is said of Venus, what is the length of her
year, and what is the mean hourly motion in her
Orbit 2 - ~, -
What is the diameter of Venus, what is the
}ength of her day, &c. 2 - !
286 GRAMMAR of ASTRONOMY.
What is the inclination of the orbit of Venus to
the ecliptic 2: What is her eccentricity in miles 2
In what time does she perform her synodic re.
volution ?
What is the mean arc of retrogradation, and
what is its duration ? +.
When is Venus a morning star, and when an .
evening star 2
What is the mean apparent diameter of Venus 2
When does a transit take place 2
=
CHAPTER VII.
Of the Earth. d)
1. The Earth is a spherical body, nearly re-
sembling the figure of a globe ; it performs its re-
volution round the Sun, in an orbit between that of
Venus and Mars, in 365 days, 5 hours, 48 minutes,
51 seconds, which is the length of the tropical year;
(Art. 14, p. 31,) and it revolves on its axis in 23
hours, 56 minutes, 4 seconds, of mean Solar time,
which is the length of a sidereal day, (Art. 6, p.
29.) The mean hourly motion of the Earth in its
orbit is about 68,000 miles, which is 90 times faster
than the velocity of sound.
In the early ages of the world, many fanciful and absurd
notions, respecting the figure of the Earth, prevailed; some
of which were adopted because they appeared to agree with
the slight and inaccurate observations of the vulgar, whilst
others represented this matter in the way which best accord-
ed with their preconceived opinions in philosophy and reli-
gion. The most general opinion was, that the Earth was a
great circular plane, extending on all sides to an infinite dis-
tance; that the firmament above, in which the heavenly
68.9 THE SOLAR SYSTEMI. 287.
bodies seem to move daily from east to west, was at no great
distance from the Earth; and that all the celestial bodies
were created solely for its use and ornament. Heraclitus
imagined the Earth to have the shape of a canoe; Anaximan-
der supposed it to be cylindrical; and Aristotle, the great
oracle of antiquity, gave it the form of a timbrel. Such of
the ancients, however, as understood any thing of astrono-
my, and especially the doctrine of eclipses, must have been
acquainted with the round figure of the Earth; as the an-
cient Babylonian astronomers, who had calculated eclipses .
long before the time of Alexander, and Thales, the Grecian,
who predicted an eclipse of the Sun. -
A very little reflection, and a very little travelling either
by sea or land, must soon convince any one that the Earth is
of a spherical form. For let a person occupy any station in
a level country, and mark carefully the objects within the
range of his horizon, let him then advance in any direction,
and as he moves the objects behind him gradually disappear,
and new objects in front come in view. Before he has tra-
velled twenty miles in the same direction, he will find that
every object that was at first visible to him is lost to his
view, and that he is now in the centre of a new horizon.
As a similar change takes place at every part of the globe
where the same experiment has been tried, it follows that
the Earth is a spherical body. The same inference may be
deduced from observing the appearance of a ship at a dis-
tance at sea, or from observing the gradual rising of the
coast as the ship approaches the shore. In the ſormer case,
the top of the mast is first seen, and as the vessel approaches
the land, the whole of her gradually becomes visible. In the
latter, the hills, or the higher parts of the buildings, are first
discovered, but by degrees-every part of the building and
even the beach itself is seen. These are appearances which
can only be reconciled with the spherical figure of the Earth.
The same conclusion may be drawn from observing the alti-
tude of the pole star, after travelling north or south a consi-
derable number of miles. In travelling northward its alti-
tude will be increased; but in travelling south it will be
diminished. - -
The globular figure of the Earth is also inferred from the
operation of levelling, in which it is found necessary to make
aſ fllowance for the difference between the true and appx.
'reſs level; and the allowance which is made, and found to
answer, is on the principle that the Earth is spherical.
28S GRAMMAR 61, ASTRONOMY.
Another proof of the Earth being of a spherical form, is
obtained from its shadow in an eclipse of the Moon; for
when the shadow of the Earth falls on the Moon she is eclips-
ed, and the shadow always appears circular upon the face of
the Moon, when she is not totally eclipsed, although the
Earth is constantly turning on its axis. Hence it follows,
that the body which projects the shadow, must be spherical.
But the most convincing proof of the spherical figure of
the Earth, is, that many navigators have sailed round it; not
on an exact circle, it is true, because the winding of the
shores would not admit of it, but by going in and out as the
shores happened to lie, and still keeping the same course,
they have at last arrived at the port from which they depart-
ed. The first who succeeded in this daring enterprise was
Ferdinand Magellan, a Portuguese, in the year 1519, and
who completed his voyage in 1124 days; in the year 1557,
Francis Drake performed the same in 1056 days; in the year
1586, Sir Thomas Cavendish made the same voyage in 777
days; in the year 1598, Oliver Noort, a Hollander, in 1077
days; Wan Schouten, in the year 1615, in 749 days; Jac.
Heremites and Joh. Huygens, in the year 1623, in 802
days: and many others have performed the same navigation,
particularly Anson, Bougainville, and Cook.
Some of these navigators sailed eastward, some westward,
till they again arrived in Europe, whence they set out; and
- in the course of their voyage observed, that all the phenome- .
na, both of the heavens and Earth, confirmed the doctrine of
the spherical figure of the Earth. The unevenness or irre-
gularity of the Earth's surface, such as mountains and val-
leys, afford no objection to its being considered as a globular
body; for the loſtiest mountains bear no greater proportion
to the vast magnitude of the Earth, than grains of sand to the
size of an artificial globe of thirteen inches in diameter. This
is the reason that no deviation from the spherical figure of
its shadow is perceptible in an eclipse of the Moon.
2. From the most accurate measurement, lately
made by mathematicians, it is found that the terres-
trial meridian is nearly an ellipse; that the figure
of the Earth is not exactly a sphere, but nearly an
oblate spheroid, its equatorial diameter being about
25 miles longer than its axis or polar diameter, and
its mean diameter 7914 miles. -
\
OF - 'I' HE SOLAR, SYSTEMſ. 289
3. By the application of a new theory of most
probable results to the determination of the magni-
tude and figure of the Earth, Dr. Jīdrain has found
the ratio of the axis to the equatorial diameter to
be at 320 to 321, the true mean diameter of the
Earth, considered as a globe, to be 7918.7 miles,
and consequently its circumference 24877.4 miles,
and a degree of a great circle equal to 69.1039
miles. } . e --
According to La Place the polar diameter is to the equi-
torial as 331 to 332; he makes the equatorial diameter
792.4 miles: hence the polar diameter is 7900 miles, and
the mean diameter 79.12. In the preceding part of this work,
the mean diameter of the Earth has been taken equal to
7920 miles, its circumference 24,880 miles, and the length of
a degree 69% miles; the same numbers shall therefore be
used in the subsequent part: they are nearly those given
by Dr. Jädrain, and which are considered to be the most
exact measures of the magnitude of the Earth. -
Although every one of the observations which have just
been made, (in the preceding article) respecting the figure
of the Earth, affords sufficient evidence that the surface of
the Earth is curved, yet none of them, except, perhaps, the
form of the shadow on the disc of the Moon in a lunar
eclipse, entitles us to infer that the figure of the Earthis that
of a globe, or perfect sphere. It was natural, however, for
those who first discovered that the Earth had around shape,
to suppose that it was truly spherical. This, however, is now
known not to be the case; its true figure being that of an ob-
late spheroid, or sphere flattened a little at the poles, and
raised about the equator: so that the axis or polar diameter
is less than the equatorial. What first led to this discovery
was the observations of some French and English philoso-
phers in the East Indies and other parts, who found that pen-
dulums required longer time to perform their vibrations the
nearer they were to the equator; for Richer in a voyage to
Cayenne, near the equator, found that it was absolutely fie-
cessary to shorten the pendulum of his clock about one
eleventh part of a Paris inch, in order to make it vibrate in
the same time as it did in the latitude of Paris. . From this
it appeared that the ſorce of gravity was less at places near
the equator than at Paris; and consequently that those parts
290 - GRAMMAR OF ASTRONOMY.
are at agreater distance from the Earth’s centre. This circum-
stance put Newton and Huygens upon attempting to disco-
ver the cause, which they attributed to the revolution of the
Earth on its axis. If the Earth were in a fluid state, its ro–
tation on its axis would necessarily make it assume such a
figure, because the centrifugal ſorce being greatest at the
equator, the fluid would there rise and swell most; and that
its figure really should be so now, seems necessary to keep
the sea in the equatorial regions from overflowing the land
in those parts. . § ! -
Newton in his Principia demonstrates, that by the opera-
tion of the power, called gravity, the figure of the Earth
must be that of an oblate spheroid, if all parts of the Earth
be of a uniform density throughout, and that the proportion
of the polar to the equatorial would be 229 to 230 nearly.
As all conclusions, however, deduced from the length of
pendulums at different places on the Earth's surface; proceed
upon the supposition that the Earth is a homogeneous body,
which is very improbāble, the true figure of the Earth can
scarcely be expected to be discovered by the pendulum; and
at any rate it can be of no use in determing the magnitude
of the Earth. A solution of this important problem has, how-
ever, been attempted at various periods, by other means, and
has at last been accomplished if a most accurate and satis
factory manner, by the actual measurement of a very large
arc of a meridian circle on the Earth’s surface. The earliest
attempt of this kind of which we have any account, is that of
Eratosthenes of Alexandria, in Egypt. . By measuring the
Sun's distance from the zenith of Alexandria, on the solstitial
day, and by knowing, as he thought he did, that the Sum was
in the zenith of Syené, on the same day, he found the distance
in the heavens between the parallels of these places to be 79
12', or ºr part of the circumference of a great circle. Sup-
posing then that Alexandria and Syené were on the same me-
ridian, nothing more was required than to find the distance
between them, which multiplied by 50, would give the cir-
cumference of the globe. But it does not appear that Era-
tosthenes took any trouble either to ascertain the bearing or
the distance of the two places; for Syené is considerably
east of Alexandria, and it appears that the distance was not
measured till long afterwards, when it was done by the com-
mand of the Emperor Nero. A similar attempt was made by
Possedonius, who lived in the time of Pompey; but it is im-
oossible for us to judge how far these results correspond
$iith the most accurate measurement of the moderns, as we
of THE SOLAR SYSTEM. $291
are unacquainted with the stadium, the measure in which
the results were expressed. . . . . . . . .
The first arc of the meridian measured in modern times,
with any degree of accuracy, was by Snellius, a Dutchma-
thematician. The arc was between Bergen-op-Zoom and
Akmaar, and the length of the degree that resulted was
55,021 toises; but upon repeating the operations afterwards
with greater accuracy, the dégree came out 57,083 toises,
which is not ſap from the truth. - - *
The next who undertook this measurement was Norwood,
who, in the year 1635, measured the distance between Lon-
don and York with a chain, from whence he deduced the
length of a degree to be 57,800 toises, which has been found
to be a near approximation, considering the method he took
to determine it. . * . . . .
Picard was the first person who employed the trigonome-
trical method with any degree of accuracy; but since his
time very large arcs' of the meridian have been measured in
various parts of the world, particularly in Lapland, Peru,
India, France, and England. The arc, which has been
measured in France extends from Dunkirk, in latitude 510
2' 9" N. to Formentera, the southernmost of the Balearic,
isles, inlatitude 38o38'56"N.comprising an arc of 12023'13".
But this has lately been extended to the Shetland islands.
The whole extent of the arc is therefore above 22 degrees.
From comparing the lengths of the degrees of the meridian
which have thus been measured at different parts of the
Earth with each other, it is found that they gradually in
crease in length from the equator to the poles; which
proves, beyond the possibillity of doubt, that the true figure
of the Earth is that of an oblate spheroid, its axis or polar
diameter, according to some mathematicians, being to the
equatorial ‘as 311 to 312. And by taking the mean length
of a degree, or that measured in France in latitude 459, and
multiplying it by 360, the degrees in the circle; the circum-
ſerence of the Earth in direction of the meridian is ſound to
be 24,855.84 miles. The circumference of the equator is
24,896.16 miles, which is about 40 miles greater than the pre-
ceding. The mean diameter of the Earth is therefore 9710
nearly, and length of one degree is 69; American miles.
4. As the axis of the Earth is perpendicular to
the plane of the equinoctial, and its orbit makes an
angle of 23° 28′ with the plane of that circle, the
292 GRAMMAR OF ASTRONOMY.
axis of the Earth in every part of its revolution,
about the Sun, will make an angle of 66° 32' with
the plane of the ecliptic; and this inclination oc-
casions the successions of the four seasons, as has
already-been illustrated, in the preceding part of .
the work. . . . . . . . . .
Observations, separated by along interval, point out that
the obliquity of the ecliptic is diminishing at nearly the rate
of half a second in a year; that is, the ecliptic appears ap-
proaching the equinoctial by half a second in a year. The
secular diminution of the obliquity of the eclipfic is at this
time 50 seconds, according to Dr. JMaskelyne and JM. De la
Land. But later observations, and the calculations of La
Place, give 52', 1 for the secular diminution. . . . . .
Physical astronomy shows that this arises from a chang
in the plane of the Earth's orbit, occasioned by the action of
the planets: that this change of obliquity will never exceed
a certain limit, which limit, according to La Place, is 20
42'; and that by this action of the planets, the ecliptic, is
progressive on the equator 14" in a century. .
Besides this progressive motion of the Earth's axis
towards a perpendicular direction to the plane of the ecliptic,
it has a kind of libratory motion, by which the inclination is
continually varying, a certain number of seconds, backwards
and forwards; the period of these variations is nine years.
The tremulous motion is termed the mutation of the Earth's
axis. This motion is caused by º joint, effect of the
inequalities of the action of the Sûm and Moon upon the
spheroidal figure of the Earth. A ... w
5. The equinoctial points have a retrograde mo-
tion, at the rate of about 19, in 72 years, or more
accurately 50%," in a year; consequently the Sun
returns again to the same equinoctial point before
he has completed his revolution in the ecliptic: so
that the equinoxes precede continually the complete
apparent revolution of the Sun in the ecliptic by 20
minutes, 20 seconds of time. - -
This retrograde motion, of 50th," in a year, of the equi-
móctial points, is usually called in books of astronomy the
precession of the equinoxes; but, as Delambre very pro-

. OF THE SOLAR, SYSTEMI. 293
perly remarks, it should be called the recession or retrogra-
dation of the equinoctial points, and reserve the term preces-
sion for the anticipation of the moment of the equinox; so
that 20 minutes 20 seconds, the time which the equinoxes
precede continually the complete revolution of the Sun in
the ecliptic, in consequenge of the recession of the equinoc-
tial points, ought to be calléd the precession of the equinoxes. “
Although the place of the celestial pole among the fixed
stars-has been considered as not changed by the annual mo-
tion of the Earth, yet in a longer period of time it is ob-
served to be changed, and also the situation of the celestial
equator, while the ecliptic retains the same situation among
the fixed stars. Observation shows that this change of the
pole-and equinoctial is nearly regular. The pole of the
equinoctial appears to move with a slow and nearly uniform
motion, in a small circle, round the pole of the ecliptic,
while the intersections of the equinoctial and ecliptic move
iyackward in the ecliptic, or contrary to the order of the
signs, with a motion, nearly uniform. In consequence of
this apparent motion; all the fixed stars increase their lon
gitudes by 50th," in a year, and also change their right as
censions and declinations. Their latitudes remain the same.
The period of the revolution of the celestial equinoctial
pole about the pole of the ecliptic is nearly 25,920 years.
The north celestial pole therefore will be, about 12,960
years hence, nearly 499 from the present polar star; and
about 10,000 years hence, the bright star Vega in Lyra will
be within 50 of the north pole. This star, therefore, which
now, in the latitude of about 54 degrees, passes the meridian
within a few degrees of the zenith, and twelve hours after
is near the horizon, will then remain nearly stationary with
respect to the horizon. All which will readily appear, from
considering the celestiál concave surface as represented by
a common celestial globe. * . . . . .
This motion of the celestial pole originates ſrom a real
motion in the Earth, whereby its axis, preserving the same
inclination to its orbit, has a slow retrograde conical motion.
The cause is shown, by physical astronomy, to arise from
the attraction of the Sun and Moon on the excess of matter
at the equatorial parts of the Earth. _-
6. It has already been observed that the astro-
nomical days are not equal, and that two causes
combine to produce their difference : that is, the
2’
* 25*
2.94. GRAMMAR OF ASTRONOMY.,
obliquity of the ecliptic with respect to the equa
tor, and the unequal motion of the Earth in an el-
liptical orbit. . . -
7. That part of the equation of time, or the dif-
ference between the -mean and apparent time,
arising from the obliquity of the ecliptic is the
greatest about February 5th, May 6th, August 8th,
and November 8th; and is nothing about March
21st, June 21st, September 23d, and December
21st, or when the Sun is in the four cardinal points
of the ecliptic.
As the Earth's axis is perpendicular to the plane of the
equator, any equal portions of this circle, by means of the
Earth's rotation on its axis, pass over the meridian in equal
times; and so, in like manner, would any equal portion of
the ecliptic, provided it were parallel to, or coincident with,
the equator. But as this is not the case, the daily motion
of the Earth on its axis carry unequal portions of it over
the meridian in equal times; the difference, being always
proportional to the obliquity: and as 'some parts of the
ecliptic are much more obliquely situated with respect to
the equator than others, those differences will, therefore, be
unequal among themselves. . . .
This part of the subject may be pleasingly illustrated on
the terrestrial globe, by placing patches on the ecliptic and
equator at every tenth or fifteenth degree ; then, by turning
the globe gradually on its axis, the patches will pass under
the meridian at different times, thus exhibiting the phenome-
na already described. And that part of the equation of time
depending upon the obliquity of the ecliptic, may be found
by the terrestrial globe: thus, bring the Sun's place in the
ecliptic to the brazen meridian; count the number of degrees
from the beginning of the sign flries to the brazen meridian,
both on the equator and on the ecliptic; the difference, reckon-
ing 4 minutes of time to a degree, is the equation of time. If
the number of degrees on the ecliptic exceed those on the
equator, the Sun is faster than the clock; but if the number
of degrees on the equator exceed those on the ecliptic, the Sun
is slower than the clock. . . . . *
8. The second part of the equation of time aris-
ing from the unequal motion of the Sun in the
OF THE SOLAR SYSTEM. 295
ecliptic, is the greatest about March 30th, and Oc-
tober 3d ; and least, or nothing, about July 1st,
and December 31st; the Sun on the last two days
being in the apsides of his orbit. r
9. As the Sun moves from the apogee to the
perigee, the time shown by the Sun precedes that
shown by a well regulated clock, or mean solar
time ; but whilst the Sun moves round the perigee
to the apogee, the mean time precedes the apparent
time. . . . . . .
Illustration. Let ABCDA be the ecliptic, or the elliptical
orbit, which the Sun, by an irregular motion, describes in the
space of a year; the dotted circle abcd, the orbit of an ima-
ginary star, or sun, coincident with the plane of the ecliptic,
and in which it moves through equal arcs in equal times.
ſ'
Let HIK, also, be the Earth which revolves round its axis
every twenty-ſour hours, from west to east; and suppose the
Sun and star to set out together from A anda, in a right line
with the plane of the meridian EH; that is the Sun st Abe:
ing at his greatest distance from the Earth, at which time his
motion is slowest; and the star, or fictitious sun at a, whose
motion is equable, and its distance from the Earth always
the same. Then because the motion of the staris always uni-
form, and the motion of the Sun, in this part of his orbit, is

296 GRAMIMAR OF ASTRONOMY.
the slowest; it is plain that whilst the meridian revolves
from H. to h, according to the order of the letters, H, I, K, L,
the sun will have proceeded forward in his orbit from A to
F; and the star, moving with a quicker motion, will have
gone through a larger arc, from a to f. from which it is plain,
that the meridian EH will revolve sooner from H to h, under
the sun at F, than from H to k under the star at f, and conse-
quently it will be noon by the Sun sooner than by the clock.
As the Sun moves from A to C, the swiftness of his motion
will continually increase, till he comes to the point C, where
it will be the greatest; and the Sun C, and the star c, will be
together again, and consequently it will be noon by them both
at the same time; the meridian EH having revolved to EK.
From this point, the increased velocity of the Sun being
now the greatest, will carry him before the star; and, there-
fore, the same meridian will, in this situation, come to the star
sooner than to the Sun. For, whilst the star movés from c to g,
the Sun will move through a greater arc, from C to G ; and,
consequently, the point K has its noon by the clock when
it comes to k, but not its noon by the Sun till it comes to l.
And though the velócity of the Sun diminishes all the way
from C to A, yet they will not be in conjunction till they come
to A, and then it is noon by them both at the same instant.
From this it appears that the solar moon is always later
than the clock, whilst the Sun goes from C to A, and sooner
whilst he goes from A to C ; and at those two points, it is
noon by the Sun and clock at the same time. -
The obliquity of the ecliptic to the equator, which is the
first mentioned cause of the equation of time, would make
the Sun and clock agree on the four days of the year, which
are when he enters) Aries, Cancer, Libra, and Capricorn;
but the other causes, which arise from his unequal motion
in his orbit, would make the Sun and clocks agree only twice
a year, that is, when he is in his apogee and perigee ; and,
consequently when these two points ſall in the beginnings
of Cancer and Capricorn, or of Aries and Libra, they will
concur in making the clocks and Sun agree in those points.
But the apogee, at present, is in the tenth degree of Cancer,
and the perigee in the tenth degree of Capricorn; and,
therefore, the times shown by the Sun and clocks cannot be
equal about the beginning of those signs, nor at any other
time of the year, except when the swiftness or slowness of
equation, resulting from one of the causes, just balances
the slowness or swiftness arising from the other. About
OF THE SOLAR SYSTEMſ. 297
&*
the 3d of November, the absolute equation of time, result-
sing from both these causes, will be the greatest; the time
shown by a regular going clock, being then about 16# min-
utes slower than the time shown by the Sun.
10. The velocity of the Earth, like all the other
planets, varies in different parts of its orbit, it being
most rapid in the perihelion, about January the
1st, and slowest when in aphelion about July 1st.
The daily motion in the perihelion is 62' 12", and
in the aphelion 59' 12". -
11. This unequal motion of the Earth causes
the summer half year, north of the equator, to be
about 8 days longer than the winter half year.
Or the interval between the vernal and autumna;
equinoxes, is about 8 days longer than the interval
between the autumnal and vernal equinoxes.
“. . * days. hrs. min.
• *
From the spring equinox to the summer
solstice – - - - - - - " - 92. 21 36
From the summer solstice to the autumnal **
equinox - - - - - 93 13 58
From the autumnăl equinox to the winter . -
solstice - - - - - - - .89 16 , 51
From s the winter solstice to the spring .
, equinox - - – - - - , 89 1 24
Hence, from the spring equinox to the autumnal equinox
is 186 days, 1 hours, 34 minutes; and from the autumnal
equinox to the spring equinox is 178 days, 18 hours, 15
minutes, making a difference of 7 days, 17 hours, 29 minutes.
12. The velocity of light is to that of the Earth
in its orbit as 10313 to 1; and it is ſound by ob-
servation to be 8 minutes 7; seconds in coming
from the Sun to the Earth. •º !,
When the Earth is in its perihelion, light takes about
7 minutes, 59%. seconds in passing from the Sun to the
Earth ; at the mean distance of the Earth from the Sun, 8
minutes, 7} seconds; and at the greatest distance of the
3.arth from the Sun, 8 minutes, T5; seconds. . . .
298 GRAMMAR OF ASTRONOMY.
TABLE. l
Showing the mean longitude of the Earth, reckoning
from the mean equinow, at the epoch of mean noon, at
Paris, January 1st, 1801; longitude of the perihe-
lion, &c. - *

- - - S O / //
Longitude of the Earth - - 3 10 9 13
Longitude of the perihelion gºss 3 9 30 5
Inclination of its axis - - - - 0 66 82 2
Greatest equation — — . – 0 1 55 30
Mean daily motion - - - 0 0 59 8
Eccentricity in miles - - - - 1,618,000
Its sidereal revolution is performed in 365 days, 6 hours,
9 minutes, 11% seconds.
Its tropical revolution, or tropical year, 365 days, 5 hours,
48 minutes, 51% seconds. • . . -
The sidereal motion of the apsides is direct 19' 40”; but
the tropical motion, is direct 1' 2" nearly in a year, or 1943,
10% in one hundred years; making the length of the year to
consist of 365 days, 6 hours, 14 minutes, 2 seconds; this is
called the flnomalistic year. A complete tropical revolution
of the apsides is performed in 20,931 years. A.
As the centrifugal force is greater at the equator than near
the poles, the weight of bodies are increased as we proceed
from the equator to the poles. If the gravity of a body at
the equator be unity or 1, at or near the poles it will be
1.00569. This variation of the action of gravity in different
latitudes, also causes the same pendulum, as has already
been remarked, to vibrate slower at the equator than at or
near the poles. For a pendulum to vibrate seconds at the
equator, it must be 39 inches in length, and at or near the
poles 39.206 inches. The density of the Earth is to that
of water as 1.1 to 2. Y.
The Earth is surrounded by a rare and elastic fluid, which
is called the atmosphere; neither the temperature nor the
density of this fluid is uniform, but diminishes in proportion
to its distance from the surface of the Earth; the height of
the atmosphere is supposed to be about 45 miles. If the
density of the atmosphere were every where the same, at
its temperature at 55 degrees, and the height of the baro-
meter at 30 inches, the height of the atmosphere would be
27,600 feet. The weight of the atmosphere upon every
square foot on the Earth's surface is about 2160 pounds.
OF THE SOLAR SYSTEMI. 299 -
{*
QUESTIONS.
What is the Earth 2 -
What is the figure of the Earth, and what is its
mean diameter 2 -
What is the ratio of the Earth's axis to its equa-
torial diameter, according to Dr. Jīdrain’s com-
putation ? t * &
Is the axis of the Earth perpendicular to the
plane of the equinoctial 2 -
Have the equinoctial points a retrograde mo-
tion ? *
What are the causes of the equation of time 2
When is that part of the equation of time, which
depends upon the obliquity of the ecliptic greatest ?
When is that part depending upon the unequal
motion of the Sun greatest ?
How much longer is the summer half year, in
northern latitude, than the winter half?
How much greater is the velocity of light than
that of the earth in its orbit? •.
•===~~
CHAPTER IX.
Of JMars. 3
1. Mars is the next planet, after the Earth, in
the order of distance from the Sun; it performs
its sidereal revolution from west to east, or in
the order of the signs, round the Sun in 686 days,
23 hours, 30 minutes and 36 seconds, at the mean
rate of about 55,166 miles per hour.
300 GRAMMAR OF ASTRONOMY,
As the orbit of this planet includes that of the Earth, if
seems to move from west to east round the Earth. Its appa-
rent motion is, however, very unequal; when it begins to be
visible in the morning, a little after the conjunction, its mo-
tion is direct and most rapid; it becomes gradually slower,
and the planet when it arrives at about 136° 48' from the
Sun, is stationary; the motion then becomes retrograde,
increasing in velocity till Mars is 180° distant from the
Sun, or in opposition, so as to be on the meridian at mid-
might. This velocity then becomes a maa'imum, diminishes,
and again becomes nothing, when Mars, approaching the
... Sun, is distant from it 1360 48'. . Its motion then becomes
again direct, after having been retrograde during 73 days,
and in this interval the planet describes an arc of retrogra-
dation of about 160 12', continuing to approach the Sun, it
finishes by immerging in the evening into the Sun's rays.
.These singular phenomena are renewed at every opposition
of Mars, but with a considerable difference as to the extent
and duration of his retrogradations. See La Place’s Sys-
tem of the World. The period in which all those changes
take place, or the interval between two successive conjunc-
tions, or oppositions, is about 780 days, which is the length
of the synodical revolution of this planet.
The irregularities of Mars in its orbit, being the most
considerable of all the primary planets, Kepler fixed upon it
as the first object of his investigations respecting the nature
of the planetary orbits; and after extraordinary labour, he
at last discovered that the orbit of this planet was elliptical;
that the Sun is placed in one of the ſoci; and that there is
no point round which the angular motion is uniform. In the
pursuit of this inquiry he ſound the same thing of the Earth's
orbit; hence, by analogy, it was reasonable to think that all
the planetary orbits are elliptical, having the Sun in one of
the foci. i - •.
2. Continued and accurate observations show
that the figure of Mars is not an exact sphere, but
an oblate spheroid, whose axis or polar diameter
is to its equatorial one as 1272 to 1355, or as 15
16 nearly. The mean diameter of Mars is about
4200 miles, and this planet revolves on its axis,
from west to east in 24 hours, 39 minutes, and
21; seconds, which is the length of its day,
**------ - - - - - - -— - -
TELESCOPIC APPEARANCES 91, MARs.
- - -
-
- -
--

of THE SOLAR systEM. 301
Mars is of a red fiery colour, and gives a much duller
light than Wemus, though when he passes the meridian
about midnight, Mars equals Venus in size. -
The magnitude or size of Mars, according to Francoeur,
is .1886, its mass. 1294, and its density .715076; the size,
mass, and density of the Earth being respectively con-
sidered as unity, or 1. And a body weighing one pound on
the surface of the Earth, will weigh nearly a quarter of a
pound on the surface of Mars. . . .
Mars is the smallest and most eccentric of all the ancient
planets, except Mercury, and he is usually represented by
the character 3 , which is said to be rudely formed from a
man holding a spear protruded, representing the god of war,
which is the title of Mars in the heathen mythology. The
red colour of this planet is ascribed to the density of its at-
mosphere; for the atmosphere which surrounds Mars is not
only of great density, but of great height: that is, extends a
great way from his surface, as appears from the occulta-
tions to which the fixed stars are subject on approaching
his disc. Cassini observed a small star in the constellation
Aquarius, at the distance of 6' from the dise of Mars, that
became so faint before its occultation, that it could not be
seen by the maked eye, nor by a three feet telescope.
3. The inclination of this planet's orbit to the
plane of the ecliptic is 1° 51' 7"; and the inclination
of its axis is 59° 41'50". Its mean distance from
the Sun is nearly 15, that of the Earth being con-
sidered as 10; and the eccentricity of its orbit is
about one-eleventh of its mean distance from the
Sun.
From a series of observations, Dr. Herschel found that the
poles of Mars were distinguished by very remarkable lu-
minous spots. These he employed to determine the situa-
tion of the axis of the planet, and its inclination to the
ecliptic, &c. Their magnitude and splendour were some-
times very considerable, but subject to very great varia-
tions. He supposes that they are produced by the reflec-
tion of the Sun’s light from the snow near the poles; and
that the variations in their size and brightness is owing to
the melting of the polar ice.
The quantity of light and heat which Mars receives from
the Sun, is only about half what the Earth receives from
“
802 GRAMMAR OF ASTRONOMY.
that luminary; and the sun appears only half as large to
Mars as to the Earth. The light or heat upon the surface
ef Mars depends, however, on the density and height of its
atmosphere. To Mars, the Earth and Moon appear like
two moons, changing places with each other, and appearing
sometimes horned, sometimes half and three quarters en-
lightened, but never full; and never above a quarter of a
degree from one another, although they are, at their mean
distance 237,519 miles asunder.
If any satellite revolve round Mars, it caust be very small,
as it has not yet been discovered, notwithstanding the great
number of observations which have been made on this
planet with the most powerful telescopes.
4. The variations in the apparent diameter of
Mars is very great; its diameter when in opposi-
tion is 29", and its mean diameter about 9}". Ac-
cording to Dr. Brinkley, the apparent diameter,
when Mars is in opposition, is 26", and in conjunc-
tion, 5". -
These changes in the apparent diameter of Mars, prove
that his distance from the Earth is continually changing.
When Mars is in conjunction, he is never seen to transit or
pass over the Sun's disc. He is not subject to the same
limitations in his angular distance from the Sun as Mercury
and Venus; but recedes from the Sun to all possible angu-
lar distances. He is sometimes in opposition; then the
apparent diameter of Mars is nearly five times larger
than when in conjunction; and, therefore, he is five times
nearer the Earth in the former position than in the latter.
When Mars is viewed in a telescope, his disc changes its
form and becomes sensibly oval, according to his relative
position with respect to the Sun; sometimes appearing
wound, at other times gibbous, but never hormed. These
phenomena show, that Mars revolves in an orbit which in
cludes that of the Earth; and that he receives his light from
the Sun. -
5. The telescopic views of this planet present
a more diversified appearance than any of the
other planets; the spots on its surface are at once
numerous and extensive. Cassini observed several
spots in both hemispheres, by which he determined
OF THE SOLAR SYSTEM, 303
that the diurnal revolution was performed in 24
hours and 40 minutes, agreeing very nearly with
the subsequent observation of Dr. Herschel.
The belts and cloudy appearances on this planet are found
to change their shape and arrangement very frequently. With
regard to the bright polar spots, Dr. Herschel observes, that
the poles of the planet are not exactly in the middle of
them, though nearly so. From the appearance and disap-
pearance of the bright north polar spot of the year 1781,
we collect, that the circle of its motion was at some consi-
derable distance from the pole. By calculation its latitude
must have been about 76 or 77 degrees north. - -
The south pole of Mars could not be many degrees from
the centre of the large bright southern spot of 1781; though
this spot was of such a magnitude as to cover all the polar
regions farther than the seventieth or sixty-fifth degree.
TABLE.
Heliocentric longitude on the 1st of Ja- .
nuary, 1825, - - - - 11s. 90 38' 0",
Geocentric longitude at the same time, 10 15 39 0
Longitude of the perihelion on the 1st
of January, 1801, - - - 11 2 24 2.
Longitude of the ascending node, at the
same time, - gº º ſº º 1 18 1 27
Inclination of the orbit to the ecliptic,
January 1st, 1801, - º º 0 1 51 7
Greatest equation, tº - - 0 10 41 27
Mean daily motion, tº ºne tº 0 0 31 27
Mean distance from the Sun in American
miles, Kºe gº º * ës 144,760,806
Eccentricity in miles, – gº sº 13,463,000
The secular motion of the apsides is 1949'52", in longi-
tude according to the order of the signs. The place of the
nodes is liable to a direct secular variation in longitude of
44' 414". The inclination of the orbit to the ecliptic is sub-
ject to a small decrease of about 1%" in one hundred years.
The greatest equation is subject to a small diminution of
about 37" in a century. -
The following particulars respecting Mars are given, by
Dr. Herschel, after long and accurate observations.
1. The node of the axis of Mars is in 118. 170 47", or
17O 47' of Pisces.
304 GRAMMAR OF ASTRONOMY.
2. The obliquity of the ecliptic on the globe of Mars,
is 28O 42'. *
3. The point zero (0) or the point of the sign Aries, on
the martial ecliptic, answers to our 8s 19928, or 190 28' of
Sagittarius.
From these and some previous observations, it appears.
that the analogy between Mars and the Earth is greater than
between the Éarth and any other planet of the solar system.
Their diurnal motion is nearly the same; the obliquity of
their respective ecliptics, on which the seasons depend, are
not very different; and of all the superior planets, the dis-
tance of Mars from the Sun is by far the nearest alike to
that of the Earth; nor is the length of its year very different
from ours when compared with the years of Jupiter, Saturn,
and Uranus.
º
QUESTIONS.
-At what rate does Mars move in its orbit 2
In what time does Mars perform a complete re-
volution on its axis 2
In what proportion is the polar diameter of Mars
to its equatorial 2
What is the inclination of the orbit of Mars to
the ecliptic 2 s”
How many seconds is the mean apparent diame-
ter of Mars 2 What is the greatest apparent di-
ameter 2 &
What else is worthy of notice in this planet 2
*-ºs
CHAPTER IX.
Of the New Planets, or flsteroids, Vesta ä, Juno à,
Ceres (, , and Pallas 2.
1. Vesta is the next planet, after Mars, in the
order of distance from the sun; and it performs
its sidereal revolution in 1335 days, 4 hours, 55
minutes, and 12 seconds, which is the length of
OF THE SOLAR SYSTEMI. 305
the planet’s year. Its relative mean distance from
the sun is 24, that of the earth being considered
as 10. t -
The greatest distance of Westa from the Sun,
in miles, is reckoned sº tºº ſº- 246,450,053
Its least distance, - dº º *º 204,419,947
Its mean distance, - tºº º - 225,435,000
Eccentricity of its orbit, - º - 21,015,053
Mean hourly motion, - - - - 44,202
Mean longitude 1st of January, 1801, - 8s. 27025' 1"
Longitude of the perihelion, tº-> - 8 9 43 0
Longitude of ascending node, - - 0 7 8 46
2. The inclination of the orbit of Vesta to the
plane of the ecliptic is 7°8'46". The apparent
diameter of this planet is not quite half a second ;
and its real diameter is supposed to be 238 miles,
but according to the observations of Schroeter it
is much greater.
In a clear evening this planet may be seen by the naked
eye, like a star of the sixth magnitude, of a dusky colour,
similar in appearance to Uranus. Vesta shines with a purer
light than any of the minor planets.
This planet was discovered by Dr. Olbers, at Bremen,
on the 29th of March, 1807. , &
3. Juno is the next planet, after Westa, in the
order of distance from the sun, and it performs its
sidereal revolution round the sun in 1590 days, 23
hours, 57 minutes, and 7 seconds, which is the
length of the planet’s year. Its relative mean dis-
tance from the sun is 27, that of the earth being
considered as 10. -
The greatest distance of this planet from
the sun, in miles, is - - - - 816,968,828
Its least distance, tº tº dº ſº. 189,792,142
Its mean distance, * * * * 258,380,485
Eccentricity of its orbit, - - - 65,588,843
Mean hourly motion, - - - - - 41,170
26* &
306 GRAMMAR OF ASTRONOMY.
Mean longitude 1st of January, 1801, 9s. 200 30' 52”
Longitude of the perihelion, - - # 23 18 41
Longitude of the ascending node, - 5 21 6 38
4. The inclination of the orbit of Juno to the
plane of the ecliptic is 13° 3. 28". The real di-
ameter of this planet, according to Schroeter, is
about 1425 miles; and its apparent diameter is
about 3.057".
Juno is of a reddish colour, and appears sometimes very
brilliant. This planet, according to the observations of
Schroeter, is surrounded by an atmosphere more dense than
that of any of the planets; and he also remarks, that the
variation in the brilliancy of this planet is cºy owing to
certain changes in the density of its atmosphere, though he
thinks it not improbable that these changes may arise from
a diurnal rotation performed in 27 days. *
The planet Juno was discovered by Harding, at the obser-
vatory of Lilianthel, near Bremen, on the evening of the 1st
of September, 1804, while he was making a catalogue of
all the stars which were near the orbits of Ceres and Pallas.
5. Ceres is the next planet, after Juno, in the
order of distance from the sun; and it performs its
sidereal revolution in 1681 days, 12 hours, 56
minutes, and 10 seconds, which is the length of the
planet’s year. Its relative mean distance from the
sun is 28, that of the earth being considered as 10.
The greatest distance of this planet from the
sun, in miles, is game gº * tºº 283,501,700
Its least distance, '- tº &º - 242,305,440
Its mean distance, - - - - 262,903,570
Eccentricity of its orbit, - * * 20,598,130
Mean hourly motion, - - was - 40,932
Mean longitude 1st of January, 1801, .. 8s. 24O45' 10"
Longitude of the perihelion, - " - 4 26 39 39
Longitude of the ascending node, " - 0 10 37 34
6. The inclination of the orbit of Ceres to the
plane of the ecliptic is 10°37'34"; its real diameter,
OF THE SOLAR SYSTEMI, 307
according to Dr. Herschel, is only 163 miles, but
Schroeter makes it 1624 miles; and its apparent
diameter is about 1 second. -
Ceres is not visible to the naked eye; but when observed
by a telescope, appears of a ruddy colour, and about the
size of a star of the eighth magnitude. It also seems to be
surrounded by an extensive and dense atmosphere; but
when examined by a telescope, which magnifies it above two
hundred times, its disc may be very distinctly perceived.
Ceres was discovered on the 1st of January, 1801, by M.
Piazzi, of Palermo in Sicily. He continued to observe the
planet till the 13th of February, when he was obliged by
illness to discontinue his observations. M. Piazzi then
transmitted accounts of his observations to several celebra-
ted astronomers, in order that they might calculate the orbit
of the new star, and trace out its progress in the heavens;
but it eluded every search that was made for it, until De-
cember 7th, when it was re-discovered by the assiduous, Dr.
Zach, of Saxe-Gotha ; and soon after it was observed by
Dr. Olbers, at Bremen; by Mechain, at Paris; by the royal
astronomer, at Greenwich; by Dr. Herschel, at Slough; and
by various other astronomers. - -
7. Pallas is the next planet, after Ceres, in the
order of distance from the sun; and it performs its
sidereal revolution in 1681 days, 17 hours, and 58
seconds, which is the length of the planet’s year.
Its relative mean distance from the sun is not much
more than 28, that of the earth being considered
as 10. .# , - -
The greatest distance of this planet from the
sun, in miles, is - - 327,437,913.
Its least distance, ęse gº dº - 198,404,567
Its mean distance, sº gº º †† 262,921,240
Eccentricity of its orbit, - - - , 64,516,678
Mean hourly motion, - - - - 40,930
Mean longitude 1st of January, 1801, 8s. 12°37' 2"
Longitude of the perihelion, - - 4 1 14 1
Longitude of the ascending node, - 5 22° 32 36
30S GRAMMIAR OF ASTRONOMY
8. The inclination of the orbit of Pallas to the
plane of the ecliptic is much greater than that of
any of the planets, being about 34° 37'8". The
real diameter of this planet, according to Schroe-
ter, is about 80 miles; but, according to Dr. Her-
schel, it is about 2099 miles. w" '.
This planet is too small to be seen by the naked eye; but
when viewed in a good telescope, it appears less ruddy than
Ceres; but the light of Pallas exhibits greater variations.
The atmosphere of this planet, according to Schroeter, is
468 miles. Pallas was discovered March 28th, 1802, by
Dr. Olbers, at Bremen, in Lower Saxony.
- QUESTIONS.
How is the planet Vesta situated, and what is its
relative mean distance from the Sun, that of the
earth being considered as 102
What is the inclination of the orbit of Westa to
the plane of the ecliptic 2 --
What is the relative mean distance of Juno from
the sun, that of the earth being considered as 102.
What is the real diameter of Juno, according to
Schroeter 2 -
What is the relative mean distance of Ceres
from the sun, that of the earth being considered
as 10 ! -
In what angle is the orbit of Ceres inclined to
the plane of the ecliptic 2 -
How is the planet Pallas situated, and what is
its relative distance from the sun, that of the earth
being considered as 102 -
In what angle is the orbit of Pallas inclined to
the plane of the ecliptic 2
It appears rather extraordinary that the orbits of the four
new planets, just described, should all be nearly at the same
distance from the sun, and in a part of the heavens, where it
was conjectured, some planet might perform its revolution
f
OF THE SOLAR SYSTEM, 309
round the sun, although no astronomer had ever been so ſor-
tunate as to discover it. What led to this discovery was the
great distance between the orbits of Mars and Jupiter, a
thing so unlike the regular order in which the orbits of the
planets between the sun and Mars were disposed. Accord-
ingly, upon the discovery of Ceres, the harmony and regu-
larity of the system seemed to be established; but the sub-
sequent discovery of Pallas and Juno seemed again to over-
turn these speculations. This new difficulty suggested to
Dr. Olbers what may, perhaps, be considered a very ro-
mantic idea, namely, that the three recently discovered
planets might be fragments of a planet, which had been
burst asunder by some convulsion. This opinion seemed to
receive considerable support from a comparison of their
magnitudes with that of all the other planets; from the cir-
cumstance of their orbits being nearly at equal distances
from the sun; and from the very singular fact, that all their
orbits cross one another in two opposite points in the heavens.
To support which, this hypothesis, derived from the last
of these circumstances, is peculiarly strong and conclusive;
for it can be demonstrated, that if a planet, in motion, be
rent asunder by any internal force, however different the
inclinations of the orbits of the fragments may be, they
must all meet again in two points. Prosecuting this idea,
Dr. Olbers every year examined the small stars that were
near these points in the heavens, and was so fortunate as to
discover a fourth fragment, or the last discovered planet,
Westa. Dr. Brewster, of Edinburgh, has suggested another
view of the subject, which seems to give additional support
to the theory of Olbers. If a planet, says Dr. Brewster, be
rent asunder by any explosive force, the form of the orbits
assumed by the fragments, and their inclination to the
ecliptic, or to the orbit of the original planet, will depend
upon the size of the fragments, or the weight of their res-
pective masses: the larger masses will deviate least from
the original path, while the smaller fragments, being thrown
off with greater velocity, will revolve in orbits more eccen-
tric, and more inclined to the ecliptic. Now this is pre-
cisely what happens: Ceres and Westa are found to be the
largest, and their orbits have nearly the same inclination to
the ecliptic as some of the old planets; while the orbits of
the smaller ones, Juno and Pallas, are inclined to the eclip-
tic, about 130 and 34}o respectively.
It is, however, somewhat remarkable that the orbits of
310 GRAMMAR OF ASTRONOMY.
Ceres and Pallas cross each other, owing to the very grea
eccentricity of the orbit of Pallas; it is several millions of
miles nearer the sun in its perihelion, then Ceres in the
same point of its orbit. But when Pallas is in its aphelion,
its distance from the sun is several millions of miles greater
than that of Ceres in the same point of its orbit.
Juno is farther from the sun in its aphelion, than Ceres in
the same point of its orbit; and Westa is farther from the
sun in its aphelion, than either Juno, Ceres, or Pallas, in
their perihelions. The perihelion distance of Westa is
greater than that of Juno or Pallas. So that it appears Westa
may sometimes be at a greater distance from the sun, than
either Juno, Ceres, or Pallas, although its mean distance is
less than either of them by some millions of miles: therefore,
the orbit of Westa crosses the orbits of the other three
planets. ,
emmºmºsºm-ºs-
CHAPTER X.
Of Jupiter ||, and its Satellites.
1. Jupiter, the ninth planet in order of distance
from the sun, performs its sidereal revolution in
4332 days, 14 hours, 18 minutes, and 41 seconds,
which is the length of its year: the rotation of
this planet on its axis, from west to east, is com-
pleted in 9 hours, 55 minutes, and 494 seconds,
which is the length of its day. The mean hourly
motion of this planet in its orbit is 29,866 miles.
Jupiter is the brightest of all the planets, except Venus.
He shines with a bright white light, but does not vary in
apparent size and brightness like Mars.
2. The form of Jupiter, like that of the earth,
is an oblate spheroid, the equatorial diameter being
to the polar as 14 to 13. The mean apparent
equatorial diameter of this planet is 38"; and when
in opposition, it is equal to 47"; its real diameter
is 91,000 miles; and its relative mean distance
OF THE SOLAR sys'TEM. 311
from the sun is 52, that of the earth being con-
sidered as 10. - • -
Jupiter is the largest planet in the solar system: its rela-
tive size is 1280.9; its mass 308.94; and its density .241.19;
the size, mass, and density of the earth being respectively
considered as unity, or 1. And a body weighing 1 pound
on the surface of the earth, would, if removed to the surface
of Jupiter, weigh 24 pounds nearly. ; :
3. The inclination of the orbit of Jupiter to the
plane of the ecliptic is 1° 18' 47"; and the axis of
this planet is so nearly perpendicular to its orbit,
that it has no sensible change of season: so that
in the polar regions of Jupiter, there is perpetual
winter : and about his equator, perpetual summer.
The inclination of Jupiter’s orbit to the ecliptic has a
small diminution of about 22.6 seconds in a century; and
his path, according to La Place, deviates occasionally from
the ecliptic 2042, or 3936. - - .
4. The apparent motion of this planet is sup-
ject to inequalities similar to those of Mars; pre-
vious to, and when it is nearly 115° 12' distant
from opposition, its motion becomes retrograde,
its velocity augments till the moment of opposition ;
then diminishes, and the motion becomes direct,
when the planet, in its approach towards the sun,
is only 115° 12' distant from it. The duration of
this retrograde motion is about 121 days, and the
arc of retrogradation is 9°54'. But there are,
according to La Place, perceptible differences in
the extent and duration of the retrograde motions
of Jupiter. The synodic revolution of this pla-
met, or the time from opposition to opposition, is
398 days, 20 hours, 48 minutes, and 28 seconds.
When Jupiter is in conjunction he rises, sets, and comes
to the meridian with the sun; but is never observed to
312 GRAMMAR OF; ASTRONOMY.
transit or pass over the sun's disc; when in opposition, he
rises when the sun sets, sets when the sun rises, and comes
to the meridian at midnight. This is a sufficient º
that Jupiter revolves round the sun in an orbit which in-
cludes that of the earth. , -
Jupiter, when in opposition, appears larger and more
luminous than at other times, being then much nearer to the
earth than a little before or after his conjunction; when the
longitude of Jupiter is less than that of the sun, he will
appear in the east before the sun rises, and will then be a
morning star; but when his longitude is greater than that
of the sun, he will appear in the west after sun-set, and
will then be an evening star.
5. Jupiter, when viewed through a telescope, is
observed to be surrounded by faint substances,
called zones, or belts, which are not only parallel
to one another, but, in general, parallel to his
equator; they are, however, subject to considera-
ble variation both in breadth and number, and are
on some occasions more conspicuous than at others.
Bright and dark spots are also frequently to be
seen in the belts; and when a belt vanishes, the
contiguous spots disappear with it. The number
of belts are very variable, as sometimes only one,
at others eight may be perceived. ,
The time of the continuance of the belts is very uncer-
tain; they sometimes remain unchanged for three months;
at others, new belts have been formed in an hour or two.
In some of these belts large black spots have appeared.
which moved swiftly over the disc, from the eastern to the
western edge of Jupiter's disc, and returned in a shorl
time to the same place. By observations on these, the ro-
tation of this planet on its axis has been determined. With
a telescope of a very moderate power, the disc of Jupiter
is nearly as large as the moon; and though the surface be
diversified by regular and parallel belts, yet it appears
much smoother than that of the Moon.
Astronomers are very different in their opinions respecting
the cause of these appearances. Some consider them as the
effect of changes in the atmosphere that surround Jupiter;
while others regard them as indications of greatphysical revo-
º
:
-
º
-
|
-
º

OF THE SOLAR SYSTEMſ. 3.13
Hutions on the surface of that planet. The first of these
hypotheses appears to explain the variations in the form and
magnitude of the belts; but it by no means accounts for
their parallelism, nor for the permanence of some of the
spots. The spot first observed by the astronomer Cassini,
in 1665, which has both disappeared and re-appeared in the
same form within the space of fifty years, seems evidently
to be connected with the surface of the planet. The form
of the belt, according to some astronomers, may be ac-
counted for by supposing that the atmosphere of Jupiter
reflects more light than the body of the planet, and that the
clouds which float in it, being thrown into parallel strată by
the rapidity of his diurnal motion, form regular interstices,
through which are seen the opaque body of Jupiter, or any
of the permanent spots which may come within the range of
the opening. -
TABLE,
Showing the mean distance of Jupiter from the Sun, and
the eccentricity of his orbit in miles; longitude of the
ascending mode, &c. *
Mean distance in miles - - - - - - 402,265,155
Eccentricity of his orbit - - - - - - 28,810,000
Longitude of ascending node, January
1st, 1801 - - - - - - - - 3s. 80 25' 34"
Longitude of the perihelion at the same -
time - - - - - - - - - - 0 11 8 35
Greatest equation of the centre - - 0 5 29 J25.
Heliocentric longitude, January 1st, 1825 0 4 8 54
Geocentric longitude at the same time 0 4 8' 5
Mean daily motion - - - - - - 0 0 0, 59.
Thesecular motion of the apsides in longitude 1934'33.8",
in consequentia, or according to the order of the signs. ,
The direct secular motion of the nodes is 57' 12.4". The
greatest equation of the centre is subject to a decrease of
55% in a century. . The great bulk of this planet, and the
short interval of time in which it makes a revolution on its
axis, cause the velocity of its equatorial parts to be prodi-
giously great; not less than 26 thousand miles per hour.
6. By directing the telescope to the planet Ju-
piter, it is found to be accompanied by four small
stars, ranged nearly in a right line parallel to the
-
27 -
314 GRAMMAR OF ASTRONOMY.
*
plane of his belts. These small stars are the
moons or satellites of Jupiter, which move round
him in different periods, and at unequal distances
from their primary. .
The discovery of these satellites was made by Gallileo in
1610; and this may be considered as one of the first fruits
of the invention of the telescope. They cannot be seen by
the naked eye, but are distinctly visible with a telescope of
a moderate power. Their relative situation with regard to
Jupiter, as well as to each other, is constantly changing.
Sometimes they may be all seen on one side of Jupiter, and
sometimes all on the other, They are designated by their
distances from Jupiter, that being called the first whose
distance from Jupiter is the least, when at the greatest
elongation, and so on with the others. They are of very
different magnitudes, some of them being greater than our
Earth, while others are not so large as the Moon. Their
apparent diameters being insensible, their real magnitudes
cannot be exactly measured. The attempt has been made
by observing the time they enter, the shadow of Jupiter;
but there is a great discordance in the observations which
have been made to obtain this circumstance; and, of course,
the result of these observations must be very discordant.
The third, however, is the greatest; the fourth is the second
in magnitude; the first the third in magnitude; and the
second is the least. - * . -
The first or nearest satellite of Jupiter, completes its
mean sidereal revolution round that planet in 1 day, 18
hours, 27 minutes, and 33 seconds, at the mean distance of
264,490 miles from the centre of its primary; the second
revolves in 3 days, 13 hours, 13 minutes and 42 seconds, at
the mean distance of 420,815 miles; the third in 7 days, 3
hours, 42 minutes, and 33 seconds, at the mean distance of
671,234 miles; and the fourth in 16 days, 16 hours, 34
minutes, and 50 seconds, at the mean distance of 1,180,582
miles. The form of the orbits of these satellites is found to
be nearly circular, especially those of the first, second, and
third; and the velocity of their motions nearly uniform. In
consequence of observing periodical changes in the intensity
of the light of the satellites, Dr. Herschel inferred that they
revolved on their axis, and that the period of their rotation
is equal to the time of their revolution round Jupiter,
Of THE SOLAR SYSTEM. 315
The ſour moons or satellites of Jupiter must afford many
curious phenomena to the inhabitants of that planet, in their
nightly course through the heavens. Their apparent diame-
ters as seen from Jupiter, are as follows:
'i'ite apparent diameter of the first is - 60' 20"
The - - - - - - - second - 29 42
The - - - - - - - third - 22 2
The - - - - - fourth – 9 39
The app. mean diam. of the Earth's Moon 31 26,
When the satellites are on the right hand, or west of Ju-
piter, approaching him, or east of Jupiter, receding from him,
they are then in the superior parts of their orbits or farthest
from the Earth. ‘ On the contrary, when the satellites are
on the right hand, or west of Jupiter, receding from him, or,
cast of Jupiter, approaching him, they are then in the in-
ferior part of their orbits, or nearest the Earth.
The satellites, like the inferior planets, are sometimes,
direct, stationary, and retrograde, as seen from the Earth.
QUESTIONs.
What is the mean hourly velocity of Jupiter in its
orbit? . . . w . . . . . .
In what time does Jupiter perform a revolution
on its axis 2 * - -
What is the ratio of the equatorial diameter of
Jupiter to its polar? . . . .
What is the relative mean distance of Jupiter
from the Sun, with respect to the Earth 2
What is the inclination of Jupiter’s orbit to the
plane of the ecliptic 2'-
What is the duration of Jupiter’s retrograde mo-
tion ? r
Do the belts of Jupiter always appear perma-
ment 2 * . *
How many satellites or moons has Jupiter?
316 GRAMMAR OF ASTIRONOMY.
CHAPTER XI.
Of Saturn h, of its Rings and its Satellites.
*. f )
1. Saturn, the tenth planet in order of distance
from the Sun, performs its sidereal revolution in
10,758 days, 23 hours, and 16 minutés, 34 seconds,
which is the length of its year. The rotation of
this planet on its axis, from west to east, is com-
pleted in 10 hours, 16 minutes, and 49 seconds,
which is the length of its day. * t
Saturn shines with a very feeble light, compared with
that of Jupiter, partly on account of his great distance from
the Sun, and partly from his dull red colour.
2. The diameter of Saturn is 77,680 miles; his
shape is an oblate spheroid, like that of Jupiter, but
still more elliptical, the equatorial diameter being to
the polar as 12 to 11. The apparent mean diame-
ter of this planet is about 17"; and its relative
mean distance from the Sun is 95, that of the Earth
being considered as 10. *
Saturn, next to Jupiter, is the largest planet in the solar
system: its relative size is 974.78; its mass 93.271; and its
density .005684; the size, mass, and density of the Earth
being respectively considered as unity, or 1, . And a body
weighing 1 pound on the surface of the Earth, would weigh
a little more than 1, pounds on the surface of Saturn.
3. The inclination of the orbit of Saturn to the
plane of the ecliptic is 2° 30'18"; and the inclina-
tion of this planet's axis to its orbit is probably 60
degrees.
The inclination of Saturn's orbit is subject to a small se-
cular diminution of 15% seconds.
4. The apparent motion of Saturn in its orbit is
subject to irregularities, similar to those of Jupiter
of THE SOLAR . SYSTEM . . 31?
and Mars. It commences and finishes its retro-
grade motion when the planet before and after its
opposition is about 108°54' distant from the Sun.
The arc of retrogradation is about 60 18, and its
duration is nearly, 131 days. The synodic revolu-
tion of this planet, or the time from opposition to
opposition, is 378 days, 2 hours, and 1 minute.
TABLE,
Showing the mean distance of Saturn from the Sun, &c.
Mean distance in miles - - - - - - 906,183,000
Eccentricity - - - - - - - - - 49,000,000
Longitude of ascending mode, January w
1st, 1801 - - - - - - - - 3s. 220 4 27”
Longitude of the perihelion at the same º
time - - - - - - - - - 2 29 30 58
Greatest equation of the centre - - ,0 6 27 58
Heliocentric long. January 1st, 1825 2 5 40 0
Geocentric long. at the same time - 2 1 44 0.
Mean daily motion - - - - - -, 0 (0. 2 6
- | |
The sidereal secular motion of the apsides is 32' 17", but
their tropical motion is 1955'47" in consequentia. The se-
cular increase of the greatest.equation is 1' 50".
5. Soon aſter the invention of telescopes, a re-
markable appearance was observed about Saturn.
After a considerable interval of time, Huygens
having much improved them, discovered, by careful
observations, a phenomenon unique, as far as we
know, in the solar system. He found that Saturn
is encompassed with a broad thin ring, inclined by
a constant angle of about 30°to the plane of Saturn's
orbit; and therefore at nearly the same angle to
our ecliptic, and so always appearing to us ob-
liquely. •
When the edge of the ring is turned towards us, it is in-
visible, on account of its thinness not reflecting light enough
to be visible, except in the 'º, best telescopes. When the
3.18 GRAMMAR OF ASTRONOMY.
plane of the ring passes between the Earth and Sun, it is
also invisible, because its enlightened part is turned from
us; and when it passes through the Sun it is also invisible,
the edge only being illuminated: so that it may have, in the
same year, two disappearances and reappearances. This
takes place when Saturn is near the nodes of the ring.
The ring is a very beautiful object, seen in a good teles-
cope, when in its most open state. It then appears ellipti-.
cal, its breadth being about half its length. Through the
space between the ring and the body, fixed stars have some-
times been seen. The surface of the ring appears more
brilliant than that of Saturn.
Among the numerous discoveries of Dr. Herschel, those
he has made with respect to Saturn and his ring are not the
least. He has ascertained that the ring, which heretofore
had generally been supposed single, consists of two, exactly
in the sºi - plane, and that they both revolve on their axis
in the same time as Saturn, and in the plane of Saturn's
equator. This is, however, doubted by Harding and
Schröeter. See Dr. Brinkley's Astronomy.
Dr. Herschel also saw the ring when it has disappeared
to other observers, either from the reflection of the edge, or
from the dark side enlightened by the reflection of Saturn,
as we see the whole Moon near new Moon. He observes
that the ring is very thin, compared with its width, its
thickness being about 1000 miles.
The outside diameter of the larger ring is 200,000 miles.
Its width - - - - - - - - - , 6,700
Distance between rings - - - - - - , 2,800
Outside diameter of smaller ring - - 180,000
Its width - - - - - - - - - 19,000
At the mean distance of Saturn, the apparent diameter of
the largest ring is about 47; seconds. • * - -
6. Saturn has also certain obscure zones, or
belts, appearing at times across his disc, like those
of Jupiter. V . . ..
These zones, or belts, are supposed to be obscurations in
his atmosphere, which Dr. Herschel has observed to be of
considerable density. -
7. Saturn has seven satellites revolving about
him in orbits nearly circular ; of which the sixth
OF THE SOLAR SYSTEMI, 3I9
is seen without much difficulty, and was called the
Huygenian satellite, from having been discovered
by H. uygens. - *-
The 3d, 4th, 5th, and 7th were afterwards discovered.
Dr. Herschel discovered the 1st and 2d., -
It has long been supposed that the 7th (formerly the 5th)
satellite revolved on its axis in the time of its revolution
round Saturn. This has been confirmed by the observa-
tions of Dr. Herschel. *
These satellites, except the 6th, require a very good teles-
cope to render them visible. On which account they have
been much less attended to than the satellites of Jupiter.
The periodical revolutions and distances of these satellites
from the body of Saturn, expressed in semi-diameters of
that planet, as well as in miles, are exhibited in the follow-
ing table :- - -

Satel-| Periodic Dist. in semi-Distances
lites. times. diameters. in miles.
\| 1 Od. 22h. 37/36." 2.8 107,000)
2 : 1, 8 53, 9 || 3.5 135,000
3 1 21 18 26 4.8 170,000
4 || 2 17 .44 51 j . 6.3 217,000
5 4 12 25 .11 S.7 303,000
6 |15 22 41 14 20.3 704,000.
7 '79 7. 54 37 59.1 2,050,000
QUESTIONs.
In what time does Saturn revolve on its axis 2
What is the shape of Saturn ? •
In what angle is Saturn’s orbit inclined to the
plane of the ecliptic 2 - -
Is the apparent motion of Saturn subject to any
irregularities 2 - -
What is the inclimation of Saturn's ring to the
plane of the planet's orbit 2
How many satellites has Saturn ?
320 GRAAIAIAR OF ASTY&ONOMY.
CHAPTER XII.
Of Uranus H, and his Satellites.
T. Uranus, the most remote planet yet known in
the solar system, performs its sidereal revolutioni in
30,688 days, 17 hours, 6 minutes, and 2 seconds,
or nearly 84 years, which is the length of the
planet’s year : the inclination of its orbit to the
plane of the ecliptic is about 46%; and the time of
rotation on its axis, or the length of its day, has not
been yet ascertained. *. *.
The planet Uranus had escaped the observation of an-
eient astronomers, its distance ſrom the earth being so great,
that it cannot be seen by the naked eye, except when the at-
anosphere is very clear, and then it appears like a star of the
ºth magnitude. Its light is of a bluish white colour; it
shows no disc but with a very great magnifying power. .
I’lamstead, at the end of the last century, and Mayer and
fle Moniuer, in this, had observed Uranus as a small star.
J}ut it was not till 1781 that Dr. Herschel discovered its
motion, and soon after, by following this star carefully, it
has been ascertained to be a true planet. Like Mars, Ju-
piter, and Saturn, the apparent motion of Uranus is subject
to irregularities. Its motion, which is nearly in the plane
of the ecliptic, begins to be retrograde when, previous to the
opposition, the planet is 103° 30' distant from the sun. It
ceases to be retrograde when, after the opposition, the planet
in its approach to the sun is only 103° 30' distant from him.
'The duration of its retrogradation is about 151 days, and its
arc of retrogradation about 30 36". The synodic revolution is
completed in 369 days, 15 hours, 44 minutes, and 38 seconds.
2. The diameter of Uranus is 35,000 miles; its
apparent diameter is very small, amounting not
quite to 4 seconds; and its relative mean distance
from the sun is 192, that of the earth being con-
sidered as 10.
Uranus is much less than Jupiter, or Saturn: the relative
size of this planet is 81.26, its mass 1.6904, and its density
OF THE SOLAR SYSTEM. 321
.0208; the size, mass, and density of the Earth being re-
spectively considered as unity, or 1. And a body weighing
1 pound on the surface of the earth, would weigh .95 on the
surface of Uranus. -
TABLE,
Showing the mean distance of Uranus from the Sun, &c.
Mean distance in miles, - - - - - 1,812,413,975
Eccentricity of its orbit, - - - - - 85,052,560
Long of ascending node Jan. 1st, 1801, 2s. 12055'42"
Long. of the perihelion at the same time, 5 17 38 19
Heliocentric long. at the same time, - 9 16 10 0
Geocentric long, at the same time, - 9 17 23 0
Greatest equation, - - - - - - - 5 21 7
Mean daily motion in its orbit, - - - 42
The sidereal motion of the apsides is about 3'59" in a
century; but the tropical motion is 1927'29", according to
the order of the signs. -
The place of the nodes has a retrograde motion of 59.
58" in a century; but, owing to the recession of the equinoc-
tial points, their apparent motion is direct in the same time.
The inclination of the orbit is subject to a small increase
of about 3" in one hundred years. t
The greatest equation has a secular increase of about 11
seconds. - - . . . .
The intensity of light or heat on this distant planet is to
that on the earth, with regard to the influence of the sun’s
rays, as 276 to 100,000, or as 1 to 362 nearly.
3. Dr. Herschel has discovered six satellites
moving round Uranus, in orbits which are nearly in
the same plane, and almost at right angles to the
orbit of their primary. • t
Two of these satellites were discovered in 1787, and the
other four in 1790 and 1794.
The periodic revolutions and the distances of these satel-
lites, from the body of Uranus, expressed in semi-diameters
of that planet, as well as in miles, are exhibited in the ſol-
lowing table:—
32? GRAMMIAR OF ASTRONOMYs

Satel- Periodic Dist. in semi-|Distances
lites. times. diameters. in miles.
1. 5d. 21h. 25/21/ 13.190 , 224,155
2 S 16 57 47% 17.09% 290,821
3 10 23 3 59 19.845 239,052
4 || 13 10 56 sº 22.752 388,718
5 38 1 48 0 45.507 777,487
| 6 |107 16 39 56 91.008 | 1,555,872
Some astronomers imagine that the motion of these satel-
lites is from east to west, or directly the reverse of all the
planets, and other satellites; but this doubtless is an optical
illusion, arising from the difficulty of ascertaining which
part of the orbit inclines to the earth, and which declines
{rom it. The inclination of their orbits, and the place of
their nodes, are not correctly ascertained. -
According to Dr. Brinkley, the relation of the periodic
times, and distances of the satellites from their primary,
hold in all the secondaries of each planet respectively. -
It may also be observed, that the rotation of the sun and
planets are all in the same direction. :
* QUESTIONS.
What is the length of the day on the surface of
Uranus 2 - -
What is the diameter of Uranus in miles; and
what its apparent diameter 2 :
What is the relative mean distance of Uranus
from the sun, with respect to the earth 2
How many satellites has Uranus, and by whom
were they discovered 2
3
#
:
:
:
§f
Merc. Venus Earth Mars TVesta Ceres | Palas Jup. Sat. Uran. Sun
Names and characters. § Q 69 & § ſ] Q 2ſ P #I G)
|ºtº" " || 7 || 0 || 5 || 2 || 2 | * | * | * | * | *
- * * * * - days | Jays days days days days days days | years Tears |years
Periodic time. 87 | *4 365 | 686 1335 | 1582 | 1681 | 1681 || 12 || 29#__83___
*...*.* || 4 || 9 || 10 || 8 -*. - 110 || 100 8 1128.
Inamº to be as 1°5"| 7° 5' 13° 5' 10°27'34° 39' 1° 19 |2° 30′ 0°46’
*****"|45° 14′ |46 || 103 || rºle ||ale | rise I gº ºne is
"*" | do |* | * | * 13 is tº iſ 8 || 3 || 1 || –
Times or ſºlving On _23°30 23:56 24h 40' 9. 52' 10h 16’ 25h 10'
*:::::"...;"| 115 584 || || Tºo 503 |474 |466 466 || 399 |378 || 369;
ºlºlºſ Rºſº Rºjºſº |
Rºy Tº Tº ſº ſºlº ſº I ſº I gº gº As
*:::::"" | 30 || 23 || 19 || 15 || 13 | 12 11 || 1 || 8 6 4.
... liº 5'57"toº gº” sº - | 40” 26°18'' 15"| 4°


324 GRAMIMAR OF ASTRONOMY.
The times and arcs of retrogradation are computed on the
supposition that the orbits are circular. The apparent
diameters of the new planets have not, according to Dr.
Brinkley, been yet ascertained. They are too small to be
measured by micronometers. Dr. Herschel thinks that iſ
the diameter of any one of them amounted to of a second,
he should have been able to have ascertained it.
It may be observed, that an apparent diameter of # of a
second, in opposition, would give a real diameter of 65 miles.
Perhaps the most striking circumstance in the above table,
is the great velocity with which the planets move; and this
is more impressed, when we consider that of the earth on
which we live, the velocity of which is 90 times greater than
the velocity of sound. In contemplating these velocities, it
cannot but occur to us, how great a power is necessary to be
continually acting, to circumflect the planets about the sun,
and compel them to leave the tangential direction. A power
that acts incessantly, and is able to counteract the great
velocities of the planets, must excite our inquires as to its
origin and law of action.
We can ascertain that this power is constantly directed
towards the sun, increases in intensity as the square of the
distance from the sun decreases, and that it is the same power
which is diffused through the whole planetary system, only
varying in quantity as the square of the distance from the
Sun is varied. So far physical astronomy teaches us; but the
proximate cause of this power, or solar gravity, as it may be
called, is unknown. We cannot trace by what agency the
Supreme Being, from whom all things originate, has or-
dained the operations and laws of gravity to be executed.
By a comparison of the distances and periodic times, which
are determined independently of each other, it will be seen,
as has already been observed, that the square of the periodic
times are as the cubes of the distances. This relation was
first found out by Kepler. For a long time no necessary
connexion was discovered between the periodic times and
distances, till at last it was shown to be a consequence of
the law of gravity above-mentioned. At present we know
of no secondary cause that could have any inſluence in re.
gulating the respective distances of the planets from the sun;
yet there appears a relation between the distances, that
cannot be considered as accidental. This was first observed
by Professor Bode, of Berlin, who remarked that a planet
was wanting, at the distance at which the new planets have
since been discovered, to complete the relation.
THE TELEscopic APPEARANCE OF THE MOON.
*
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O F 4'll E. SQLAf: S YSTEM. 32.5
According to him, the distance of the planets may be ex
pressed nearly as follows, the earth's distance from the sun
being considered as 10.
Mercury - - - - - - 4 = 4
Venus - - - - - - - 4 -|- 3 × 1 = 7
Earth - - - - - - - 4 + 3 × 2 = 10
Mars - - - - - - - 4 + 3 × 2* = 16
New Planets - - - - 4 + 3 × 2* = 28
Jupiter - - - - - - 4 + 3 × 2* = 52
Saturn - - - - - - 4 + 3 × 2* = 100
Uranus - - - - - - 4 + 3 × 2* = 196
Comparing these with the mean distances above given,
we cannot but remark the near agreement, and scarcely he-
sitate to pronounce that their mean distances were assigned
according to a law, although we are entirely ignorant of thc
cxact law and of the reason for that law : Sce Dr. Bºxinſ:-
ley's Elements of Astronomy.
*-** *
CHAPTER XIII.
Of the JMoon. C
1. The JMoon, next to the Sun, is the most in-
teresting to us, of all the heavenly bodies, and is
particularly distinguished by the periodical changes
to which her figure and light are subject.
Among the ancients, Luna ) , or the Moon, was an object
of very great respect. By the Hebrews she was more re-
garded than the Sun, and it appears they regulated their
time by her motions and appearances. The new Moon was
observed as a festival among them, which was celebrated
with sound of trumpets, entertainments, and sacrifices. The
ancient bards and poets have also celebrated the praises of
the Moon under various appellations, as Cynthia, Cyllene,
Phoebe, Silver Queen of Night, &c.
2. The Moon moves round the Earth in an ellip-
tical orbit, of which the Earth is in one of the foci.
The inclination of the Moon's orbit to the plane of
2S -
326 GRAMMIAR OF AS4130 NOVIY.
the ecliptic is about 5°9'. The Moon perſorms
her mean sidereal revolution in 27 days, 7 hours, 43
minutes and 11% seconds, at the mean distance of
236,267 miles from the centre of the Earth.
The Moon also accompanies the Earth in its annual re-
volution round the Sun. This necessarily follows, if the
motion of the Earth be admitted, and is well illustrated by
the motion of the satellites of Jupiter and Saturn. The in-
climation of the Moon's orbit is very variable: the greatest
inequality sometimes extends to 8' 47". The motions of
the Moon are exceedingly irregular, her sidereal revolution
is not the same for every century. The comparison of mo-
dern with ancient observations, shows incontestibly an acce-
leration in the mean motion of the Moon; but this accelera-
tion has been proved to be periodical. . . .
3. The figure of the Moon is that of an oblate
spheroid, like the Earth; her mean diameter is
2161 miles. The apparent diameter varies according
to her distance from the Earth; when nearest to
us, it is 33' 31", but at the greatest distance, it is
about 29' 30"; so that the mean apparent diameter
is about 31' 30". - . .
. The magnitude or size of the Moon is .02, its mass .01.46,
and consequently its density .73; the size, mass, and den-
sity of the Earth being respectively considered as unity, or 1.
TABLE,
Showing the mean tropical revolution of the JMoon, mean
- diurnal motion of the perigee, &c. . -
. Mean inclination of the orbit - - - - -50 9' 3"
Greatest equation of the centre - - - 6 17 9
Mean diurnal motion of the Moon in respect
to the equinoxes - - - - - - - 13 10 35
Mean diurnal motion of the perigee - 0 6 41
Mean diurnal motion of the node - - - 0 3 10
OF THE SOLAR SYSTERI. 327
t - + dy. hr, min. Sec. .
Mean tropical revolution - - - 27
7 49 4
Mean synodic revolution - - - 29 12 44 g
Mean sidereal revolution - - - 27 7 43 11
Sidereal revolution of the perigee 83.12 11 11 39
Sidereal revolution of the node 18223 7 13 17
Eccentricity in miles - - - - - - - - - 12960
Obs. 1. The line of the apsides has a motion according to
the order of the signs when the Moom is in syzygies, and
contrary, in quadratures. But in a whole revolution of the
Moon, the progress exceeds the regress. They go forward.
with the greatest velocity, when the line of the apsides is in
the nodes; and if they do go back when in the modes, their
regression is then slowest of all, in the same revolution.
When the line of the apsides is in the quadratures, they
are direct, with the least velocity when the Moon is in
syzygies; but they return the swiftest in the quadratures ;
and in this case, the regress exceeds the progress, in one
entire revolution of the Moon. . . . . . . . . . .
2. Considering one entire revolution of the Moon, cºeteris
paribus, the nodes move in antecendentia, with the greatest
velocity, when she is in the syzygies; then slower and slower
till they are at rest, when she is in the quadratures. In one
whole revolution of the Moon, the nodes go back very fast
when they are in quadratures; then slower till they come to
rest, when the time of the nodes is in syzygies. . . .
3. The inclination of the Moon's orbit is changed by the
same force as that by which the nodes are moved; being
increased as the Moon recedes from the node, and diminish-
ed as she approaches it. - . . . . .
The inclination of the orbit is least of all when the modes
are come to the syzygies. For, in the motion of the nodes.
from the syzygies to the quadratures, and in one entire re-
volution of the Moon, the force which increases the inclina-
tion, exceeds that which diminishes it; therefore, the in-
clination is increased, and it is the greatest of all when the
nodes are in quadratures. -
4. The eccentricity of the Moon's orbit undergoes various
changes every revolution. It is greatest of all when the
line of the apsides is in the syzygies, and the least when
that line is in the quadratures. This variation of the ec-
centricity affects the equation of the centre.
5. As to the inequality of the Moon's motion, she moves
$2}} GRANIMAR OF ASTRONOMY.
swifter, and, by the radius drawn from her to the Earth, (or
yadius vector of the Moon) describes a greater arc in pro-
portion to the time, also has an orbit less curved, and by
that means comes nearer to the Earth in her syzygies than
in the quadratures: her motion is also swifter in the
Earth's aphelion than in its perihelion. "The Moon also
perpetually changes the figure of her orbit, or the species
ef the ellipse in which she moves. , *
6. There are also a great many other inequalities in the
motion of this satellite, which it is very diſficult to reduce
to any certain rule; and which render the calculations of
her true place in the heavens a work of considerable labour.
There are nearly thirty equations to be applied to the mean
longitude to obtain the true, and about 24 for her latitude
and parallax. . . . . . . . " . . " .
4. When the Moon is in conjunction with the
Sun, it is then invisible; when moving from the
Sun towards the east, it is first visible, it is then
called the new Moon, and appears like a crescent;
when 90 degrees from the Sun, it is halved, or as it
is usually called dichotomised; when more distant it
is gibbous; and when in opposition, it shines with
a full face, and is then called the full Moon : ap-
proaching the Sun towards the east, it becomes
again gibbous, then halved, and lastly crescent, after
which it disappears from the superior lustre of the
Sun, and the smallness of the illuminated part which
is turned towards the Earth.
The phases of the Moon are particularly interesting; the
luminous crescent being always turned towards the Sun,
evidently indicates that the Moon receives its light from the
Sun; and the law of the variation of its phases, which in-
crease in a certain ratio of the angular distance of the Moon
from the Sun, proves that the Moon is spherical. The en-
lightened part varies nearly as the versed sine of the angle
of elongation from the Sun. . . . . . .
The cause of the appearance of the whole Moon, observed
a few days before and after the new Moon, is the reflection
of light from the Fayth. When the Moon becomes consis
“OF THE SOLAR SYSTEM. 329
derably elongated from the Sun, it is then out of the way of
this reflection. * . . . . . . .
5. The time between two conjunctions, or two
oppositions, called a lunation, and synodic month, is
greater than the time of a revolution in the orbit, or
the time of return to the fixed star. Because, when
the latter time is completed, the Moon has to move
a farther space to overtake the Sun. . .
Let S=period of Sun's apparent motion round the Earth.
P= period of Moon's motion about the Earth. . . .
L=period between conjunction and conjunction, or of a
łunation. . . . . . .
Then S : P : : 4 right angles: angle described by Sun in
the Moon's periodic time = angle gained by the Moon in
the time L – P. . . . .
But the angles gained by the Moon are as the times of
gaining them. Therefore, 4 right angles: angle gained by
Moon in time L – P : ; L : L – P. Hence, S ; P : : L.
L – P, or S : S — P: ; L : P, therefore • . -
SXP 365.25×27.32 . . . . . . . . .
L = - = = 29 days, 12 hours, and 42.
S.–P 337.93 . .
minutes. . . . . . . .
6. In 19 solar years, of 365 days, there are 235
lunations and one hour. Therefore, considering
only the mean motion, at the end of 19 years, the
full moon falls again upon the same days of the
month, and only one hour sooner. This is called
the JMetonic cycle, from Meton, who published it at
the Olympic Games, in the year 433, before the
Christian 62T8... . . . .
This period of 19 years has been always in much estima-
tion for its use in forming the calendar; and from that cir-
cumstance, the numbers of this cycle have been called the
golden number. - , r
One of the earliest attempts upon record to discover the
distance of the sun from the earth, was from observing when
the moon was exactly halved or dichotomised. At that time
the angle at the moon, formed by lines drawn from the moon.
to the sun and earth, is exactly a right angle; therefore, if
28*
330 GRAMMAR OF AS'FIRON ONIY.
the elongation of the moon from the sun be exactly observed,
the distance of the sun from the earth will be had, that of the
moon being known, by the solution of a right angled triangle;
that is, sun’s distance : moon’s distance: ; radius : cosine
moon’s elongation. The uncertainty in observing when the
moon was exactly dichotomised, rendered this method of
little value to the ancients. However, by the assistance of
micrometers, it may be performed with considerable accu-
racy. Wendelinus, observing at Majorca, the climate of
which is well adapted to observation, determined in 1650,
the sun's distance, by this method, very considerably nearer
than had been done at that time by any other method.
This method is particularly worthy of attention, being the
first attempt for the solution of the important problem of
finding the sun's distance. It was used by Aristarchus of
Samos, who observed at Alexandria, about 280 years before
the commencement of the christian era. -
7. Viewing the moon with a telescope, several
curious phenomena offer themselves. Great vari-
ety is exhibited on her disc. There are spots dif-
fering very considerably in degrees of brightness.
Some are almost dark. Many of the dark spots
must necessarily be excavations on the surface or
valleys between mountains, from the circumstances
of the shades of light which they exhibit.
There is no reason to suppose that there is any large col-
łection of water in the moon; for if there were, when the
boundary of light and darkness passes through it, it must
mecessarily exhibit a regular curve, which is never observed.
The non-existence of large collections of water is also
probable, from the circumstance of no change being observed
on the moon’s surface; such as would be produced by
vapours or clouds; for, although, as will be remarked, the
atmosphere of the moon is comparatively of small extent,
yet it is probable that an atmosphere does exist.
8. That there are lunar mountains is strikingly
apparent, by a variety of bright detached spots al-
most always to be seen on the dark part, near the
separation of light and darkness.
‘Shese are tops of eminences enlightened by the sun, while
of THE solar systEM. 331
their lower parts are in darkness. But sometimes light spots
have been seen at such a distance from the bright part, that
they could not arise from the light of the sun. Dr. Herschel
has particularly taken notice of such at two or three differ-
ent times. These, he supposes, are volcanoes. He mea-
sured the diameter of one, and found it equal to 3", which
answers to four miles on the surface of the moon. . .
The heights of lunar mountains may be ascertained by
measuring with a micrometer the distance between the top
of the mountain, at the instant it first becomes illuminated,
and the circle of light and darkness. This measurement is
to be made in a direction perpendicular to the line, joining
the extremities of the horns. See Dr. Brinkley's Elements
of Astronomy. , , , , , . . . . . :
According to Ricciolus, the top of the hill, called St.
Catherine's, is nearly 8 miles in height. But later astrono-
mers are not inclined to allow of so great an elevation to any
of the lunar mountains. Dr. Herschel investigated the
height of a great many; and he thinks that, a few excepted,
they generally do not exceed half a mile. But there seems
to be little doubt that there are mountains on the surface of
the moon, which must exceed those on the surface of our
earth, taking into consideration the relative magnitudes of
the moon and earth. Schroeter determined the height of
one, called Leibnitz, to be 25,000 feet, whereas the height
of Chimborazo is not 22,000 feet; so that taking into consi–
deration the relative magnitudes of the earth and moon, this
lunar mountain will be five times higher than any of the
terrestrial mountains. ,
9. It is not the least remarkable circumstance of
the moon, that it always exhibits nearly the same
face to us. We always observe nearly the same
spots, and that they are always nearly in the same
position with respect to the edge of the moon.
Therefore as we are certain of the motion of the
moon round the earth, we conclude that this must
revolve on an axis nearly perpendicular to the plane
of his orbit, in the same time that she performs her
synodic revolution. . . . . . . • V . .
This must necessarily take place in order that the same
face may be continually turned towards the earth during a
3.32 GRAMMAR OF ASTRONOMY.
whole revolution in her orbit. The motion of the moon in
her orbit is not equable, therefore if the rotation on her axis
be equable, there must be parts in her eastern and western
edges, which are only occasionally seen. These changes,
called the moon’s libration in longitude, are found to be such
as would agree with an equable motion of rotation. .
There are parts about her poles only occasionally visible.
This, called her libration in latitude, arises from her axis
being constantly inclined to the plane of her orbit in an angle
of 860. A diurnal libration also takes place; at rising, a
part of the western edge is seen, that is invisible at setting,
and the contrary takes place with respect to the easterſ,
edge. This is occasioned by the change of place in the
spectator, on account of the earth's rotation.
10. At the full moon nearest the autumnal equi-
nox, the moon is observed to rise nearly at Sun-set,
for several nights together. This moon, for its
uses in lengthening the day, at a time when a con-
tinuance of light is most desirable to assist the
husbandman in securing the fruits of his agricultu-
ral labour, is called the harvest moon.
. The rising and setting of the moon is most interesting at
and near full moon. At full moon, it is in or near that part
of the ecliptic, opposite to the sun. Hence, at full moon,
at mid-summer, it is in or near the most southern part of the
ecliptic, and consequently appears but for a short time above
the horizon; and so there is little moon-light in summer,
when it would be useless. In mid-winter, at full, it is near
or in the northernmost part of the ecliptic, and therefore re-
mains long above the horizon, and the quantity of moon-light
is then greatest when it is most wanted; and this is the more
remarkable, the nearer the place is to the north pole. There
at mid-winter the moon does not set for 15 solar days to-
gether, namely, from the first to the last quarter.
The moon, by its motion from west to east, rises later
every day, but the retardations of rising are very unequal.
In northern latitudes, when the moon is near the vernal
equinox, or the beginning of the sign Aries, the retardation
of rising is least, and when near the beginning of Libra,
greatest. This will appear by considering that when Aries
is rising, the part of the ecliptic below the horizon makes the
heast angle with the horizon, and when Libra is rising, the
oF THE solar systEM. 333
greatest. This may be satisfactorily illustrated by the
celestial globe. . . . . . . .
The variation of the retardation of rising, according as the
moon is in or near different parts of the ecliptic, being under-
stood, the explanation of the harvest moon is very easy.
The moon, at full, being near the part of the ecliptic, op-
posite to the sun, and at the autumnal equinox the sun be-
ing in Libra : consequently the mogn must be then near
Aries, when, from what has been stated, the retardation of
her rising amounts only to a few minutes; and as the moon
at full always rises at sun-set, the cause of the whole pheno-
menon is still more striking, and there it is of greater use
where the changes of seasons are much more rapid.
In some years the phenomenon of the harvestmoon is much
more perceptible than in others, even although the moon
should be füll on the same day, or in the same point of her
orbit. This is owing to a variation in the angle which the
moon’s orbit makes with the horizon of the place where the
phenomenon is observed. . If the moon moved exactly in the
ecliptic, this angle would always be the same at the same time
of the year. But as the moon’s orbit intersects the ecliptic,
and makes an angle with it of 509', the angle formed by the
moon’s orbit and the horizon of any place is not exactly the
$
same as that made by the ecliptic and horizon.
When the ascending node happens to be in Aries, the
harvest moon will appear to the greatest advantage; but,
when the descending node is in Aries, the phenomenon will
be the least remarkable. º
At places near the equator, this phenomenon does not hap-
pen; for every point of the ecliptic, and nearly every point
pſ the moon’s orbit, makes the same angle with the horizon,
both at rising and setting, and therefore equal portions of it
will rise and set in equal times. As the moon’s modes make
a complete circuit of the ecliptic in about 18 years and 225
days, it is evident, that when the ascending node is in the
first point of Aries at any given time, the descending node
must be in the same points about 9 years and 112 days after-
wards; consequently, there will be a regular interval of
about 9 years between the most beneficial and least benefi-
cial harvest moons. -
11. The moon, when at, or near, the horizon,
appears much larger than , when at, or near, the
zenith ; and yet it can be demonstrated that the
334 GRAMMAR OF ASTRONOMY.
horizontal moon is the semi-diameter of the earth,
‘farther from the spectator than the moon in the
zenith, and consequently ought to appear smaller.
* Accordingly, by actual measurement, this will be found
to be really the case. This apparent increase of magnitude
in the horizontal moon must therefore be considered as an
optical illusion, arising from the concavity of the heavens,
appearing to the eyeº be a less portion of a spherical sur-
face than a hemisphere. . . . .
Many astronomers formerly denied the existence of an at-
mosphere at the moon; principally, from observing no varia-
tion of the appearance on the surface, like what would take
place, did clouds exist as with us; and also, from observing
Ino change in the light of the fixed stars on the approach of
the dark edge of the moon. The circumstance of there be-
ing no clouds, proves either that there is no atmosphere
similar to that of the earth, or that there are no waters on
its surface to be converted into vapour: and that the lustre
of the stars not being changed, proves that there can be no
dense atmosphere. But astronomers now seem to agree
that an atmosphere does surround the moon, although of
small density, when compared with that of the earth. M.
Schroeter has observed a small twilight in the moon, such
as would arise from an atmosphere capable of reflecting the
rays at the height of about a mile. S .
Had the moon an atmosphere of considerable density, it
would readily be discovered by the durations of the occulta-
tions of the fixed stars. The duration of an occultation
would be sensibly less than it ought to be, according to the
diameter of the moon. The light of the star passing by the
moon, would be refracted by the lunar atmosphere, and the
star rendered visible when actually behind the moon; in the
same manner as the refraction by the earth's atmosphere
enables us to see the celestial objects for some minutes after
they have actually sunk below our horizon, or ‘before they
have risen above it. Now the duration is certainly never
less than eight seconds of time, which proves that horizon-
tal refraction at the moon must be less than 2"; for the dura-
tion being lessened by 8", the beginning of the occultation
would be retarded 4" of time, during which the moon moves
over 20 of space. This, therefore, shows that if a lunar at-
mosphere exists, it must be 1000 times rarer than the
atmosphere at the surface of the earth, because the horizon-
ta} refraction by the earth's atmosphere is nearly 2000",
OF THE SOLAR SYSTEM. (335
With such a rare atmosphere, the lunar inhabitants must be
deprived of many of the advantages which we enjoy, from
the existence of our own. Indeed the loss of one advantage,
that of twilight, is, on account of the length of their day,
not of much consequence, and from the apparent irregulari-
ties of the lunar surface so much light may be reflected,
that the assistance of the atmosphere to make daylight, may
not be so necessary as on the surface of the earth.
QUESTIONs. . . . -
Which of the heavenly bodies most frequently
changes its appearance 2
In what time does the moon perform her sidereal
revolution ? * - … .
What is the real diameter of the moon in miles 2
In what part of the heavens, in a clear evening,
must we look for the new moon 2
In what part of the heavens is the full moon
shortly after sunset 2 . . . . . . . r
Why is a synodic revolution greater than a side-
real revolution ? . . . . . . -
What is the Metonic cycle 2 *
Have any mountains, or other irregularities, been
observed upon the surface of the moon 2
‘Why is that moon whose full happens nearest the
autumnal equinox, called the harvest moon?
Why does the moon appear larger when in or
near the horizon, than when in or near the zenith?
CHAPTER XIV.
- Of the Tides.
1. That periodical flux, or reflux, caused by the
action of the sun and moon, but more particularly
by that of the latter, upon the waters of the ocean,
is called the Tides. . . .
336 GRAMMAR OF ASTRONOMY.
The tides have been always found to follow, periodically,
the course of the sun and moon; and hence it has been sus-
pected, in all ages, that the tides were, some way or other,
produced by these bodies. - - i
The celebrated Kepler was the first person who formed
any conjectures respecting their true cause. But what
Kepler only hinted, has been completely developed and de-
monstrated by Sir Isaac Newton.
After his great discovery of the law of gravitation, he found
it an easy matter to account for the whole phenomena of the
tides; for, according to this law of nature, all the particles of
matter which compose the universe, however remote from one
another, have a continual tendency to approach, each other,
with a force directly proportional to the quantity of matter they
contain, and inversely proportional to the square of their dis-
tance asunder. It is therefore evident, from this, that the earth
will be attracted both by the sun and moon. But, although
the attraction of the sun greatly exceeds that of the moon, yet
the sun being nearly 400 times more distant from the earth
than the moon, the difference of his attraction upon different
parts of the earth, is not nearly so great as that of the moon;
and therefore the moon is the principal cause of the tides.
2. There are two tides every 24 hours, 50minutes,
and 28 seconds, agreeing with the mean interval
from the moon’s leaving the meridian of any place till
it returns to the same meridian again. Or, which
amounts to the same thing, it is high water at any
place every 12 hours, 25 minutes, and 14 seconds.
The mean retardation of the tides, or of the moon’s coming
to the meridian in 24 hours, is about 48' 45.7"; and the mean
interval between two successive tides is 12 hours, 25 minutes,
and 14 seconds: hence the mean daily retardation of high
water is 50 minutes and 28.4 seconds.
The retardation in the time of high water, or the tide,
varies with the phases of the moon.
About the time of new and full moon the interval is least,
being only 12 hours, 19 minutes, 28 seconds; and at the
quadratures the interval is the greatest, being 12 hours, 30
minutes, and 7 seconds. . . . - *
If all parts of the earth were equally attracted by the
moon,the waters of the ocean would always retain a spherical
form, and there would be notides, except those which would
OF THE SOLAR SYSTEMI. - 337
be produced by the action of the sun. But the action of the
moon being unequal on different parts of the earth, those
parts being most attracted that are nearest the moon, and
those at the greatest distance least, the spherical figure must
suffer some change from the moon’s action. Now as the
waters of the ocean directly under the moon are nearer to
her than the central parts of the earth, they will be more
attracted by the moon than the central parts. For the same
reason the central parts will be more attracted than the
watérs on the opposite side of the earth, and, therefore, the
distance between the earth’s centre and the waters on its
surface, both under the moon and on the opposite side will
be increased; or the waters will rise higher, and it will
then be flood or high water at those places.
But this is not the only cause that produces the rise of the
waters at these two points; for those parts of the ocean
which are 900 from them, will be attracted with nearly the
same force as the centre of the earth, the effect of which
will be a small increase of their gravity towards the centre
of the earth. Hence, the waters of those places will press
towards the zenith and nadir, or the points where the gra-
vity of the waters is diminished, to restore an equilibrium,
and thus occasion a greater rise at those places.
But in order to know the real effect of the moon on the
ocean, the motion of the earth on its axis must be taken into
account. For if it were not for this motion, the longest
diameter of the watery spheroid would point directly to the
moon's centre; but by reason of the motion of the whole
mass of the earth on its axis, from west to east, the most
elevated parts of the waters no longer answer precisely to
the moon, but are carried considerably to the eastward in
the direction of the rotation. The waters also continue to
rise after they have passed directly under the moon, though
the immediate action begins them to decrease; and they do
mot reach their greatest height till they have got about 459
farther. After they have passed the point, which is 909
distant from the point below the horizon, they continue to
descend, although the force which the moon adds to their
gravity, begins there to decrease. For still the action of
the moon adds to their gravity, and makes them descend
till they have got about 450 farther; the greatest elevations,
therefore, do not take place at the points which are in a
line with the centres of the earth and moon, but about half
338 GRAMMAR OF ASTRONOMY.
ºl quadrant to the east of these points, in the direction of
the motion of rotation. . . . .
. Thus it appears, if the earth were entirely covered by the
ocean, that the spheroidal form which it would assume,
would be so situated, that its longest diameterywould point to
the east of the moon; or, which amounts to the same thing,
the moon would always be to the west of the meridian of the
parts of greatest elevation. And as the moon apparently
shifts her position from east to west in going round the earth
every revolution, the longer diameter of the spheroid ſol-
lowing her motions, will occasion two floods and two ebbs
in the interval of 24 hours, 48 minutes, 45", as above.
3. The action of the moon in raising the watérs
of the ocean, is to that of the Sun nearly as 4% to 1.
Therefore when the actions of the sum and moon are
in the same direction as at the time of new and full
moon, the tides rise higher than at any other time,
and are called spring tides. But when the moon is
in the quarters, the action of the sun diminishes that
of the moon, because his action is opposed to that
of the moon; consequently, the effect must be to
depress the waters where the moon’s action has a
tendency to raise them. These tides are considerably
lower than at any other time, and are calledneap tides.
The spring tides do not take place on the very day of the
new and full moon, nor the meap tides on the very day of the
quadratures, but a day or two after ; because in this case, as
in some others, the effect is neither the greatest nor least
when the immediate influence of the cause is greatest or
least: as the greatest heat, for instance, is not on the solsti-
tial day, when the immediate action of the sun is greatest,
but some time after it. And, although the actions of the sun
and moon were to cease, yet the ocean would continue to
ebb and flow for some time, as its waves continue in violent
motion for some time after a storm. -
The high water at a given place does not always answer to
the same situation of the moon, but happens sometimes sooner
and sometimes later than if the moon alone acted on the ocean.
This proceeds from the action of the sun not conspiring
with that of the moon. The different distances of the moon
from the earth also occasion a sensible variation in the tides,
or THE solar systEM. 339
When the moon approaches the earth, her action in every
part increases, and the differences in that action, upon which
the tides depend, likewise increase. For the attraction of
anybody is in the inverse ratio of the square of its distance;
the nearer, therefore, the moon is to the earth, the greater is
her attraction, and the more remote, the less. , Hence, her
action on the nearest parts increases more quickly than it
does on the more remote parts, and therefore the tides in-
crease in a higher proportion as the distance of the moon
diminishes. . . . . . . . .
Newton has shown that the tides increase as the cubes of
the distances decrease; so that the moon at half her present
distance, would produce a tide eight times greater. Now the
moon describes an ellipse about the earth, and, of course,
must be once in every revolution nearer the earth than in
any other part of her orbit; consequently, she must produce
a much higher tide when in this point of her orbit than in the
opposite point. This is the reason that two great spring
tides never take place immediately after each other; for if
the moon be at her least distance at the time of new moon,
she must be at her greatest distance at the time of full
moon, having performed half a revolution in the intervening
time, and therefore the spring tide at the full will be much
less than that at the preceding change. For the same rea-
son, if a great spring tide happens at the time of full moon,
the tide at the following change will be less. -
The spring tides are highest, and the neap tides lowest
about the beginning of the year; for the earth being nearest
the sun about the ist of January, must be more strongly
attracted by that body, than at any other time of the year;
hence, the spring tides which happen about that time will
be greater than at any other time. And should the moon
be new or full in that part of her orbit which is nearest to
the earth, at the same time the tides will be considerably
higher than at any other time of the year. . .
When the moon has north declination, the tides are higher
in northern latitudes; when she passes the meridian above
the horizon, than when she passes the meridian below it;
but when the moon has southern declination, the reverse
takes place.
JNewton has shown that the moon raises the waters 8 feet
7 inches, while the sun and moon together raise them 10%
feet, when at their mean distances from the earth; and
about 12 feet when the moon is at her least distance. Such
340 GRAMMAR OF ASTRONOMY
would the tides regularly be, if the earth were all covered.
with the oeean to a great depth; but as this is not the case,
it is only in places situated on the shores of large oceans,
where such tides, as above described, take place.
The tides are also subject to very great irregularities
from local circumstances; such as, meeting with islands,
shoals, headlands, passing through straits, &c. In order
that they may have their full motion, the oceanin which they
are produced ought to extend 90° from east to west, because
that is the distance between the greatest elevation, and the
greatest depression produced in the waters by the moon.
Hence, it is that the tides in the Pacific Ocean exceed those
of the Atlantic, and that they are less in that part of the
Atlantic which is within the torrid zone, between America.
and Africa, than in the temperate zones, on either side of it
where the ocean is much broader. . . . . . -
In the Baltic, the Mediterranean, and the Black Seas,
there are no sensible tides; for they communicate with the
ocean by so narrow inlets, and are of so great extent, that
they cannot speedily receive, and let out water enough to
raise or depress their surfaces in any sensible degree.
At London the spring tide rises 19 feet, at St. Maloes, in
France, they rise 45 feet, and in the bay of Fundy, in Nova
Scotia, about 60 feet. . . . . . . . . . . . . . . . .
CHAPTER xv.
Of Refraction, Parallar, &c.
1. The density of the atmosphere surrounding
the Earth continually decreases, and at a few miles
high becomes very small; and a ray of light pass-
ing out of a rarer medium into a denser, is always
bent out of its course towards the perpendicular to
the surface, on which the ray is incident. It fol-
lows, therefore that a ray of light must be continu-
ally bent in its course through the atmosphere, and
describe a curve, the tangent to which curve, at
the surface of the Earth, is the direction in which
the celestial object appears. Consequently the
apparent altitude is always greater than the true
OF THE SOLAR SYSTEM. 34}
2. The refraction or deviation is greater, the
greater the angle of incidence, and therefore great-
est when the object is in the horizon. The hori-
zontal refraction is 32; at 45° in its mean quantity
it is 57% seconds. -
The refraction is affected by the variation of the quantity
or weight of the superincumbent atmosphere at a given
place, and also by its temperature. In computing the quan-
tity of refraction, the height of the barometer and thermome-
ter must be noted. The quantity of refraction at the same
Zenith distânce varies nearly as the height of the barometer,
the temperature remaining constant. The effect of a varia.
tion of temperature is to diminish the quantity of refraction
about ºf part, for every increase of one degree in the height
of the thermometer. Therefore, in all accurate observa-
tions cf altitude, or zenith distance, the height of the baro-
‘meter and thermometer must be attended to. . . . .
The refraction may be found by observing the greatest
and least altitudes of a circumpolar star. The sum of these
altitudes, diminished by the sum of the refractions corres-
ponding to each altitude, is equal to twice the altitude of the
pole; from whence, if the altitude of the pole be otherwise
known, the sum of the refractions will be had; and from
the law of variation of refraction, known by theory, the
proper refraction to each altitude may be assigned.
Otherwise, when the height of the pole is not known, the
ingenious method of Dr. Bradley may be followed, who
observed the zenith distances of the Sun at its greatest de-
clinations, and the zenith distances of the pole star above
and below the pole. The sum of these four quantities
must be 1809 diminished by the sum of the four refractions,
and then by theory apportioned the proper quantity of re-
fraction to each zenith distance. In this manner he con-
structed his table of refraction. º
The ancients made no allowance for refraction, although
it was in some measure known to Ptolemy, who lived in the
second century. He remarks, a difference in the times of
rising and setting of the stars in different states of the at-
mosphere. This, however, only shows that he was ac-
quainted with the variation of refraction, and not with the
quantity of refraction itself. - - . .
Alhazen, a sºn ºf of Spain, in the 9th cen-
*...*
342 GRAMMAR OF ASTRONOMY.
tury, first observed the different effects of refraction on the
height of the same star, above and below the pole. Tycho
Brahe, in the 16th century, first constructed a table of re-
fractions. This was a very imperfect one.
3. As the atmosphere refracts light, it also re-
flects it, which is the cause of a considerable por-
tion of the daylight we enjoy. After sun-set the
atmosphere also reflects to us the light of the Sun,
and prevents us from being involved in instant
darkness, upon the first absence of the Sun. .
Repeated observations show that we enjoy some twilight
till the Sun has descended 18O below the horizon. From
whence it has been attempted to compute the height of the
atmosphere, capable of reflecting rays of the Sun sufficient
to reach us; but there is much uncertainty in the matter.
If the rays come to us after one reflection, they are reflected
from a height of about 40 miles; if aſter two, or three, or
four, the heights will be twelve, five, and three miles. The
computation requires the assistance of the theory of terres-
trial refractions. .
The duration of twilight depends upon the latitude of the
place, and declination of the Sun. The Sun's depression be-
ing 180 at the end of twilight, we have the three sides of a
spherical triangle to find an angle, viz. the Sun's zenith dis
tance (108°,) the polar distance, and the complement of lati
tude, to find the hour angle from noon. At or near the equa-
tor, the twilight is always short, the parallels of declina-
nation being nearly at right angles to the horizon. At the
poles, the twilight lasts for several months: at the north
pole, from the 22d of September to the 12th of November,
and from the 25th of January to the 20th of March. When
the difference between the declimation and complement of
latitude of the same name is less than 189, the twilight
lasts all night. , . . . - -
4. Refraction is the cause of the oval figures
which the Sun and Moon exhibit, when near the
horizon. The upper limb is less refracted than
the lower, by 5, or nearly of the whole diameter,
while the diameter parallel to the horizon remains.
the same. . . . . . . . . . . . . .
The rays, from objects in the horizon, pass through a
OF 'FHE SOLAR SYSTEMI, 343
greater space of a denser atmosphere than those in the
zenith, hence they must appear less bright. According to
Bougier, who made many experiments on light, they are
1300 times fainter, whence it is not surprising that we can
look upon the Sun in the horizon without injuring the sight.
5. A spectator observing a planet notin his zenith,
refers it to a place among the fixed stars, different
from that to which a spectator at the centre of the
Earth would refer it. The observed situation of
the body is called its apparent place, and the place
seen ſtom the centre of the Earth, is called its true
place. The arc of the great circle, intercepted
between these two imaginary points, is called the di-
ºurnal parallaw. This parallax, when the apparent
zenith distance of the body is 90°, or when the body
is in the horizon, is called the horizontal parallaa.
Let C be the centre of the Earth, H the place of a spec-
tator on its surface, P any object, Wumnrs the sphere of the
fixed stars, to which the places of all the bodies in our sys-
tern are referred; W the zenith, and HS the horizon.

344 GRAMMAR OF ASTRONOMY.
Now, drawing CPm, m is the place of P as seen from the
centre, and m from the surface; the arc mn is the diurnal
parallaº of the object when seen from H, in the position P.
7\nd, when the planet appears in the horizon at h, the arc
Ys is the horizontal parallaw. . . . . .
6. The diurnal parallax is equal to the angle
subtended at the planet, by the place of the spec-
tator and centre of the Earth ; and, therefore, the
horizontal parallax is greatest, and is equal to the
angle under which the semi-diameter of the Earth
would appear at the planet.
For, to a spectator at H, (see the last figure) a fixed star
in the direction HV is in the zenith, and the distance of the
planet from this star is equal to the angle VHP; but at the
centre, the distance is equal to the angle WCP, and the dif-
ference of these is the angle HPC. Now, CP : CH : : sin.
PHV, (or sine CHP) : sin. HPC, the parallax; therefore,
. . . . . - CH X sin. PHW ; ... .
sine of the parallax HPC = — - EP — . As CH is
constant, supposing the Earth to be a sphere, the sine of the
parallax varies as the sine of the zenith distance directly,
and the distance of the body from the centre of the Earth
inversely. Hence, a body in the zenith has no parallax,
and at h, in the horizon, the parallax is greatest, being then
equal to the angle which the semi-diameter of the Earth.
subtends at the planet. . . . . . . . -
The nearer a body is to the Earth the greater is its paral-
lax; hence, the Moon on this account has the greatest pa-
rallax, and the fixed stars, from their vast distance, have no
parallax, the semi-diameter of the Earth appearing at that
distance no more than a point. .
7. The diurnal parallax depresses, an object; a
planet at rising appears to the eastward of its true
place, and at setting to the westward, whence the
term diurnal, parallax. And for different altitudes
of the same body, supposing it to continue at the
same distance from the Earth, the sine of the di-
urnal parallax, or parallax in altitude, is equal to
the sine of the horizontal parallax multiplied by
the sine of the apparent zenith distance.
Ol' 3"HE SOLAR SYSTEMſ. 345 *
For the parallax varies as the sine s of the apparent.
zenith distance; therefore, if p = the horizontal parallax,
and radius be unity, we shall have 1 : 8::p : ps, the sine of
the diurnal parallax. To ascertain, therefore, the parallax
at all altitudes, we must find it at some altitude...
To find the parallaº of the Sun, JMoon, or any of the
lanets. Let a body P be observed from two places H and
'S on the same meridian, (see the fig, page 843) then the an-
gle HPS is the effect of parallax between the two places.
Now, the angle HPS = horizontal parallac X sin. PHW, .
taking the angle HPC for the sine of HPC, and the parallax
or angle SPC = hor, par. X PSr.; hence, the horizontal pa-
rallax X (sin. Z. PHV-- sin. PSr) = HPS. Therefore, they
horizontal parallax = Z. HPS, divided by the sum of those
two simes. If the distance between the two places be known,
in degrees, the angle HPS = WHP + rSP – HCS. -
Supposing the distance between the two places Hand Sto be
74046'30", equal HCS; the zenith distance WHP=32O, and
rSP=440. Then, the angle HPS = 32O+440–74O46'30"
= 769–740.46' 30" = 1°13'30"=73.5. But the horizon-
s 73.5 73.5/ *
talparallas-Hºs I sin. 445-52992-E.63466"
- 73.5/ / - { ; . . w &
— = .2//. $ *
is = 60
Or, the angle which the disc of the Earth subtends at a
planet may be obtained; and, hence, the horizontal parallax
is also given. Thus, to find the angle which two distant pla-
ces, in the same terrestrial meridian, subtend at a planet. Let
H and S be two places, P a planet in the celestial meridian
of these places. Hv, and Sn the directions in which the fixed
star, also in the meridian at the same time, is seen at the
two places. The star made use of is supposed to be very
nearly in the same parallel of declination as the planet, that
is, not differing in declination more than a few minutes.
. Now, because Hv and Sn are parallel, the angle HmS is
equal to the angle m|Hv; therefore, Z. HPS = HnS + nSP
= vBIP + PSn = the sum of the apparent distances of the
planet and star, (the place to which the planet is vertical
being supposed to be between the places of observations.)
These distances can be observed with great accuracy by
means of a micrometer. We have thus the principal things
necessary to enable us to advance by a most important step,
346 GRAMMAR OF ASTRONOMY.
viz. to obtain the angle which the disc of the Earth sub-
tends, as seen from the planet. . . . . . . . . . .
It may easily be demonstrated thatthis angle,º equals
fice availov is –o s &–*—
twice the parallaxis – 4. Hrs x sin. VHP+ sin. PSr.
See Dr. Brinkley’s Elements of Astronomy. . . .
Thus to obtain the angle which the earth's disc subtends
at the planet, it is necessary to know the angle VHP and PSr,
or zenith distances of the planet at the two places. But it.
is not necessary that these angles should be observed with
much precision, since it is easy to see that an error of even a
few minutes, in the quantities of these anº will make no
t & . . . . . . aCl. . . . .
. . . . . . - . Z. WHP + sin. Z-PS,"
The above is on the suppositions, 1st, that, the star and
planet are on the meridian together: 2nd, that the two
places are in the same.terrestrial. If the star and planet
are not in the meridian together, yet their difference of de-
climation being observed, it is the same as if there had been
a star on the meridian, with the planet. If the two places
are not in the same terrestrial meridian, an allowance must
be made for the planet's motions in the interval between its
passages over the two meridians, and we obtain the dif-
ference of declimations that would have been observed at
two places under the same meridian. . . . . .
The Cape of Good Hope is nearly in the same meridian
with many places in Europe, having observatories for astro-
nomical purposes, and therefore a comparison of the observa-
tions made there, with those made in Europe, furnishes us
with the means of practising this method. By a comparison
of the observations of De La Caille, made at the Cape of
Good Hope, with those made at Greenwich, Paris, Bologna,
Stockholm, and Upsal, the angles which the earth's disc sub-
tend at Mars and at the moon, have been obtained with very
considerable precision. Comparisons of observations will
also furnish the same for the sun and other planets. But
knowing the angle which the earth’s disc subtends at any one
planet, we can readily'find it for the sun, or any other planet.
The last method that has been described for finding the
parallaxes of the bodies in the solar system, yields only to
one other method in point of accuracy; viz. to that ſur-
mished by the transit of Venus over the Sun's disc. See
Dr. Brinkley's Elements of flstronomy, Art. 263.
sensible error in the quantity sin
QF THE SOLAR SYSTEMI, 34?
~~
ſ The Sun = 17 sec.
Mercury = 28
---- Venus = 42
, ; Mars = 42
-- * Ceres i
The diameter of the . = 9
earth, when nearest to, and 4 V.
seen from Jupiter = 4 \
Saturn = 2
* Uranus = 1
UThe Moon =2°2'
A planet, therefore, appearing to us as small as the earth
appears to the inhabitants of Saturn and Uranus, would not
have been observed except by the assistance of the telescope.
8. The distance of acelestial body from the centre
of the earth, is equal to the semi-diameter of the
earth, divided by the sine of the horizontal parallax.
For, in the triangle hEIC (see the fig. p. 343) rightangled at
H, are given CH and the angles H and h; therefore, as sin.
Z h : radius (= sin. 900 = 1): : CH: Ch = CH
Bem. di th in ZTE =
ten man earn, the distance of the body from the centre
sin. hor, par. *
of the earth. Hence, as the semi-diameter of the earth has
Deen determined to be 3960 miles; when the horizontal
parallax of a body is known, its distance from the centre of
#he earth is easily found. ſº ſ
Example. Supposing the horizontal parallax of the moon
to be 57, what is its distance from the earth, the semi-di-
Ameter of the latter body being 3960 miles \-
Solution. As sin. Z. h = 57 : radius 1 (= sin. H = 'sin.
909) : : C H (= 3950 miles): Ch. But the natural sine of
|
37' = .01658; hence Ch = # == 238,842 miles, the
distance of the moon from the centre of the earth when her
borizontal parallax is 57. w
Or, by logarithms :
As sine 57 - - - " - - S.219581
Is to radius, or sin. 90° es ºs - 10.000000
So is 3960 miles - - - - 3.597695
".
To 238,842 - - - - 5,378114
848 GRAVIMAR OF ASTRONOMY.
Ex. 2. What is the distance of the moon from the earth,
when her horizontal parallax is the greatest, or 61' 32", the
semi-diameter of the earth being 3960 miles 2
Ea. 3. What is the distance of the moon from the earth,
when her horizontal parallax is the least, or 53'52" 2
Ea. 4. What is the distance of the sun from the earth,
supposing his horizontal parallax to be 83 seconds :
} ~\
º
I , . . . CHAPTER XVI.
} * Of Eclipses.
1. The Eclipses of the sun and moon, of all the
celestial phenomena, have most and longest en-
gaged the attention of mankind. They are now,
in every respect less interesting than formerly: at
first they were objects of superstition;-next, be-
fore the improvements in instruments, they served
for perfecting astronomical tables; and last of all,
they assisted geography and navigation. Eclipses
of the sun still continue to be of importance for
geography, and in some measure for the verifica-
tion of astronomical tables. *. t
As every planet belonging to the solar system, both pri-
mary and secondary, derives its light from the sun, it must
cast a shadow to that part of the heavens which is opposite
to the sun. This shadow is of course nothing but a priva-
tion of light in the space hid from the sun by the opaque
body, and will always be proportionate to the relative mag-
nitudes of the sun and planet. If the sun and planet were
both of the same size, the form of the shadow cast by the
planet would be that of a cylinder, the diameter of which
would be the same as that of the sun or planet, and it would
never converge to a point. If the planet were larger than
the 'sun, the shadow would continue to spread or diverge;
but as the sun is much larger than any of the planets, the
shadow cast by any one of these bodies must converge to a
point, the distance of which from the planet will be propor-
tionate to the size and distance of the planet from the sun.
OF THE SOLAR SYSTEMI. 349.
The magnitude of the sun is such that the shadow cast by
each of the primary planets always converges to a point
before it reaches any other planet; so that not one of the pri-
mary planets can eclipse another. The shadow of any planet
which is accompanied by satellites may, on certain occa-
sions, eclipse these satellites; but it is not long enough to
eclipse any other body. The shadowoſasatellite or moon may
also, on certain occasions, fall on the primary and eclipse it.
2. Eclipses of the JMoon. An eclipse of the moon.
being caused by the passage of the moon through
the comical shadow of the earth; the magnitude
and duration of the eclipse depend upon the length
of the moon’s path in the shadow. -
Let AB and TE
be sections of the
sun and earth, by a
plane perpendicular
to the plane of the
ecliptic. Let ATV
and BEW touch these
sections externally,
and BPG and AMN
internally. Uet these
lines be conceived
to revolve about the
axis CKW ; then
TVE will form the
conical shadow, from
every point of which
the light of the sun
will be excluded,
more of it from the
parts near TV and
EV than from those
near PG and MN.
The semi angle
of the cone (TVK)
= sem. diam. Sun
(CTA) — horizontal
parallax of the Sun º
(TCK.) The angle
subtended by the se-
mi-diameter of the

30
350 - GRAMINIAR OF ASTRON ONIY.
section = SKW = TSK–KVT = horizontal parallax of
the moon -- horizontal parallax of the sun — semi-diame-
ter of the sun. The angle of the come being known, the
height of the shadow may be computed. For height of the
shadow : radius of earth : : rad. : tang. # angle of cone;
also the diameter of section of the shadow at the moon is
known, for 4 SO : dist. moon :: tang. semi-diam. of section
of shadow :: radius.
The height of the shadow varies from 218 to 220 semi-
diameters of the earth, and nearly varies inversely as the
apparent diameter of the sun.
3. When the moon is entirely immersed in the
shadow, the eclipse is total; when only part of it
is involved, partial; and when it passes through
the axis of the shadow, it is said to be central and
total. The breadth of the section of the shadow,
at the distance of the moon, is about three diame-
ters of the moon; therefore when the moon passes
through the axis of the shadow, it may be entirely
in the shadow for nearly two hours. -
The angle SKW is, when greatest, about 46' : therefore,
as the moon’s latitude is sometimes above 59, it is evident
an eclipse of the moon can only take place when it is near
its nodes.
The circumstances of an eclipse of the moon can be
readily computed. The latitude of the moon at opposition,
the time of opposition, the horizontal parallax of the moon,
and diameters of the sun and moon are known from the
tables. By the tables we can compute the angular velocity
of the moon relatively to the sun at rest. Thence we can
find the time from the beginning of the eclipse to opposi-
tion, and the time from opposition to the end. And, as the
time of opposition is known, the times of beginning and
ending of the eclipse are known. Sec Dr. Brinkley’s As-
ironomy.
4. The greatest distance of the moon, at oppo-
sition, from its node, that an eclipse can happen,
is about 11% degrees, and is called its ecliptic
Himit.
OF THE SOLAR SYSTEM. 351
When the moon is nearest the earth, let CD represent
the semi-diameter of the shadow at the moon, and LD the
semi-diameter of the moon touching it; LN the apparent
path of the moon, and N the place of the node. Then NC
is the limit of the distance of the node from conjunction, at
which an eclipse can happen. -
Sin. angle N (5° 17'): rad. : : sin. CL (semi-diam. moon
-- semi-diam, section = 63 when greatest): sin. NC, 11.
degrees. -
5. If the moon’s modes were fixed, eclipses
would always happen at the same time of the year,
as we find the transits of Mercury and Venus do,
and will continue to do for many ages: but as the
nodes perform a revolution backward in about 18;
years, the eclipses happen sooner every year by
about 19 days. - - i
In 223 lunations, or 18 years, 10 days, 7 hours, and 43
minutes, or 18 years, 11 days, 7 hours, and 43 minutes, ac-
cording as there are five or four leap years in the interim,
the moon returns to the same position nearly with respect to
the sun, lunar nodes, and apogee ; and therefore the eclipses
return nearly in the same circumstances: this period was
called the Chaldean Saros, being used by Chaldeans for
foretelling eclipses. -
From the refraction of the sun’s light by the atmosphere
of the carth, we are enabled to see the moon in a total eclipse.
when it generally appears of a dusky red colour. The
moon has, it is said, entirely disappeared in some eclipses.
The Penumbra makes it very difficult to observe accu-

352 GRAMMAR OF ASTRONOMY, f
rately the commencement of a total eclipse of the moon; an
error of above a minute of time may easily occur. Hence
lunar eclipses now are of little value for finding geographi-
cal longitudes. The best method of observing an eclipse
of the moon is by noting the time of entrance of the differ-
ent spots into the shadow, which may be considered as so
many different observations.
‘6. Eclipses of the Sun. From what has been
said of the earth’s shadow, it is easy to see that the
angle of the moon’s shadow is nearly equal to the
apparent diameter of the sun. Hence we compute
that the length of the conical shadow of the moon
varies from 60% to 55% semi-diameters of the earth.
The moon’s distance varies from 65 semi-diameters
to 56. - - •
Therefore, sometimes when the moon is in conjunction
with the sun, and near her node, the shadow of the moon
reaches the earth, and involves a small portion in total
darkness, and so occasions a total eclipse of the sun. The
part of the earth involved in total darkness is always very
small, it being so near the vertex of the cone; but the part
involved in the penumbra extends over a considerable por-
tion of the hemisphere turned towards the sun : in these
parts the sun appears partially eclipsed.
7. The length of the shadow being sometimes
less than the moon’s distance from the earth, no
part of the earth will be involved in total darkness;
but the inhabitants of those places near the axis
of the come will see an annual eclipse, that is, an
annulus of the sum’s disc will only be visible.
Thus, let HF, LU, the sections of the sun and moon.
Produce the axis SW of the cone, to meet the earth in B :
from B draw tangents to the moon, intersecting the sun in I
and N. The circle, of which IN is the diameter, will be
invisible at B, and the annulus, of which IH is the breadth,
will be visible, • .
OF THE SOLAR SYSTEM. 353
It has been computed, that a
total eclipse of the sun can
never last longer, at a given
place, than 7° 38', nor be annu-
lar longer than 12 24". The
diameter of the greatest sec-
tion of the shadow that can L'
reach the earth is about 180-7
miles. -
The general circumstances
of a solar eclipse may be re-
presented by projection with
considerable accuracy, and a.
map of its progress on the sur-
face of the earth constructed.
See Vince’s Astronomy, vol. I.
The phenomena of a solar
eclipse at a given place may
be well understood by consi-
dering the apparent diameters
of the sun and moon on the
concave surface, and their
distances as affected by paral-
lax. When the apparent di-
ameter of the sun is greater
than that of the moon, the
eclipse cannot be total, but it
may be annular. As the be-
ginning, end, and magnitude
of an eclipse of the sun can- - s
not be computed without the aid of astronomical tables
calculated for that purpose, it is here unnecessary to take
any farther notice of those computations. t
8. The ecliptic limit of the sun, (the greatest dis-
tance of the conjunction from the node when an
eclipse of the sun can take place,) is 17O 12 near-
ly. And the ecliptic limit, when an eclipse must
happen, is 15° 19'.
Let CN and NL be the ecliptic and moon’s path, and CN
the distance, when greatest, of the conjunction from the
node ; as the angle N, the inclination of the orbit may be
considered as constant, when CN is greatest; CL, the true
latitude of the moon is greatest. The true latitude=ap-

30°
3.54 GRAMMAR OF ASTItONOMY.
parent latitude + parallax in latitude = (when an eclipse
barely takes place,) sum of the semi-diameters + parallax
in latitude. Therefore, at the ecliptic limits the parallax
in altitude is the greatest possible, that is, when it is equal
to the horizontal parallax. -
ence, CL=semi-diameter T.
moon -- semi-diam. Sun +
hor, par. moon. Therefore,
CL, (when greatest,) = 88
-- 61' = 1° 34' nearly. And
because sin. NC =
cot. N × tan. LC,
- rad.
we find NC = 170 12 nearly; 2
an eclipse may happen within - S.
i..'. '...'...N. C
= 80' + 54 (the least diameters and least parallax) = 10
24, we find NC = 150 19, and an eclipse must happen
within this limit.
9. There must be two eclipses, at least, of the
sun every year, because the Sun is above a month
in moving through the solar ecliptic limits. But
there may be no eclipse of the moon in the course
of a year, because the Sun is not a month in
moving through the lunar ecliptic limits.
When a total aud central eclipse of the moon happens,
there may be solar eclipses at the new moon preceding and
following; because, between new and full moon, the sun
moves only about 150, and therefore the preceding and
following conjunctions will be at less distances from the
node than the limit for eclipses of the sun. As the same
may take place at the opposite node, there may be six
eclipses in a year. Also when the first eclipse happens
early in January, another eclipse of the sun may take place
near the end of the year, as the nodes retrograde nearly 200
in a year. Hence, there may be seven eclipses in one
year, five of the sun, and two of the moon.
, 10. Thus more solar than lunar eclipses happen,
but few solar are visible at a given place.
A total eclipse of the sun, April 22d, 1715, was seen in
most parts of the south of Europe. A total eclipse of the sun

OF THE SOLAR SYSTEMI. 355
has not been seen in London since the year 1140. The
eclipse of 1715 was a very remarkable one; during the total
darkness, which lasted in London 3'28", the planets Jupiter,
Mercury, and Venus, were seen; also the fixed stars Capella
and Aldebaran. Dr. Halley has given a very interesting
account of this eclipse, which is said by Maclaurin to be the
best description of an eclipse thatastronomical history affords.
A particular account is also given in the Phil. Trams. by
Maclaurin, of an annular eclipse of the sun, observed in
Scotland, February 18, 1737. He remarks that this pheno-
menon is so rare, that he could not meet with any particu-
lar description of an annular eclipse recorded. This eclipse
was annular at Edinburgh during 5' 48".
The beginning and end of a solar eclipse can be observed
with considerable exactness, and are of great use in deter-
mining the longitudes of places; but the computation is com-
plex and tedious, from the necessary allowances to be made
for parallax. -
11. When Jupiter and any of his satellites are in
a line with the sun, and Jupiter between the satellite
and the sun, the satellite disappears, being then
eclipsed, or involved in Jupiter's shadow. When
the satellite comes into a position between Jupiter
and the sun, it sometimes casts a shadow on the disc
of that planet, which is seen by a spectator on the
earth as an obscure round spot. And when the
satellite is in a line between Jupiter and the earth,
it appears on his disc as a round black spot, and a
transit of the satellite takes place. - “.
The instant of the disappearance of the satellite by en-
tering into the shadow of Jupiter, is called the immersion
of that satellite; and the emersion signifies the first instant
of its appearance at coming out of the same.
Obs. 1. Before the opposition, the immersions only of the
first satellite are visible; and after the opposition, the emer-
sions only. .
2. The first three satellites are always eclipsed, when
they are in opposition; but sometimes the fourth satellite,
hke our moon, passes through opposition without being
eclipsed. - - - * *
8. As these phenomena appear at the same moment of
353 GRAMMAR OF ASTRONOMY.
absolute time at all places on the earth to which Jupiter is
then visible, but at different hours of relative time, according
to the distance between the meridians of the places at which
ºbservations are made; it follows that this difference of
time converted into degrees, will be the difference of longi-
tude between those places. &
4. The instant of immersion or emersion, is more pre-
eisely defined than the beginning or end of a lunar eclipse;
; therefore, the longitude is more accurately found by the
Ornièl', -- .
5. For this purpose all the eclipses of the four satellites
of Jupiter, that are visible in any part of the world, are
given in the Nautical Almanac. The times of the immer-
sions and emersions are calculated with great accuracy, for
the meridian of Greenwich, from the very excellent tables
of De Lambre.
6. The first satellite is the most proper for finding the
longitude, its motions being best known, and its eclipses oc-
euring most frequent. . . -
7. When Jupiter is at such a distance from conjunction
with the sun as to be more than eight degrees above the
Morizon, when the sun is 80 below, an eclipse of the satellites
will be visible at any place; this may be determined near
enough by the celestial globe. * &
8. The immersion or emersion of any satellite being
carefully observed at any place according to mean time, the
łongitude from Greenwich is found immediately, by taking
the difference of the observation from the corresponding
tirne shown in the ephemeris, which must be converted into
degrees, &c., by allowing 150 for every hour: and will be
east or west of Greenwich, as the time observed is more or
jess than that of the ephemeris. 4. -
cHAPTER XVII.
of Comets.
1. Čomets are planetary bodies moving about the
sun in elliptic orbits, and following the same laws as
the planets; so that the areas described by their
sadii vectores are equal in equal times.
of THE SoLAR systEM. 357
When a comet appears, the observations to be made ſor
ascertaining its orbit are of its declinations and right ascen-
'sions, from which the geocentric latitudes and longitudes are
obtained. These observations of right ascension and declina-
tion must be made with an equatorial instrument, or by
measuring with a micrometer, the differences of the declina-
tion and right ascension of the comet, and a neighbouring
fixed star. The observations, according to Dr. Brinkley,
ought to be made with the utmost care, as a small error may
occasion a considerable one in the orbit.
From the beginning of the christian era to the present
time, there has appeared not less than 500 comets; but the
elements of not more than 99 have been computed, and of
the latter number, 22 passed between the sun and Mercury
in their perihelia; 40 between Mercury and Venus; 17
between Venus and the earth; 16 between the earth and
Mars; and 4 between Mars and Jupiter. -
The appearance of one comet has been several times re-
corded in history, viz. the comet of 1680. The period of
this comet is 575 years. It exhibited at Paris a tail 620
long, and at Constantinople one of 90°. When nearest the
sun, it was only one-sixth part of the diameter of the sun
distant from his surface; when farthest, its distance ex-
ceeded 138 times the distance of the sun from the earth.
2. As the orbits of the comets are. very eccen-
tric, the aphelion distance of a comet is so great,
compared with its perihelion distance, that the
small portion of the ellipse which it describes near
its perihelion, or during its appearance, may, with-
out any sensible error, be supposed to coincide
with a parabola, and thus its motion during a short
interval may be calculated as if that portion of the
orbit was parabolical. • *
Dr. Halley makes the perihelion distance of the comet of
1680 to be to its aphelion distance, nearly as 1 to 22412; so
that this comet was twenty-two thousand four hundred and
twelve times farther from the sun in its aphelion than in its
perihelion.
According to the laws of Kepler, the sectors described in
the same time by two planets, are to each other as the areas
of their ellipses divided by the square of the times of the
358 GRAMMAR OF ASTRONOMY.
revolution, and these squares are as the cubes of their semi-
imajor axes. It is easy to conclude, that if we imagine a
planet moving in a circular orbit, of which the radius is
equal to the perihelion distance of a comet; the sector de-
scribed by the radius vector of the comet, will be to the
corresponding sector described by the radius vector of the
planet, as the square root of the aphelion distance of the
comet is to the square root of the semi-major axis of its
orbit, a relation which, when the ellipse changes to a para-
bola, becomes that of the square root of 2 to unity.
The relation of the sector of the comet to that of the
imaginary planet is thus obtained, and it is easy by what
has been already said, to get the proportion of this last
sector, to that which the radius vector of the earth describes
in the same time. The area described by the radius vector
of the comet may then be determined for any instant what-
ever, setting out from the moment of its passage through
the perihelion, and its position may be fixed in the parabola,
which it is supposed to describe. Nothing more is neces-
sary, but to deduce from observation the elements of the
parabolic motions.
3. The elements of a comet are, the perihelion
distance of the comet, the position of the perihelion,
the instant of its passage through the perihelion, the
inclination of its orbit to the plane of the ecliptic,
and the position of its nodes.
Elements of the Comet of 1811.
Time of Comet's passage through its
º
perihelion, Sep. sº &ºi= - - 12d. 9h. 48m.
Place of the perihelion, - - - 749 12' 00"
Distance of the perihelion - - - 1 .02241
Place of the ascending node - - 1400 13' 00"
Inclination of the orbit to the plane of the
ecliptic - º tº *-*. --> - 72 12 00
its heliocentric motion retrograde.
The investigation of these five elements presents much
gyeater difficulties than that of the elements of the planets,
which being always visible, and having been observed during
a long succession of years may be compared when in the most
favourable position for determining these elements, instead
()]? 'I'll E. SOLAYP SYSTEM. . .
3
59
of which cornets appear only for a short time, and frequently
in circumstances where their apparent motion is rendered
very complicated, by the real motion of the earth, which
always carries us in a contrary direction. -
Notwithstanding all these difficulties, it is possible to del,
termine the elements of the orbits of comets by different
methods. Three complete observations are sufficient for
this object; others only serve to confirm the accuracy of
these elements, and the truth of the theory which has been
just explained. Above ſour and twenty comets, the nume-
rous observations of which are exactly represented by this
theory, have confirmed it beyond all doubt. It appears,
therefore, that comets which have been considered as me-
teors, for many years, are of the same nature as planets;
their motions and their returns are regulated by the same
laws as planetary motions.
4. Comets do not always move in the same di.
rection like the planets. The real, or heliocentric
motion of some is direct, or according to the order
of the signs; and of others, retrograde. But the
geocentric motion of the same comet may be either
retrograde or direct according to the position of the
earth with respect to the comet, and their relative
velocities. -
The heliocentric motion of half the comets, whose elements
have been computed, is retrograde, and of the others, direct,
The inclination of their orbits is not confined within a nar-
row zone like that of the planetary orbits; they present
every variety of inclination from an orbit nearly coincident
with the plane of the ecliptic, to that perpendicular to it,
A comet is recognised when it re-appears by the identity
of the elements of its orbit with those of the orbit of a come!
already observed. If its perihelion distance, the position of
its perihelion, its nodes, and the inclination of its orbit are
very nearly the same, it is probable that the comet which
appears is that which has been observed before, and which,
having receded to such a distance as to be invisible, returns
to that part of its orbit nearest to the sun. The duration of
the revolution of comets being very long, and having been
observed with very little care, till within about two centh-
ries; the period of the revolution of one comet only, is known
360 GRAMMIAR OF ASTRONOMIY.
with certainty, that of 1682, which had been already ob-
served in 1607 and 1531, and which has re-appeared in
1759. This comet takes about 76 years to return to its
perihelion; therefore, taking the mean distance of the sun.
from the earth as unity, the greater axis of its orbit is 35.9,
and as its perihelion distance is only 0.58, it recedes from
the sun at least 35 times more than the earth, describing a
very eccentric ellipse. Its return to the perihelion has been
longer by thirteen months from 1531 to 1607, than from
1607 to 1682; it has been 18 months shorter from 1607 to
1682, than from 1682 to 1759.
. The real or heliocentric motion of this comet was retro-
grade, and the elements of the orbit deduced by Dr. Halley
from the observations of Apian in 1531, of Kepler in 1607,
and of himself in 1682, also the elements deduced from the
observations in 1759, were as follows:

Per. dist.
Passage through Earth's per Place of Place of Inclinitiou
Perihelion. dist. unity. Perihelion! Node. to ecliptic.
*
\
3 O o ' )
d. h. 5 O '
1531 Aug. 21 18 . 567 10 1 39|| 19 30, 17 51
1607 Oct. 26 8 . 537 | 10 2 1611 20 2 tº 17 2
|1682 Sep. 14 4 .583 |10 2 521 21 16, 17 58
(1759 Mar. 1214 .583 to 3 gll 23 451 17 40
This comet was retarded by the action of Jupiter, as Dr.
Halley had foretold. This retardation was more exactly
computed by Clairaut, who also calculated the retardation
by Saturn. The result of his computation published before
the return of the comet, fixed April 15, for the time of the
passage through perihelion: it happened on March 12.
Dr. Halley's computation appears also very exact, when it
is considered that he did not allow for the retardation by
Saturn. We may be nearly certain that this comet will re.
appear again in 1834. -
The return of some other comets has been suspected: the
most probable of these returns was that of the comet of
i532, which has been believed to be the same with that of
1661, and the revolution of which was fixed at 129 years;
but this comet not having re-appeared in 1790, as was ex-
pected, there is great reason to believe that these two comets
were not the same.
The preceding part of the present Chapter has been
principally extracted from Laplace’s System of the World.
1811.
THE COMET OF
-
-
|×
…）
，
， ， ,

OF 'ſ HE SOLAR SYSTEMI, 36%
An ingenious computation has been made by Laplace,
from the doctrine of chances, to show the probability of two
comets being the same, from a near agreement of the ele-
ments. It is unnecessary to detail at length the method here.
It supposes that the number of different comets does not ex-
ceed one million, a limit probably sufficiently extensive.
The chance that two of these, differing in their periodic
times, agree in each of the five elements within certain
limits, may be computed by which it was found to be as
1200: 1. that the comets of 1607 and 1682 were not differ-
ent, and thus Halley was justly almost confident of its re-
appearance in 1759. As it did appear then, we may ex-
pect, with a degree of probability, approaching almost with-
out limit to certainty, that it will re-appear again at the
completion of its period.
But with respect to the comet predicted for 1789, from
the supposition that those of 1661 and 1532 were the same,
the case is widely different. From the discrepancy of the
elements of these comets, the probability that i. were the
same is only 3 to 2, and we cease to be surprised that we
did not sce one in 1789. See Dr. Brinkley's Elements of
Astronomy. w
Comets that appeared in 1264 and 1556 are supposed to
have been the same, whence this comet may again be ex-
pected in 1848. © -
A comet appeared in 1770 very remarkable from the re-
suit of the computations of Lexell, which indicated a period
of only 5 years; it has not been observed since. There
can be no doubt that the periodic time of the orbit which it
described in 1770, was justly determined ; for M. Burck-
hardt has since, with great care, re-computed the observa-
tions, and his result gives a periodic time of 55 years.
Lexell has remarked, that this comet, moving in the
orbit he had investigated, must have been near Jupiter in
1767, and would also be very near it again in 1779, from
whence he concluded that the ſormer approach changed the
perihelion distance of the orbit, by which the comet became
visible to us, and that in consequence of the latter approach,
the perihelion distance was again increased, and so the
comet again became invisible, even when near its perihelion.
This explanation has been in a manner confirmed by the
calculations of Burckhardt, from formulas of Laplace. He
has found, that before the approach of Jupiter, in 1767, the
perihelion distance might have been 5.08, and that aſter the
approach in 1779, it may have become 3.33, the eash's dis
362 'GRAMMAR OF ASTRONOly.I.Y.
tance being unity. With both these perihelion distances,
the comet must have been invisible during its whole revolu-
tion. The perihelion distance in 1770 was 0.67.
This comet was also remarkable by having approached .
nearer the earth than any other comet that has been ob-
served: and by that approach having enabled us to ascer-
tain a limit of its mass or quantity of matter. Laplace has
computed, that, if it had been equal to the earth, it would
have shortened the length of our year by # of a day. Now
it has been perfectly ascertained, by the computations of
Delambre on the Greenwich observations of the Sun, that
the length of the year has not been changed, in consequence
of the approach of that comet by any perceptible quantity,
and thence Laplace has concluded that the mass of that
comet is less than stºrm of the mass of the earth. The
smallness of its mass is also shown by its having traversed
the orbits of the satellites of Jupiter without having occa-
sioned an alteration in their motions. From those and other
circumstances, it seems probable that the masses of the
comets are in general very inconsiderable; and therefore,
as Dr. Brinkley remarks, that astronomers need not be under
apprehensions of having their tables deranged in conse-
quence of the near approach of a comet to the earth or
moon, or to any bodies of the solar system. -
5. The motion of a comet, like that of a planet,
is accelerated, when moving from its aphelion to its
perihelion, and retarded from its perihelion to
its apheliom. On account of the great eccentricity
of a comet's orbit, its motion in the perihelion is
prodigiously swiſt, and in the aphelion proportiona-
bly slow. ! . •
According to Newton, the velocity of the comet of 1680,
which came nearest to the sun of any upon record, was eight
hundred and eighty thousand miles an hour. On taking the
perihelion distance of this comet, equal to .00603, as given
by Pingré, (proportioned according to the present mean
parallax of the sun deduced from the transit of Venus of
1769,) I find, says Squire in his Astronomy, by two different
calculations, that the velocity of this comet in its perihelion
was no less than 1,240,108 miles per hour ; at which time
it was only 572,850 miles from the centre of the sun, or
abott 130,000 miles ſºom his surface.
of THE SOLAR systEM. 363
'The velocity of this comet in its perihelion was so great,
that, if continued, would have carried it through 124 degrees
in an hour. But its actual hourly motion during that inter-
val, before and after it passed its perihelion, was 81° 46'52".
From Dr. Halley’s determination of the orbit of this comet,
it cannot be less than 13,000 millions of miles from the sun
when in its aphelion. -
According to Pingré, the elements of the orbit of the comet_
of 1680, were as ſollows: this comet passed through its
perihelion December 18th, at 1 minute, 2 seconds aſter 12
o'clock at noon mean time at Greenwich ; place of the
perihelion 8s 220 40' 10", or 22° 40' 10" of Sagittarius; and
its distance from the sun when in the perihelion, .00603, the
mean distance of the earth ſrom the sun being considered as
unity or 1 ; the longitude or place of the ascending node 9
signs, 1957'13", or 1957' 13" of Capricornus; and the in-
clination of the orbit to the plane of the ecliptic 619 22' 55".
It appears from the great diurnal motion of some comets,
that they must have come very near the earth. For, ac-
cording to Regiomontanus, the comet of 1472 moved over .
an arc of 1200 in one day. And the comet of 1759 described
the apparent arc of 410 in the same interval of time.
The comet of 1811 was first seen at Viviers, by Flauger-
gues, on the 25th of March, and was visible till the end of
May ; it must have been very faint and near the horizon all
the time, it having during that interval great southern lati-
tude. The Earth was in about 5 degrees of Libra, on the
25th of March, and therefore the comet must be nearly in
opposition to the Sun, which certainly was the most favour-
able position for seeing it. It was then moving towards its
perihelion, but its motion being slow, and the Earth re-
treating from it, it was lost sight of when the Earth arrived
at the beginning of Sagittarius. The comet passed the as-
cending node on July 11th, when the Earth was between
Capricornus and Aquarius; it was then approaching its
conjunction with the Sun, and was invisible from the end
of May till the 31st of August, when, between 3 and 4 o’clock
that morning, it was observed by Bouvard, at the imperial
observatory; its right ascension was 147° 18', and declina-
tion 32O 53' north. The comet was first observed at Green-
wich, on the 5th of September ; its geocentric longitude at
that time was. 1450 3' 10", and its geocentric latitude 280
36' 39". The comet was at its perihelion, at a distance of
97,128,950 miles from the Sun on the 12th September.
364 GRAM SIAR OF ASTRONOMY.
On October 26, the comet was 26933 from the perihelion;
its heliocentric longitude was 41° 58' and latitude 720 1/;
having two days before passed the higher part of its orbit, or
90 degrees from the node. The Earth at the same time was
in about 90 of Aries; and the geocentric longitude of the
comet was 1740 37, and its geocentric latitude 5405'. The
comet’s distance from the Sun was 102,532,550, and from the
Earth 120,413,930 miles. The comet was nearest the Earth
on the 11th of October, when its distance was 113,630,450
miles, its apparent motion in longitude at this time was nearly
foui degrees in twenty-four hours. On the 12th, the comet
was 379 33' from the perihelion, having a rapid geocentric
motion in longitude, the direction of the Earth and comet:
conspiring to produce that effect. Itsgeocentric longitude was
203C 46', and latitude 610 39'; the Earth at the same time
was 18040' in the sign Aries. The comet’s distance from the
Sun was 108,842,464, and from the Earth 118,948,225 miles.
On January 1st, 1812, the comet was 89° 11’ from the perihe-
lion; its heliocentric longitude was 328° 15', and latitude 230
83. The Earth was about 10° 21' in Cancer; the greatest
geocentric longitude of the comet was 312° 2', and latitude
17O 18'. Its distance from the Sun was 190,520,000, and
from the Earth 259,614,500 miles. See, for a delineation of
a portion of this comet’s orbit, Squire's Astronomy.
Though the real or heliocentric motion of this comet was
not within the sphere of the Earth’s orbit, yet its geocentrie
track, when referred to the ecliptic, crossed the orbit of the
Earth; hence, the apparent place of the comet, during the
greater part of the time it was visible, was towards the op-
posite part of the heavens to its true place. -
From the true and apparent places of the comet, given
above, for particular days, its real and visible path may be
traced upon the celestial globe. Dr. Herschel makes the
planetary body of this comet not more than 428 miles in
diameter; but the real diameter of the head he makes to be
about 127,000 miles. :
The apparent motion of this comet was direct, yet very
unequal, for when it first became visible after passing the
ascending node, it was nearly stationary, and the same
about the time of its disappearance, but when nearest the
Farth it equalled that of Mercury. t
This comet was visible a longer time than almost any other
upon record, and therefore none has ever afforded such cer-
tain means of information with respect to its orbit. Had its
ineliocentric notion heen direct, it would have been visible
() F TIIL SOLAR SYSTEM1. - 365
much longer, and would have passed within 44,485,850
miles of the Earth, had it crossed the line of its nodes at the
same time. The comet would then have appeared a large
nebulous body, but without a tail, as that appendage would
have been projected in a direct line from behind its body.
6. The most striking phenomena, that makes the
comets objects of attention to all mankind, is the
tail of light which they often exhibit. When ap-
proaching the Sun, a nebulous tail of light is seen
to issue from them, in a direction opposite to the
Sun. This, after having increased, again de-
creases till it disappears. The stars are visible
through it.
The nebulosity with which those comets are almost al-
ways surrounded, seems to be formed by the vapours which
the solar heat raises on their surface. It is imagined that
the great heat which they experience towards their perihe-
ion, rarifies the particles which have been congealed by the
.xcessive cold of the aphelion. -
t appears also that the trains of comets are only these va-
pours elevated to a considerable height by this rarefaction,
combined either with the solar rays or with the dissolution of
those vapours in the fluid, which reflects the zodaical light
to us. This seems to result from the direction of their trains,
which are always beyond the comets, relatively to the Sun,
and which only becoming visible near their perihelion, are
not at a maximum till after their passage through this point,
when the heat communicated to the comet by the Sun, is
increased by its duration, and by the proximity to this
luminary. -
Dr. Hamilton supposes the tails of comets, the aurora bo-
realis, and the electric fluid to be matter of the same kind.
He supports this opinion by many strong arguments, which
are found in his ingenious essay on the subject. According
to this hypothesis, it would follow that the tails are hollow;
and there is every reason to suppose this, from the scarcely
perceptible diminution of the lustre of the stars seen through
them. He supposes that the electric matter, which continu-
ally escapes from the planets, is brought back by the assis-
tance of the comets. --
But much is yet to be known on this subject. Objections
31* **
366 GRAMIMAR OF ASTRONOMIY.
may be made to his hypothesis, although so ingeniously
supported. According to the opinion of Kepler, the rays of
the Sun carry away some gross parts of the comets, which re-
fiedt other rays of the Sun, and give the appearance of a tail.
****
CHAPTER XVIII.,
Of the Firmanent of Fived Stars.
1. The number of stars visible to the naked eye,
as has already been remarked, is not more than
2000. We observe, says Dr. Brinkley, about 3000
stars visible to the naked eye, very irregularly scat-
tered over the concave surface of the heavens.
“There are seldom above 2000 visible at once, even
on the most favourable star-light night.
‘This may at first appear incredible to some, because ai.
first sight they seem to be innumerable; but the deception
arises from looking upon them hastily, without reducing them
into any kind of order. For let a person look steadily for
some time upon a large portion of the heavens, and count the
number of stars in it, and he will be surprised to find the
number so small. And if the moon be observed for a short
interval of time, she will be found to pass very few in her
way, although there are as many about her path as in any
other part of the heavens. Flamstead’s Catalogue contains
only 3000 stars, and many of those are not visible without a
telescope. But although the number of stars may be small
when examined with the naked eye, yet when examined with
a powerful telescope, the number exceeds, all computation.
$or a good telescope, directed to almost any part of the hea-
vens, discovers multitudes that are lost to the naked eye. In
some places, however, they are crowded together; and in
others, there are considerable spaces where no stars can be
seen. In the small group called the Pleiades, in which only
6 or 7 stars can be seen by the naked eye, Dr. Hook, with a
telescope of 12 feet long, discovered 78 stars. And F. de
Rheita affirms, that he has observed more than 2000 stars in
the constellation Orion; and above 188 in the Pleiades."
or THE FIRMAMENT OF l'IXED STARs. 367
That which appears only a single star in Orion's sword,
Huygens found, by the telescope, to consist of 12 stars very
near together. Galileo found 80 in the belt of Orion's sword,
21 in the nebulous star of his head, and about 500 in another
part of the constellation within the compass of one or two
degrees, and more than 40 in the nebulous star Praesepe.
Others, even in the best telescopes, appear still as small lu-
minous clouds. There is a very remarkable one in the con-
stellation Orion, which the best telescopes show as a spot
uniformly bright. It is a singular and beautiful phenomenon.
So great is the number of telescopic.stars in some parts of
the milky way, that Dr. Herschel observed 588 stars in his
telescope at the same time, and they continued equally mu-
merous for a quarter of an hour. In a space of about 10
degrees long, and 2% degrees wide, he computed 258,000
Stars. Phil. Trams. 1795. -
2. The appearance of the stars seen in a teles-
cope, is very different from that of the planets.
The latter are magnified and show a visible disc.
The stars.appear with an increased lustre, but with
mo disc. Some of the brighter fixed stars appear most
beautiful objects, from the vivid light they exhibit.
Dr. Herschel tells us that the brightness of the fixed stars,
of the first magnitude, when seen in his largest telescope, is
too great for the eye to bear. When the bright star. Sirius
was about to enter the telescope, the light was equal to that
on the approach of sun-rise, and upon entering the telescope,
the star appeared in all the splendour of the rising sun, so
that it was impossible to behold it without pain to the eye.
The apparent diameter of a fixed star is only a deception
arising from the imperfections of the telescope. The
brighter stars appear sometimes in bad telescopes to subtend
an angle of several seconds, and this has led astronomers
into mistakes respecting their apparent diameters.
The more perfect the telescope, the less this irradiation
of light. We know with certainty that some of the brighter
stars do not subtend an angle of 1", from the circumstance
of their instantly disappearing, on the approach of the dark
edge of the moon. Dr. Herschel attempted to measure the
diameter of Vega in Lyra, and imagined it to be about fºr
of a second. - * t
That the diameter of the sun may appear less than a
3.68 GRAMMAR OF ASTRONOMY.
second, it must be removed 1900 times farther from us than
at present; which is an argument in favour of the vast dis-
tance of the fixed stars. - .
Although the superior light of the sun effaces that of the
stars, yet by the assistance of telescopes we can observe the
brighter stars at any time of the day. The aperture of the
telescope collects the light of the star, so that the light re
ceived by the eye, ſrom the star, is greater than when the
eye is unassisted. The darkness in the tube of the telescope
also in somé measure assists. See Dr. Brinkley's Astronomy.
3. Some stars appearing single to the naked eye,
when examined with a telescope, appear double or
triple ; that is, consisting of two or three stars
very close together : such are Castor, & Hercules,
the Pole Star, &c. Seven hundred, not noticed
before, have been observed by Dr. Herschel.
In viewing these double stars a singular phenomenon dis-
covers itself, first noticed y Dr. Herschel; some of the
double stars are of different colours, which, as the images
are so near each other, cannot arise from any defect in the
telescope. & Herculis is double, the larger red, the smaller
blue; 5 Lyrae is composed of four stars, three white and one
red; y Andromedae is double, the larger reddish white, the
smaller a fine sky blue. Some single stars evidently differ
in their colour. Aldebaran is red, Sirius a brilliant white.
From a series of observations on double stars, Dr. Her-
schel has found that a great many of them have changed
their situations with regard to each other; that the one per-
forms as revolution round the other, and that the motion of
some is direct, while that of others is retrograde. He has
observed that there is a change in more than 50 of the double
stars, either in the distance of the two stars, or in the angle
made by a line joining them with the direction of their
daily motion. - • *
The following are the observations that have been pub-
lished relative to six double stars, a Gemenorum, (Castor,) y
Leonis, s Boötes, & Herculis, 6 Serpentis, y Virginis. In re-
spect to Castor, the first of these, Dr. Herschel thinks it
highly probable, that the orbits in which the two stars move
round their common centre of gravity are nearly circular,
and at right angles to the line in which we see them; and that
the time of a whole apparent revolution of the small star
oF THE FIRMAMENT OF FIXED STARs. 369
round Castor will be nearly 342 years and 2 months, in a
retrograde direction. * - ;
Of the two stars which compose y Leonis, the smaller
one revolves round the larger in an apparent elliptical orbit,
and performs a retrograde revolution in 1200 years.
The beautiful double star, a Boötes, is composed of 2
stars, one of which is of a light red, and the other of a fine
blue, having the appearance of a planet and its satellite.
From observation Dr. Herschel concludes, that the orbit of
the small star is elliptical, and performs its revolution, ac-
cording to the order of the signs, in 1681 years.
The double star, & Herculis is composed of a greater and
lesser star; the former being of a beautiful bluish-white, and
the latter of a fine ash colour. The smaller one revolves
round the larger, nearly in the plane of the spectator. On the
11th of April, 1803, it was nearly occulted by the larger star.
The double star, 6 Serpentis, has, like g Bootes, undergone
a considerable change in the angle of position, without any
variation in the distance between the two stars. Dr. Her-
schel computes the period of the smaller star round the
larger to be 375 years. \
The double star, y Virginis, which has long been known
to astronomers, is composed of two nearly equal stars; the
smaller, according to Dr. Herschel, completes its revolution
in about 708 years. -
When we take into consideration the very small angle
which the apparent distance of these double stars subtends,
and the slow motion of the revolving stars, we must conclude
that the period of their respective revolutions cannot be ascer-
tained with any great degree of accuracy. Squire's flstronomy.
4. From former observations, it appears consi-
derable changes have taken place among the fixed
stars. Stars have disappeared, and new ones have
appeared. { *
The most remarkable new star recorded in history, was
that which appeared in 1572, in the chair of Cassiopeia. It
was for a time brighter than Venus, and then seen at mid-
day: it gradually diminished its lustre, and after 16 months
disappeared. That the circumstances of this star were
faithfully recorded we can have no doubt, since many diffe-
rent astronomers of eminence saw and described it. Cor
nelius Gemma viewed that part of the heavens, the sky
370 GRAMMAR OF ASTRONOMY.
being very clear, and saw it not. The next night it ap-
peared with a splendour exceeding all the fixed stars, and
scarcely less bright than Venus. Its colour was at first white
and splendid, afterwards yellow, and in March, 1573, red
and fiery like Mars or Aldebaran; in May of a pale livid
colour, and then became fainter and fainter till it vanished.
Another new star, little less remarkable, appeared in Oct.
1604. It exceeded every fixed star in brightness, and even
appeared larger than Jupiter. Kepler wrote a dissertation
on it. Changes have also taken place in the lustre of the
fixed stars; 3 Aquilae is now considered less bright than y.
A small star near & Ursa Majoris is now probably more
bright than formerly, from the circumstance of its being
named Alcor, an Arabic word, which signifies sharp-sight-
edness in the person who could see it. It is now very visible.
Several stars also change their lustre periodically. O Ceti,
in a period of 333 days, varies from the 2d to the 6th mag-
nitude. The most striking of all is Algol, or 3 Persei.
Goodricke has with great care determined its periodical va-
riations. Its greatest brightness is of the 2d, and least of
the 4th magnitude ; its period is only 2 days, 21 hours: it
changes from the 2nd to the 4th magnitude in 34 hours, and
back again in the same time, and so remains for the rest of
the 2d. 21 hours. These singular appearances may be
explained, by supposing the fixed star to be a body revolv-
ing on an axis, having parts of its surface not luminous.
The following are some of the most remarkable variable
stars, viz.:- - * &’
New star of 1572 in Cassiopeia, which changes from the
1 to 0; that is, from the first magnitude to be invisible; pe-
riod 150 years. -
0 Of the Whale, from 2 to 0; period 333 days.
New star of 1604, in the east foot of Serpentarius, ſrom
1 to 0; period not known. . • *
8 Lyrae, from 3 to 5; period 6 days, 9 hours.
New star of 1670, in the Swan's head, which has not
been seen since 1672.
ºn Antinoi, from 3 to 5; period 7 days, 4 hours, 15 minutes.
× In the Swan's neck, from 5 to 0; period 369 days, 21
hours.
Another in the same constellation, near y in the breast;
from 3 to 0; period 18 years.
ô Chephei, from 3 to 5; period 5d. 8h. 37%m.
Some stars, like 3 in the Whale, have gradually in-
of THE FIRMAMENT OF FIXED STARs. 37 i
creased in brilliancy; others, like Ö in the Great Bear, have
been constantly diminishing in brightness. ſº
5. The number of nebulae is very considerable.
Dr. Herschel has discovered above 2000: before
his time only 103 were known. But far the greater
part of these 2000 can be seen only with telescopes
equal to his own. - *
He has given an account of several phenomena, which he
calls nebulous stars, stars surrounded with a faint luminous
atmosphere. He describes one observed Nov. 13, 1790, in
the following manner. A most singular phenomenon: a star
of the 8th magnitude, with a faint luminous atmosphere, of a
circular form, and of about 3’ diameter; the star is exactly
in the centre, and the atmosphere is so diluted, ſaint, and
equal throughout, that there can be no surmise of its con-
sisting of stars; nor can there be a doubt of the evident
connexion between the atmosphere and the star. Another
star, not much less in brightness, and in the same field with
the above, was perfectly free from any such appearance.
6. As the earth moves in an orbit, nearly cir-
cular, round the sun, an observer on its surface in
one situation, is nearer some stars by the diameter
of the earth’s orbit, than in another, and consé-
quently the angular distances of those stars ought
to appear greater. But the angular distances of
the fixed stars, observed at different seasons of the
year, always remain the same, even when observed
with the most exquisite instruments. Hence, the
diameter of the earth’s orbit, which is about 190
millions of miles, bears no sensible proportion to
their distance. *
The greatest angle which the diameter of the Earth's
orbit subtends at any fixed star, is called its annual parallaw,
and sometimes only parallaa. r
According to the observations of Dr. Bradley, the annual
parallax of y Draconis, a star of the second magnitude,
situate nearly in the solstitial colure, about 150 from the pole
of the ecliptic, is imperceptible. The observations of Pond,
the present astronomer at Greenwich, and those of Dr.
372 GRAMMAR OF ASTRONOMY.
brinkley, of Trinity College, Dublin, agree also as to this
star, in showing that the annual parallax is imperceptible.
Now, admitting the annual parallax of the nearest fixed
star, suppose Sirius, to be 2", then its distance from the Earth
would be no less than 9,797,587,500,000 miles, or nearly ten
million million of miles. But admitting the parallax of the
nearest fixed star to be only 1", which is probably too great,
then its distance will be nearly twenty million million of miles.
The parallax of any fixed star has been, till lately,
thought imperceptible. Piazzi, from his observations made
at Palermo, suspected a parallax of a few seconds in several
stars. Dr. Brinkley, who has paid particular attention to
this subject, says, that his observations made with the
circle, eight feet in diameter, belonging to the observatory
of Trinity College, Dublin, appeared to point out a paral-
lax in several stars; and that the agreement of results, ob-
tained by different sets of observations, seemed to leave no
doubt on this head. However, observations made elsewhere
do not confirm his results.
The distance of the fixed stars, proved by the motion of
the Earth, is indeed wonderful, yet there is nothing contrary
to reason and experience in admitting it. Why should we,
as Dr. Brinkley justly observes, limit the bounds of the
universe by the limits of our senses? We see enough in
every department of nature, to deter us from rejecting any
hypothesis, merely because it extends our ideas of the
creation and divine Creator. , , ' ' ,
Our knowledge of the fixed stars must be.much more cir-
cumscribed than of the planets, since the best telescopes do
not magnify the fixed stars so as to submit their diameters to
measurement; but it is well ascertained that the apparent
diameter of the brightest of them is less than 1". The fixed
stars, as we have seen, are at immeasurable distances from
us, at distances compared with which the whole solar system
is but a point. Their diameters are less than we can
measure, yet their light is more intense than that of the pla-
mets. We conclude, therefore, that they are selſ-shining
Bodies, and according to a high degree of probability, like
our Sun, the centre of planetary systems. Admitting this,
the multitudes of ſixed stars that may be discovered with the
most inferior telescopes, show us an extent of the universe
that our imagiuation can scarcely comprehend; but what is
even this, compared to the extent that the discoveries and
conjectures of Dr. Herschel point out 2 We cease to have
of THE FIRMAMENT OF FIXED STARs. 373
distinct ideas, when we numerate by ordinary measures the
distances of the fixed stars, and we require the aid of other
circumstances to enable us to comprehend them. Thus, we
compute that the nearest of the fixed stars is so far distant,
that light, which moves at the rate of 192,900 miles in a
second, will take above a year in coming from the star to the
Earth; that the light of many telescopic stars may have
been many hundred years in reaching us; and still farther,
that, according to Dr. Herschel, the light of some of the me-
bulae, just perceptible in his forty feet telescope, has been
above a million of years on its passage. The limit of the
distance of the nearest fixed star, may be considered as well
ascertained; but anything advanced with respect to the dis-
tances of the others, must be in a manner conjectural.
The brighter fixed stars have been supposed to be nearer
to us than the rest. Besides their superior lustre leading to
this conclusion, many of them were discovered to have small
motions, called proper motions, that could only be explained
by supposing them to arise from a real motion in the stars
themselves, or in the Sun and solar system, or from a motion
compounded of both these circumstances.
Now, whichever of these suppositions was adopted, it
was reasonable to suppose, that the cause of the smaller
stars not appearing to be affected, could only arise from the
greater distance of those stars. However, it is now ascer-
tained that some of the smaller stars appear to have proper
motions, much greater than those of the brightest stars.
Hence, conclusions deduced from the proper motions of the
bright stars, respecting the relative distances of those stars,
must tend to weaken conclusions that might be deduced
from their brightness and apparent magnitudes.
There is a double star of the sixth magnitude, the 61st
star of the Swan, which consists of two stars, within a few
seconds of each other. Each of these stars are moving near-
ly at the same rate, that is, at the rate of 6" in a year. It is
likely they are also moving about their common centre of
gravity. At present they preserve nearly the same distance
from each other. This proper motion is far greater than has
been observed in any of the brighter stars, or indeed in any
star. It might be supposed, on this account, that these stars
(61 cygni) are nearer to us than the brighter stars. To as-
certain this point, Dr. Brinkley has made observations of
the zenith distances, at the opposite seasons, and he could
not discover any sensible parallax in these stars.
374 GRAMIMAR OF ASTRONOMY.
*
Bessel has compared these and some of the neighbouring
stars by observations on the right ascensions, and found no
sensible parallax. Still the arguments formerly adduced,
for the brighter fixed stars being nearer to us, are considera-
bly weakened by the great proper motions observed in some
of the smaller stars.
The star 40 Eridani has a proper motion of about 4" in a
year. The annual proper motion of Arcturus is about 2/.
In many of the stars there is no proper motion perceptible.
Besides the proper motions, it has been remarked by Dr.
Herschel, that in several instances, the line joining two stars
very near together, changes its position. This is in some
cases explained by a proper motion in the brighter star; in
other cases it seems to indicate, as has already been obser-
ved, the revolution of one star round another. The double
star Castor is a striking instance: during the last fifty years,
the line joining the two stars, which are about 5” asunder,
has had a motion of rotation at the rate of about one degree
in a year, while the interval between the stars has remained
nearly the same. Of the three circumstances which explain
the apparent motion of a star, that which supposes it to arise
from a combination of the motion of the solar system and of
the star is most probable. The Sun and nearest fixed stars
are probably all in motion round a centre, the centre of gra-
vity, perhaps of a nebula, or cluster of stars, of which the
Sun is one, and the milky way a part, as Dr. Herschel sup-
poses, while this nebula revolves with other nebulae about a
common centre. The direction of the motion of our system
cannot with certainty be ascertained, because from the whole
motion we observe in a fixed star, we have nothing to help
us in assigning that which belongs to the Sun. -
Dr. Herschel has particularly considered this subject, and
has concluded that our Sun.is moving towards a point in the
constellation Hercules, the declination of which is 400, and
rig' ascension 2469. His arguments are very ingenious,
b: ... there is necessarily so much hypothetical in them, that
the mind cannot feel much confidence in his conclusion.
That our system is in motion, there can be no doubt; the
difficulty is to ascertain the precise direction and velocity:
and from the circumstances of the case, there seems to be
little probability that the knowledge will ever be here at-
tained by man. y - . . . . . . .
Dr. Herschel conjectures that the distances of the fixed
stars are nearly inversely as their apparent magnitudes.
of THE FIRMAMENT of FIXED STARS, 375
From thence, and a train of ingenious reasoning, relative to
the faintest nebulae discoverable by his forty feet telescope,
he has concluded that the distances of these nebulae are so
great, that light issuing from them must have been two mil-
lions of years in reaching the Earth. But the recent disco-
veries relative to the proper motions of the smaller fixed
stars must, as has been said, in some measure weaken the
conclusions formerly adopted respecting the relative dis-
tances of the fixed stars.
The discoveries of Dr. Herschel have also made us ac-
quainted with many nebulae, which are not resolvable into
stars, but apparently formed of luminous matter, gradually
condensing, by the principle of universal attraction, into
masses, as if about to form the suns of future systems.
Distant ages only can appreciate these conjectures. Dr.
Brinkley's Elements of flstronomy.

THE END,
DUPL
A 426962

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