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ELEMENTS OF ASTRONOMY,
A N A B R ID G M E N T
| OF
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K E IT H 'S N E W T R E A T IS E
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ON THE
USE OF THE GLOBES.
wew AMERICAN EDITION, wrt H. ADDITIONS AND IMPRovements, AND
AN EXPLANATION OF THE ASTRONOMICAL PART OF THE
A MERICAN ALMAN A.C.
THIRTIETH EDITION.
PHILADELPHIA :
THOMAS, COWPERTHWAIT, & CO.
1845. *
QB
@9%
1646
*-*.
3Entered according to the 3ct of Congress in the year 1832,
by KEY & BIDDLE, in the Clerk's Office of the District Court of
the Eastern District of Pennsylvania.
gººd-
*
Stacks
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+ 13,73.
10-24705 -94/PREFACE.
THAT ASTRONOMY is now considered a needful and im-
portant branch of knowledge for every well educated person,
will be readily allowed; for however some minds, totally
uncultivated, may, “with brute unconscious gaze,” raise
their eyes to the starry firmament, or behold the various
phaenomena that result therefrom, still, to those who hold a
respectable rank in society, a general acquaintance at least,
with the order of the heavenly bodies, and the laws by which
they are governed, must at some time necessarily become a
part of their inquiries.
Hence, where it is practicable, it seems highly desirable
that that which must be known should be begun early, or
made a branch of school education; at least the elements of
the science, or great leading principles should be then in-
culcated. - - -
That there are many great and scientific works, and some
popular volumes already published, is well known; and iſ
this compendium is added to the number, it is not for the
sake of obtruding the author once more before that public
which has so favourably countenanced his former works, but
because he has not, after a solicitous search, found any trea.
tise expressly designed and practically drawn up as a class
book for schools.
He acknowledges the free use which has been allowed
him of some works on the subject, from which he has ex-
tracted valuable materials. Indeed, in a few instances, it
will be seen that he has preferred rather to select verbatiºn
from respectable authorities, than to distort the sentences
(as is sometimes done) for the sake of an apparent originality.
Far, however, from attempting to set aside the use of those
valuable works which should have a place in every library,
this is intended only to become the handmaid to them.
3.
iy PREFACE,
As the study of the same branch of science is often com-
menced by persons, not only of different ages, but of different
capacities, and variously circumstanced in point of assistance,
so must the modes of instruction, and the treatises propor-
tionably vary. That treatise which may be well adapted to
the solitary and self-taught student, or that which may, by
its diversified reflections, captivate a leisure hour, may not
be the best suited to the boy who studies in conjunction with
his class fellows, and with the elucidations of a master
always at hand.
As an elementary work, care has been taken to avoid two
very common evils, that of extreme brevity on the one
hand, and of a too great prolixity on the other. A mere out-
line, or brief mention of a very few leading particulars, could
not prove satisfactory, either to teacher or learner; it would
call forth no exertion, excite no interest, afford no pleasure,
impress no lasting improvement. On the other hand, to
swell the volume with complicate calculations, and by the
discussion of subjects too abstruse for juvenile comprehen-
sion, would occasion the Tyro to stumble at the threshold,
and recoil from the study in hopeless disgust.
The text or larger print, may be considered to contain the
general principles and well authonticated facts; or at least,
so much of the outline of the science as should be first known.
This therefore may be appoiated for the learner's first course.
The smaller print, except what refers to illustrations of
the plates may be omit.ed, or not formally insisted on, till the
second course; as its ontains matters either less known, or of
less immediate importance; or else more difficult to be com-
prehended.
Perhaps there is not a point in which instructors more
widely differ than in their opinion of the quantum proper to
be put before the pupil. The vast dissimilarity in the buſ.
of elementary treatises, on any one subject, proves the truth
of this assertion. One teacher prefers a volume for his pupil
PREFACE, V
that contains almost every minutia, though it may require
the toil of years to wade through it;-another presents him
with a meagre outline that will not require the labour of as
many months.
While this difference of opinion exists, and it will more or
less ever exist, it may be desirable to meet, as much as pos-
sible, the views of each. This has been attempted in some
late publications; and the plan is here followed by a distinc-
tion in the type. It is herein intended, that the text, if
perused alone, should contain in itself a connected and tole-
rable complete outline; and if read with the smaller type,
that the work should exhibit but a more enlarged whole.
This simplicity in the arrangement will, it is hoped, render
it more accommodating to instructors, and suit it to the pur-
poses of scholars of different classes, capacities and ages.
That work must surely possess some advantages, that can be
perused by the younger scholar without perplexity, and by
the more advanced student without deficiency.
General principles only of an art or science, it is well
known, are the parts proper to be first committed to memory;
and that too, perhaps, at an age when their utility is not
known, nor to what purposes they are applicable. This is
best effected, as Dr. Lowth observes, “by some short and
clear system.” Every one is aware of the impropriety of
surcharging the bodily organs,—but overloading the yet un-
expanded faculties of the mind, by an attempt to fill it with
a too great redundancy of ideas in a first course, is equally
fruitless and injurious.
It is particularly recommended that those young persons
who wish to derive information from this treatise, will not
only peruse it deliberately, and digest what they read, bus
make a study of it, so as to be able to answer with consider-
able correctness the questions subjoined. From a mere cur-
sory perusal, neither information nor entertainment can be
expected.
A 2
wi PREFACE.
It is hoped that the numerous well executed plates which
accompany this work will be deemed appropriate to elucidate
the subjects; and that the complete series of questions will
prove generally acceptable to instructors, and contribute to
facilitate their labours.
It is presumed that most of the interesting parts of Astro-
nomy have been introduced. To have illustrated the method
of calculating Eclipses, and the transits of Mercury and We-
nus; or of finding the longitude and the periodic times and
distances of Jupiter's satellites, &c. might have enhanced
the work in the public estimation, but to the learner it would
prove not only useless, but perplexing and obscure. f
Indeed, to have handled the subject more abstrusely, and
to have written in all the technical phraseology of the science,
would have been much more easy than was the frequent la-
bour of verbal discrimination, of casting into shade some
parts which would only dazzle and bewilder, and of clothing
other parts in a language, not less pure it is hoped, but at
least more suited to the youthful comprehension.
CONTENTS.
CHAPTER I.
Preliminary Definitions
CHAPTER II.
Of the Heavenly Bodies
The Sun * @ &
CHAPTER III.
Mercury * tº e
Venus g &
CHAPTER IV.
The Earth . . ſº
Tº e Moon sº
CHAPTER V.
Mars . tº gº º
Asteroids * &
CHAPTER VI.
Jupiter . . . .
Jupiter's Satellites
CHAPTER VII,
Saturn . * º
Satellites of Saturn
Saturn's Ring * *
CHAPTER VIII.
The Georgium Sidus, or Her-
schel . g * gº *
The Herschel's Satellites
The Proportional Magnitude
and Distance of the Planets
CHAPTER IX.
Comets . g ſº tº
CHAPTER X.
The Fixed Stars . g
CHAPTER XI.
Constellations º tº
Northern Constellations e
Southern Constellations
Zodiacal Constellations .
CHAPTER XII.
Different Systems . . .
CHAPTER XIII.
Of the Motions of the Planets
§
10
11
J4
15
17
18
20
21
22
23
ib.
Inferior and Superior Con-
junctions of the Planets
CHAPTER XIV.
The Plane of an Orbit, Pla-
nets, Nodes, &c. *
The Transits of Mercury
Venus & & *
CHAPTER XV.
The Ecliptic, Zodiac, and
Equator, &c. . *
Of the Ephemeris .
CHAPTER XVI.
Definitions, Degrees, Poles, &c.
CHAPTER XVII.
Planets' Orbits Elliptical .
Attraction of Gravitation
” CHAPTER XVIII.
Of Attractive and Projectile
forces. & g &
CHAPTER XIX.
On the Centre of Gravity .
and
The Horizon .
CHAPTER XX.
Day and Night . . §
CHAPTER XXI.
Of the Atmosphere
CHAPTER
Refraction . 4 * * *
CHAPTER XXIII.
Parallax º * * *
CHAPTER XXIV
Equation of Time . . .
CHAPTER XXV.
The Seasons . wº * &
CHAPTER XXVI.
The Seasons, continued
& CHAPTER XXVII.
The Moon's Months, Phases,
&c. - ſº
7
37
38
40
al
48
ol
ib.
54
57
58
59
61
63
65
69
71
W111 CONTENTS.
The Phases of the Moon
CHAPTER XXVIII.
Eclipses . . tº º
Eclipse of the Moon
Eclipse of the Sun.
CHAPTER XXIX.
Polar Day and Night, &c.
CHAPTER XXX.
Umbra and Penumbra in
Eclipses . . .
CHAPTER XXXI.
The Transit of Venus .
Occultation of the Fixed Stars
CHAPTER XXXII.
The Harvest Moon *
CHAPTER XXXIII.
The Harvest Moon, continued
CHAPTER XXXIV.
Of Leap-year . . .
74
81
86
87
90
92
CHAPTER XXXV.
The Tides * º
CHAPTER XXXVI.
The Tides, continued . . 98
CHAPTER XXXVII.
The Tides, continued
CHAPTER XXXVIII.
The Precession of the Equinox 104
CHAPTER XXXIX.
The Precession of the Equi-
nox, continued { }
CHAPTER XL.
The Obliquity of the Ecliptic,
&c. . g º § e
. 95
psy
d
109
CHAPTER XLI.
To find the Proportionate
Magnitudes of the Planets 111
To find the Planets Distances
from the Sun . . . ib.
Questions for Examination . 113
EXPLANATION OF SIGNS.
G). The Sun.
Q} The Moon.
{B The Earth.
§ Mercury.
2 Venus.
3 Mars.
ii Jupiter.
ELEMENTS OF ASTRONOMY.
CHAPTER I.
PRELIMINARY DEFINITIONS.
ASTRONOMY is that branch of natural philosophy
which treats of the heavenly bodies: it consists of two
parts, namely, descriptive and physical Astronomy.
Descriptive Astronomy, comprises an account of the
phenomena of the heavenly bodies.
Physical Astronomy consists in the investigation of
the causes of their motions, &c.
A Circle is a plain figure, bounded by a uniform
curve line, called the circumference, which is every
where equidistant from a certain point within, called
its centre, as A B C D (pl. 1. fig. 1.)
The circumference itself is often called a circle, and also the peri
phery.
The Radius of a circle is a line drawn from the
centre to the circumference; as A E, E B, or E C
(fig. 1.)
The Diameter of a circle is a line drawn through the
centre, and terminated at both ends by the circum-
ference, as A. E.C (fig. 1.)
Every Diameter is double the radius, and divides the circle into two
equal parts. The terminating points of the diameter are sometimes
called its Poles, as A and C.
An Arc of a circle is any part of the circumference
as F D G (fig. 1.)
2 DEFINITIONS.
A Chord of a circle is a right line joining the ends
of an arc ; dividing the circle into two unequal parts,
as FG (fig. 1.)
A Semicircle is half the circle, or a segment cut off
by the diameter, as A B C (fig. 1.)
The half circumference is sometimes called the Semicircle.
A Quadrant is half a semicircle, or one fourth part
of a whole circle ; as A E B, or B E C.
A quarter of the circumference is sometimes called a Quadrant.
All circles, great or small, are supposed to be di-
vided into 360 equal parts, called degrees (marked *;)
each degree into 60 minutes (marked ';) each minute
into 60 seconds (marked ".) Hence a semicircle con-
tains 180 degrees, and a quadrant 90 degrees.
An Angle is the meeting of two lines in a point, as
A (plate 1, fig. 2.)
The point where they meet is called the angular point, and the lines
A Band A C, are called sides or legs.
A Right Angle is that which is made by one line
perpendicular to another, or, when the angles on each
side are equal to one another, they are right angles;
as the angles M and N (fig. 3.)
The measure of a right angle is a quadrant of 90 degrees.
An Acute Angle is less than a right angle, as the
angle S (fig. 4.)
An Obtuse Angle is greater than a right angle, as
the angle R (fig. 4.)
Parallel Lines, whether straight or circular, are
lines in the same plane, which are every where at the
same distange from one another; and which, though
drawn ever so far, both ways, will never meet: thus
*
I) EFINITIONS, 3
a b and c d and ef (fig. 5,) are three parallel lines;
and g h and i k (fig. 6,) are two parallel semicircles.
A Globe or Sphere is a round body, every part of
whose surface is equally distant from a point within,
called its centre. º:
A Spheroid is a figure nearly spherical, either ob-
long or oblate. The earth is a spheroid, having its aa is
or diameter at the poles shorter than at the equator.
A Great Circle, A B D E, of a sphere, is one whose
plane passes through its centre C. (See plate 2, fig. 1.)
A Small Circle of a sphere, F G H I, is that whose
plane does not pass through its centre.
A Diameter, N C S, of a sphere, perpendicular to
any great circle, is called the axis of that great circle,
and the extremities, NS, of the axis, are called its
poles. (Plate 2, fig. I.)
Hence the pole of a great circle is 90° from every point of the di-
ameter upon the sphere; because every angle, as NCA, being a right
angle, the arc, N A, is every where 90 degrees.
Any two great eircles bisect each other; for the planes of both
passing through the centre of the sphere, their common section must
be a diameter of each; and every diameter bisects a circle.
The Aacis of the earth is that diameter about which
it performs its diurnal revolution.—See plate 2, fig. 2,
where pe p q represent the Earth, and p O p the axis.
CHAPTER II.
ASTRoNOMY is that science which teaches the know
ledge of the celestial bodies, the sun, moon, planets,
comets, and fixed stars; with their magnitudes, mo-
t-Gns, distances, periods, eclipses, and order.
gº.
4 DEFINITIONS.
#
=
The general opinion of astronomers of the present day is, that the
universe is composed of an infinite number of systems of worlds: in
each of which there are certain bodies moving in free space, and re-
volving, at different distances, round a sun, placed in or near the centre
of each system ; and that these suns are the stars which are seen in
the heavens.
-->
Among the heavenly bodies the Sun and Moon
are termed luminaries ; the others are called stars.
Stars are also distinguished into planets and fixed
Stars.
The PLANETs, though they appear like the fixed
stars, are all opaque, or dark bodies, moving in a regu-
lar order round the sun, from west by south, to east,
receiving their light from him, and shining by reflecting
his light.
Some of the planets have attendants or satellites
moving round them, as their centres, and with them
round the sun. There is also another order, called
comets, with blazing tails, which pursue very eccen-
tric courses.
The names of the planets are Mercury, Venus, the
Earth, Mars, Jupiter, Saturn, and Uranus or Herschel;
with four smaller ones, called Asteroids, namely,
Vesta, Ceres, Pallas, and Juno.
Vesta, though the last discovered of the asteroids, is, according to
some authorities, nearer to Mars than either of the other three; but,
according to others, Juno is placed the nearest.
These are all called primaries; and there are also
eighteen satellites or moons, called secondaries. The
Earth has one ; Jupiter, four; Saturn, seven; and
Uranus, six. No moons have hitherto been disco-
vered to belong to the other planets.
=#E
_*:::::::::::::=
page 4. Plate 2

THE SUN, 5
Correctly speaking, the satellites are planets, as well as those round
which they revolve; for planet is derived from the Greek word
wyzwarns, signifying rowing or wandering.
THE SUN,
THE SUN is the source of light and heat, and the
centre of our Solar or Planetary System. His form is
nearly that of a sphere or globe. His diameter is
about 883,210 miles, and his circumference 2,774,692
miles.
According to some authorities the Sun's diameter is 893,522 miles.
For the definition of a globe or sphere, see the Preliminary Definitions,
Chap. I. The Sun's diameter is equal to 112 diameters of the earth.
His distance from the earth is 95,000,000 of miles;
and he is 1,400,000 times larger than our earth. The
Sun was for ages, and till lately, thought to be a globe
of real fire ; but it is now supposed to be an opaque
body, surrounded by a luminous atmosphere.
Though to the Sun our earth is indebted for light and heat, life and
vegetation, and without its genial influence it would become a dark
inert mass, yet Dr. Herschel supposes the Sun to be an opaque body.
surrounded by a lucid and transparent atmosphere; that this luminary
differs but little in his nature from the planets; and that it is an in-
habitable world.
A number of maculae, or dark spots, may sometime''
be seen, by means of a telescope, on different parts
of the Sun's surface. These consist of a nucleus,
which is much darker than the rest, surrounded by a
mist or smoke ; and they are so changeable as fre-
quently to vary during the time of observation. Some
of the largest of them seem to exceed the bulk of the
whole earth, and are often seen, at intervals of a fort-
night, for three months together. The darker spots are
termed maculae, and the brighter faculae.
6 THE sun.
The maculae have been supposed by some, to be cavities in the body
of the Sun; the nucleus being in the bottom of the excavation; and the
shady zone surrounding it, the shelving sides of the cavity. Others
have supposed maculae to be large portions of opaque matter moving
in the fiery fluid. Some again have taken them for the smoke of vol-
canoes in the Sun, or the scum floating upon a huge ocean of fluid
matter. Facula, on the contrary, have been called clouds of light, and
luminous vapours. But Dr. Herschel supposes that the Sun is surround-
ed by an atmosphere of a phosphoric nature, composed of various trans-
parent and elastic fluids, by the decomposition of which, light is pro-
duced, and lucid appearances formed, of different degrees and intensity.
The Sun has two motions; the one is a periodical
motion, in nearly a circular direction round the com-
mon centre of all the planetary motions (see the arti-
cle, Centre of Gravity, Chap. XIX.)—the other motion
is a revolution upon its axis, which is completed in
about twenty-five days.
The Sun's motion about its axis renders it spheroidical, having its
diameter at the equator longer than at the poles. --
The method of ascertaining the Sun's revolution on
his axis is, by observing the motion of some of those
remarkable spots which are seen on his disc. If these
spots are observed uniformly to change their places,
and to appear on one side and disappear on the other,
there is not any other means of explaining such phe-
nomena, but that of a rotation about his axis.
The time of rotation may be found by observing the
arc described by any spot in a given time, and then find
by proportion the time of describing the whole circle.
Or the return of the spot to the same position with re-
spect to the earth may be observed, which will give the
time of an entire rotation.
The Sun, if viewed from any other system in the
universe, would appear as a fixed star does to us.
MERCURY. 7
CHAPTER III.
MERCURY.
MERCURY” is the smallest of the inferior planets,
and the nearest planet to the sun. His diameter is
above one third of the diameter of our earth, or about
3,000 miles. He revolves about the sun in 87 days,
23 hours, and #, at the distance of about 37,000,000
of miles from that luminary; moving in his orbit at
the amazing rate of above 112,000 miles an hour, OT
31 miles in a second.
By the term orbit is meant, the path described by a
planet in its course round the sun, or by a moon round
its primary planet.
For an illustration of the planets' orbits, see the Frontispiece.
Some authorities make Mercury's diameter 200 miles more, and
others as much less. His mean distance from the sun is to that of the
earth from the sun, as 387 to 1,000, or considerably more than one-third.
Though small, he has a bright appearance, with a
light tint of blue; he never departs much more than
30° from the sun, and on that account is usually hid in
the splendour of that luminary. *
The sun's diameter will appear, if viewed from Mercury, nearly
three times as large as from the earth. And the sun's light and heat at
Mercury, have been calculated at above seven times those of the earth:
upon the supposition that the materials of which Mercury is composed,
are of the same nature as those of our globe.t
Mercury’s diurnal motion, or time of rotation on his
sº-
* Mercury, was considered, mythologically, as the messenger of the
gods.
t These degrees of heat and light are presumed, upon the long and
generally received opinion, that the sun is a globe of fire.
8 VENUS.
axis is 24 hours and 5 minutes, and the inclination of
his axis to his orbit is very small.
Mercury changes his phases in a manner similar to
the moon, according as he is stationed with regard to
the earth and sun.
This planet, however, never appears to us quite full; because, when
his bright side is turned fully to us, he is lost in the sun's beams. From
these different phases it is clear that he does not shine by his own light;
for if so, he would appear always round.
As the orbit of this planet is between the earth's or.
bit and the sun, he will at times appear to pass exactly
between them; and this appearance is denominated the
transit of Mercury over the sun's disc: the planet then
appearing like a black spot moving across the face of
the sun.
As the planes of the earth and Mercury's orbits are not coincident,
this appearance does not often happen. The last transit happened, Nov.
5, 1822; a second will happen, May 5, 1832; and another, Nov. 7, 1835.
VENUS.
VENUs is the second planet from the sun, and is
easily distinguished by her superior brightness and
whiteness. Her mean distance from that luminary is
about 69,000,000 of miles, and she completes her an-
nual revolution in less than 225 days, with a rotation
about her axis in 24 hours nearly.
Hence, the length of her year is not quite two-thirds of ours, Bian-
chinimakes a complete rotation on her axis to be 24 hours 8 minutes; but
the Cassinis, 23 hours 20 minutes; and Schroeter 23 hours 21 minutes.
The circumference of her orbit is at least 433,000,000 of miles.
Her magnitude is nearly the same as that of the earth;
her diameter being about 7,900 miles; and she moves
in her orbit at the rate of 75,000 miles in an hour.
VENUS, 9
The quantity of light and heat which this planet re-
ceives from the sun, may be supposed to be double that
of the earth. Her lustre is so great that she has been
seen in the day-time, when the sun shines; and at night
she usually projects a real shade.
Venus, when viewed through a telescope, is neve
seen to shine with a bright full face. But she ha
phases changing like the moon; for sometimes she ap-
t)62arS gibbous, at others, horned like the new moon, and
her illumined part is constantly towards the sun; which
proves that she moves, not round the earth, but round
the sun.
Venus is a morning star when seen by us westward of
the sun, for then she rises before him; and an evening
star when eastward of that luminary, for then she sets
after him.* She is alternately the one and the other
about 290 days.
In her seasons there must be a very considerable
difference; much more, indeed, than is experienced by
us. The axis of our earth is inclined only 23# degrees,
whereas that of Venus inclines about 75 degrees to the
plane of her orbit.
Venus appears much larger at sometimes than at others; and the
great variations of her apparent diameter demonstrate that her distance
from the earth is exceedingly variable. This great inequality, with
respect to distance between her superior and inferior conjunctions,
will appear from an inspection of plate 7 fig. 2. See also page37.
The orbit of Venus, like that of Mercury, lying be-
tween the earth and sun, there will happen, at times,
* When a morning star, she is called, in the language of the poets,
Phosphorus, or Lucifer; and Hesperus or Vesper, when an evening star.
B 2
10 THE EARTH,
what is denominated the transit of Venus, or the pass-
ing of this planet over the sun's disc, in the form of a
dark round spot: this occurs only twice in about 120
years.
One was seen in England in 1639, one m 1761, and one in 1769:
only two will happen in the present century, viz. the first in 1874, the
last in 1882.
By this phaenomena astronomers have been enabled to ascertain the
distance of the earth from the sun; and hence the distances of the
other planets are easily found. Kepler was the first person who predict-
ed the transits of Venus and Mercury over the suns disc. And the
first time Venus was ever seen upon the sun, was or Nov. 16, 1639,
by our countryman, Mr. Horrox, who was educated at Emanuel Col-
lege, Cambridge. See a fuller Illustration, Chap. XXXI.
CHAPTER IV.
THE EARTH.”
THE EARTH is the third planet from the sun; its mean
distance from him being about 95,000,000 of miles; its
diameter is found to be 7,920 miles, and its circum-
ference to be 24,880 miles.
Doubtless, to a person placed on the planet Venus, the Earth would
have as much the appearance of a star as Venus has to us.
The Earth has two constant motions; the one about
its axis, and the other through its orbit round the sun.
It moves in its orbit at the rate of 68,000 miles an
hour, which is nearly 20 miles each moment; and per-
forms an entire revolution in nearly 365+ days, which
*The Earth by the ancients was called Terra; and by astronomers
Tellus, f
TIHE MOON, 11
is the length of our year. A complete rotation upon its
axis forms a natural day of 24 hours.
The more exact time of its annual motion is 365 days, 5 hours, 48
minutes, and 49 seconds.
Hence the division of time into days and years are prescribed by the
motions of the Earth; the former depending upon the rotation of the
Sarth upon its axis; the latter upon its revolution in its orbit.
The form of the Earth is not that of an exact globe
or sphere, but of a spheroid, i. e. a little flatted at the
poles, having the diameter at the equator, 26 miles
longer than at the poles.
The earth was formerly supposed to be a wide extended plane,
firmly fixed upon something, which it was impossible to describe; but
from more recent observations, which will hereafter be explained, it is
proved to be nearly globular.
The earth serves as a great satellite to the moon, and
subject to nearly the same changes as that body under-
goes. But the Earth appears more than thirteen times
larger when viewed from the moon, than the moon ap-
pears to us; and hence far more luminous. So that
when it is new moon to our earth, it is a full earth to
the moon, and the contrary.
It may, perhaps, be inaccurate to denominate the larger body a sa-
tellite to the smaller.
For an illustration of the motions of the Earth, causing the different
lengths of days, and nights, and of the different seasons, see Chap.
XXV., &c.
THE MOON.
THE Moon is a satellite to the earth we inhabit,
about which it revolves in an elliptic orbit, from one
new moon to another, in 29 days, 12 hours, and 44 mi-
nutes, very nearly.
The above is called a synodical month. But the Moon revolves
12 THE MOON,
from one point in the heavens to the same point again, in 27 days, 7
hours, and 43 minutes, which is called a siderizl or periodical month.
These distinctions will be illustrated in Chap. XXVII.
The Moon's mean distance from the earth is 240,000
miles; and she moves in her orbit at the rate of about
2,290 miles in an hour.
Her diameter is 2,160 miles ; and her bulk
about a fiftieth part of the earth's. She always keeps
the same side towards the earth ; hence her rotation on
her axis is performed in the same time as her revolution
through her orbit; and hence it appears also that her
day and night, taken together, are just as long as our
lunar month; each being as long as from new moon to
full moon.
She accompanies the earth in its annual orbit; and
during that period, goes herself nearly thirteen times
round the earth in an orbit of her own. Hence her
year does not consist of quite thirty days. The different
forms of increase and decrease which she presents, du-
ring the time of each revolution, are called the phases
of the Moon.
The Moon, like the other planets, is a dark, or opaque
body, borrowing her light from the sun; hence, only
that half which is turned towards him at any time,
can be fully illuminated; the opposite half would re-
main in darkness, if it were not for the light reflected
from our earth. Therefore, as the light of the Moon,
visible on the earth, is on that part of her body turned
towards us, we shall, according to her different posi-
tions, perceive different degrees of illumination. Hence
she appears sometimes waning, sometimes horned, then
half round. If, on the contrary, the moon were a lu-
THE MOON. 13
minous body, she would always shine with a full orb, as
the sun does.
It has been already noticed that our earth is a satellite to the Moon,
as is evident soon after the change; for then her hemisphere towards
us is illuminated by light which the earth reflects.”
The Moon's axis is almost perpendicular to the plane
of the ecliptic; consequently she can have no diversity
of seasons.
The inclination of her axis is only 1943
The shades which appear on the face of the Moon,
are found, when viewed through a telescope, to result
from the diversity of mountains and valleys.
Some of the mountains in the Moon were formerly supposed to be
five miles high; but Dr. Herschel has determined with greater precision
than former astronomers, that very few of them exceed half a mile in
perpendicular elevation. He has also observed several volcanoes in
the Moon, emitting fire, as those on the earth do. Two of them ap-
peared to him nearly extinct, but a third showed an actual eruption of
fire, or luminous matter. When the Moon is either horned or gibbous,
the irregularity of her surface is clearly discerned by the border of the
Moon appearing indented or jagged, especially about the edge of the
illumined part. See plate 18.
The Moon at her conjunction is invisible to us: her
first appearance afterwards is called new moon ; in op-
position her whole disc is enlightened; it is then called
full moon.
One remarkable circumstance relating to the Moonis, that the hemi-
sphere next the earth, can never be really dark; for when it is turned
from the sun, it continues illuminated by light reflected from the earth,
in the same manner as we are enlightened by a full moon. But the other
hemisphere of the Moon has a fortnight's light, and a fortnight's dark-
ness by turns.
* The Greeks gave to the Moon the name of Selene.
14 MARS,
The sun and stars rise and set to the inhabitants of
the Moon, in a manner similar to what they do to us;
and we are led to conclude that, like the earth, the
Moon is also inhabited.
Ne large seas or tracts of water have been observed in the Moor,
by Dr. Herschel, or any other astronomer, nor did he notice any indi
cations of a Lunar atmosphere. Recent observations, however, on the
occultations of Jupiter and Venus by the Moon, render it highly proba-
ble that the Moon, as well as the earth, is surrounded by an atmosphere.
On April 5th, 1824, Mr. Ramage, of Aberdeen, Captain Ross, of the
Navy, and Mr. Comfield, at Northampton, observed, with excellent
telescopes, the occultation of Jupiter, and to all of them the disc of the
planet appeared distorted when it approached the limb of the Moon; and
Mr. Comfield, at Clapham, on Oct. 30th, 1825, observed, on the emer
sion of Saturn from behind the dark limb of the Moon, first the disc
of the planet, and then the eastern extremity of the ring decidedly flat-
tened, a phaenomena perfectly analogous to what would be produced
by refraction, and therefore rendering it highly probable that the Moor.
is surrounded by an atmosphere.
CHAPTER. W.
MARS.*
THE orbit of MARs is next above that of the earth,
and he is the first of what are called superior planets.
He is known in the heavens by a dusky red appearance.
His distance from the sun is 143,000,000 of miles; and
the length of his year is about 687 of our days.
The cause of his dusky red colour has not been clearly ascertained:
whether it arises from a thick atmosphere, or from his being of a na-
ture the better to reflect the red rays of light. The mean distance of
Mars from the sun is more than half as far again as that of our earth :
* The ancients have given the same name to the heathen God of war
ASTEROIDS, I 5.
that is, if the distance of the earth be considered to consist of 100 parts,
that of Mars would be 152.
He moves in his orbit at the rate of 53,000 miles
in an hour. The diurnal motion of this planet on
its axis is performed in 24 hours and 39 minutes. His
diameter is only 4,189 miles; and owing to his distance
he is supposed not to possess one half of the light and
meat which we enjoy.
The diurnal motion of Mars is ascertained by several spots that are
seen in him, when he is in that part of his orbit which is opposite to the
sun and earth. Dr. Hook first discovered them, and Cassini and Her
schel have from them, at length, determined his motion on his axis.
Though Mars, when viewed through a telescope, ap-
pears mostly full, yet he is seen, at times, to increase
and decrease somewhat like the moon; with this excep-
tion, that he is never horned. Hence we infer that he
shines not by his own light;-that his orbit exceeds
that of the earth, and includes both the earth and the
sun. No satellites or moons have been discovered to
attend on Mars. See plate 5.
Mars, when in the part of the heavens opposite to the sun, appears
about five times larger than when he is near the sun; which proves
that he must be much nearer to the earth in one situation than in an-
other. This will receive illustration by an inspection of plate 7, fig.
2, where the great inequality, with respect to distance, is seen between
his opposition and conjunction. It is evident, also, that it is not the earth
that is in the centre of his motion, but the sun.
ASTEROIDS.
BETwPEN the orbits of Mars and Jupiter, four small
planets, called Asteroids, have lately been discovered,
viz. Vesta, Ceres, Pallas, and Juno.
VESTA, though the last discovered, is nearer to Mars
than the other three : its mean distance from the sun
16 ASTEROIDS,
being 225,000,000 miles; and the revolution through
its orbit is performed in 1,326 of our days. Its incli-
nation to the ecliptic is 7+ degrees, being rather more
than that of Mercury. The size of this planet is not
yet ascertained.
Vesta was discovered by Dr. Olbers, a physician of Bremen, in Ger
many, early in 1807. This planet is much smaller than our moon.
CEREs’s mean distance from the sun is 263,000,000
miles, not quite three times that of the earth. Its
time of revolution is 4 years, 7 months, and 10 days;
its diameter 1,582 miles, and it is inclined to the eclip-
tic in an angle of about 103 degrees.
Ceres was discovered by M. Piazzi, of Palermo, in Sicily, Janu-
ary 1, 1801.
PALLAs's mean distance from the sun is nearly the
same as that of Ceres; not quite three times that of
the earth, namely 263,000,000 miles. Its revolution
is made in about four years. Its orbit is inclined to
the ecliptic, in an angle of about 34% degrees; and its
diameter is 2,280 miles. -
Pallas was discovered by Dr. Olbers, in March 1802.
JUNO’s mean distance from the sun is 252,000,000
miles; and its size nearly equal to that of Ceres. It
revolves round the sun in 4 years and 4 months; and
its diameter is 1,393 miles. Its inclination to the
ecliptic is 13 degrees and it appears like a star of the
eighth magnitude.
Juno was discovered by M Harding of Lilienthal near Bremen,
Sept. 1st, 1804.
*
ºpº
Fig. 2


JUPITER, 17
CHAPTER VI.
JUPITER,+
JUPITER’s orbit lies between those of Mars and Sa.
turn ; he is the largest of all the planets, and is easily
distinguished by his peculiar magnitude and brilliancy.
He exceeds all the planets in brightness, except some-
times Venus. The distance of Jupiter from the sun
's estimated at more than 490,000,000 of miles.
Jupiter's mean distance from the sun is 52 of those parts of which
the earth's distance is 10; hence, he is full five times farther from the
sun than the earthis. And if it be admitted that light and heat dimin-
ish in proportion as the squares of the distances increase, the inhabit-
ants of Jupiter receive but a 25th part of the sun's light and heat that
we enjoy. See plate 18.
Jupiter’s diameter is more than ten times that of the
earth, it being 89,170 miles; and therefore his magni-
tude is about 1,300 times that of the earth.
His year is nearly equal to 12 of ours, for he makes
one revolution round the sun in 4,332 days and a half:
consequently he travels at the rate of more than 25,000
miles in Rn hour.
Jupiter revolves on his axis, which is perpendicular
to its orbit, in less than 10 hours, at the amazing rate
of 26,000 miles an hour, a velocity 25 times greater
than the earth's. Hence, by this swift diurnal rota-
tion, his equatorial diameter is 6,000 miles greater than
his polar diameter. And as the variety in the seasons
of a planet depends upon the inclination of its axis to
its orbit, and as Jupiter has no inclination, there can be
* The great heathen deity is characterized by this name.
C
18 JUPITER’s SATELLITEs.
no difference in his seasons, nor any variation in the
length of his days and nights.
Jupiter's days and nights are always 5 hours each, in length, and
about his equator there is perpetual summer; and an everlasting win-
ter in his polar regions. If the axis of this planet were inclined to his
orbit any considerable number of degrees, it might be less habitable
about the poles; for then each pole would be nearly six years together
in darkness.
When viewed through a telescope, Jupiter is per-
ceived to be surrounded by faint substances, called
zones or belts. These belts are generally parallel to
its equator, and which is very nearly parallel to the
ecliptic. They are subject to great variations both in
number and figure. Sometimes eight have been seen at
once; sometimes only one. Sometimes they continue
for three months with little or no variation, and some-
times a new belt has been seen in less than two hours.
From their being subject to such changes, it is inferred
that they do not adhere to the body of Jupiter, but ex-
ist in his atmosphere.
This planet, even on the most careless view through
a good telescope, appears to be oval, the longer diame-
ter being parallel to the direction of the belts.
Professor Struve of Dorpat, by the most accurate ad-
measurements, has determined the proportion between
the greatestand least diameters to be as 1,371, to 1,000.
JUPITER’s SATELLITEs.
THIS planet has four satellites revolving about him
at different distances, and in different periods of time;
the nearest making a revolution in less than two days,
and the most distant in little more than sixteen: hence
JUPITER’s SATELLITEs. 19
their relative situation changes every instant. Conse
quently, these satellites, like our moon, are subject to
be eclipsed, and their eclipses are of considerable im-
portance to astronomers. They were first discovered
by Galileo in 1610.
Galileo took them, at first, for telescopic stars; but farther observa-
tion convinced him and others that they were planetary bodies. The
periodical time of the first satellite is in about one day and 18 hours,
the second in 3 days 13 hours, the third in 7 days 3 hours; and the fourth
in 16 days 16 hours.
The angles under which the satellites appear at the
mean distance of the planet from the earth, have been
determined with great precision by Struve, to be first,
1,018", second 0,914", third 1,492", fourth 1,277".
These numbers represent also the proportions of the
diameters of the satellites. It hence appears, that the
second is the smallest, the third the largest, and the
fourth larger than the first.
By means of the eclipses of Jupiter's satellites, a
method has been obtained for determining the longi-
tude of places, with facility and some accuracy; and
also for demonstrating that the motion of light is pro-
gressive, and not instantaneous as was once supposed.
The velocity of light is more than a million of times
greater than of a ball issuing from a cannon. Rays of
light come from the sun to the earth in less than 8
minutes; which is at the rate of about 12,000,000 of
miles in a minute.
5 SATELLITES OF SATURN.
CHAPTER VII.
SATURN,+
*.
SATURN till of late years was esteemed the sixth and
the most remote planet of the solar system. He shines
with a pale dead leaden light. His mean distance
from the sun is about 9% times farther off than that
of the earth, being nearly 900,000,000 of miles. Of
course the light and heat he derives from the sun, are
about 90 times less than at the earth.
It has been calculated, however, that the light of the sun at Saturn
is 500 times greater than that which we enjoy from our full moon.
While our day-light is calculated to exceed that of our full moon 90,000
times.
The diameter of Saturn is nearly 80,000 miles, and
his magnitude almost a thousand times that of the
earth. He performs his revolution in his orbit round
the sun in less than 30 of our years (10,759 days,)
consequently he must travel nearly 21,000 miles an
hour. He revolves about his axis in 12 hours and 13%
minutes.
Cassini and others attempted, but without success, to determine the
rotation of Saturn about his axis; but Dr. Herschel's observations have
at length ascertained it. The Phil. Trans, of 1794 say 10h 16' 0"4; but
later accounts say 12h 134'.
SATELLITEs of SATURN.
SATURN is attended by seven Satellites or Moons,
whose periodical times differ very much. The one
nearest to him performs a revolution round the primary
* This name is given to the supposed father of the Heathen gods
page 20 Plate 3
Relative Sizes of the Planets.
§§ §
&º
º Perus O
lſ (ranſas `---
... O
2-
C O |
- Earth & Moon. ))
Q & Mercury



SATURN’s RING. 21
planet in 22 hours and a half; and that which is most
remote takes 79 days 7 hours.
The last Satellite is known to turn on its axis, and in its rotation to
be subject to the same law which our moon obeys; that is, it revolves
on its axis in the same time in which it revolves about the planet.
SATURN’s RING.
SATURN is also encompassed with a kind of Ring,
or, according to Dr. Herschel, with two concentric
rings, situated in one plane, which is not much inclin-
ed to the equator of the planet. They may probably be
of considerable use in reflecting the light of the sun to
him. See plate.
From numerous observations it has been concluded, that the near
est is 21,000 miles distant from Saturn, and that the breadth of the inner
ring is 20,000 miles; that of the outer ring 7,200 miles; and the vacant
space between the two rings 2,839 miles.
Dr. Herschel conjectures that it is no less solid than the planet itself;
and he has found that it casts a strong shadow upon the planet. The
light of the ring he has observed brighter than that of the planet; for the
ring appears sufficiently bright for observation at times, when the tele-
scope scarcely affords light enough to give a fair view of Saturn.
Professor Struve has made some interesting obser-
vations on this planet, with a superb refracting teles-
cope.—The results of his admeasurements are, that at
the mean distance of the planet,
The external diameter of the external ring is 40.215
The internal diameter of the external ring is 35.395
The external diameter of the internal ring is 34.579
The internal diameter of the internal ring is 26.748
The equatorial diameter of Saturn is . . 18.045
The breadth of the external ring is . . . 2.410
The breadth of the chasm between the rings is 0.408
G 2
22 THE GEORGIUM SIDUS.
The breadth of the internal ring is . . . . 3.915
The distance of the ring from Saturn is . . 4.352
He adds, “it is remarkable that the outer ring is much
less brilliant than the inner. The inner one too, to-
wards the planet, seems less distinctly marked, and to
grow fainter; so that I am inclined to think that the
Inner edge is less regular than the others.”
The Ring has a rotation about its axis, or, which is
the same thing, revolves about the planet, in the same
time that Saturn turns round on his axis.
CHAPTER VIII.
URANUS, OR HERSCHEL.
THIs is the most remote planet yet discovered in our
Solar system. He appears of a bluish white colour,
and can rarely be seen but by means of a telescope.
He may be best perceived, by the naked eye, in a very clear might
when the moon is absent.
To Dr. Herschel the world is indebted for the discovery of this planet,
on the 13th of March, 1781. The Doctor, in honour of George III.
king of England, named it the Georgium Sidus, (or Georgian Star.)
though by astronomers it is called the Herschel, in testimony of re-
spect to the discoverer. American astronomers call it Uranus.
The distance of this planet from the sun is more than
1,800,000,000 miles; or about nineteen times that of
the earth.
The distance given by some authors, is 1,812,000,000 miles. The
light and heat which he derives from the sun, are supposed to be about
the 361st part of those at our earth (for the square of 19 is 361; which
PRoPort IoMAL MAGNITTołº, &c. of PLANETS. 23
see explained in a future chapter)—that is, about equal to the effect of
249 of our full moons.
He performs his annual revolution in 3,069 days, or
about 84 of our years; consequently he must travel at
the rate of 16,000 miles an hour.
The time of his completing a revolution has been ascertained by a
series of observations. When first discovered in March 1781, he was
in Gemini; and in August 1803, he had advanced to 11° of Libra; or
through more than a fourth part of his orbit.
His diameter is found to be 35,865 English miles;
but his diurnal rotation has not yet been discovered.
THE HERSCHEL's SATELLITEs.
THE HERSCHEL, or URANUs has sia: Satel-
lites; the one nearest the planet performs his revolution
round the primary in less than six days; and that which
is the most remote in rather more than 107 days and a
half.
Though the light of these Satellites or Moons is, as Dr. Herschel
observes, extremely faint, yet they are, probably, of great benefit to the
inhabitants of that planet; for it is reasonable to conclude that there is
scarcely any part of his orb but what is constantly enlightened by one
or other of them.
The proportional Magnitude and Distance of the
PLANETs.
THE Earth is fourteen times as large as Mercury;-very little larger
than Venus;–three times as large as Mars; more than a million times
as large as Pallas. But Jupiter is more than fourteen hundred times as
large as the Earth. Saturn above a thousand times as large, exclusive
of his ring; and the Georgian eighty times as large.
As the DISTANCEs of the planets when given in miles, are such a
burthen to the memory as seldom to be retained, astronomers often ex-
press their mean distances in a shorter way, by supposing the distance
of the earth from the sun to be divided into ten parts. Mercury may
24 COMETS•
then be estimated at nearly four of such parts from the sun. Venus at
seven, the Earth at ten, Mars at full fifteen, Jupiter at fifty-two; Saturn
at nunety-five, and the Georgian one hundred and ninety parts. [See
the scale on the frontispiece.] These are calculated by multiplying the
respective distances of the planets by 10, and dividing by 95, the mean
distance of the earth from the sun. For the relative magnitudes of the
planets see plate 3.
CHAPTER IX.
COMETS.
CoMETs, like the orbs already mentioned, are sup-
posed to be planetary bodies forming a part of our sys-
tem; for, like the planets, they revolve round the sun;
not, indeed, in orbits nearly circular, but in very dif.
ferent directions, and in extremely long elliptic curves,
having the sun in one of their foci ; approaching some-
times near the sun, at others stretching far beyond the
orbit of the remotest planet. The periods of their revo-
lutions are so long that only three are known with any
degree of certainty.
Some suppose them, not adapted for the habitation of animated be.
ings, on account of the great extremes of heat and cold, to which, in
their course, they appear to be subject.
The name of Cometis derived from Cometa, “hairy;”
because Comets appear with long tails, somewhat re-
sembling hair. This appearance is supposed to be no-
thing more than vapour arising from the body in a line
opposite to the sun; some indeed have been seen with-
out such appendage, and as round as the regular planets.
The knowledge, however, which we have of Comets, is
COMETs. 25
very imperfect, as they afford but few observations on
which to ground conjecture.
By common people they are called blazing stars, and by some they
are thought to be portentous; presaging some extraordinary event. But
they can have no such tendency, nor can there be any apprenension
that they can injure the earth we inhabit, by coming into contact. Even
the tail of the Comet cannot come near our atmosphere, unless it should
be at its inferior conjunction very nearly at the time when it is in its
node; circumstances so extremely unlikely, that there are some mil-
lions to one against such a conjunction.
It was thought that the periods of three of the Comets had been dis-
tinctly ascertained; the first of these appeared in 1531, 1607, and 1682,
and it was expected to return every 75th year; and one did appear in
1758, which was supposed to be the same. -
The second of them appeared in 1532 and 1661, and was again
expected in 1789, but in this the astronomers were disappointed.
The third was that which appeared in 1680, and its period being es-
timated at 575 years, cannot, upon that supposition, return till 2255.
This Comet, at its greatest distance, is 11,200,000,000 of miles from the
sun; and its least distance from the sun's centre was but 490,000 miles;
in this part of its orbit it travelled at the rate of 880,000 miles in an hour.
Comets differ much in their magnitude, though most
of those which have been observed are less than the
moon; but their dimensions are not determined with
accuracy. } *
The head of the Comet of 1807 was ascertained to
be about 538 miles in diameter; and that of 1811,
about the size of the moon.
According to Sir Isaac Newton, comets are of an
opaque nature, and consist of a very compact, durable,
and solid substance, capable of bearing exceedingly
great degrees of heat and cold. The Comet seen by
him in 1680, was observed to approach so near the sun
that its heat was estimated by him to be 2,000 times
greater than that of red hot iron. And it has been said
26 THE FIXED STARS.
that a globe of red hot iron as large as our globe would
scarcely cool in 50,000 years.
Notwithstanding the above supposition the appearance of the two
brilliant Comets, of late, seems to overturn that theory. Of that in 1807,
Dr. Herschel says, we are authorized to conclude that the body of the
Comet, on its surface is self luminous, from whatever cause this quality
may be derived. The vivacity of the light of the Comet, also, had a
much greater resemblance to the radiance of a star, than to the mild
reflection of the sun's beams upon the moon.
Comets consist (according to modern observation) of the nucleus, the
head, the coma, and the tail. The nucleus is a small and brilliant part
in the centre; the head includes all the very bright surrounding light;
the coma is the hairy appearance surrounding the head; and the tail,
which is of great length, is supposed to consist of radiant matter, such
as that of the aurora borealis.
The tail of the Comet in 1807, was ascertained to be more than
9,000,000 of miles in length; and that in 1811, to be full 33,000,000 in
length. The distance of this Comet from the sun was 95,000,000 of
miles, and from the earth upwards of 142,000,000 of miles.
CHAPTER X.
THE FIXED STARS.
ALL the heavenly bodies beyond our system are
called Fiated Stars, because, except some few, they
never appear to move or to change their places, with
regard to each other, as the planets do. As they are
placed at immense distances from our system, they
must be bodies of great magnitude, and doubtless shine
by their own light. They are probably suns, like our
sun, to different systems of planets: each fixed star
being supposed to be the géntre of its own system.
That the fixed stars shine by their own light is concluded; being at
such vast distances from the sun, they could not possibly receive from
him so strong a light as they shine with. So great is their distance.
page 26
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THE FIXED STARS, 27
that though tha orbit of the earth is twice 95,000,000 of miles across, and
we are consequently 190,000,000 of miles nearer to some stars at one
time than we are at another, yet the stars always appear in the same
places, and with the same magnitude. See plate IV. fig. 2. Let * * *
represent the fixed stars, and A B C D, the earth's annual course; then
will the earth in that part of its orbit at B, be 190,000,000 of miles nearer
to the fixed stars, than when at D.
The distance of Sirius, or the Dog-star, the nearest
of the fixed stars, cannot be less than two millions of
millions of miles. A cannon ball flying from that star
at the rate of 400 miles an hour, would not reach usin
570,000 years.
Professor Vince says, “the nearest fixed star cannot be less than
400,000 times farther from us than the sun is.” Hence 400,000, multi-
plied by 95,000,000, give 38 millions of millions of miles for the near-
est fixed star.
Dr. Herschel says, that several of the fixed stars revolve on their
2X6S.
The fixed stars, then, are most probably suns, which,
like our sun, serve to enlighten, warm, and sustain
other systems of planets, and their dependent satellites.
They are usually classed into six magnitudes, which
include all that can be seen without a telescope; the
largest are called stars of the first magnitude, and the
smallest, those of the sixth. There are seldom so many
as a thousand visible at one time, to the naked eye,
even in a clear star-light night.
The number of stars appears to us at times innumerable; but this is
a deception, occasioned from their being observed by us in a confused
manner, or by the refraction and reflection of the rays of light, passing
from them through our atmosphere.
Many of the fixed stars, which to the naked eye ap-
pear as single stars, are found to consist of two, and
some even of three, or more.—Not that they are really,
28 THE FIXED STARs.
double or treble, but they are stars at different dis.
tances, which appear nearly in a right line. There are
also clusters of stars, called nebulae: the most remark-
able of these is, that broad zone, called the Milky way.
In this bright track, Dr. Herschel has seen 116,000
stars pass over the field of his telescope, in a quarter of
an hour.
The Magellanic clouds, near the south pole, which resemble two
whitish spots in the heavens, are of the order of nebulae, and are well
known to sailors.
Since the introduction of telescopes, the number of fixed stars has
heen considered as immense; and by the greater perfection of our
glasses, still more stars are discovered; so that there appear to be no
bounds to their number, or to the extent of the universe.
There are two methods of discovering which are
planets, and which are fixed stars: the first is by their
twinkling or not ; for every fixed star twinkles, but a
planet does not. The second is by the nature of their
motions: they all, indeed, appear to rise and set; but,
besides that, the planets have a motion from one part
of the heavens to another, sometimes among the fixed
stars in one constellation, at other times among those
of another; whereas the fixed stars keep constantly the
same relative distance from each other.
Many conjectures have been offered as to the cause of the furinkling
of the fixed stars; perhaps it may be the unequal refraction of light, in
consequence of inequalities and undulations in the atmosphere.
‘Several stars mentioned by ancient astronomers are
not now to be found, and several are now observed
which do not appear in their catalogues.
The most ancient observations of a new star is that by Hipparchur,
THE FIXED STARS. 29
about 120 years before Christ. Some others have been noticed in later
times; but the first new star we have any accurate account of, is tha.
which was discovered by Cornelius Gemma, in 1572, in the Chair of
Cassiopeia. It exceeded Sirius in brightness, and was seen at mid-day.
It first appeared larger than Jupiter, but it gradually decayed; after six-
teen months it entirely disappeared.
Some fixed stars have been noticed alternately to ap-
pear and disappear, and others have been subject to
great periodical variations in their magnitudes.
In 1600, a changeable star was discovered by W. Jansenius, in the
neck of the Swan, which appeared visible for many years; but from 1640
to 1650 was invisible. It was seen again in 1655, increased till 1660,
then grew less, and disappeared. In 1665 re-appeared; disappeared in
1681. In 1715, it appeared of the sixth magnitude, as it is seen at present.
To mention one more instance, among many, 8 Lyrae was discovered
by Mr. Goodrich, to be subject to a periodic variation. It completes all
its phases in 12 days, 19 hours, during which time it undergoes the fol-
lowing changes: 1. It is of the third magnitude for about two days.
2. It diminishes in about 14 day. 3. It is between the fourth and fifth
magnitude for less than a day. 4. It increases in about two days. 5. It
is of the third magnitude for about 3 days. 6. It diminishes in about one
day. 7. It is something larger than the fourth magnitude for a little less
than a day. 8. It increases in about one day and three quarters to the
first point, and so completes a whole period. See Phil. Trans. 1785.
In whatever part of the universe we are, we appear
to be in the centre of a concave; that is, a hollow sphere,
where all remote objects appear at equal distances from
us; so that, whether we are on the planet Venus, or on
the earth, or on any planet or star in the universe, the
effect in this particular would be the same.
As a proof of this, the sun, moon, and stars, appear
at equal distances; whereas the sun (as has been men-
tioned) is 400 times farther off than the moon, and the
fixed stars at least 200,000 times farther from us than
the sun.
If transplanted to a planet of any other system, sup:
D
eſſe
-f
30 CONSTELLATIONS,
*
pose to one belonging to Sirius; then Sirius, which now
appears only as a star, would prove a sun. Our sun
would then appear as a star, and the earth, with all the
other planets, would be invisible.
The vulgar error, that all these stars were placed in the heavens only
to afford us light, must be erroneous, since thousands of them are invisi-
ble to us without the help of a telescope, and we receive more light
from the moon, than from all the stars together.
CHAPTER XI.
CONSTELLATIONS.
THE ancients, in reducing astronomy to a science,
formed the fixed stars into constellations, or collections
of stars, and represented them by animals, and other
figures, according to the ideas which the dispositions
of the stars suggested.
This arrangement took place very early; for some kind of division
must have been suggested by necessity, in order thatastronomers might
describe any particular star so as to be understood. Neither, without
some such division, could the situation of the planets have been point-
ed out, as they are continually changing their places. We find mention
made of Orion and Pleiades by Job. Homer and Hesiod also make
mention of some of them; but Aratus enumerates almost all the an-
cient ones.
The number of the ancient constellations was about
fifty, but the present number upon the globe is eighty.
The heavens are usually distinguished by three re-
gions, called the Northern and Southern hemispheres,
and the Zodiac. The number of the constellations,
in the northern hemisphere, is 36; in the southern, 32;
and in the zodiac, 12. Stars not comprehended in any
of these, are called unformed stars.
CONSTELLATIONS, 31
NoRTHERN ConstELLATIONs.
NUMBER OF STARS,
Ursa Minor. The Little Bear . . . . . . 24
Draco. The Dragon . . . . . . . . . 80
Cepheus . . . . . . . . . . . . . 85
Lacerta. The Lizard . . . . . . . . . 16
Cassiopeia. The Lady in her Chair . . . . 55
Perseus . . . . . . . .
Caput Medusae. Medusa's Head . . . . .
Camelopardalus. The Camelopard . . . . . 58
Lynx. The Lynx . . . . . . . . . . 44
Ursa Major. The Great Bear . . . . . . 87
Cor Caroli. Charles’s Heart
Leo Minor. The little Lion . . . . . . . 53
Coma Berenices. Berenice's Hair . . . . . 43
Asterion and Chara. The Greyhound . . . . 25
Boötes . . . . . . . . . . . . . 54
Corona Borealis. The Northern Crown . . . 21
Hercules. Hercules kneeling . . . . . . . 13
Cerberus. The Three Headed Dog . . . . 9
Lyra. The Harp . . . . . . . . . . 21
Cygnus. The Swan . . . . . . . . . 81
Velpecula et Anser. The Fox and Goose . . 35
Sagitta. The Arrow . . . . . . . . . 18
Delphinus. The Dolphin . . . . . . . . 18
Pegasus. The Flying Horse . . . . . . 89
Andromeda . . . . . . . . . . . . 66
Triangulum Boreale. The Northern Triangle . 16
Musca. The Fly
Auriga. The Wagonner . . . . . . . 66
Mons Maenalus The Hill Maenalus
59
32 CONSTELLATIONS.
NUMBER OF STARS,
Serpens. The Serpent . . . . . .
Serpentarius. The Serpent Bearer . .
Scutum Sobieski. Sobieski’s Shield . .
Taurus Poniatowski. Poniatowski’s Dull
Antinoùs & ſº tº e º e C. Q
Aquila. The Eagle . . . . . .
Equulus. The Colt . . . . . .
THE SouTHERN ConstELLATIONS.
Piscis Australis. The Southern Fish .
Cetus. The Whale . . . . . . .
Eridanus. The River Po . . . . . .
Orion . . . . . . . . . . . .
Lepus. The Hare . . . . . . . .
Canis Major. The Great Dog . . . .
Monoceros. The Unicorn . . . . .
Canis Minor. The Little Dog . . . .
Hydra. The Hydra . . . . . . .
Sextans. The Sextant . . . . . . .
Crater. The Cup . . . . . . . .
Corvus. The Crow . . . . . . . . . .
Argo Navis. The Ship Argo . . . .
Crux. The Cross
Centaurus. The Centaur . . . . . .
Lupus. The Wolf . . . . . . . .
Ara. The Altar . . . . . . .
Corona Australis. The Southern Crown .
Columba Noachi. Noah's Dove . . . .
Robur Carolinum. The Royal Oak . .
Apis. The Bee . . . . . . . . .
º
*
64
74
8
34
12
10
24
97
84
78
19
31
39
14
60
41
31
64
24
#
9
12
10
12
p
º
*2
32
ye
4
Write
P.
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A
9. *
Aºi (
't

CONSTELLATIONS. 33
NUMBER OF STARS.
Triangulum Australe. The South Triangle . . 5
Apus. The Bird of Paradise . . . . . . 11
Pavo. The Peacock . . . . . . . . . 14
Indus. The Indian . . . . . . . . . 12
Grus. The Crane . . . . . . . . . . 13
Phoenix. The Phoenix . . . . . . . . 14
Toucon. The American Goose . . . . . . 9
Hydrus. The Water Snake . . . . . . . 10
Dorado. The Sword Fish . . . . . . . 6
Piscis Wolans. The Flying Fish . . . . . 8
Chamaeleon. The Cameleon . . . . . . . 10
THE ZoDIACAL CoNSTELLATIONs.
Aries. The Ram. . . . . . . . . . . 66
Taurus. The Bull . . . . . . . . . . 141
Gemini. The Twins . . . . . . . . . 85
Cancer. The Crab . . . . . . . . . . 83
Leo. The Lion . . . . . . . . . . . 95
Virgo. The Virgin . . . . . . . . . 110
Libra. The Balance . . . . . . . . . 51
Scorpio. The Scorpion . . . . . . . . 44
Sagittarius. The Archer . . . . . . . 69
Capricornus. The Goat . . . . . . . . 51
Aquarius. The Waterman . . . . . . . 108
Pisces. The fishes . . . . . . . . . 113
Some of the principal fixed stars are distinguished by
particular names, as Regulus, Arcturus, Sirius, &c.,
others are denoted by the letters of the Greek alphabet.
the first letter being put to the greatest star in each
constellation; the second letter to the next greatest, and
e D 2
34 DIFFERENT SYSTEMS.
so on; and when any more letters are wanted, the Italic
letters are generally used.
By this contrivance the place of any particular star in the heavens
may be found, with the greatest ease and precision.
CHAPTER XII.
DIFFERENT SYSTEMS.
THE system we have been describing, and which is
now universally received, is called the Copernican. It
was formerly taught by Pythagoras, a Greek philoso-
pher, born in the island of Samos, 590 years before
Christ, and Philolais, his disciple, finding it impossible
any other way to give a consistent account of the hea-
venly motions.
This system, however, was so extremely opposite to
all the prejudices of sense and opinion, that it never
made any great progress in the ancient world till re-
vived by Copernicus.
Ptolemy, an Egyptian philosopher, who flourished
130 years after Christ, supposed at first that the earth
was perfectly at rest near the centre; and that all the
other bodies, namely, the sun, moon, planets, comets
and fixed stars, revolved about it in circles every day.
But as their retrograde motions and stationary appear-
ances could not thus be solved, he afterwards supposed
them to revolve in epicycloids.
Epicycloids are curves generated by the revolution of the periphery
ofa circle along the concave or convex parts of another circle.
The full illustration of this motion may exceed the present compre-
hension of the learner, but he may conceive it to be not much unlike

DIFFERENT SYSTEMS. 35
the curve line, a, b, c, d, e,f, &c., plate XV. fig. 1. Now it is evident
that at the points b and c, and also d and e, the planet's motion would
appear stationary and retrograde from b to c, and from d to e, and at other
times direct.
But though this system will not solve the phases of Venus and Mer-
cury, and for other reasons cannot be true, it was maintained from the
time of Ptolemy till the revival of learning in the sixteenth century.
The Egyptians received also the following system:—
That the earth is immoveable in the centre, about
which revolve, in order, the Moon, Sun, Mars, Jupiter
and Saturn; and about the sun, revolve Mercury and
Venus. This disposition will account for the phases
of Mercury and Venus, but not for the apparent motions
of Mars, Jupiter, and Saturn.
At length Copernicus, a native of Poland, adopted
the Pythagorean system, and published it to the world
in 1530. This doctrine had been so long in obscurity,
that the restorer of it was considered the inventor.
Copernicus placed the Sun in the centre of the sys-
tem, and about it, the other bodies in the following
order: Mercury, Venus, the Earth, Mars, Jupiter and
Saturn.
Europe, however, was still immersed in ignorance,
and the general ideas of the world were not able to keep
pace with those of a refined philosophy. This occa-
sioned Copernicus to have few abettors, but many op-
ponents. t:
Tycho Brahe, a noble Dane, and eminent philoso-
pher, sensible of the defects of the Ptolemaic system
but unwilling to acknowledge the motion of the earth,
endeavoured, about 1586, to establish a new system of
his own, in which the earth was supposed the centre
of the sun and moon; that Mercury, Venus, &c. re-
36 of THE MOTION of THE PLANETs.
volved about the sun, and that the sun and planets,
together, turned round the earth in 24 hours. But as
this proved to be still more absurd than that of Ptolemy,
it was soon exploded, and gave way to the Copernican,
or true solar system.
Some of Tycho's followers, seeing the absurdity of supposing all the
heavenly bodies daily to revolve about the earth, allowed a rotary mo-
tion to the earth, in order to account for their dhurnal motion, and this
was called the Semi-Tychonic system.
Thus the solar system, now adopted, after having
been taught by Pythagoras, and revived by Copernicus,
was confirmed by Galileo, Kepler, and Descartes, and
fully established by Sir Isaac Newton. See Planeta-
rium, plate 6.
CHAPTER XIII.
OF THE MOTIONS OF THE PIANETS:
DIRECT, STATIONARY, AND RETROGRADE.
THE planets, Mercury, Venus, the Earth, &c. if seen
from the sun, would appear to pass from star to star,
through the constellations, in a uniform and regular
Iſlaſt 1101’,
But as seen from the earth, they apparently move
very irregularly ; sometimes they appear to go forward,
at other times to remain stationary, and then to recede.
To give some idea of this, suppose yourself placed in the centre of a
circular course, keepińg your eye on the horse while going round; it
is evident that he would appear to run round the whole course in a
regular manner. Again; imagine yourself placed at a considerable
distance on the outside of the course, and the horse's motions would
oF THE MOTION of THE PLANETs. } .
appear no longer uniform. on the opposite side of the course alone
“would he seem regular: then alone would it appear the same as when
you stood in the centre. When he approached you, he would scarcely
seem to move; in that part of his course next to you, he would move
in a direction contrary to what he did at first; and again, when going
from you, his motion would be scarcely visible.
When the planets are farthest from us, their motion
is said to be direct; when nearest to us retrograde,
because they appear to be moving back again ; and
when either approaching us, or going from us, we say
they are stationary, because, if then observed in a line
with any particular star, they will continue so for a con-
siderable time; now these appearances could not hap-
pen if they moved round the earth as their centre. See
plate VII. fig. 1. -
Inferior and Superior Conjunctions of the PLANETs.
WHEN Mercury or Venus is nearest to us, that is,
in a line between us and the sun (see plate VII. fig. 2.)
we say it is in inferior conjunction ; when farthest
from us, and the sun is between us and the planet, in
superior conjunction.
The superior planets, namely, those whose orbits
include that of the earth, have alternately a conjunction
and an opposition; a conjunction, when the sun is be-
tween the earth and the planet; and an opposition,
when the earth is between the sun and the planet, that
is, when the planet is nearest to us, and appears to be
opposite to the sun.
Hence, when a planet is in conjunction, it rises and
sets nearly with the sun ; but in opposition, it rises
nearly when the sun sets, and sets when he rises.
38 THE PLANE OF AN or BIT, PLANETs, &c.
We say nearly, because it cannot be exactly, except when the
planet is in or near its mode; or, which is the same thing, when the
sun, earth and planet, are in a right line, which seldom happens.
As only that side of a planet which is turned to the
sun can be enlightened by him it is evident, that as
viewed with a telescope from the earth, its appearance
must vary; thus Venus, just before and after her supe-
rior conjunction, would be seen nearly with a full face,
when stationary, she would appear only half enlight-
ened, like the moon, at the first quarter, because an
equal portion of the bright and dark sides will be turn-
ed towards us; the bright parts will be decreasing till
her inferior conjunction, and then only the dark side
will be turned towards us, and consequently she will
be for a short time invisible : by-and-by she will be.
come again stationary, and appear like the moon ather
third quarter.
It is true, both Mercury and Venus may at times be seen even when
in their inferior conjunctions, but it can be only in their transits, which
will be explained in a future chapter.
These appearances refer to the inferior planets only,
Mercury and Venus. The superior planets always ap-
pear with nearly a full face.
CHAPTER XIV.
THE PLANE OF AN ORBIT, PLANETS, NODES, ETC.
THE earth, as seen from the sun in its periodical re-
volution, will describe a circle among the stars, which
astronomers call the ecliptic ; and sometimes the sun's
THE PLANE OF AN or BIT, PLANETs, &c. 39
annual path, because the sun, as seen from the earth,
always appears in that line.
Suppose the earth, if seen from the sun, to appear in Cancer, then
the sun, if viewed from the earth, will appear in Capricorn; or, if the
earth appear in Aries, the sun will appearin Libra. See plate IV. fig, 1.
By the plane of a circle may be understood that sup-
posed surface which would lie evenly between every
part of the circumference.
Any flat and smooth surface is a plane; hence the edge of a round
table may represent the ecliptic, and the surface of the table its plane.
Though the orbit of the earth and the ecliptic are in
the same plane, they are not the same thing; for the
ecliptic is supposed to extend far beyond that of the
earth to the fixed stars.
If the edge of a round table be made to represent the ecliptic, then
a circle within, drawn from the centre of the table, may represent the
orbit of the earth, and they will be both in the same plane, though of
unequal dimensions.
The orbits of the planets are not in the same plane
as that of the earth; in other words, the planets do not
move in the ecliptic. They are in every revolution
one-half of their periods a little above the ecliptic, and
the other half as much below it. This is called the in-
clination of their orbits (see plate VIII. fig. 1.) where S
represents the sun; A B C D the orbit of the earth;
and EFG H the orbit of one of the inferior planets,
suppose of Venus; the half, FG H, rises above, and the
other half, HEF, sinks below it, from the points H F,
which are in a line with the orbit of the earth.
The dotted line b H F a, is called the line of the
nodes; and the points H F, the nodes of the planet.
The point F is called the ascending node, because the
40 THE TRANSITS OF MERCURY AND VENUS.
planet is then ascending or rising above the orbit of the
earth; or, which is the same thing, above the ecliptic.
When in H it is descending below it, whence that point
is called the descending node.
As the planes of the planets’ orbits vary a little from
each other, so their nodes or intersections are at dif-
ferent parts of the plane of the ecliptic.
The dotted line, c def, may represent the orbit of
any other planet, and convey some faint idea of the way
in which they intersect each other.
Not that we are to suppose, when speaking of the
plane of the ecliptic, or plane of the earth's orbit, that
it is a real and visible flat surface; nor in speaking of
the orbits of the planets, that we mean solid rings; for
the planets perform their revolutions with the utmost
regularity in unbounded space.
The Transits of MERCURY and VENUs.
If Venus were in her ascending node at F, (plate
VIII. fig. 1) when the earth is at a, or in her descend-
ing node at H, when the earth is at b, she would be in
a line with the sun, and on the sun's disc she would
appear a dark round spot passing over it. These ap'
pearances are called transits; they happen very se!-
dom, because Venus is very seldom in or near her nodes
at her inferior conjunctions. -
That there are great variations in the apparent dia.
meter of Venus may be demonstrated thus: suppose S
(plate VII, fig. 1.) to be the sun, E the earth in its or-
bit, and a b c d, &c. Venus in her’s : now it is evident
that when Venus is at a between the sun and earth.
e 4/
'S
• Telescopic Fleus of Venu


THE ECLIPTIC, zoDIAC, AND EquaTor, &c. , 41
she would, if visible, appear much larger than when
she is at c in superior conjunction, because so much
nearer in the former case than in the latter; being in
the situation a, but 27,000,000 miles from the earth,
E; but at e, 163,000,000.
As Venus passes from a Shrough b c d to e, she may be observed
by a good telescope to have all the same phrases as the moon has
in passing from new to full; therefore when she is at e she is full.
Also, during her journey from c through f to g, she will appear to havo
a direct motion in her orbit; from g to Å, and from b to c to be nearly
stationary, but from h to b, her motion, thºugh still really direct, will
appear to a spectator at E, to be going back again, of rerograce, swas
shown before.
Mercury is seen in the same manner, which is a prool
that their orbits must be within that of the eanth.
CHAPTER XV.
THE ECLIPTIC, ZODIAC, AND EQUATOR, ETC.
THE ECLIPTIC is an imaginary great circle in the
heavens, which the sun appears to describe in the
course of the year, among the stars. -
The following are the most conspicuous stars that lie
near to the ecliptic:-The Ram's Horn, called, a Arie-
tis—Aldebaran, in the Bull's Eye—Castor and Pollux—
Regulus, or the Cor Leonis—Spica Virginis—Antares,
or the Scorpion's Heart—also, which lie more distant,
• Altair, in Aquila—Fomaehaut, in the Fish's Mouth,
‘and Pegasus.
The above nine stars are considered as the most conspicuous near
the moon's orbit—from these the moon's distance is calculated, and
hence the tables in the Nautical Almanac are constructed for the use
E. Ö
42 THE ECLIPTIC, zoDIAC, AND EQUAToR, &c.
of navigators. The Ecliptic is so called, because all the eclipses must
necessarily happen in this line, where the sun always is.
The Ecliptic and Equator, being great circles, must
bisect, or equally divide each other; and their inclina-
tion is called the obliquity of the Ecliptic. Also the
points where they intersect are called the equinoctial
points, and the times when the sun comes to these
points are called the equinoaces.
The ZoDIAC is an imaginary broad circle, or belt,
surrounding the heavens, extending about 8° on each
side the ecliptic, in which the planets, with the exception
of Ceres, Pallas, and Juno, constantly revolve.
The term Zodiac is derived from a Greek word zaštaxos; from Keov,
“an animal,” because each of the twelve signs formerly represented
some animal; that which we now call Libra being by the ancients
reckoned a part of Scorpio.
For the definitions of degrees, &c. see preliminary definitions.
The names and characters of the twelve signs, with
the time of the sun’s entrance into them, are as follow :
1. Aries, ‘P, or the Ram; March 20th.
2. Taurus, 8, the Bull; April 20th.
3. Gemini, II, the Twins; May 21st
4. Cancer, g3, the Crab ; June 21st.
5. Leo, Sl, the Lion; July 23d.
6. Virgo, Iſſ, the Virgin; August 23d.
7. Libra, -e-, the Balance; September 23d.
8. Scorpio, 11, the Scorpion; October 23d.
9. Sagittarius, 1, the Archer; November 22d.
10. Capricornus, V3, the Goat; December 21st.
11. Aquarius, x, the Waterman; January 20th.
12, Pisces, 96, the Fishes; February 19th.
#
THE ECLIPTIC, zodiac, AND EQUATOR, &c. 43
Dr. Watt's lines, “The Ram, the Bull,” &c. are well known; but,
perhaps, to learn the signs in the above order will answer a better
purpose, and be but little extra labour.
The order of these is according to the motion of the sun. The first
point of Aries coincides with one of the equinoctial points, and the first
point of Libra with the other.
The first six are called northern signs, lying on the
north side of the equator; and the last six southern,
lying on the south side.
The signs W5, 3%, 36, ‘P, 8, II, are called ascend-
ing, because the sun approaches our north pole while
it passes through them ; and 95, Sl, ſſ, C-, 1/1, 4, are
called descending, the sun receding from our pole as it
passes through them. -
Each of the 12 signs of the Zodiac contains 30 de-
grees.
The EquaTor is either terrestial or celestial.
The terrestial Equator is an imaginary great cir-
cle of the earth, perpendicular to its axis; hence the
axis and poles of the earth are the axis and poles of
the equator. This circle is equally distant from the
two poles, and separates the globe into the northern
and southern hemispheres.
The celestial Equator, called also the equinoctial, is
a plane of the terrestial equator extended to the fixed
stars; and if the axis of the earth be produced in like
manner, they will be the poles of the celestial equator.
And the star nearest to the north pole is called the pole
star, as P. P. fig. 2, plate II.
44 THE EPHEMERIS.
OF THE EPHEMERIS,
The Astronomical Ephemeris being frequently alluded to in
the use of the globes and the study of astronomy, a short ex,
planation of the astronomical part of the only work of this kind
published in this country, viz. the American Almanac, may be
acceptable, taking, for example, that for the current year, 1832.
The first thirty-five pages, which are occupied by the relations
of the planets, the time of the entrance of the Sun into the signs
of the Zodiac, the length of each of the four seasons, the ca-
lendars of the Jews and Mahometans, the eclipses of the Sun,
Moon, and satellites of Jupiter; the occultations of the fixed stars
by the moon, the elements of the two comets of short period,
known as Encke's and Biela’s : the position and magnitude of the
rings of Saturn, the aspects of the planets, the height of the
greatest tides, the usual height of the spring tides at several
places on the American coast, the difference between the time
of high water at these places and at Boston, the latitude and lon-
gitude of most of the principal places in the United States, and
with the length of the longest and shortest days thereat, will, it
is supposed, require no illustration.
Of the calendar pages, those (36 and 37) for the month of
January may be taken as an example. On the top of the left
hand page will be found the apparent time of the beginning and
end of twilight, or the time when the Sun is 18 degrees below
the horizon before sunrise, and after sunset, for every sixth day,
at Boston, New York, Washington, Charleston, and New Orleans;
which places being situated in different latitudes, renders the al-
manac equally useful to every part of the United States. It may
however be proper to remark, that the twilight will not in general
be sufficiently strong to be visible, unless the Sun is considerably
less than 18 degrees below the horizon. On the 1st of January
it appears that the twilight begins at New Orleans at 27 minutes
after 5 in the morning, and ends at 27 minutes before 7 in
the evening. Under the above, will be found the time of the
Moon's apogee and perigee, or the time in each lunation, when
page 44
Plate 7
&E
Conjunction
crior (ºfton, 2.2
*/
Sup



THE EPHEMERIS. 45
she is farthest from, and nearest to the Earth, with the dis-
tance between the Earth and Moon, at those times, in English
miles. •
Next below are placed the phases of the Moon, or the mean
time at Washington of her conjunction, quadratures, and oppo-
sitions with the Sun: under these are placed the columns of the
calendar, viz. the day of the month and the corresponding day
of the week, also the apparent time of the rising and setting of
the Sun, and the mean time of the rising or setting of the Moon,
calculated for the same cities for which the twilight was com-
puted: thus, on the 2d of January the Sun rises at Boston at
21 minutes after 7, and sets 31 minutes before 5; at New Orleans,
he rises 57 minutes after 6, and sets 57 minutes before 6; the
Moon sets the same day at Boston at 39 minutes after 4 in the
afternoon, and at New Orleans 5 minutes after 5. By doubling
the time of the Sun's rising we have the length of the night, and
by doubling that of his setting, the length of the day; hence,
at Boston on the 2d of January, the length of the day, or the in-
terval between the rising and setting of the centre of the Sun,
exclusive of the effect of refraction, is 8 hours 58 minutes, and
at New Orleans 10 hours 6 minutes: want of room is the reason
assigned in the almanac for expressing the beginning and end of
twilight and the rising and setting of the Sun in apparent time
Apparent time is, however, readily converted into mean, by apply-
ing the equation (third long column right hand page) according
to the direction at the head of the column; and mean into ap-
parent, by applying the equation contrary to the direction: thus,
on the 2d of January the equation being 4 minutes to be added
to apparent for mean time, and consequently to be subtracted from
mean for apparent; the Sun rose that day at Boston, in mean
time, at 35 minutes after 7 and sat 27 minutes before 5; and the
Moon sat the same day, in apparent time, at 30 minutes after 4.
The column of the equation of time shows the quantity by
which a well regulated clock is fast or slow of the Sun, and by
it watches or clocks may be regulated, by comparing them with
a good dial at any time when the Sun shines thereon, and ex-
46 THE EPHEMERIS.
amining if the difference between them agrees with the figures in
this column: thus, on the first day of January 1832; a clock did
not show true mean time unless it was 13 minutes 42 seconds
faster than the time by the dial, or unless when the shadow in-
dicated noon, the clock was 13 minutes 42 seconds past 12.-For
further illustrations see the chapter on the equation of time, page 65.
The second long column of the right hand page gives the
mean time of the daily passage of the Moon over the meridian
of Washington, or the instant her centre bears down South at
that place. On the day of conjunction with the Sun, the Moon
the planets, and the fixed stars come to the meridian very nearly
at the same moment with him; and if the conjunction takes
place precisely at noon, the two bodies will be on the meridian
precisely at the same time; in all other positions than when in
conjunction, the Moon, planets, and stars will pass the meridian
before, or after the Sun, according as the Sun's right ascension
is greater or less. The mean time of the passage of any hea-
venly body over the meridian, is easily found by subtracting the
siderial time at the moment of the passage, from the right ascen-
sion of that body at the same moment.
The fourth, fifth, and sixth of the long columns contain the
mean time of high water at Boston, New York, and Charleston,
of that tide which arrives when the Moon is near to the meri
dian. The 7th long column contains the remarkable days in the
month, the conjunction of the Moon with fixed stars and planets,
that may be occultations in some part of the United States, and
other phenomena interesting to the astronomer. At the top
of the right hand page, will be found the mean time of the pass-
age of the planets over the meridian of Washington, with their
declinations or distance from the equator at that time, ou every
sixth day. By the assistance of this table, the places of the
planets may be easily found in a celestial globe; it being borne in
mind, that north declinations are designated by the sign + and
south by —. +.
On pages 60, 61, 62, 63, are the Sun's declination, and the
siderial time, which are given for every day, at noon, at Berlin;
THE EPHEMERIS. 47
or about six in the morning at Washington, the former in appa-
rent, the latter in mean time; the greatest declination (23° 273')
will be found on the 21st of June and December: about the
20th of March, and 23d of September, the declination ap-
pears to be nothing; the Sun's centre is, therefore, then but for
a single moment in the celestial equator, which is vulgarly termed
crossing the line ; the exact moment of the Sun having no
declination, may be thus ascertained. On the 20th of March,
1832, at apparent noon at Berlin, in Prussia, it appears by the
almanac, the declination of the Sun's centre was 2'59.2” south,
and on the 21st 20' 41.3' north; then by proportion as 23' 40.5” .
(the variation in 24 hours) is to 2'59.2", so is 24 hours to
3 hours 1 minute 40 seconds; consequently the Suai's centre was
in the celestial equator at Berlin, March 20th, 3 hours 1 minute
40 seconds apparent, or 3 hours 9 minutes 14 seconds mean time
in the afternoon: from which subtracting the difference of longi-
tude, 6 hours 1 minute 41 seconds, (Washington being west of
Berlin,) we have the corresponding time at Washington, March
20th, 9 hours 7 minutes 33 seconds, mean time, in the morning.
. The Sun's siderial time, is what the Sun's right ascension
would be, if the Earth moved uniformly in her orbit, and in the
plane of the celestial equator; it therefore is the Sun's actual
right ascension, diminished or increased by the equation of time.
It is of the greatest importance for the determination of the mean
time of the passage of the Moon, planets, or stars over the me-
ridian, by subtracting it from the right ascension of the Moon,
planet, or star, at the moment of the passage. If the latter be
the greater, the passage will be after; and if less, before that
of the Sun. For example, the star Aldebaran will be on the
meridian of Washington, August 28th, 1832, at 5 hours 59 mi-
nutes 38 seconds mean time, in the morning, its right ascension
at that moment being 4 hours 26 minutes 18 seconds; and the
siderial time 10 hours 26 minutes 40 seconds. -
48 IPOLES AND TROPICS.
CHAPTER XVI.
A DEGREE is the 360th part of a circle; and the
measure of an angle is an arc, or part of the circum-
ference of a circle, whose angular point is the centre;
and so many 360th parts as an arc contains, so many
degrees the measure of an angle is said to be : *
Thus, let A B (plate IX. fig. 3) represent the plane of the ecliptic,
and N C S the axis of the earth, Z C P will make an angle of 23#9, be-
cause the arc, Z P, contains 23; parts of 360, the whole circle; and as
A N contains the same number of degrees as Z P, its inclination must
be 23#9.
The Poles are the extremities of the earth's axis,
(plate IX, fig. 3;) N the north pole, S the south pole,
P the north pole star, to which, and to the opposite part
of the heavens, the axis always points. These extremi-
ties in the heavens appear motionless, while all the
other parts seem in a continual state of revolution.
The circle of motion in the heavenly bodies seems to
increase with the distance from the poles.
The Tropics are two small circles parallel to the equa-
tor, at 23% degrees distance from it; that to the north
is called the tropic of Cancer, and that to the south the
tropic of Capricorn.
The Polar circles circumscribe the poles of the
world, at the distance of 23% degrees. That on the
north is called the Arctic, and that on the south the
Antarctic circle. -
The distance of these polar circles from the poles being fixed at 23°
(the same as the tropics from the equator) is because it is the line of
boundary between light and darkness, when the sun is on either of the
tropics, and throws his beams over and beyond the pole.
page 49
Plate 6
AY(?/?/ſ/）, ±√AW）”/„Af

MERIDIANs, colurEs, &c. 49
The Meridians are so called because, as the earth
revolves on his axis, when any one of them is opposite
to the sun it is mid-day or noon along that line. Twen-
ty-four of these lines are usually drawn on the globes,
to correspond with the twenty-four hours of the day.
Not that these are the only ones that can be imagined,
for every place that lies ever so little east or west of
another place has a different meridian.
Suppose the upper 12 (plate IX. fig. 3) to be opposite the sun, it
will of course be noon along that line; and the next meridian marked 1,
being 150 east, will have passed the meridian 1 hour, consequently it
will there be one in the afternoon, and so on, according to the order of
the figures, to the lower 12, which being the part of the earth turned
directly from the sun, it will be midnight on that meridian: as you pro-
ceed round, the next meridian will be one in the morning, the next two.
and so on, till you arrive at the upper 12, where you set off Hence
there must be a continual succession of day and night.
Note. This difference of time between places, lying under different
meridians, is called longitude; or,
Longitude is an arc of the equator between the me-
ridian of any place and the first meridian. In English
geographers the first meridian passes through London
or Greenwich, and the distance is reckoned east or
west thence; fifteen degrees of longitude being equal
to one hour of time.
To all places eastward of the first meridian, the time
will be before London; if west, after London.
To reduce longitude to time divide by 15.
As the earth makes a complete revolution on its axis in 24 hours, it
must pass over 360° in that time: and if you divide 360 by 24, the quo-
tient, 15, will be the number of degrees passed over in an hour: hence
300 will be equal to two hours, 459 to three hours, &c.
Then if it be 12 o'clock at London, at Barbadoes, lying nearly 60°
west of London, it will be 4 hours earlier, or 8 o'clock in the morning.
At Petersburgh, 300 east, it will be 2 hours ºater, or 2 o'clock in th
50 LATITUDE, coluREs, &c.
afternoon; and at Calcutta, almost 900 east, nearly 6 hours later in the
afternoon.
To reduce time to longitude, multiply by 15.
A captain arriving at the Bermudas, finds the difference of time be-
tween them and London to be 4 hours and 20 minutes, which, multi-
plied by 15 (or by 3 and 5) will give 659.
Latitude is the distance of any place from the equa-
tor, either north or south, or it is equal to the elevation
of the pole above the horizon. The latitude of the
heavenly bodies is reckoned from the ecliptic, and ter-
minates in the arctic and antarctic circles, and their
longitude begins at the point Aries.
The Colures are two meridians, which pass through
the poles of the world; one of them through the points
of Aries and Libra, and therefore called the Equinoc-
tial Colure; the other through the solstitial points,
Cancer and Capricorn, and therefore called the Solsti
tial Colure.
The Zones are five; namely, one torrid, two temperate,
and two frigid.—The torrid is all that space between the
tropics, and so called from its excessive heat; the tem-
perate zones extend from the tropics to the polar cir-
cles; the frigid zones are comprised between the polar
circles and the poles.
Solstitial points are the first points of Cancer and
Capricorn; so called because the sun, when he is near
either of them, seems to stand still, or to be at the
same height in the heavens at noon for several days
together.
Equinoctial points are the first points of Aries and
Libra; so called, because when the sun is near either
of them the days and nights are equal
PLANETs' or BITS ELLIPTICAL. 51
As it is presumed that the pupil will have previously gone through
a course of geography and the globes, the above short definitions may
be sufficient. though they could not be omitted altogether.
CHAPTER XVII.
PLANETS’ ORBITS ELLIPTICAL.
THE orbits or paths described by the revolution of
the planets round the sun, are not true circles, (as plate
VIII. fig. 3,) but somewhat elliptical, that is, longer
one way than another.
In a circle the periphery, or circumference, is equal-
ly distant from a point within, called its centre, A.; but
an ellipsis has two points called the focuses, or foci, as
BC. In one of these, called its lower focus, is the sun.
Hence, in every revolution of the planet it must be
nearer the sun in one part of its orbit than it is at an-
other. -
Let S (plate VIII, fig. 5,) represent the sun, A B CD
a planet in different parts of its orbit; when it is nearest
the sun, as at A, it is said to be in its perihelion; when
at B its aphelion; but when at C or D, its middle or
mean distance; because the distance S C or S D is the
middle between A S, the least, and B S the greatest;
and half the distance between the two focuses is called
the eccentricity of its orbits, as SE or E F.
ATTRACTION OF GRAVITATION,
By attraction is meant that property, in bodies by
which they have a tendency to approach each other.
52 ATTRACTION OF GRAVITATION,
Thus the magnet attracts the needle; this is called attraction of mag
netism : and thus the feather suspended near the electrical conductor
is attracted by it; this is termed attraction of electricity. And that pro-
perty which connects or firmly unites the different particles of matter,
of which the body is composed (as that of a stone,) is attraction of cohe.
sion.
Attraction of Gravitation is a power by which bo-
dies in general tend toward each other; and the at-
traction is in proportion to the quantity of matter which
they contain; but the earth, being so immensely large
in comparison of all other substances in its vicinity, de-
stroys the effect of this attaction between smaller bo-
dies by bringing them all to itself.
By attraction of gravitation, the sun, the largest body,
attracts the earth and all the other planets, and they
again gravitate or have a tendency to approach the Sun
The earth being larger than the moon, attracts her, and
she gravitates towards the earth.
Upon this. principle, a stone, when thrown from earth, is brought
by the earth's attraction and its own gravitating power to the earth
again.
The waters in the ocean, and indeed all the terrestrial bodies, gra-
vitate towards the centre of the earth; and it is by this power that we
stand on all parts of the earth, with our feet pointing to the centre. In
short, it is by the attraction of gravity that a marble falls from the hand,
a brick from the top of a building, or an apple from the tree. All bo-
dies, by the power of gravity, have a tendency or disposition towards
the earth.
One law of attraction is, “That attraction decreases
as the squares of the distances from that centre in-
crease.”
Any number multiplied into itself is a square number; thus, the
square of 2 is 4, the square of 3 is 9, of 4 is 16, &c.
Suppose a planet at B (plate X, fig. 4) to be twice
ATTRACTION OF GRAVITATION, 53
as far from the sun as at A ; then, as the square of the
distance 2 is 4, the attraction at B will be four times
less than at A, or, which is the same thing, A will be
attracted with four times the force it would be at B.
Again, if the distance at A (fig. 5,) were four times
less than at B, then, as the square of 4 is 16, the at-
traction at A would be sixteen times greater than at B.
The second law of gravity is, “That bodies attract
one another with forces proportional to the quantities
of matter they contain.” All bodies of equal magnitude
contain not equal quantities of matter, for a ball of cork
of equal bulk with one of lead, being more porous, does
not contain so much matter.
So the sun, though a million of times as big as the
earth, not being so compact and dense a body, contains
a quantity of matter only 200,000 times as great, and
hence attracts the earth with a force only 200,000
times more than the earth attracts him.
Hence suppose there are in a river two boats of
equal bulk at any distance, suppose twenty yards, from
each other, and that a man in one boat pulls a rope
which is fastened to the other, the boats will meet in
a point which is half way between them. If one boat
were three times the bulk of the other, then the lighter
would move three times as far as the heavier, or fifteen
yards, while the heavier moved only five.
F
54 ATTRACTIVE AND PROJECTILE FORCES.
CHAPTER XVIII.
OF ATTRACTIVE AND PROJECTILE FORCES.
THE sun, being so immense a body, would, by the
power of attraction draw all the planets to him, if the
attractive power were not counteracted by another force.
It must therefore be observed that all simple motion is
naturally rectilineal, that is, all bodies, if there were
nothing to prevent them, would move in straight lines.
But the planets’ motiora are circular, which is a com-
pound of two forces, the one called the attractive or
centripetal force; the other the projectile or centrifugal
force.
Suppose a marble be shot from the hand along a smooth floor, if it
meet with no impediment it will move straight forward; this is termed
the projectile force, and its motion will be rectilineal. But if a ball be
thrown into the air, unless projected perpendicularly, it will not con-
tinue to move in a straight line, but incline towards and ſall to the
earth; for the resistance of the air, and the attraction of the earth retard
its progress: otherwise it would continue to move in a straight line,
with a velocity equal to that which was at first impressed upon it.
The joint action of the attractive or projectile forces
retains the planets in their orbits; the primaries round
the sun, and the secondaries round their primaries.
*When a stone is whirled round in a sling, its motion is circular. If
the stone flies out, it will go off in a straight line.
This straight line is what is called the tangent of a circle, as A a, B
b, &c. (Plate VIII, fig. 4;) for all bodies moving in a circle have a
natural tendency to fly off in that direction. Thus a body at A will
tend towards a, at B towards b, and so on, its rectilineal motion; but
the central force (the action of the hand) acting against it, preserves
its circular motion.
The moon and all the planets move by this law; and
...itrº-
ATTRACTIVE AND PROJECTILE FORCES, 55
the attractive or centripetal force of the sun being
equal to the projectile or centrifugal force of the plan-
ets, they are, by attraction, prevented from moving on in
a straight line, and, as it were, drawn towards the sun;
and by the projectile force from being overcome by at-
traction. They must therefore revolve in nearly circu-
lar orbits.
If, for instance, the projectile force were to cease acting upon the
earth, it must fall to the sum: on the contrary, if the force of gravity
were to cease upon the earth, it would fly off into infinite space.
The secondary planets are governed by the same
laws in revolving round their respective primaries; for
as by the attractive power of the sun, combined with
the projectile force of the primary planets, they are
retained in their orbits; so also the action of the pri-
maries upon their respective secondaries, together with
their projectile force, preserves them in their orbits.
If the attractive power of the sun were uniformly the
same in every part of their orbits, they would be true
circles, and the planets would pass over equal portions
in equal times; but the attractive power of the sun is
not uniformly the same; hence the orbits of the planets
are not true circles, but a ſittle elliptical, and they
must pass over unequal parts of their orbits in equal
portions of time.
By passing over equal portions in equal times may be understood pas
sing from B to C, or from C to A, in the same time as from A to D, of
from D to B-(Plate VIII. fig. 5.)
By unequal portions in equal times, the centrifugal force would carry
a planet from A to a, in the same time as it would from B to b. And
In 1ts orbit from A to c, as soon as from B to d.
A double velocity will balance a quadruple or fourfold
power of gravity or attraction.—Hence, as the centri
56 ATTRACTIVE AND PROJECTILE FORCES.
petal force is four times as great at A as at B, the cen-
trifugal force is twice as great; and would describe the
area or space contained between the letters A S c, in
the same time as the area or space BS d. For accord-
ing to the laws of the planetary motions, in their re.
volutions they always describe equal areas in equal
times.
By equal areas is meant, that if the earth moves from A to c in the
same time as from B to d, then the area of A S c will be equal to the
area of BS d.
The orbits of the comets being very elliptical, the
irregularity of their motions must be exceedingly great.
When near the sun, or in their perihelion, the cen-
tripetal force must act powerfully on the comet, and
that force must be equalled by the projectile force;
hence they will then move with amazing celerity; but
when arrived at their aphelion, where the influence of
the sun is weak, their motion is exceedingly slow, and
the sun must appear little more than a fixed star.
If a body at rest receives two impulses at the same time, from forces in
different directions, it will be made to move in a line that lies between
the direction of the forces impressed. If on the ball A (Plate IX. fig.
1,) a force be impressed sufficient to make it move with a uniform ve-
locity to the point B, in a second of time; and if another force be also
impressed on the ball which would make it move to C, in the same
time, the ball by means of the two forces acting together, will describe
the line A a D.
In the beginning the Grand Mover impressed such a degree of mo-
tion upon these bodies as, if not controlled, would have whirled them
onwards in straight lines to endless lengths, till they would have been
lost to imagination in the abyss of space; but the gravitating power
combined with the projectile. determines their courses to an elliptical
form, and obliges these bodies to perform their destined rounds.
f
page 57 - Plaze 9
A. Fig. I B
* . a.
C N D
=C-
S
w


ON THE CENTRE OF GRAVITY, 57
CHAPTER, XIX.
ON THE CENTRE OF GRAVITY.
THE Centre of Gravity is that point of the body, in
which its whole weight is, as it were, concentrated, and
upon which, if the body be freely suspended, it will
rest.
A weight of 1 cwt. at 10 feet from a prop, will balance another of
10 cwt. at 1 foot from it; or
Let two weights (Plate X. fig. 6) be nicely poised on
a centre, round which they may freely turn : the
heaviest, of 10 cwt., would move in a circle whose ra-
dius or distance from the centre would be one foot,
while the lightest, of 1 cwt., would move in a circle
whose radius would be 10 feet; the centre round which
they move is the centre of gravity.
And thus the sun and planets move round an ima-
ginary point as a centre, always preserving an equilib-
rium.
If the earth were the only attendant on the sun, as his quantity of
matter is 200,000 times as great as that of the earth, he would revolve
in a circle a 200,000th part of the earth's distance from him, in the
same time as the earth is making one revolution in its orbit, or one
year; but as the planets in their orbits must vary in their positions,
the centre of gravity cannot be always at the same distance from the
SUlll.
The quantity of matter in the sun so far exceeds that
of all the planets together, that even if they were all
on one side of him, he would never be more than his
own diameter distant from his centre of gravity; there-
fore the sun is considered as the centre of the system.
As the secondary planets are governed by the same
F 2
58 THE HORIZON.
laws as their primaries, they, also, with their primaries,
move round a centre of gravity. * *
Every system in the universe is supposed to revolve
in like manner, and all these together to move round
One common centre.
THE HORIZON.
The Horizon is that distant boundary of our sight
where the heavens and the earth seem to meet all
around us. •
There are two horizons, termed the rational and the
sensible. The rational horizon applies to the rising,
setting, &c. of the sun, moon and stars. This horizon
is supposed to encompass the globe exactly in the mid-
dle, or to be in a line with its centre H O, and to di-
vide the heavens into two equal parts, being 90° distant
from a point Z, over our heads, called the zenith,
and the opposite point N, in the heavens directly under
our feet called the nadir. (See Plate IV. fig. 2.)
The rational horizon is represented on the artificial globes by the
broad paper circle or wooden horizon.
The sensible horizon respects land and water, and
terrestrial objects. The extent of this horizon is great-
er or less, according as the spectator is more or less
elevated.
Leta B c, (Plate IV. fig. 2) represent the sensible horizon, and B the
‘olace of the spectator. Them an eye placed at 5 feet above the sur-
face of the sea, sees 23 miles each way; but if it be elevated twenty
feet, that is ſour times the height, it will see 5% miles, or twice the
distance. —º *
The difference of the two horizons is this: the sensible is seen from
the surface of the earth; the rational is supposed to be viewed from
its Centre. - - -
zºº.
DAY AND NIGHT, 59
Though the heavenly bodies can be viewed by the
spectator only from the sensible horizon (or surface of
the earth) as at B, yet they are really seen to rise and
set when they are on the rational horizon, HO. This
is owing to their vast distances from the earth, which
occasion the difference arising from the positions of
the surface or the centre to vanish.
The semi-diameter of the earth is not 4,000 miles; but 4,000 miles,
compared with 95,000,000, the distance of the sun from the earth, is so
little, that the difference of time is not discernible, not to mention the
greater distance of the fixed stars. Even the rising and setting of the
moon respects the rational horizon, whose distance is but 240,000 miles,
which bears a proportion to 4,000, as 60 to 1.
CHAPTER XX.
DAY AND NIGHT.
THE form of the earth, as has been already noticed,
approaches nearly to that of a true globe or sphere;
and the cause of the succession of day and night, is
the rotation of the earth upon its aris once in twenty-
four hours.
For the meaning of globe, or sphere, aris, &c. see Preliminary Defini-
tions, chap. 1.
A common observer may imagine that the sun, moon, and starry fir. .
mament revolve daily about the earth, while the earth remains at rest"
but their apparent motions are accounted for much more rationally.
Suppose A B C D (plate IV. fig. 2) to be the earth
revolving on its axis according to the order of the let-
ters, that is, from A to B, from B to C, &c. If the sun
be fixed in the heavens at Z, and a line, HO, be drawn
through the centre of the earth E, it will represent the
60 DAY AND NIGHT,
circle, which, when extended to the heavens, is called
the rational horizon.
The sun always illuminates one hemisphere of the
earth, while the other hemisphere remains in darkness.
Therefore if the sun be supposed at Z, it will illu-
minate by its rays all that part of the earth that is above
the horizon H. O. To the inhabitants at A, its western
boundary, it will appear just rising; to those situated
at B, it will be moon ; and to those in the eastern part
of the horizon C, it will be setting.
A spectator cannot from any spot behold more than
a semicircle of the heavens at any one time. If placed
at A, he will see the concave hemisphere ZO N ; and
on the boundary of his view will be N and Z; conse-
quently the sun at Z will be just coming into sight, or
rising.
Then by the rotation of the earth, he will in a few
hours come to B, when to him it will be noon ; and
those who live at B will have descended to C.
In this situation they will behold the hemisphere
N H Z, and the sun, Z, will to them be setting ; con-
sequently it will be night to them till they return to A,
when the sun will again appear to rise.
Therefore, however a spectator may imagine that the sun and
heavenly bodies are moving around him from east to west, this is only
apparent; just as a person passing swiftly in a carriage, or sailing
near the shore, sees the houses, trees, and other fixed objects moving
the contrary way; but he knows that this is merely a deception, and
that it is himself only that moves.
This daily motion of the earth round its axis accounts
equally for the apparent motions of the whole starry
firmament about the earth every twenty-four hours.
GN THE ATMOSPHERE. 61
By this motion the inhabitants of London are carried at the rate of
810 miles an hour, and those upon the equator about 1040.
The only points in the heavens that keep their posi-
tions, are the two celestial poles, which are opposite to
the poles of the earth.
The stars above our horizon are as numerous by day
as by night; but they cannot be discerned, because
the sun’s rays are so powerful as to render those coming
from the fixed stars invisible.
Though our year consists of 365 days, the earth
makes 366 revolutions on its axis, whilst it is going
once round the sun.
Though the earth makes a complete revolution daily
on its axis, yet we are not at all sensible of its motion.
If its motion were irregular, it would no doubt be per-
ceptible; but as it meets with no obstruction, the
motion must be so uniform as not to be perceived.
That the earth may have such a motion, and we not be in the least
sensible of it, is evident; for even the motion of a ship on smooth water
is not sensibly perceived by those on board.
CHAPTER XXI.
OF THE ATMOSPHERE.
THE Atmosphere is a thin, transparent, and fluid
body, surrounding this terraqueous globe, and covering
it to a considerable height. It possesses permanent
elasticity and gravity, and is most dense or heavy near
the earth, but becomes gradually rarer or lighter, the
higher we ascend; so much so that at the tops of some
high mountains it is difficult to breathe.
62 OF THE ATMOSPEIERE,
The whole mass of the atmosphere contains a heterogeneous col-
lection of particles, exhaled from all solid or fluid bodies on the surface
of the earth.
It serves not only to suspend the clouds, furnish us
with wind and rain, and answer the common purposes
of breathing, but is also the cause of the morning and
evening twilight, and of all the glory and brightness of
the firmament.
Experiments upon the air-pump prove, that without the air or atmo-
sphere no animal could exist; without its aid all vegetation would
cease. Sound could not be produced without it, nor would there be
any rains or dews to moisten the ground.
Without an atmosphere, only that part of the sky
would appear light in which the sun was placed ; and
if a person should turn his back, the heavens would
appear dark as night, and the least stars would be seen
to shine. But the atmosphere being strongly illuminated
by the sun, reflects the light back upon us, and causes
the whole heavens to shine with such splendour as to
render the light of the stars invisible.
The height to which the atmosphere extends has not
been exactly ascertained; but at a greater height than
45 miles it will not refract the rays of light from the sun.
The sun’s rays falling upon the higher parts of it be-
fore rising, causes by reflection a faint light, which in-
creases till he appears above the horizon; and in the
evening decreases after he sets, till he is eighteen de-
grees below the horizon, where the morning twilight
begins, and the evening twilight ends.
The beginning and end of twilight is also said to be when the least
stars, viz. those of the 6th magnitude begin to appear and disappear.
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REFRACTION. 63
CHAPTER XXII.
REFRACTION.
THE rays of light, in passing out of one medium into
another of a different density, deviate from a rectilineal
course ; and if the density of this latter medium con-
tinually increase, the rays of light, in passing through
it, will deviate more and more from a right line towards
a curve, in passing to the eye of an observer.
From this cause all the heavenly bodies, but the moon,
except when in the zenith, appear higher than they
really are. This apparent elevation of the heavenly
bodies above their true altitude, is caused by Refrac-
tion.
Let A B C (plate XI. fig. 1.) represent the surrounding atmosphere,
a the true place of a star, b the apparent place. Let a ray fall from a
on the surface of the atmosphere at A, and it will be refracted in the
direction of the curve A D, because the density of the atmosphere in-
creases as it approaches the earth's surface. Hence an observer at Yº
will see the object at b.
It is in consequence of the refraction of the atmo-
sphere, that all heavenly bodies, eaccept the moon, are
seen for a short time before they rise in the horizon,
and also after they have sunk below it.
At some periods of the year the sun appears three
minutes longer, morning and evening, than he would
do were there norefraction; and about two minutes every
day at a mean rate. Hence, when the sun is at T below
the horizon, a ray of light T I, proceeding from him.
comes straight to I, where falling on the atmosphere,
it is turned out of its direct, or rectilineal course, and
is so bent down to the eye of the observer at I), the
64 PARALLAX,
the sun appears in the direction of the refracted ray
above the horizon at S.
The effects of refraction may be seen thus: immerse a staffin a tub
of water; if it be placed perpendicularly there will be no refraction;
that is, it will not seem bent at all:—incline it a little towards the edge
of the tub, and it will appear a little bent at the surface of the water;
incline it still more, and the refraction will be greater.
Refraction is also shown in that well known experiment of putting
any small object, as a shilling, &c., at the bottom of a basin or tub, then
walking backward till the object is just lost sight of, and there stand-
ung while another person pours water into the basin, and the money
will appear Now if the edge of the basin be called the horizon, the
water the atmosphere, and the shilling the moon, it is clear that it will
be seen above the horizon when really below it.
CHAPTER, XXIII.
PARALLAX.
THE Parallaa of the sun and moon is the difference
between the altitude of either object observed at the
same instant of time by two spectators; one on the sur-
face of the earth, and the other placed at the earth's
centre.
The place of an object as observed from the earth's surface is called
its apparent place; and as observed from the centre, its true place.
The parallax of the heavenly bodies is greatest when
in the horizon; hence called the horizontal parallaa.
The sun's mean parallax being only 86, is seldom made use of in
nautical calculations, except to determine the longitude, by means of
observing the angular distance between the sun and moon.
The fixed stars, on account of their vast distance from the earth.
have no parallax.
As the parallax of the sun or moon or planets de
presses, or causes them to appear lower than they really
* *
EQUATION OF TIME, 65
are, the difference must be added to their apparent al-
titudes, to obtain their true altitudes.
Let C (fig. 2, plate XI.) represent the centre of the
earth; F D E, part of the moon's orbit; G d e, part of
a planet's orbit; Z K, part of the starry heavens: now,
to a spectator at A, upon the surface of the earth, let
the moon appear at E, in the horizon of A, and it will
be referred to K; but if viewed from the centre C, it
will be referred to I: the difference between these
places, or the arc I K, is called the parallaa, in alti-
tude; and the angle A E C, is the parallactic angle.
The parallax will be greater or less, as the objects
are more or less distant from the earth; thus the paral-
lax I K, of E, is greater than the parallax f K, of e.
Also, with respect to any one object, when it is in
the horizon, the parallax is the greatest, and diminishes
as the body rises to the zenith, where the parallax is
nothing. Thus, the horizontal parallax of E and e, is
greater than that of D and d, but the objects F and G,
as seen from either A or C, appear in the same place
Z, or in the zenith.
CHAPTER XXIV.
EQUATION OF TIME.
OUR summer half year is longer than the winter
half year, by about eight days; occasioned by the
inequality of the earth's annual motion. This in-
equality and the obliquity of the ecliptic are the
causes of the difference of time between the sun and
a well regulated clock, The clock keeps equal time,
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66 EQUATION OF TIME.
while the sun is constantly varying, and shows only ap
parent time. The difference of these is called the
equation of time.
Equal time is measured by a clock that is supposed to measure ex-
actly 24 hours from noon to noon. And apparent time is measured by
the apparent motion of the sun in the heavens, or by a good sun-dial.
This difference between equal and apparent time de-
pends, first, upon the inclination of the earth's axis to
the plane of its orbit; and secondly, upon the elliptic
or oval form of the earth's orbit; for the earth's orbit
being an ellipse, its motion (as has been already shown)
is quicker in its perihelion than in its aphelion.
The rotation of the earth upon its axis is the most
equable motion in nature, and is completed in 23 hours,
56 minutes, and 4 seconds. This space is called a
sidereal day, because any meridian on the earth will
revolve from a fixed star to that star again in this time.
Hence, if the earth had only a diurnal motion, the day would be
nearly four minutes shorter than it is.
But a solar, or natural day, which our clocks are in-
tended to measure, is the time which any meridian on
the earth will take in revolving from the sun to the sun
again, which is about 24 hours, sometimes a little more,
sometimes less. This is occasioned by the earth's ad-
vancing nearly a degree in its orbit, in the same time
that it turns eastward on its axis; and hence the earth
must make more than a complete rotation before it can
come into the same position with the sun, that it had
the day before.
Some idea of this may be formed by the hands of a clock; suppose
both of them to set off together at twelve o'clock, the minute hand
EQUATION OF TIME. 67
must travel more than a whole circle before it will overtake the hour
hand; that is, before they will be in the same relative position
Again, it must be observed that only four times a year
the degrees on the ecliptic and the equation are equal; in
other words, but four times a year is the sun's longitude
and right ascension the same in degrees ; and that is
when he passes through the equator and the tropics,
and then the sun and clocks go together, as far as re-
gards this cause; but at other times they differ, because
equal portions at the ecliptic pass over the meridian in
unequal parts of time, on account of its obliquity.
To those who are acquainted with the globes this will appear evi-
lent by inspection. First, find the sun's longitude on the eclip-
tic, then his right ascension on the equator, and it will be seen that
the number of degrees will be nowhere equal, except at the first point
of Aries, Cancer, Libra and Capricorn. Or, it may be illustrated by the
globe, thus: (plate IX, fig. 2.) Let Y? and -- represent the equator.
‘Y”, Qö, -o- the northern half of the ecliptic, and QP, V5, -o, the southern
half. Make chalk or other marks, as at a b c de fgh, all round the
equator and ecliptic at equal distances (suppose at 20 or 30 degrees from
each other,) beginning at Aries; now, by turning the globe on its axis,
it will be seen that all the marks in the ecliptic, from Aries to Cancer,
come sooner to the brazen meridian than their corresponding marks on
the equator: those from the 1st of Cancer to Libra, come later;-those
from Libra to Capricorn sooner, and those from Capricorn to Aries later.
Note: Time, as measured by the sun-dial is represented by the
marks on the ecliptic; that measured by a good clock, by those on the
equator.
Hence it may be supposed, that while the sun is in
the first and third quarters (plate IX. fig. 2,) that is,
between ºp and gö, and - and V5, it will be faster than
the clocks, and while in the other two quarters it will
be slower; because equal portions of the ecliptic come
sooner to the meridian in the 1st and 3d, and later in
the 2d and 4th; but on account of the elliptic form o
68 EQUATION OF TIME.
the earth’s orbit, this will not be always exactly the
CàSee
If the difference between time measured by the dial and clock, de-
pend solely on the inclination of the earth's axis to the plane of its orbit,
the clocks and dials ought to be together both at the equinoxes and the
solstices (that is, on the 20th March, 21st June, 23d September, and 21st
December;) but owing to the elliptic form of the earth's orbit, they co-
incide on other days not far distant.
An Ephemeris will show this: on the 20th March, and 23d of Sep-
tember, instead of the clocks and dials agreeing, there will be a varia-
tion of 6 or 8 minutes: and their times of coinciding will happen seve-
ral days later in the vernal, and earlier in the autumnal equinox.
If the earth’s motion in its orbit were uniform, which
it would be if the orbit were circular, then the whole
difference between equal time by the clock, and appa-
rent time by the sun, would arise from the inclination
of the earth’s axis. But this is not the case; for the
earth travels when nearest the sun, that is in the winter,
more than a degree in 24 hours;–and when farthest
from the sun, that is in summer, less than a degree in
the same time.
From this cause the natural day would be of the
greatest length when the earth was nearest the sun, for
it must continue turning the longest time after an en
tire rotation, in order to bring the meridian of any place
to the sun again; and the shortest day would be when
the earth moves the slowest in her orbit.
The above inequalities, combined with those arising
from the inclination of the earth's axis, make up that
difference which is shown by the equation table in one
of the outside columns of an Ephemeris.
*
THE SEASONS. 69
CHAPTER XXV,
THE SEASONS.
THE aſcis of the earth is not upright or perpen-
dicular to the plane of the ecliptic, but inclines to
it 23# degrees, as Z C P, making an angle with it of
664 degrees, P C B, (plate IX. fig. 3.) The axis of
the earth, in its annual orbit, always keeps parallel to
itself.
See plate XII, fig. 2, where the earth is represented in four different
parts of its orbit, still preserving its parallelism; see also plate XIII.
fig. 1.
Although the earth's orbit is 190,000,000 of miles in
diameter, yet the axis of the earth always points to the
same part of the heavens; because compared with the
distance of the fixed stars, 190,000,000 of miles is but
a mere point.
As some illustration of this: suppose two parallel lines are drawn
upon an elevation, three or four yards from each other. If we look
along them they will both seem to point directly to the moon in the ho-
rizon, and perhaps three or four yards will bear as great a proportion
to the moon's distance, as 190,000,000 of miles to the fixed stars.
What a striking proof of the inconceivable distance of the fixed stars,
when, notwithstanding the earth in the course of the year continues
to move from one part of its orbit to the other, yet the north pole ap-
pears at all times to point in exactly the same direction towards the po-
lar star!
It is known that the earth has an annual course round
the sun, because the sun, if seen to be in a line with a
fixed star, any day or hour, will in a few weeks, by the
motion of the earth, be found considerably to the east
of such star, and he may be thus traced round the hea-
vens to the same fixed star from which he set out.
G 2
70 THE SEASON Se
These observations may be made in the day-time, because through
the shaft of a very deep mine the stars are visible by day as well as by
night. They are also rendered visible in the day by telescopes pro-
perly fitted up for the purpose.
The variety of the seasons depends upon the length
of the days and nights, and upon the position of the
earth with respect to the sun.
If the axis of the earth N S (plate X, fig. 1) were
perpendicular to a line E Q, drawn through the cen-
tres of the sun and earth, there would happen equal
day and night throughout the year; for as the sun al-
ways enlightens one half, every part must be half its
time in the light, and the other half in darkness.
'The two poles must be excepted, because to a person there situated,
the sun would never appear to rise or set, but would always be mov-
ing round the horizon.
If the earth were thus situated, the rays would fall at
all times vertically on the equator: and the heat excit-
ed by the sun being greater or less, in proportion as the
rays fall more or less perpendicularly, the parts about
the equator would be heated to a high degree, while
the regions around the poles would be desolated by
perpetual winter.
The proportion of heat materially depends on the degree of perpen
dicularity of the sun's rays. Let plate X, fig. 3, represent summer and
winter rays in the latitude of London. It is evident that the summer
rays strike more directly, and with greater force, as well as in greater
numbers, on the same place.
The axis of the earth being inclined 2339 as in plate
X. fig. 2, represents the position of the earth in our
summer season, when all the parallel circles, except
the equator, are divided into two unequal parts; and
the length of their days and nights in each latitude will
THE SEASONS. 71
bear a proportion to the greater or less portion of their
circumference in the enlightened and dark hemisphere.
I*, for instance, a b represent that circle of latitude in which London
s situated, it is evident that about two-thirds of it is in the light, and
only one-third in darkness; hence, the sun will be two-thirds or 16
hours above the horizon, and 8 hours below it.
The parallel above a b is entirely in the light, and from thence to
the pole there is continual day for some time; and at the pole the sun
shines for six months together.
During that time the south pole is involved in darkness.
To those who live in equal latitudes, the one north,
the other south, the length of the days to one will be
always equal to the length of the nights to the other.
All parts of the globe enjoy the presence of the sun
for the same length of time, in the course of the year.
CHAPTER XXVI.
THE SEASONS, CONTINUED.
THE figure plate XII. fig. 2, represents the earth
in four different parts of its orbit, or as situated with
respect to the sun in the months of March, June, Sep-
tember, and December. The earth appearing nearer
the sun in winter than in summer.
We are more than 3,000,000 of miles nearer to the sun in December
than we are in June; and as the apparent diameter of any object in
creases in proportion as our distance from it is diminished, so the sun's
apparent diameter is greater in our winter than in summer. In winter
"t is 32' 36", in summer but 31' 31".
It is ascertained that our summer (that is, the time
that passes between the vernal and autumnal equinoxes)
is nearly eight days longer than our winter, or the time
72 THE SEASONS,
between the autumnal and vernal equinoxes; conse-
quently the motion of the earth is slower in summer
than in winter, and therefore it must be a greater dis-
tance from the sun.
The coldness of our northern winters (though nearer to the sun,)
compared with our summers, arises from the rays falling upon us so
very obliquely, as was before noticed ; and also from the length of the
summer days and shortness of the nights; for the earth and air become
heated by day, more than they can cool by night.
Both the hottestand coldest seasons of the year are not in the long-
est and shortest days, but a month after those times; for a body once
heated does not grow cold instantaneously, but gradually, and vice
versa. And as long as more heat comes from the sun in the day than
is lost in the night, the heat will increase.
In June the north pole of the earth inclines to the
sun (plate XII. fig. 2,) and consequently brings all the
northern parts of the globe into the light; then to the
people of those parts it is summer. But in December,
when the earth is in the opposite part of its orbit, the
north pole declines from the sun, and the south pole
comes into light. It is then winter to us, and summer
to the inhabitants of the southern hemisphere.
In March and September the axis of the earth neither
inclines to, nor declines from the sun (plate XII, fig.
2,) but is perpendicular to a line drawn from its cen-
tre.
It is then equal day and equal night at all places,
except at the poles, which are in the boundary of light
and darkness, and the sun being directly vertical to,
or over the equator, makes equal day and night at all
places.
In March the real place of the earth is Libra, consequently the sun
will appear in the opposite sign, in Aries, and be vertical to the equator
As the earth proceeds from March to June, its northern hemisphere
THE MOON's MonTHs, PHASEs, ETC. 73
comes into light, and on the 21st of that month, the sun is vertical to
the tropic of Cancer.
In September the sun is again vertical to the equator, and of course
the days and nights are again equal.
Following the earth in its journey to December, or when it has ar-
rived at Cancer, the sun appears in Capricorn, and is vertical to the
tropic of Capricorn. Now the southern pole is enlightened, and all the
circles on that hemisphere have their larger parts in light. Of course
At is summer to the southern, and winter to the northern hemisphere.
For the increase and decrease of days and nights
we are indebted to the inclination of the earth's axis,
and its preserving its parallelism. Hence from the
20th of March to the 21st of June the sun is vertical
successively to all places between the equator and the
tropic of Cancer, and consequently the days must grad-
ually lengthen. From June to September the sun is
again successively vertical to the same parts of the
earth, but in a reverse order.
From September to December the sun is sucessively vertical to all
places between the equator and the tropic of Capricorn, which causes
the days to lengthen in the southern hemisphere.
CHAPTER XXVII.
THE MOON'S MONTHS, PHASES, ETC.
THE time which the moon takes in performing her
journey round the earth, is called a month, of which
there are two kinds; a periodical month of 27 days, 7
hours, 43 minutes, and a synodical month of 29 days,
12 hours, 44 minutes, nearly.
This difference arises from the earth’s annual motion
in its orbit.
74 PHASES OF THE MOON,
Suppose (plate XII, fig. 1.) S the sun; T the earth, in a part of its
Orbit QTL. Let E be the position of the moon. If the earth had no
motion, the moon would move round its orbit, EFG, &c. into the po-
sition of E again in 27 days, 7 hours, 43 minutes; but while the moon
is describing her journey, the earth is passing through nearly a twelfth
part of its orbit. This the moon must also describe, before the two
bodies can come again into the same position that they before held
with respect to the sun; and this takes up so much more time as to
make her synodical month equal to 29 days, 12 hours, and 44 minutes.
This is the cause of the division of time into months.
N. B. The moon's orbit is elliptical.
THE PHASES OF THE MOON,
The sun always enlightens one half of the moon;
and though sometimes its whole enlightened hemis-
phere is seen by us, yet sometimes only a part, and at
other times none at all, is discernible, according to her
different positions in the orbit, with respect to the
earth.
Suppose (plate XII, fig. 1) A B C D E, &c. to represent the moon
in different parts of her orbitround the earth, in which one half is con-
stantly seen to be enlightened, as would appear if seen from the sun;
then will the enlightened parts of the outside figures represent the ap-
pearance of the moon as seen from the earth.
When the moon is at E, no part of its enlightened
side is visible to the earth. It is then new moon or
change. And the moon being in a line between the
sun and the earth, they are said to be in conjunction.
The outside figure opposite E is wholly dark, to show that the moon
is invisible at change.
The whole illuminated hemisphere at A is turned to
the earth, and this is called full moon, and the earth
being between the sun and moon, they are said to be in
opposition.
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ECLIPSES, 75
When at F, a small part only will be seen from the
earth, and that will appear horned; at G, one-half of
the enlightened hemisphere is visible; it is then said
to be in quadrature.
At H, three-fourths of the enlightened part are visi-
ble, and it is then said to be gibbous; and at A, the
whole enlightened face is said to be full, and so of the
rest.
The horns of the moon just after change, or conjunction, are turned
to the east; after full moon, or opposition, they are turned to the west.
The various phases of the moon are often represented by a small
globe or ivory ball suspended by a string. Let your eye represent the
earth, and the candle the sun; then moving it round you, the full and
the change will appear, and the different degrees of illumination in her
orbit as seen from the earth. This will also illustrate the manner in
which the moon, by keeping the same face always towards the earth,
makes one complete revolution on her axis while she makes one inher
orbit.
The moon’s apparent motion is that of rising in the
east and setting in the west, but this is owing to the
revolution of the earth upon its axis. The moon’s real
motion round the earth is from west by south to east.
Her real motion may be known by remarking, when she is near any
particular star, she will approach it from west to east, then be in con
junction with it, and then pass eastward of it.
CHAPTER XXVIII.
ECLIPSES.
THE term Eclipse implies a privation of light, and
in Astronomy the obscuration of the luminaries of
heaven Eclipses are either of the sun or moon.
.76 ECLIPSE. OF THE Moon.
ECLIPSE of THE Moon.
An Eclipse of the Moon is occasioned by the inter.
position of the earth between the sun and moon, and
consequently it must happen when the moon is in op-
position to the sun, that is, at the full moon, as plate
XIV. fig. 1.
If the plane of the moon’s orbit coincided with the
plane of the ecliptic, there would be an eclipse at every
opposition and conjunction; but as that is not the case,
there can be no eclipse at opposition or conjunction,
unless at that time the moon be at or near the node.
The orbit of the moon does not coincide; for one-half is elevated
more than 5 degrees and one-third above that of the earth; and the
other half is as much below it. Hence she mostly passes either above
or below the shadow of the earth.
The greatest distance from the node at which an
eclipse of the moon can happen is 12 degrees. When
she is within that distance, there will be a partial or
total eclipse, according as a part or the whole disc or
face of the moon falls within the earth's shadow. If
the eclipse happen exactly when the moon is full in
the node, it is called a central or total eclipse.
The duration of the eclipse lasts all the time the
moon is passing through the earth's shadow; and the
shadow being considerably wider than the moon's di-
ameter, an eclipse of the moon sometimes lasts three
or four hours. -
The shadow is also of a conical shape, and as the
moon's orbit is an ellipse, and not a circle, the moon
will at different times be eclipsed when she is at differ
ent distances from the earth.
ECLIPses of THE sun. 77
And accordingly as the moon is farther from, or nearer to the earth,
the eclipse will be of a greater or less duration; on account of the
slower motion of the moon, when more distant from the earth.
An eclipse of the moon always begins on the moon's
left side, and goes off on her right side.
This may be conceived by pre-supposing that the earth casts a
shadow far beyond the moon's orbit; and as the moon's course is from
west to east, her eastern edge must necessarily first enter that shadow.
By knowing exactly at what distance the moon is
from the earth, and of course the width of the earth's
shadow at that distance, it is that all eclipses are calcu-
lated with accuracy for many years before they happen.
It is found also, that in all eclipses the shadow of the earth is conical,
which is a demonstration that the body which casts it is of a spherical
form, for no other sort of figure would, in all positions, cast a conical
shadow. This is mentioned as another proof that the earth is a spheri-
cal body. The conical form of the shadow proves also that the sun
must be a larger body than the earth; for if two bodies were equal to
one another (as plate XIV. fig. 3) the shadow would be cylindrical;
and if the earth were the larger body (as fig. 14) its shadow would be
of the figure of a cone which had lost its vertex. .
ECLIPSE OF THE SUN.
An Eclipse of the Sun happens when the moon, pass
ing between the sun and the earth (plate XIV. fig. 2,
intercepts the sun's light from coming to the earth,
which can happen only at the change, or, when the moon
is in conjunction. -
This may be illustrated by suspending a small globe, or ivory ball,
in a right line between the eye and the candle.
The ball intercepting the light of the candle, represents an eclipse
of the sun; for as light passes in a right line, the sun is hidden from
that part of the earth which is under the moon, and therefore he must
be eclipsed.
If the whole of the sun be obscured by the body of
H
78 ECLIPSE OF THE SUN.
the moon, the eclipse is total: if only a part be dark-
ened, it is a partial eclipse; and so many twelfth
parts of the sun's diameter, as the moon covers, so
many digits are said to be eclipsed.
The word digit means a twelfth part of the diameter of either the
sun or the moon.
It is only when the moon is in perigee and very
near one of the nodes, that she can cover the whole disc
of the sun, and produce a total eclipse ; and no eclipse
of the sun can happen but when she is within 17 de-
grees of either of her nodes. At all other new moons
she passes either above or below the sun, as seen from
the earth; and at all other full moons above or below
the earth's shadow.
An eclipse of the moon, if central, must be total;
but an eclipse of the sun may be central and not total.
Hence there are what are termed annular eclipses, when
a ring of light appears round the edge of the mòon
during an eclipse of the sun. It has its name from the
Latin word annulus, “a ring.” This kind of eclipse is
occasioned by the moon being at her greatest distance
from the earth at the time of an eclipse; because in
that situation, those who are under the point of the
dark shadow will see the edge of the sun, like a fine
luminous ring, all around the dark body of the moon.
It is only when the moon is nearest the earth at an
eclipse of the sun, that the eclipse can be total : a total
eclipse is, therefore, a very curious and uncommon
spectacle. Total darkness cannot last more than six
or seven minutes.
There must be two solar eclipses in a year, and there
may be but two. But there may not be one lunar eclipse
THE HARVEST MOON, 87
}
and then, if the difference of the latitudes of the moon
and the star exceed 1° 20', there cannot be any occult
ation ; but if this difference be less than 51", there
must be an eclipse of the star on some part of the
earth : between these limits the occultation may or
may not take place.
In very different places of the earth, a great difference will result
from the change in the moon's parallax, and this difference may be even
so great as altogether to prevent the obscuration from taking placa
CHAPTER XXXII.
THE HARVEST MOON.
Owing to the daily progress the Moon is making in
her orbit from west to east, she rises about 50 minutes
later every day, when near the equator, than on the
day preceding. But in places of considerable latitude
there is a remarkable difference, especially about the
time of harvest, when at the season of full moon she
rises to us for several nights together only from 17 to
25 minutes later on the one day than on that immedi-
ately preceding.
To those who live in the latitude of London, when the moon is in
the 10th of Pisces, she rises 25 minutes later than on the day pre-
ceding; the 23d of Pisces, 20 minutes later; the 7th of Aries, 17 minutes
later; the 20th, 17 minutes; the 3d of Taurus, 20 minutes; and the
16th, 24 minutes later.
To persons who live at considerable distances from
the equator, the autumnal full moon rises very soon af-
ter sun-set for several nights together; and by thus
succeeding the sun before the twilight is ended, the
moon prolongs the light, to the great benefit of those
88 THE HARVEST MOON,
that are engaged in gathering in the fruits of the earth.
Hence the full moon at this season is called the Har-
pest Moon.
It is believed that this was observed by persons engaged in agricul
ture at a much earlier period than that in which it was noticed by as
tronomers. The former ascribed it to the goodness of the Deity, not
doubting but that he had so ordered it for their advantage.
About the equator, where there is no such variety
of seasons, and where the weather changes but seldom,
and at stated times, moonlight is not wanted for gather-
ing the fruits of the earth, and there the moon rises
throughout the year at nearly the equal intervals of 50
minutes, as before observed.
At the polar circles, the autumnal full moon rises at
sun-set, from the first to the third quarter; and at the
poles, where the sun is for half a year absent, the win-
ter full moons shine constantly without setting, from
the first to the third quarter.
The moon's path may be considered as nearly coin
ciding with the ecliptic; and all these phenomena are
owing to the different angles made by the horizon and
different parts of the moon’s orbit, or in other words,
by the moon's orbit lying sometimes more oblique to
the horizon than at others. In the latitude of London,
as much of the ecliptic rises about Pisces and Aries in
two hours as the moon goes through in six days; there-
fore while the moon is in these signs, she differs but
two hours in rising for six days together, that is, one
day with another, about 20 minutes later every day than
on the preceding.
* These parts or signs of the ecliptic which rise with
the smallest angles, set with the greatest, and vice versa-
THE HARVEST MOON. 8ſ.
And whenever this angle is least, a greater portion of
the ecliptic rises in equal times than when the angle is
larger. This may be seen by elevating the pole of
the globe to any considerable latitude, and then turning
it round on its axis. |
Consequently when the moon is in those signs which rise or set with
the smallest angles, she rises or sets with the least difference of time;
and on the contrary, with the greatest difference in those signs which
rise or set with the greatest angles,
Let plate XV, fig. 2, represent the globe, the north pole being ele-
wated to about 5139, with Cancer on the meridian, and Libra rising in
the east. In this position the ecliptic has a high elevation, making an
angle with the horizon of 629.
But let the globe be turned half round on its axis till Capricorn
comes to the meridian, and Aries rises in the east, then the ecliptic
will have the low elevation, above the horizon (fig. 2) making an angle
of only 150 with it. This angle is 470 less than the former angle, equa
to the distance between the tropics.
In northern latitudes, the smallest angle made by the
ecliptic and horizon is when Aries rises, at which
time Libra sets; the greatest when Libra rises, at which
time Aries sets. The ecliptic rises fastest about Aries,
and slowest about Libra. Though Pisces and Aries
make an angle of only about 15° with the horizon when
they rise, to those who live in the latitude of London
they make an angle of 62° with it when they set. The
Moon, quitting Pisces and Aries, arrives in about four-
teen days at the opposite signs, Virgo and Libra, and
then she differs almost four times as much in rising;
being one hour and about fifteen minutes later every
day or night than on the preceding.
Those who are acquainted with the globes will easily demonstrate
this problem by putting small patches on the ecliptic, at distances from
each other equal to the moon's daily course; which (deducting for the
sun's advance) is little more than 129. Then (after rectifying the globe
I
90 THE HARVEST MOON,
for the latitude, and setting the hour-index to 12) by turning the globe
round, and observing the time of the appearing and disappearing of the
patches, the variation in the time of the moon's rising or setting will be
shown on the hour circle.
As the moon can never be full but when she is op-
posite to the sun, and the sun is never in Virgo or Li-
bra but in our autumnal months, September and Octo-
ber, it is evident that the moon is never full in the op-
posite signs, Pisces and Aries, but in those two months.
Therefore we can have only two full moons in a year,
which rise, for a week together, very near the time of
sun-set. The former of these is called the Harvest
Moon, and the latter the Hunter’s Moon.
CHAPTER, XXXIII.
THE HARVEST MOON, CONTINUED.
THough there are but two full moons in the year
that rise with so little difference of time, yet the phe-
nomenon of the moon's rising for a week together so
nearly in point of time, occurs every month, in some
part or other of her course.
In Winter the signs Pisces and Aries rise about noon; and the sun,
In Capricorn, is then only a quarter of a circle distant. Therefore the
moon, while passing through them, must be only in her first quarter
Hence her rising is neither regarded nor perceived.
In Spring, these signs rise with the sun, because he is then in them,
and as the moon changes while passing through the same sign with the
sum, it must then be the change, and hence invisible.
In Summer, they rise about midnight, for the sun being three signs,
or a quarter of a circle before them, the moon is in them, or about her
third quarter. Hence rising so late, and giving but little light, her rising
passes unobserved.
THE TERRESTRIAL, GLOBE, 97
ern semicircle of the horizon, and the number of de-
grees from the sun's place to the west point of the hori-
zon will be the setting amplitude.
OR, BY THE ANALEMMA.
Elevate the pole so many degrees above the horizon
as are equal to the latitude of the place; bring the day
of the month on the analemma to the eastern semicircle
of the horizon: the number of degrees from the day of
the month to the east point of the horizon will be the
rising amplitude : bring the day of the month to the
western semicircle of the horizon, and the number of
degrees from the day of the month to the west point of
the horizon will be the setting amplitude.
ExAMPLEs. 1. What is the sun's amplitude at Lon.
don on the 21st of June?
Answer. 390 48' to the north of the east, and 390 48' to the north of
the west.
2. On what point of the compass does the sun rise
and set at London on the 17th of May?
3. On what point of the compass does the sun rise
and set at the Cape of Good Hope on the 21st of De-
cember 7
4. On what point of the compass does the sun rise
and set on the 21st of March 7
5. On what point of the compass does the sun rise
and set at Washington on the 21st of October?
6. On what point of the compass does the sun rise
and set at Petersburg on the 18th of December ?
7. On December 22d, 1827, in latitude 31° 38' S.
and longitude 83° W., if the sun set on the S. W. point
of the compass, what is the variation?
º X
98 PROBLEMIS PERFORMED WITH
8. On the 15th of May 1827, if the sun rise E. by
N. in latitude 33° 15' N. and longitude 18° W., what
is the variation of the compass?
PROBLEM XLIV.
To find the sun's azimuth and his altitude at any place,
the day and hour being given.
RULE. Elevate the pole so many degrees above the
horizon as are equal to the latitude of the place, and
screw the quadrant of altitude on the brass meridian,
over that latitude ; find the sun's place in the ecliptic,
bring it to the brass meridian, and set the index of the
hour-circle to twelve ; then if the given time be before
noon, turn the globe eastward* as many hours as it
wants of noon; but, if the given time be past noon,
turn the globe westward as many hours as it is past
noon, bring the graduated edge of the quadrant of alti-
tude to coincide with the sun’s place, then the number
of degrees on the horizon, reckoned 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 from the horizon to
the sun's place, will be the sun's altitude.
* Whenever the pole is elevated for the latitude of the place, the pro-
per motion of the globe is from east to west, and the sun is on the east
side of the brass meridian in the morning, and on the west side in the
afternoon; but when the pole is elevated for the sun's declination, the
motion is from west to east, and the place is on the west side of the me
ridian in the morning, and on the east side in the afternoon,
THE TERRESTRIAL, GLOBE, 99
OR, BY THE ANALEMMA.
Elevate the pole so many degrees above the horizon
as are equal to the latitude of the place, and screw the
quadrant of altitude on the brass meridian, over that
latitude; bring the middle of the analemma to the brass
meridian, and set the index of the hour-circle to
twelve ; then, if the given time be before noon, turn
the globe eastward on its axis as many hours as it wants
of noon; but, if the given time be past noon, turn the
globe westward as many hours as it is past noon; bring
the graduated edge of the quadrant of altitude to coin-
cide with the day of the month on the analemma, then
the number of degrees on the horizon, reckoned from
the north or south point thereof to the graduated edge
of the quadrant, will show the azimuth ; and the num-
ber of degrees on the quadrant, counting from the ho-
rizon to the day of the month, will be the sun's altitude.
ExAMPLEs. 1. What is the sun’s altitude, and his
azimuth from the north, at London, on the 1st of May,
at ten o'clock in the morning?
Answer. The altitude is 479, and the azimuth from the north 1369
or from the south 449.
2. What is the sun’s altitude and azimuth at Peters-
burg on the 13th of August, at half past five o'clock
in the morning" *
3. What is the sun’s azimuth and altitude at Anti-
gua, on the 21st of June, at half past six in the morn-
ing, and at half past ten ?
4. At Barbadoes on the 21st of June, required the
sun's azimuth and altitude at 8 minutes past 6, and at
100 PROBLEMS PERFORMED WITH
# past 9 in the morning ; also at # past 2, and at 52
minutes past 5 in the afternoon.
5. On the 13th of August at half past eight o'clock
In the morning, at sea, in latitude 57° N. the observed
azimuth of the sun was S. 40° 14' E., what was the
sun's altitude, his true azimuth, and the variation of
the compass?
6. On the 14th of January, in latitude 33° 52' S,
at half past three o'clock in the afternoon, the sun’s
magnetic azimuth was observed to be N. 68° 51" W.;
what was the true azimuth, the variation of the com-
pass, and the sun’s altitude 7
PROBLEM XLV.
The latitude of the place, day of the month, and the
sun's altitude being given, to find the sun's azimuth
and the hour of the day.
RULE. Elevate the pole so many degrees above the
horizon as are equal to the latitude of the place, and
screw the quadrant of altitude on the brass meridian,
over that latitude; bring the sun's place in the ecliptic
to the brass meridian, and set the index of the hour-
circle to twelve; turn the globe on its axis till the sun’s
place in the ecliptic coincides with the given degree
of altitude on the quadrant; the hours passed over by
the index of the hour-circle will show the time from
noon, and the azimuth will be found on the horizon,
as in the preceding problem.
OR, BY THE ANALEMMA.
Elevate the pole to the latitude of the place, and
screw the quadrant of altitude ove" that latitude : bring
THE TERRESTRIAL, GLOBE, 101
the middle of the analemma to the brass meridian, and
set the index of the hour-circle to twelve ; move the
globe and the quadrant till the day of the month coin-
cides with the given altitude, the hours passed over by
the index will show the time from noon, and the azi-
muth will be found in the horizon as before.
ExAMPLEs. 1. At what hour of the day on the 21st
of March is the sun's altitude 22#9 at London, and
what is his azimuth? The observation being made in
the afternoon.
Answer. The time from noon will be found to be 3 hours 30 ml-
nutes, and the azimuth 590 1" from the south towards the west. Had
the observations been made before noon, the time from noon would
have been 33 hours, viz. it would have been 30 minutes past eight in
the morning, and the azimuth would have been 590 1" from the south
towards the east.
2. At what hour on the 9th of March is the sun’s al-
titude 25° at London, and what is his azimuth'ſ The
observation being made in the forenoon.
3. At what hour on the 18th of May is the sun’s al-
titude 30° at Lisbon, and what is the azimuth ! The
observation being made in the afternoon.
4. Walking along the side of Queen-square in Lon-
don on the 5th of August in the forenoon, I observed
the shadows of the iron-rails to be exactly the same
length as the rails themselves; pray what o'clock was
it, and on what point of the compass did the shadows
of the rails fall '!
5. At what hour of the day on the 20th of Septem-
ber, is the sun’s altitude 21° at Quebec, and what is
its azimuth, the observation being made in the
morning?
102 PROBLEMS PERFORMED WITH
6. At what hour on the 15th of June is the sun's al
titude 30° at Philadelphia, and what is the azimuth
the observation being made in the afternoon :
PROBLEM XLVI.
Given the latitude of the place, and the day of the month
to find at what hour the sun is due east or west.
RULE. Elevate the pole so many degrees above
the horizon as are equal to the latitude of the place,
find the sun's place in the ecliptic, bring it to the brass
meridian, and set the index of the hour-circle to twelve;
screw the quadrant of altitude on the brass meridian,
over the given latitude, and move the lower end of it
to the east point of the horizon; hold the quadrant in
this position, and move the globe on its axis till the
sun's place comes to the graduated edge of the qua
drant; the hours passed over by the index from twelve
will be the time from noon when the sun is due east,
and at the same time from noon he will be due west.
ExAMPLEs. 1. At what hour will the sun be due
east at London on the 19th of May; at what hour will
he be due west; and what will his altitude be at these
times?
Answer. The time from 12 when the sun is due east, is 4 hours 54
minutes; hence the sun is due east at six minutes past seven o'clock in
the morning, and due west at 54 minutes past four in the afternoon;
the sun's altitude will be ſound at the same time, as in Problem XLIV
In this example it is 25° 26'.
2. At what hours will the sun be due east and west
at London on the 21st of June, and on the 21st of De-
cember; and what will be his altitude above the hor.
zon on the 21st of June 7
THE TERRESTRIAL GLOBE, 103
3. Find at what hours the sun will be due east and
west, not only at London, but at every place on the
surface of the globe, on the 21st of March and on the
23d of September?
4. At what hours is the sun due east and west at
Buenos Ayres on the 21st of December ?
PROBLEM XLVII.
Given the sun's meridian altitude, and the day of the
month, to find the latitude of the place.
RULE. Find the sun's place in the ecliptic, and
bring it to that part of the brass meridian which is
numbered from the equator towards the poles; then,
if the sun was south of the observer when the altitude
was taken, count the number of degrees from the sun’s
place on the brass meridian towards the south point of
the horizon, and mark where the reckoning ends; bring
this mark to coincide with the south point of the hori-
zon, and the elevation of the north pole will show the
latitude. If the sun was north of the observer when
the altitude was taken, the degrees must be counted in
a similar manner, from the sun's place towards the
north point of the horizon, and the elevation of the
south pole will show the latitude.
OR, witHouT A GLOBE.
Subtract the sun's altitude from ninety degrees, the
remainder is the zenith distance. If the sun be south
when his altitude is taken, call the zenith distance
north; but, if north, call it south; find the sun's de-
104 PROBLEMS PERFORMED WITH
clination in an ephemeris or a table of the sur’s de-
clination, and mark whether it be north or south; then,
If the zenith distance, and declination have the same
name, their sum is the latitude, but, if they have con-
trary names, their difference is the latitude, and it is
always of the same name with the greater of the two
quantities.
ExAMPLEs. On the 10th of May, 1827, I observed
the sun’s meridian altitude to be 50°, and it was south
of me at that time; required the latitude of the place 3
Answer. 570 29' north.
By calculation.
900 0/
50 0 S., sun's altitude at noon.
40 0 N., the zenith's distance.
17 29 N., the sun's declination 10th May 1827.
57 29 N., the latitude sought.
2. On the 10th of May, 1827, the sun's meridian al-
titude was observed to be 50°, and it was north of the
observer at that time; required the latitude of the
place {
Answer. 22923 south.
By calculation.
990 0/
50 0 N., sun's altitude at noon.
40 0 S., the zenith's distance.
17 29 N., the sun's declination 10th May 1827.
gºssmº-ºsmº
22 31 S., the latitude sought.
3. On the 5th of August, 1827, the sun's meridian
altitude was observed to be 74° 30' north of the ob-
server; what was the latitude 1
THE TERRESTRIAL, GLOBE, 105
4. On the 19th of November, 1827, the sun's meri-
dian altitude was observed to be 40° south of the oh-
server; what was the latitude 7
5. At a certain place, where the clocks are two hours
faster than at London, the sun's meridian altitude was
observed to be 30 degrees to the south of the observer
on the 21st of March ; required the place 7
6. At the place where the clocks are 5 hours slower
than at London, the sun’s meridian altitude was ob-
served to be 60° to the south of the observer on the
16th of April, 1827; required the place
PROBLEM XLVIII.
The length of the longest day at any place, not within
the polar circles, being given, to find the latitude of
that place.
RULE. Bring the first point of Cancer or Capricorn
to the brass meridian (according as the place is on the
north or south side of the equator,) and set the index
of the hour-circle to twelve : turn the globe westward
on its axis till the index of the hour-circle has passed
over as many hours as are equal to half the length of
the day: elevate or depress the pole till the sun's place
(viz. Cancer or Capricorn) comes to the horizon; then
the elevation of the pole will show the latitude.
NotE. This problem will answer for any day in the year, as well
as the longest day, by bringing the sun's place to the brassmeridian and
proceeding as above.
OR, Bring the middle of the analemma to the brass meridian, and
set the index of the hour-circle to 12; turn the globe westward on its
axis till the index has passed over as many hours as are equal to half
the length of the day; elevate or depress the pole till the day of the
106 PROBLEMIS PERFORMED WITH
month coincides with the horizon, then the elevation of the pole will
show the latitude.
ExAMPLEs. 1. In what degree of north lätitude,
and at what places is the length of the longest day 16%
hours?
Answer. In latitude 529, and all places situated on, or near that pa-
rallel of latitude, have the same length of the day.
2. In what degree of south latitude, and at what
places is the longest day 14 hours ?
3. In what degree of north latitude is the length of
the longest day three times the length of the shortest
night 7
4. There is a town in Norway where the longest day
is five times the length of the shortest night; pray what
is the name of the town 7 *
5. In what latitude north does the sun set at seven
o'clock on the 5th of April 7
6. In what latitude south does the sun rise at five
o'clock on the 25th of November 7
7. In what latitude north is the 20th of May 16
hours long?
8. In what latitude north is the night of the 15th of
August 10 hours long?
PROBLEM XLIX.
The latitude of a place and the day of the month being
given, to find how much the sun's declination must
vary to make the day an hour longer or shorter than
the given day.
RULE. Find the sun's declination for the given
day, and elevate the pole to that declination: bring the
THE TERRESTRIAL GLOBE, 107
given place to the brass meridian, and set the index of
the hour circle to twelve : turn the globe eastward on
its axis till the given place comes to the horizon, and
observe the hours passed over by the index. Then, if
the days be increasing, continue the motion of the
globe eastward till the index has passed over another
half hour, and raise or depress the pole till the place
comes again into the horizon, the elevation of the pole
will show the sun's declination when the day is an hour
longer than the given day; but, if the days be decreas-
ing, after the place is brought to the eastern part of
the horizon, turn the globe westward till the index has
passed over half an hour, then raise or depress the
pole till the place comes a second time into the hori-
zon, the last elevation of the pole will show the sun's
declination when the day is an hour shorter than the
given day.
OR,
Elevate the pole to the latitude of the place, find the
sun's place in the ecliptic, bring it to the brass meri-
dian, and set the index of the hour-circle to twelve;
turn the globe westward on its axis till the sun's place
comes to the horizon, and observe the hours passed
over by the index; then, if the days be increasing,
continue the motion of the globe westward till the in-
dex has passed over another half hour, and observe
what point of the ecliptic is cut by the horizon; that
point will show the sun's place when the day is an hour
longer than the given day, whence the declination is
readily found: but, if the days be decreasing, turn the
globe eastward till the index has passed over half an
108 PROBLEMS PERFORMED WITH
hour, and observe what point of the ecliptic is cut by
the horizon; that point will show the sun's place when
the day is an hour shorter than the given day.
OR, BY THE ANALEMMA.
Proceed exactly the same as above, only, instead of
bringing the sun's place to the brass meridian, bring
the analemma there, and instead of the sun's place, use
the day of the month on the analemma.
ExAMPLEs. 1. How much must the sun's declina-
tion vary that the day at London may be increased one
hour from the 24th of February 1
Answer. On the 24th of February the sun's declination is 9° 38'
south, and the sun sets at a quarter past five; when the sun sets at three
quarters past five, his declimation will be found to be about 44° south,
answering to the tenth of March: hence the declination has decreased
50 23, and the days have increased 1 hour in 14 days.
2. How much must the sun's declination vary that
the day at London may decrease one hour in length
from the 26th of July 1
Answer. The sun's declination on the 26th of July is 19938 north,
and the sun sets at 49 min. past seven; when the sun sets at 19 min.
past seven, his declination will be found to be 149 43' north, answering
to the 13th of August: hence the declination has decreased 5° 55', and
the days have decreased one hour in 18 days
3. How much must the sun's declination vary from
the 5th of April, that the day at Petersburg may in-
crease one hour?
4. How much must the sun's declination vary from
the 4th of October, that the day at Stockholm may de-
crease one hour?
5. What is the difference in the sun's declination,
THE TERRESTRIAL, GLOBE, 109
when he rises at seven o'clock at Petersburg, and when
he sets at nine 7
PROBLEM L.
To find the sun's right ascension, oblique ascension, ob-
lique descension, ascensional difference, and time of
rising and setting at any place.
RULE. Find the sun's place in the ecliptic, and
bring it to that part of the brass meridian which is
numbered from the equator towards the poles; the de-
gree on the equator cut by the graduated edge of the
brass meridian, reckoning from the point Aries east-
ward, will be the sun’s right ascension.
Elevate the poles so many degrees above the horizon
as are equal to the latitude of the place, bring the sun's
place in the ecliptic to the eastern part of the horizon,
and the degree on the equator cut by the horizon,
reckoning from the point Aries eastward, will be the
sun's oblique ascension. Bring the sun’s place in the
ecliptic to the western part of the horizon, and the de-
gree on the equator cut by the horizon, reckoning from
the point Aries castward, will be the sun's oblique de-
scension.
Find the difference between the sun's right and ob-
lique ascension; or, which is the same thing, the dif.
ference between the right ascension and oblique de-
scension, and turn this difference into time by multi-
plying by 4: then, if the sun's declination and the
latitude of the place be both of the same name, viz.
both north or both south, the sun rises before six and
sets after six, by a space of time equal to the ascen:
k X- *
110 PROBLEMIS PERFORMED WITH
sional difference; but if the sun's declination and the
latitude be of contrary names, viz. the one north and
the other south, the sun rises after six and sets before
six.
ExAMPLEs. 1. Required the sun's right ascension,
oblique ascension, oblique descension, ascensional dif-
ference, and time of rising and setting at London, on
the 15th of April 7
Answer. The right ascension is 23030, the oblique ascension is 9°
45, the ascensional difference (23°30'—99 45/-) 13045', or 55 minutes
of time; consequently the sun rises 55 minutes before 6, or 5 min, past
5, and sets 55 min. past 6. The oblique descension is 37° 15'; conse-
quently the descensional difference is (370 15–23° 30'-) 13045, the
same as the ascensional difference.
2. What are the sun’s right ascension, oblique ascen-
sion, and oblique descension, on the 27th of October
at London; what is the ascensional difference, and at
what time does the sun rise and set !
3. What are the sun’s right ascension, declination,
oblique ascension, rising amplitude, oblique descen-
sion, and setting amplitude at London, on the 1st of
May; what is the ascensional difference, and at what
time does the sun rise and set !
4. What are the sun's right ascension, declination
oblique ascension, rising amplitude, oblique descen-
sion, and setting amplitude, at Petersburg, on the 21st
of June; what is the ascensional difference, and what
time does the sun rise and set !
5. What are the sun's right ascension, declination,
oblique ascension, rising amplitude, oblique descen-
'sion, and setting amplitude, at Alexandria, on the 21st
THE TERRESTRIAL GLOBE. 111
of December ; what is the ascensional difference and
what time does the sun rise and set ! *
PROBLEM LI.
Given the day of the month and the sun's amphtude
at sunrise to find the latitude of the place of ob-
servation.
RULE. Find the sun's place in the ecliptic, and
bring it to the eastern or western part of the horizon,
(according as the eastern or western amplitude is
given,) elevate or depress the pole till the sun's place
coincides with the given amplitude on the horizon,
then the elevation of the pole will show the latitude.
OR, THUs:
Elevate the north pole to the complement” of the
amplitude, and screw the quadrant of altitude upon the
brass meridian over the same degree : bring the equi-
noctial point Aries, to the brass meridian, and move
the quadrant of altitude till the sun's declination for
the given day (counted on the quadrant) coincides with
the equator; the number of degrees between the point
Aries, and the graduated edge of the quadrant, will be
the latitude sought.
ExAMPLEs. 1. The sun's amplitude at sunrise was
observed to be 39° 48' from the east towards the north,
on the 21st of June ; required the latitude of the place {
*The complement of the amplitude is found by subtracting the ampli.
plitude from 90°. This rule is exactly the same as above: for it is
formed from a right-angled spherical triangle, the base being the com:
plement of the amplitude, the perpendicular the latitude of the place,
and the hypothenuse the complement of the sun's declination,
112 PROBLEMs PERFORMED with
Answer. 51932 north.*
2. The sun's amplitude was observed to be 15° 30
from the east towards the north, at the same time his
declination was 15° 30'; required the latitude 7
3. On the 29th of May, when the sun's declination
was 21° 30' north, his rising amplitude was known to
be 22° northward of the east; required the latitude 1
4. When the sun's declination was 2° north, his ris-
ing amplitude was 4° north of the east; required the
latitude 7
PROBLEM LII.
Given two observed altitudes of the sun, the time elapsed
between them, and the sun's declination, to find the
latitude. ->
RULE. Find the sun's declination, either by the globe
or an ephemeris; take the number of degrees contain-
ed therein from the equator with a pair of compasses,
and apply the same number of degrees upon the meri
dian passing through Libraf from the equator northward
or southward, and mark where they extend to: turn
the elapsed time into degrees,f and count those de-
grees upon the equator from the meridian passing
through Libra; bring that point of the equator where
the reckoning ends to the graduated edge of the brass
meridian, and set off the sun’s declination from that
*See Keith's Trigonometry, fourth edition, page 285.
t Any meridian will answer the purpose as well as that which passes
through Libra; on Adams' and on Cary's globes this merdian is divided
like the brass meridian. r
4 See the method of turning time into degrees. Prob. XIX.
THE TERRESTRIAL, GLOBE, 11:
point along the edge of the meridian, the same way as
before; then take the complement of the first altitude
from the equator in your compasses, and, with one foot
in the sun’s declination, and a fine pencil in the other
foot, describe an arc; take the complement of the
second altitude in a similar manner from the equator,
and with one foot of the compasses fixed in the second
point of the sun’s declination, cross the former arc:
the point of intersection brought to that part of the
brass meridian which is numbered from the equator
towards the poles, will stand under the degree of lati-
tude sought.
ExAMPLEs. 1. Suppose on the 4th of June, 1827,
in north latitude, the sun's altitude at 29 minutes past
10 in the forenoon, to be 65°24', and at 31 minutes
past 12, 74° 8': required the latitude 1
Answer. The sun's declination is 22° 22′ north, the elapsed time
two hours two min. answering to 30° 30'; the complement of the first
altitude 240 36, the complement of the second altitude 15° 52', and the
latitude sought 360 57 north. -
2. Given the sun's declination 19° 39' north, his al-
titude in the forenoon 38° 19, and, at the end of one
hour and a half, the same morning, the altitude was
50° 25'; required the latitude of the place, supposing
it to be north 1
3. When the sun's declination was 22° 40' north,
his altitude at 10 h. 54 m. in the forenoon was 53°29',
and at 1 h. 17 m. in the afternoon it was 52°48'; re-
quired the latitude of the place of observation, sup-
posing it to be north 1 +
4. In north latitude, when the sun's declination was
22° 23' south, the sun's altitude in the afternoon was
k 2 Y 2
114 PROBLEMIS PERFORMIED WITH
observed to be 14°46', and after 1 h. 22 m. had elapsed,
his altitude was 8° 27'; required the latitude 7
PROBLEM LIII.
The day and hour being given when a solar eclipse
will happen, to find where it will be visible.
RULE. Find the sun's declination, and elevate the
pole agreeably to that declination; bring the place at
which the hour is given to that part of the brass meri-
dian which is numbered from the equator towards the
poles, and set the index of the hour-circle to twelve ;
then, if the given time be before noon, turn the globe
westward till the index has passed over as many hours
as the given time wants of noon; if the time be past
noon, turn the globe eastward as many hours as it is
past noon, and exactly under the degree of the sun's
declination on the brass meridian you will find the
place on the globe where the sun will be vertically
eclipsed:* at all places within 70 degrees of this place,
the eclipse may f be visible “specially if it be a total
eclipse.
ExAMPLE. On the 11th or February, 1804, at 27
min. past ten o'clock in the morning at London, there
was an eclipse of the sun, where was it visible, sup-
*The effect of parallax is so great, that an eclipse may not be visi.
ble even where the sun is vertical.
t When the moon is exactly in the node, and when the axis of the
moon's shadow and penumbra pass through the centre of the earth, the
breadth of the earth's surface under the penumbral shadow is 70°20';
but the breadth of this shadow is variable; and if it be not accurately
determined by calculation, it is impossible to tell by the globe to what
extent an eclipse of the sun will be visible. , - r - ,
THE TERRESTRIAL GLOBE. 115
posing the moon's penumbral shadow to extend north-
ward 70 degrees from the place where the sun was
vertically eclipsed?
Answer. London, &c.
PROBLEMI LIV.
The day and hour being given when a lunar eclipse will
happen, to find where it will be visible.
RULE. Find the sun's declination for the given day
and note whether it be north or south; if it be north, ele-
vate the south pole so many degrees above the horizon
as are equal to the declination; if it be south, elevate
the north pole in a similar manner; bring the place at
which the hour is given to that part of the brass meri-
dian which is numbered from the equator towards the
poles, 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 ; if after
noon, turn the globe eastward as many hours as it is
past noon ; the place exactly under the degree of the
sun's declination will be the antipodes of the place
where the moon is vertically eclipsed, set the index
of the hour-circle again to twelve, and turn the globe on
its axis till the index has passed over twelve hours;
then to all places above the horizon the eclipse will be
visible; to those places along the western edge of the
horizon, the moon will rise eclipsed; to those along
the eastern edge she will set eclipsed; and to that place
immediately under the degree of the sun's declination,
reckoning towards the elevated pole, the moon will be
vertically eclipsed.
116. PROBLEMIS PERFORMED WITH
ExAMPLE. On the 26th of January, 1804, at 58 min
past seven in the afternoon at London, there was an
eclipse of the moon; where was it visible?
Answer. It was visible to the whole of Europe, Africa, and the
continent of Asia.
PROBLEM LV.
To find the time of the year when the Sun or Moon will
be liable to be eclipsed.
RULE 1. Find the place of the moon’s nodes, the
time of new moon, and the sun's longitude at that time,
by an ephemeris; then if the sun be within 17 de-
grees of the moon’s node, there will be an eclipse of
the sun. ar
2. Find the place of the moon's nodes, the time of
full moon, and the sun's longitude at that time, by an
ephemeris: then, if the sun's longitude be within 12
degrees of the moon’s node, there will be an eclipse of
the moon.
OR, wrthouT THE EPHEMERIs.
The mean annual variation of the moon’s nodes is
19°19'44" and the place of the node for the first of
January 1827 being 2° 2' in 2-, its place for any other
time may therefore be found.
ExAMPLEs.1. On the 9th of June, 1827, there will be
a full moon, at which time the place of the moon's
node is 7° in as and the sun's longitude 8, 17°48'; will
an eclipse of the moon happen at that time !
Answer. Here the sun's longitude is not within 12 degrees of the
THE TERRESTRIAI, GLOBE, 117
moon's node, therefore there will be no eclipse of the moor. —When
the sun is in one of the moon's nodes at the time of full moon, the moon
is in the other node, and the earth is directly between them.
2. There will be a new moon on the 7th of June,
1827, at which time the place of the moon's node will
be --, 12° 43' and the sun’s longitude 8 15°54'; will
there be an eclipse of the sun at that time !
3. There will be a new moon on the 18th of De-
cember 1827, at which time the place of the moon’s
node will be ~ 2° 24′ and the sun's longitude Iſſ, 25°
51'; will there be an eclipse of the sun at that time !
4. On the 3d of November, 1827, there will be a
full moon, at which time the place of the moon's node
will be so- 4° 56', and the sun’s longitude -- 10° 18';
will there be an eclipse of the moon at that time !
5. On the 25th of April, 1827, there will be a new
moon, at which time the place of the moon’s node is -a-
15° 19' and the sun's longitude ºp 4°29'; will there be
an eclipse of the sun at that time ! -
6. On the 20th of October, 1827, there will be a
new moon, at which time the place of the moon's node
is -o- 5° 38' and the sun's longitude Iſ! 26° 19'; will
there be an eclipse of the sun at that time?
PROBLEM LVI.
To ea plain the phenomenon of the harvest moon.
DEFINITION 1. The harvest moon, in north latitude
is the full moon which happens at, or near the time of
the autumnal equinox; for, to the inhabitants of north
latitude, whenever the moon is in Pisces or Aries (and
she is in these signs twelve times in a year,) there is
118 PROBLEMS PERFORMED WITH
very little difference between her times of rising for
several nights together, because her orbit is at these
times nearly parallel to the horizon. This peculiar
rising of the moon passes unobserved at all other times
of the year except in September and October; for there
never can be a full moon except the sun be directly
opposite to the moon; and as this particular rising of
the moon can only happen when the moon is in Bé Pisces
or ºp Aries, the sun must necessarily be either in Tſſ.
Virgo or -o- Libra at that time, and these signs answer
to the months of September and October.
DEFINITIon 2. The harvest moon, in south latitude,
is the full moon which happens at, or near, the time of
the vernal equinox; for, to the inhabitants of south la-
titude, whenever the moon is in Iſſ, Virgo or ~ Libra
her orbit is nearly parallel to the horizon: but when
the full moon happens in Iſſ, Virgo or ~ Libra, the sun
must be either in 3é Pisces or ºp Aries. Hence it ap-
pears that the harvest moons are just as regular in south
latitude as they are in north latitude, only they happen
at contrary times of the year.
RULE FOR PERForMING THE PROBLEM.–1. For north
latitude. Elevate the north pole to the latitude of the
place, put a patch or make a mark in the ecliptic on
the point Aries, and upon every twelve degrees pre-
ceding and following that point, till there be ten or ele-
ven marks; bring that mark which is the nearest to
Pisces to the eastern edge of the horizon, and set the
index to 12; turn the globe westward till the other
marks successively come to the horizon, and observe
THE TERRESTRIAL, GLOBE, 119
the hours passed over by the index; the intervals of
time between the marks coming to the horizon will
show the diurnal difference of time between the moon’s
rising. If these marks be brought to the western edge
of the horizon in the same manner, you will see the
diurnal difference of time between the moon’s setting:
for, when there is the smallest difference between the
times of the moon's rising, there will be the greatest
difference between the times of her setting; and, on
the contrary, when there is the greatest difference be-
tween the times of the moon’s rising, there will be the
least difference between the times of her setting.
NoTE. As the moon's nodes vary their position and form a complete
revolution in about nineteen years, there will be a regular period of
all the varieties which can happen in the rising and setting of the moon
during that time. The following table (extracted from Ferguson's As-
tronomy,) shows in what years the harvest moons are the least and most
beneficial, with regard to the times of their rising, from 1823 to 1860.
The columns of years under the letter L are those in which the har-
vest moons are least beneficial, because they fall about the descending
node; and those under M are the most beneficial, because they fall
about the ascending mode.
L L L L M M M M \
1826 1831 1845 1849 1823 1837 1842 1856
1827 1832 1846 1850 1824 1838 1843 1857
1828 1833 1847 1851 1825 1839 1853 1858
1829 1834 1848 1852 1835 1840 1854 1859
1830 1844 - 1836 1841 1855 1860
2. For south latitude. Elevate the south pole to the
latitude of the place, put a patch or make a mark
on the ecliptic on the point Libra, and upon every
twelve degrees preceding and following that point, till
there be ten or eleven marks; bring that mark which
is the nearest to Virgo, to the eastern edge of the hori-
zon, and set the index to 12; turn the globe westward
120 PROBLEMs PERFORMED with
till the other marks successively come to the horizon,
and observe the hours passed over by the index; the
intervals of time between the marks coming to the ho-
rizon will be the diurnal difference of time between
the moon's rising, &c. as in the foregoing part of the
problem.*
PROBLEM LVII.
The day and hour of an eclipse of any one of the satel-
lites of Jupiter being given, to find upon the globe all
those places where it will be visible.
RULE. Find the sun's declination for the given day,
and elevate the pole to that declination; bring the
place at which the hour is given to the brass meridian
and set the index of the hour-circle to 12 ; then, if the
given time be before noon, turn the globe westward as
many hours as it wants of noon; if after noon, turn the
globe eastward as many hours as it is past noon; fix
the globe in this position : THEN,
1. If Jupiter rise after the sun, f that is, if he be an
evening star, draw a line along the eastern edge of the
horizon with a black lead pencil, this line will pass over
all places on the earth where the sun is setting at the
* This solution is on a supposition that the moon keeps constantly in
the ecliptic, which is sufficiently accurate for illustrating the problem.
Otherwise the latitude and longitude of the moon, or her right ascension
and declination, may be taken from the ephemeris, at the time of full
moon, and a few days preceding and following it; her place will then
be truly marked on the globe. - -
tJupiter rises after the sun, when his longitude is greater than the
sun's longitude. -
THE TERRESTRIAL GLOBE, 121
given hour; turn the globe westward on its axis till
as many degrees of the equator have passed under the
brass meridian as are equal to the difference between
the sun's and Jupiter's right ascension; keep the globe
from revolving on its axis, and elevate the pole as many
degrees above the horizon as are equal to Jupiter's de-
clination, then draw another line with a pencil along
the eastern edge of the horizon : the eclipse will be
visible to every place between these lines, viz. from
the time of the sun's setting to the time of Jupiter's
setting.
2. If Jupiter rise before the sun,” that is, if he be
a morning star, draw a line along the western edge of
the horizon with a black lead pencil, this line will pass
over all places of the earth where the sun is rising at
the given hour; turn the globe eastward on its axis
till as many degrees of the equator have passed under
the brass meridian as are equal to the difference be-
tween the sun's and Jupiter's right ascension; keep
the globe from revolving on its axis, and elevate the
pole as many degrees above the horizon as are equal
to Jupiter’s declination, then draw another line with a
pencil along the western edge of the horizon; the
eclipse will be visible to every place between these
lines, viz. from the time of Jupiter's rising to the time
of the sun's rising.
ExAMPLEs. 1. On the 13th of January, 1805, there
was an immersion of the first satellite of Jupiter at
* Jupiter rises before the sun when his longitude islesthan themn's
longitude. -
l Z
122 PROBLEMs PERFORMED witH
9 m. 3 sec. past five o'clock in the morning at Green-
wich; where was it visible? -
Answer. In this example the longitude of the sun exceeds the lon-
gitude of Jupiter, therefore Jupiter was a morning star, his declination
being 190 16 S. and his longitude 7 signs 290 46, by the Nautical Al-
manac; his right ascension and the sun's right ascension may be found
by the globe; for, if Jupiter's longitude in the ecliptic be brought to the
brass meridian, his place will stand under the degree of his declina-
tion;” and his right ascension will be found on the equator, reckoning
from Aries. This eclipse was visible at Greenwich, the greater part
of Europe, the west of Africa, Cape Verd islands, &c.
2. On the 5th of January, 1827, at 44 min. 2 sec.
past seven o'clock in the morning, at Greenwich, there
will be an immersion of the first satellite of Jupiter;
where will the eclipse be visible 7 Jupiter's longitude
at that time being 6 signs 13° 41' and his declination
4° 10' south.
3. On the 5th of June, 1827, at 14 min. 8 sec. past
eight o'clock in the evening, at Greenwich, there will
be an emersion of the first satellite of Jupiter; where
will the eclipse be visible 7 Jupiter's longitude at
that time being 6 signs 4° 31' and his declination 0°
30' south.
4. On the 2d of December, 1827, at 39 min. 4 sec.
past six o'clock in the morning, at Greenwich, there
will be an immersion of the first satellite of Jupiter;
where will the eclipse be visible 7 Jupiter's longitude
*This is on supposition that Jupiter moves in the ecliptic, and, as he
deviates but little therefrom, the solution by this method will be suf.
ficiently accurate. To know if an eclipse of any one of the satellites
aſ Jupiter will be visible at any place; we are directed by the Nauti
cal Almanac to “find whether Jupiter be 80 above the horizon of the
place, and the sun as much below it.” $
THE TERRESTRIAL, GLOBE, 123
at that time being 7 signs 3° 59' and his declination
1° 5' north.
PROBLEM LVIII.
To place the terrestrial globe in the sun-shine, so that
it may represent the NATURAL POSITION of the earth.
RULE. If you have a meridian line” drawn upon a
horizontal plane, set the north and south points of the
wooden horizon of the globe directly over this line ;
or, place the globe directly north and south by the ma-
riner's compass, taking care to allow for the variation;
bring the place in which you are situated to the brass
meridian, and elevate the pole to its latitude ; then the
globe will correspond in every respect with the situa-
tion 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.
While the sun shines on the globe, one hemisphere
will be enlightened, and the other will be in the shade:
thus, at one view, may be seen all places on the earth
which have day, and those which have night.f
If a needle be placed perpendicularly in the middle
of the enlightened hemisphere, (which must of course
* As a meridian line is useful for fixing a horizontal dial, and for
placing a globe directly north and south, &c. the different methods of
drawing a line of this kind will precede the problems on dialling.
t For this part of the problem it would be more convenient if the
globe could be properly supported without the frame of it, because the
shadow of its stand, and that of its horizon, will darken several parts of
the surface of the globe, which would otherwise be enlightened
124 PROBLEMIS PERFORMIED WITH
be upon the parallel of the sun’s declination for the
given day,) it will cast no shadow, which shows that
the sun is vertical at that point; and if a line be drawn
through this point from pole to pole, it will be the me-
ridian of the place where the sun is vertical, and every
place upon this line will have noon at that time; all
places to the west of this line will have morning, and
all places to the east of it afternoon. Those inhabitants
who are situated on the circle which is the boundary
between light and shade, to the westward of the meri-
dian where the sun is vertical, will see the sun rising;
those in the same circle to the eastward of this meri-
dian will see the sun setting. Those inhabitants to-
wards the north of the circle, which is the boundary
between light and shade, will perceive the sun to the
southward of them, in the horizon; and those who are
in the same circle towards the south, will see the sun
in a similar manner to the north of them.
If the sun shine beyond the north pole at the given
time, his declination is as many degrees north as he
shines over the pole; and all places at that distance
from the pole will have constant day, till the sun's de-
clination decreases, and those at the same distance
from the south pole will have constant night.
If the sun do not shine so far as the north pole at
the given time, his declination is as many degrees south
as the enlightened part is distant from the pole; and
all places within the shade, near the pole, will have
constant night, till the sun’s declination increases
northward. While the globe remains steady in the po-
sition it was first placed when the sun is westward of
THE TERRESTRIAL GLOBE. 125
the meridian, you may perceive on the east side of it,
in what manner the sun gradually departs from place
to place as the night approaches; and when the sun is
eastward of the meridian, you may perceive on the
western side of it, in what manner the sun advances
from place to place as the day approaches.
PROBLEM LIX.
The latitude of a place being given, to find the hour of
the day at any time when the sun SHINEs.
RULE 1. Place the north and south points of
the horizon of the globe directly north and south
upon a horizontal plane, by a meridian line, or by a
mariner's compass, allowing for the variation, and ele-
vate the pole to the latitude of the place; then, if the
place be in north latitude, and the sun's declination be
north, the sun will shine over the north pole ; and if a
long pin be fixed perpendicularly in the direction of the
axis of the earth, and in the centre of the hour-circle,
its shadow will fall upon the hour of the day, the figure
XII of the hour-circle being first set to the brass meri-
dian. If the place be in north latitude, and the sun’s
declination be above ten degrees south, the sun will
not shine upon the hour-circle at the north pole.
RULE 2. Place the globe due north and south upon
a horizontal plane, as before, and elevate the pole to
the latitude of the place; find the sun's place in the
ecliptic, bring it to the brass meridian, and set the in-
dex of the hour-circle to XII; stick a needle perpen-
dicularly in the sun's place in the ecliptic, and turn
the globe on its axis till the needle casts no shadow;
fix the globe in this position, and the index will show
l 2 z 2
126 PROBLEMS PERFORMED WITH
the hour before 12 in the morning, or after 12 in the
afternoon. -
RULE 3. Divide the equator into 24 equal parts
from the point Aries, on which place the number VI;
and proceed westward VII, VIII, IX, X, XI, XII, I, II,
III, IV, V, VI, which will fall upon the point Libra,
VII, VIII, IX, X, XI, XII, I, II, III, IV, V;% elevate
the pole to the latitude, place the globe due north and
south upon a horizontal plane, by a meridian line, or
a good mariner's compass, allowing for the variation,
and bring the point Aries to the brass meridian ; then
observe the circle which is the boundary between light
and darkness westward of the brass meridian ; and it
will intersect the equator in the given hour in the morn-
ing; but, if the same circle be eastward of the brass
aeridian, it will intersect the equator in the given hour
in the afternoon. r *
OR, Having placed the globe upon a true horizontal
plane, set it due north and south by a meridian line;
elevate the pole to the latitude, and bring the point
Aries to the brass meridian, as before ; then tie a small
string, with a noose, round the elevated pole, stretch
its other end beyond the globe, and move it so that the
shadow of the string may fall upon the depressed axis;
at that instant its shadow upon the equator will give
the hour.i.
* On Adams' globes the antarctic circle is thus divided, by which
the problem Inay be solved.
+The learner must remember that the time shown in this problem
is solar time, as shown by a sun-dial; and, therefore, to agree with a
good clock or watch, it must be corrected by a table of equation of time.
See a table of this kind among the succeeding problems.
THE TERRESTRIAL GI, OBE, 127
PROBLEM LX.
To find the sun's altitude, by placing the globe in the
SUN-SHINE,
RULE. Place the globe upon a truly horizontal
plane, stick a needle perpendicularly over the north
pole,” in the direction of the axis of the globe, and
turn the pole towards the sun, so that the shadow of
the needle may fall upon the middle of the brass meri-
dian ; then elevate or depress the pole till the needle
casts no shadow; for then it will point directly to the
sun; the elevation of the pole above the horizon will be
the sun's altitude.
PROBLEM LXI.
To find the sun's declination, his place in the ecliptic,
and his azimuth, by placing the globe in the SUN-
SHINE,
RULE. Place the globe upon a truly horizontal
plane, in a north and south direction by a meridian
line, and elevate the pole to the latitude of the place;
then, if the sun shine beyond the north pole, his decli-
nation is as many degrees north as he shines over the
pole ; if the sun do not shine so far as the north pole,
his declination is as many degrees south as the enlight-
ened part is distant from the pole. The sun's declina-
tion being found, his place may be determined by
Problem XX.
* It would be an improvement on the globes were our instrument
makers to drill a very small hole in the brass meridian over the north
pole.
128 PROBLEMS PERFORMED WITH
Stick a needle in the parallel of the sun’s declina-
tion for the given day,” and turn the globe on its axis
till the needle casts no shadow : fix the globe in this
position, and screw the quadrant of altitude over the
latitude; bring the graduated edge of the quadrant to
coincide with the sun's place, or the point where the
needle is fixed, and the degree on the horizon will
show the azimuth.
CHAPTER III.
PROBLEMS PERFORMED WITH THE CELESTIAL GLOBE.
PROBLEM LXII.
To find the right ascension and declination of the sun,
Or a Staſ”.
RULE. Bring the sun or star to that part of the brass
meridian which is numbered from the equinoctial to-
wards the poles; the degree on the brass meridian is
the declination, and the number of degrees on the
equinoctial, between the brass meridian and the point
Aries, is the right ascension.
OR, Place both the poles of the globe in the horizon,
bring the sun or star to the eastern part of the horizon;
then the number of degrees which the sun or star is
northward or southward of the east, will be the decli-
nation north or south; and the degrees on the equinoc-
* On Adams' globes the torrid zone is divided into degrees by dotted
lines, so that the parallel of the sun's declination is instantly found: in
using other globes, observe the declination on the brass meridian, and
stick aneedle perpendicularly in the globe under that degree.
THE CELESTIAL GLOBE. 129
tial, from Aries to the horizon, will be the right ascen
sion. *
ExAMPLEs. 1. Required the right ascension and
declination of a Dubhe, in the back of the Great Bear.
Answer. Right ascension 162° 49', declination 62o 48 N.
2. Required the right ascensions and declinations
of the following stars? *
», Algenib, in Pegasus. », Bellatriæ, in Orion.
2, Scheder, in Cassiopeia. 2, Betelgeua, in Orion.
3, Mirach, in Andromeda. 2, Canopus, in Argo Na
2, Acherner, in Eridanus. wis. $,
2, Menkar, in Cetus. 2, Procyon, in the Little
3, Algol, in Perseus. Dog.
2, Aldebaran, in Taurus. | y, Algorab, in the Crow.
2, Capella, in Auriga. 2, Arcturus, in Boötes.
3, Rigel, in Orion. s, Wendemiatria, in Virgo.
PROBLEM LXIII.
To find the latitude and longitude of a star.”
RULE. Place the upper end of the quadrant of alti-
tude on the north or south pole of the ecliptic, ac-
cording as the star is on the north or south side of the
ecliptic, and move the other end till the star comes, to
the graduated edge of the quadrant: the number of de-
grees between the ecliptic and the star is the latitude;
and the number of degrees on the ecliptic, reckoned
eastward from the point Aries to the quadrant, is the
longitude.
OR, Elevate the north or south pole 66%% above the
horizon, according as the given star is on the north or
*The latitudes and longitudes of the planets must be found from an
ephemeris.
130 PROBLEMIS PERFORMED WITH
south side of the ecliptic; bring the pole of the eclip-
tic to that part of the brass meridian which is number.
ed from the equinoctial towards the pole : then the
ecliptic will coincide with the horizon; screw the
quadrant of altitude upon the brass meridian over the
pole of the ecliptic ; keep the globe from revolving on
its axis, and move the quadrant till its graduated edge
comes over the given star: the degree on the quadrant
cut by the star is its latitude; and the sign and degree
on the ecliptic cut by the quadrant show its longitude.
ExAMPLEs. 1. Required the latitude and longitude
of . Aldebaran in Taurus 7
Answer. Latitude 5o 28 S. longitude 2 signs 60 53'; or 60 53' in
Gemini. - ,
2. Required the latitudes and longitudes of the fol-
lowing stars 7
2, Markab, in Pegasus.
&, Scheat, in Pegasus.
•, Fomalhaut, in the S.
Fish.
2, Deneb, in Cygnus.
•, Altair, in the Eagle.
8, Albireo, in Cygnus.
•, Vega, in Lyra.
×, Rastaben, in Draco.
•, Antares, in the Scor-
pion.
2, Arcturus, in Boötes.
8, Pollua, in Gemini.
3, Rigel, in Orion.
ProBLEM LXIV.
The right ascension and declination of a star, the moon,
a planet, or of a comet, being given, to find its place
on the globe.
RuLE. Bring the given degrees of right ascension
to that part of the brass meridian which is numbered
from the equinoctial towards the poles: then under
THE CELESTIAL, GLOBE. 131
the given declination on the brass meridian you will
find the star, or place of the planet. *
ExAMPLEs. 1. What star has 261°29' of right as-
cension, and 52° 27' north declination?
Answer. 8 in Draco.
2. On the 31st of January, 1825, the moon's right
ascension was 91° 21', and her declination 23°19';
find her place on the globe at that time.
Answer. In the milky way, a little above the left foot of Castor.
3. What stars have the following right ascensions
and declinations?
Right Ascensions. Declinations. Right Ascensions. Declinations.
7o 19' 55° 26' N. 83° 6' 34°11' S.
11 11 59 38 N. 86 13 44 55 N.
25 54 19 50 N. 99 5 16 26 S.
46 32 9 34 S. 110 27 32 19 N.
53 54 23 29 N. : 113 16 28 30 N.
76 14 8 27 S. 129 2 7 8 N.
4. On the 1st of December, 1827, the moon's right
ascension at midnight will be 50° 58', and her de
clination 16° 58' N.; find her place on the globe.
5. On the 1st of May, 1827, the declination of Ve-
nus will be 1° 11’S. and her right ascension 0°4',
find her place on the globe at that time.
6. On the 19th of January, 1827, the declination of
Jupiter will be 4° 21' S. and his right ascension 12°
55'; find his place on the globe at that time.
132 PROBLEMIS PERFORMED WITH
PROBLEM LXV.
The latitude and longitude of the moon, a star or a
planet, given, to find its place on the globe.
RULE. Place the division of the quadrant of altitude
marked 0, on the given longitude in the ecliptic, and
the upper end on the pole of the ecliptic ; then, under
the given latitude, on the graduated edge of the qua-
drant, you will find the star, or place of the moon or
planet. *
ExAMPLEs. 1. What star has 0 signs 6° 16' of lon-
gitude, and 12° 36' N, latitude?
Answer. Y in Pegasus. r
2. On the 5th of June, 1827, at midnight, the moon’s
longitude will be 6' 23°41'; and her latitude 1° 49
S.; find her place on the globe.
3. What stars have the following latitudes and longi-
tudes 7
Latitudes. Longitudes. Latitudes. Longitudes.
120 35' S. 1; 11° 25' | 39° 33' S. 3' 11° 13'
5 29 S. 2 6 53 10 4. N. 3 17 21
31 8 S. 2 18 56 0 27 N. 4 26 57
22 52 N. 2 18 57 44 20 N. 7 9 22
16 3 S. 2 25 51 || 21 6 S. 11 0 56
4. On the first of June, 1827, the longitudes ana
latitudes of the planets will be as follow: required their
places on the globe 7 .
Longitudes. Latitudes. Longitudes. Latitudes.
§ 2° 0° 54' 0°29' S. A 6' 4° 28′ 1927' N.
2 1 7 1 1 52 S. h 3 5 47 0 32 S.
3 222 12 0 46 N. Hi 9 27 52 2.1 5 S.
THE CELESTIAL, GLOBE, 133
PROBLEM LXVI.
The day and hour, and the latitude of a place being
given, to find what stars are rising, setting, culmina-
ting, &c.
RULE. Elevate the pole to the latitude of the place,
find the sun's place in the ecliptic, bring it to the brass
meridian, and set the index of the hour-circle to 12;
then, if the time be before noon, turn the globe east-
ward on its axis till the index has passed over as many
hours as the time wants of noon; but, if the time be
past noon, turn the globe westward till the index has
passed over as many hours as the time is past noon :
then all the stars on the eastern semi-circle of the ho-
rizon will be rising, those on the western semi-circle
will be setting, those under the brass meridian above
the horizon will be culminating, those above the hori-
zon will be visible at the given time and place, those
below will be invisible.
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 equinoctial, at a distance
from it equal to the degrees in the remainder, they
will be the circles of perpetual apparition and occulta:
tion. *
ExAMPLEs. 1. On the 9th of February, when it is
nine o'clock in the evening at London, what stars are
ſº 2 A
134 PROBLEMIS PERFORMED WITH
rising, what stars are setting, and what stars are on the
meridian 7
Answer. Alphacca, in the northern Crown is rising; Arcturus and
Mirach, in Boötes, just above the horizon; Sirius on the meridian;
Procyon and Castor and Pollux a little east of the meridian. The con-
stellations Orion, Taurus, and Auriga, a little west of the meridian:
Markab, in Pegasus, just below the western edge of the horizon, &c.
2. On the 20th of January, at two o'clock in the morn-
ing at London, what stars are rising, what stars are
setting, and what stars are on the meridian 7
Answer. Vega in Lyra, the head of the Serpent, Spica Virginis, &c.
are rising; the head of the Great Bear, the claws of Cancer, &c. on the
meridian; the head of Andromeda, the neck of Cetus, and the body of
Columba Noachi, &c. are setting.
3. At ten o’clock in the evening at Edinburgh, on
the 15th of November, what stars are rising, what stars
are setting, and what stars are on the meridian
4. What stars do not set in the latitude of London,
and at what distance from the equinoctial is the circle
of perpetual apparition ?
5. What stars do not rise to the inhabitants of Edin-
burgh, and at what distance from the equinoctial is the
circle of perpetual occultation?
6. What stars never rise at Otaheite, and what stars
never set at Jamaica?
7. How far must a person travel southward from
London to lose sight of the Great Bear?
8. What stars are continually above the horizon at
the north pole, and what stars are constantly below the
horizon thereof? -
THE CELESTAL GLOBE. I35
PROBLEM LXVII.
The latitude of a place, day of the month, and hour
being given, to place the globe in such a manner as
to represent the heavens at that time; in order to find
out the relative situations and names of the constella-
tions and remarkable stars.
RULE. Take the globe out into the open air, on
a clear star-light night, where the surrounding horizon
is uninterrupted by different objects; elevate the pole
to the latitude of the place, and set the globe due north
and south by a meridian line, or by a mariner's com
pass, taking care to make a proper allowance for the
variation ; find the sun's place in the ecliptic, bring it
to the brass meridian and set the index of the hour-
circle to 12; then, if the time be after noon, turn the
globe westward on its axis, till the index has passed
over as many hours as the time is past noon; but, if
the time be before noon, turn the globe eastward till
the index has passed over as many hours as the time
wants of noon; fix the globe in this position, then the
flat end of a pencil being placed on any star on the
globe so as to point towards the centre, the other end
will point to that particular star in the heavens.
PROBLEM LXVIII.
To find when any star, or planet, will rise, come to the
meridian, and set at any given place. .
RULE. Elevate the pole so many degrees above the
horizon as are equal to the latitude of the place; find
136 PROBLEMIS PERFORMED WITH
the sun's place in the ecliptic, bring it to the brass
meridian, and set the index of the hour-circle to 12.
Then if the star or planet be below the horizon, turn
the globe westward till the star or planet comes to the
eastern part of the horizon, the hours passed over by
the index will show the time from noon when it rises;
and, by continuing the motion of the globe westward
till the star, &c. comes to the meridian, and to the west-
ern part of the horizon successively, the hours passed
over by the index will show the time of culminating
and setting.
If the star, &c. be above the horizon and east of the
meridian, find the time of culminating, setting, and
rising, in a similar manner. If the star, &c. be above
the horizon west of the meridian, find the time of set-
ting, rising, and culminating, by turning the globe
westward on its axis.
ExAMPLEs. 1. At what time will Arcturus rise,
come to the meridian, and set, at London, on the 7th
of September ?
Answer. It will rise at seven o'clock in the morning, come to the
meridian at three in the afternoon, and set at eleven o'clock at night.
2. On the 1st of August, 1805, the longitude of Ju-
piter was 7 signs 26 deg. 34 min., and his latitude 45
min. N. ; at what time did he rise, culminate, and set,
at Greenwich, and whether was he a morning or an
evening star?
Answer. Jupiter rose at half past two in the afternoon, came to the
meridian at about ten minutes to seven, and set at a quarter past eleven
in the evening. Here Jupiter was an evening star, because he setaſter
the sun.
THE CELESTIAL, GLOBE, 137
3. At what time does Sirius rise, set, and come to
the meridian of London, on the 31st of January 7
4. On the 1st of January, 1827, the longitude of
Venus will be 8 signs 27 deg. 10 min. and her latitude
1 deg. 29 min. N.; at what time will she rise, culminate,
and set at Paris, and whether will she be a morning or
an evening star
5. At what time does Aldebaran rise, come to the
meridian, and set at Dublin, on the 25th of November?
6. On the first of February, 1827, the longitude of
Mars will be 11 signs 26 deg. 26 min., and latitude 0
deg. 32 min. S.; at what time will he rise, set, and
come to the meridian of Greenwich 7
PROBLEM LXIX.
To find the amplitude of any star, its oblique ascension
and descension, and its diurnal arc for any given day.
RULE. Elevate the pole to the latitude of the place,
and bring the given star to the eastern part of the ho-
rizon; then the number of degrees between the star
and the eastern point of the horizon will be its rising
amplitude; and the degree of the equinoctial cut by
the horizon will be the oblique ascension: set the index
of the hour-circle to 12, and turn the globe westward
till the given star comes to the western edge of the ho-
rizon; the hours passed over by the index will be the
star's diurnal arc, or continuance above the horizon.
The setting amplitude will be the number of degrees
between the star and the western point of the º rizon,
and the oblique descension will be representedt
in 2 2 A 2

I38 PROBLEMIS PERFORMED WITH
degree of the equinoctial which is intersected by the
horizon, reckoning from the point Aries.
ExAMPLEs. 1. Required the rising and setting am-
plitude of Sirius, its oblique ascension, oblique descen-
sion, and diurnal arc, at London 7
Answer. The rising amplitude is 27 deg. to the south of the east;
setting amplitude 27 deg. south of the west; oblique ascension 120 deg.;
oblique descension 77 deg.; and diurnal arc 9 hours 6 minutes.
2. Required the rising and setting amplitude of Al-
debaran, its oblique ascension, oblique descension, and
diurnal arc, at London 7
3. Required the rising and setting amplitude of
Arcturus, its oblique ascension, oblique descension,
and diurnal arc, at London 7
4. Required the rising and setting amplitude of x.
Bellatrix, its oblique ascension, oblique descension,
and diurnal arc, at London 7
PROBLEM LXX.
To find the distances of the stars from each other in
degrees.
RULE. Lay the quadrant of altitude over any two
stars, so that the division marked o may be on one of
the stars; the degrees between them will show their
distance, or the angle which these stars subtend, as
seen by a spectator on the earth.
ExAMPLEs. 1. What is the distance between Vegain
Lyra, and Altair in the Eagle'ſ
Answer. 34 degrees.
2. Required the distance between 8 in the Bull's
Horn, and y Bellatrix in Orion's shoulder?
THE CELESTIAL, GLOBE, 139
3. What is the distance between 3 in Pollux, and •
in Procyon?
4. What is the distance between n, the brightest of
the Pleiades, and 3 in the Great Dog's Foot?
5. What is the distance between in Orion's girdle,
and 3 in Cetus?
6. What is the distance between Arcturus in Boötes,
and 3 in the right shoulder of Serpentarius!
PROBLEM LXXI.
To find what stars lie in or near the moon’s path, or
what stars the moon can eclipse, or make a near ap-
proach to.
RULE. Find the moon’s longitude and latitude, or
her right ascension and declination, in an ephemeris,
for several days, and mark the moon's places on the
globe; then by laying a thread, or the quadrant of alti-
tude, over these places, you will see nearly the moon’s
path, and consequently, what stars lie in her way.
ExAMPLEs. 1. What stars were in, or near, the
moon’s path, on the 10th, 11th, 13th, and 16th of De-
cember, 1805 !
10th, 5's longitude Q 20° 12' latitude 3° 34' S.
11th, - - iſ 4 22 - - 4 25 S.
13th, - =~ 1 39 º - 5 15 S.
16th, º * m 10 11 - - 4 26 S.
Answer. The stars will be found to be Cor Leonis or Regulus, Spi-
ca Virginis, 2 in Libra, &c. See page 47, White's Ephemeris.
2. On the 1st, 2d, 3d, 4th, and 5th of April, 1827,
what stars will lie near the moon's way?
140 PROBLEMIS PERFORMED WITH
1st, 5's right ascension, 72° 6' declination 19°55'N
2d, - º- 84 41 - - 19 59 N.
3d, - tº 97 14 - - 19 9 N.
4th, * 109 44' º - 17 28 N.
5th, - - 122 8 - - 14 58 N
PROBLEM LXXII.
Given the latitude of the place and the day of the
month, to find what planets will be above the horizon
after sun-setting.
RULE. Elevate the pole so many degrees above the
horizon as are equal to the latitude of the place; find
the sun's place in the ecliptic, and bring it to the
western part of the horizon, or to ten or twelve degrees
below ; then look in the ephemeris for that day and
month, and you will find what planets are above the
horizon, such planets will be fit for observation on that
night.
ExAMPLEs. 1. Were any of the planets visible after
the sun had descended ten degrees below the horizon
of London, on the 1st of December, 1805 ! Their lon-
gitudes being as follow :
# 8, 22° 30' 1ſ 8, 15° 27' Y's longitude at
2 9 23 40 H. 6 24 50 midnight 0" 9°
3 8 25 21 # 6 24, 5
Answer. Venus and the moon were visible.
2. What planets will be above the horizon of Lon
don when the sun has descended ten degrees below,
on the 1st of January, 1827 ? Their longitudes being
as follow:
THE CELESTIAL, GLOBE. 141
# 8 17°51' At 6' 12°13 5's longitude at
9 8 27 10 # 3 2 1 midnight 11° 5°9'
3 11 2 48 # 9 23 22
PROBLEM LXXIII.
Given the latitude of the place, day of the month, and
hour of the night or morning, to find what planets
will be visible at that hour.
RULE. Elevate the pole so many degrees above the
horizon as are equal to the latitude of the place; find
the sun's place in the ecliptic, bring it to the brass me-
ridian, and set the index of the hour-circle to 12; then,
if the given time be before noon, turn the globe eastward
till the index has passed over as many hours as the
time wants of noon; but if the given time be past noon,
turn the globe westward on its axis till the index has
passed over as many hours as the time is past noon:
let the globe rest in this position, and look in the
ephemeris for the longitudes of the planets, and, if any
of them be in the signs which are above the horizon,
such planets will be visible.
ExAMPLEs. 1. On the 1st of December, 1805, the
longitudes of the planets, by an ephemeris, were as
follow ; were any of them visible at London at five
o'clock in the morning 7
$ 8, 22° 30' Aſ 8, 15° 27' y's longitude at
2 9 23 40 # 6 24 50 midnight 0" 9° 15'.
3. 8 25 21 # 6 24 5
Answer. Saturn and the Georgium Sidus were visible, and both
nearly in the same point of the heavens, near the eastern horizon, Sa-.
turn was a little to the north of the Georgian. J
142 PROBLEMIS PERFORMED WITH
2. On the first of June, 1827, the longitudes of the
planets in the fourth page of the Nautical Almanac are
as follow: will any of them be visible at London at ten
o'clock in the evening?
§ 2 0°54' 2| 6’ 4°28' X's longitude at
2 1 7 1 % 3 5 47 midnight 5' 0° 25'.
3 2 22 12 Hi 9 27 52
PROBLEM LXXIV.
The latitude of the 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 latitude of the place; find
the latitude and longitude of Venus in an ephemeris,
and mark her place on the globe; find the sun's place
in the ecliptic, and bring it to the brass meridian; then,
if the place of Venus be to the right hand of the me-
ridian, 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
n its axis till Venus coincides with the western edge
of the horizon; and the hours passed over by the index
will show how long Venus sets after the sun.
When Venus is a morning star. Bring the sun's place
to the eastern edge of the horizon, and set the index
of the hour-circle to 12; turn the globe eastward on
its axis till Venus comes to the eastern edge of the
THE CELESTIAL, GLOBE, 143
morizon, and the hours passed over by the index will
show how long Venus rises before the sun.
NoTE. The same rule will serve for Jupiter, by mark-
ing his place instead of that of Venus.
ExAMPLEs. 1. On the first of March, 1805, the
longitude of Venus was 10 signs, 18 deg. 14 min., or
18 deg. 14 min. in Aquarius, latitude 0 deg. 52 min.
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
the sun set !
Answer. Venus was a morning star, and rose three quarters of an
hour before the sun.
2. On the 25th of October, 1805, the longitude of
Jupiter was 8 signs 7 deg. 26 min., or 7 deg. 26 min.
in Sagittarius, latitude 0 deg. 29 min. north: whether
was he a morning or an evening star 7 If a morning
star, how long did he rise before the sun at London 7
If an evening star, how long did he shine after the sun
set !
Answer. Jupiter was an evening star, and set 1 hour and 20 min.
after the sun.
3. On the 1st of January, 1827, the longitude of
Venus will be 8 signs 27 deg. 10 min., latitude 4 deg.
29 min. north : will she be a morning or an evening
star? If she be a morning star, how long will she rise
before the sun at London? If an evening star, how
long will she shine after the sun sets 7
4. On the seventh of July, 1827, the longitude of
Jupiter will be 6 signs 5 deg. 46 min., latitude 1 deg.
19 mia, north; will he be a morning or an evening
144 PROBLEMS PERFORMED WITH
star If he be a morning star, how long will he rise
before the Sun? If an evening star, how long will he
shine after the sun sets?
PROBLEM LXXV.
: The latitude of a place and day of the month being given
to find the meridian altitude of any star or planet.
RULE. Elevate the pole so many degrees above the
horizon as are equal to the latitude of the given place;
then,
For a star. Bring the given star to that part of the
brass meridian, which is numbered from the equinoc-
tial towards the poles; the degrees on the meridian
contained between the star and the horizon will be the
altitude required.
For the moon or a planet. Look in an ephemeris for
the planet's latitude and longitude, or for its right as-
cension and declination, for the given month and day,
and mark its place on the globe; bring the planet's
place to the brass meridian; and the number of degrees
between that place and the horizon will be the altitude.
ExAMPLEs. 1. What is the meridian altitude of Al-
debaran in Taurus, at London 1
Answer. 549 36.
2. What is the meridian altitude of Arcturus in
Boötes, at London 7
3. On the first of February, 1827, the longitude of
Jupiter will be 6 signs 14 deg. 25 min., and latitude
1 deg. 27 min, north : what will his meridian altitude
be at London f
4. On the first of November, 1827, the longitude of,
k
THE CELESTIAL, GLOBE, 145
Saturn will be 3 signs 20 deg. 18 min., and latitude
0 deg. 21 min. south : what will his meridian altitude be
at London 7
5. On the first of April, 1827, at the time of the
moon’s passage over the meridian of Greenwich, her
right ascension is 67° 49', and declination 19° 40' N.
required her meridian altitude at Greenwich 3
6. On the 21st of December, 1827, the moon will
pass over the meridian of Greenwich at 56 minutes
past two o'clock in the evening ; required her meridian
altitude 7
The X's right ascension at noon being 440 49, declination 150 51' N.
Do. at midnight - - - - - 50 58 - - - 16 58 N.
PROBLEM LXXVI.
To find all those places on the earth to which the moon
will be nearly vertical on any given day.
RULE. Look in an ephemeris for the moon’s lati-
tude and longitude for the given day, and mark her
place on the globe (as in Prob. LXV.); bring this
place to that part of the brass meridian which is num-
bered from the equinoctial towards the poles, and ob-
serve the degree above it; for all places on the earth
having that latitude will have the moon vertical (or
nearly so) when she comes to their respective meri-
'dians.
OR: Take the moon’s declination from page VI. of
the Nautical Almanac, and mark whether it be north
or south, then, by the terrestrial globe, or by a map,
find all places having the same number of degrees of
latitude as are contained in the moon's declination,
18 2 B
*
**
146 PROBLEMIS PERFORMED WITH
and those will be the places to which the moon will be
successively vertical on the given day. If the moon's
declination be north, the places will be in north latitude;
if the moon’s declination be south, they will be in south
latitude.
ExAMPLEs. 1. On the 15th of October, 1805, the
moon's longitude at midnight was 3 signs 29 deg. 14
min., and her latitude 1 deg. 35 min. south; over what
places did she pass nearly vertical ?
Answer. From the moon's latitude and longitude being given, her
declination may be found by the globe to be about 199 north. The
moon was vertical at Porto Rico, St. Domingo, the north of Jamaica,
O'why'hee, &c.
2. On the 9th of September, 1827, the moon’s lon-
gitude at midnight will be 1 sign 10 deg., and her
latitude 0 deg. 22 min. south; over what places on the
earth will she pass nearly vertical ?
3. What is the greatest north declination which the
moon can possibly have, and to what places will she be
then vertical!
4. What is the greatest south declination which the
moon can possibly have, and to what places will she be
then vertical ?
PROBLEM LXXVII.
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. Elevate the pole so many degrees above the
horizon as are equal to the latitude of the place, and
screw the quadrant of altitude upon the brassmeridian
over that latitude: find the sun's place in the ecliptic
THE CELESTIAL GIOBE, * 147
bring it to the brass meridian, and set the Index of the
hour-circle to 12; bring the lower end of the quadrant
of altitude to that side of the meridian on which the
star was situated when observed ; turn the globe west-
ward till the centre of the star cuts the given altitude
on the quadrant; count the hours which the index has
passed over, and they will show the time from noon
when the star has the given altitude : the quadrant will
intersect the horizon in the required azimuth.
ExAMPLEs. 1. At London, on the 28th of Decem-
ber, the star Deneb in the Lion's tail, marked 3, was
observed to be 40 deg. above the horizon, and east of
the meridian : what hour was it, and what was the star's
azimuth'ſ
Answer. By bringing the sun's place to the meridian, and turning
the globe westward on 1ts axis till the star cuts 40 deg. of the quadrant
east of the meridian, the index will have passed over 14 hours; conse-
quently, the star has 40 deg. of altitude east of the meridian, 14 hours
from noon, or at two o'clock in the morning. Its azimuth will be 62;
deg. from the south towards the east.
2. At London, on the 28th of December, the star 8,
in the Lion’s tail, was observed to be westward of the
meridian, and to have 40 deg. of altitude : what hour
was it, and what was the star's azimuth?
Answer. By turning the globe westward on its axis till the star cuts
40 deg, of the quadrant west of the meridian, the index will have passed
over 20 hours; consequently, the star has 40 deg. of altitude west of
the meridian, 20 hours from noon, or at eight o'clock in the morning.
Its azimuth will be 62% deg. from the south towards the west.
3. At London, on the 1st of September, the altitude
of Benetnach in Ursa Major, marked n, was observed
to be 36 degrees above the horizon, and west of the
meridian ; what hour was it, and what was the star's
azimuth 1 *
148 PROBLEMS PERFORMED WITH
4. On the 21st of December, the altitude of Sirius,
when west of the meridian at London, was observed to
be 8 deg. above the horizon ; what hour was it, and
what was the star's azimuth?
5. On the 12th of August, Menkar in the Whale's
jaw, marked *, was observed to be 37 deg. above the
horizon of London, and eastward of the meridian;
what hour was it, and what was the star's azimuth
PROBLEM LXXVIII.
Given the latitude of a place, day of the month, and hour
of the day, to find the altitude of any star, and its
azimuth.
RULE. Elevate the pole so many degrees above the
horizon as are equal to the latitude of the place, and
screw the quadrant of altitude upon the brass meridian
over that latitude ; find the sun's place in the ecliptic,
bring it to the brass meridian, and set the index of the
hour-circle to 12; then, if the given time be before
noon ; turn the globe eastward on its axis till the in-
dex has passed over as many hours as the time wants
of noon ; if the time be past noon, turn the globe west-
ward till the index has passed over as many hours as
the time is past noon: let the globe rest in this posi-
tion, and move the quadrant of altitude till its gradua-
ted edge coincides with the centre of the given star;
the degrees on the quadrant, from the horizon to the
star, will be the altitude; and the distance from the
north or south point of the horizon to the quadrant,
counted on the horizon, will be the azimuth from the
north or south.
THE CELESTIAL GI, OBE, 149
ExAMPLEs. 1. What are the altitude and azimuth
of Capella at Rome, when it is five o'clock in the morn-
ing on the 2d of December?
Answer. The altitude is 41 deg. 58 min. and the azimuth 60 deg.
50 min. from the north towards the west.
2. Required the altitude and azimuth of Altair in
Aquila on the 6th of October, at nine o'clock in the
evening, at London 7
3. On what point of the compass does the star Alde-
baran bear at the Cape of Good Hope, on the 5th of
March, at a quarter past eight o'clock in the evening;
and what is its altitude 7
4. Required the altitude and azimuth of Acyone in
the Pleiades marked n, on the 21st of December, at four
o'clock in the morning, at London
PROBLEM LXXIX.
Given the latitude of the place, day of the month, and
azimuth of a star, to find the hour of the night and
the star's altitude,
RULE. Elevate the pole so many degrees above the
horizon as are equal to the latitude of the place, and
screw the quadrant of altitude upon the brass meridian
over that latitude; find the sun's place in the ecliptic,
bring it to the brass meridian, and set the index of the
hour-circle to twelve; bring the lower end of the qua-
drant of altitude to coincide with the given azimuth on
the horizon, and hold it in that position; turn the globe
westward till the given star comes to the graduated
edge of the quadrant, and the hours passed over by the
index will be the time from noon; the degrees on the
n 2 2 B 2
150 PROBLEMS PERFORMED WITH
quadrant, reckoning from the horizon to the star, wil,
be the altitude.
ExAMPLEs. 1. At London, on the 28th of Decem-
ber, the azimuth of Deneb in the Lion's tail marked 3,
was 62% deg. from the south towards the west; what
hour was it, and what was the star's altitude 7
Answer. By turning the globe westward on its axis, the index will
pass over 20 hours before the star intersects the quadrant; therefore
the time will be 20 hours from noon, or eight o'clock in the morning;
and the star's altitude will be 40 deg.
2. At London, on the 5th of May, the azimuth of
Cor Leonis, or Regulus, marked 2, was 74 deg. from
the south towards the west; required the star's altitude,
and the hour of the night?
3. On the 8th of October, the azimuth of the star
marked 3, in the shoulder of Auriga, was 50 deg. from
the north towards the east; required its altitude at Lon-
don, and the hour of the night?
4. On the 10th of September, the azimuth of the
star marked , in the Dolphin, was 20 deg. from the
south towards the east; required its altitude at London,
and the hour of the night?
PROBLEM LXXX.
Two stars being given, the one on the meridian, and the
other on 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 brass meridian ; keep the globe
from turning on its axis, and elevate or depress the
pole till the other star comes to the eastern or western
THE CELESTIAL, GLOBE, 151
part of the horizon ; then the degrees from the ele-
wated pole to the horizon will be the latitude.
ExAMPLEs. 1. When the two pointers of the Great
Bear, marked 2 and 3, or Dubhe and 3, were on the
meridian, I observed Vega in Lyra to be rising; re-
quired the latitude 7
Answer. 27 deg. north.
2. When Arcturus in Boötes was on the meridian,
Altair in the Eagle was rising; required the latitude 7
3. When the star marked 3 in Gemini was on the
meridian, in the shoulder of Andromeda was setting;
required the latitude?
4. In what latitude are 2 and 3, or Sirius and 3 in
Canis Major rising, when Algenib, or 2, in Perseus, is
on the meridian 7
PROBLEM LXXXI.
The latitude of the place, the day of the month, and
two stars that have the same azimuth, being given, to
find the hour of the night.
RULE. Elevate the pole so many degrees above the
horizon as are equal to the latitude of the place, and
screw the quadrant of altitude upon the brass meridian
over that latitude; find the sun's place in the ecliptic,
bring it to the brass meridian, and set the index of the
hour-circle to 12 ; turn the globe on its axis from east
to west till the two given stars coincide with the gra-
duated edge of the quadrant of altitude; 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.
152 PROBLEMIS PERFORMEED WITH
ExAMPLEs. 1. 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?
Answer. By bringing the sun's place to the meridian, &c. and turn-
ung the globe westward, the index will pass over 15 hours before the
stars coincide with the quadrant; hence they will have the same azi-
muth at 15 hours from noon, or at three o'clock in the morning; and
the azimuth will be 42} deg. from the south towards the east.
2. On the 10th of September, what is the hour at
London, when Deneb in Cygnus, and Markab in Pe-
gasus, have the same azimuth, and what is the azimuth 7
3. At what hour on the 15th of April will Arcturus
and Spica Virginis have the same azimuth at London,
and what will that azimuth be 7
4. 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 7
5. On the 21st of December, what is the hour at
Dublin when 2 or Algenib in Perseus, and 3 in the
Bull's horn, have the same azimuth, and what is the
azimuth
PROBLEM LXXXII.
The latitude of the place, the day of the month, and two
stars that have the same altitude, being given, to find
the hour of the night.
RULE. Elevate the pole so many degrees above the
horizon as are equal to the latitude of the place, and
screw the quadrant of altitude upon the brass meridian
over that latitude; find the sun's place in the ecliptic,
bring it to the brass meridian, and set the index of the
hour-circle to 12; turn the globe on its axis from east
THE CELESTIAL GI.O.B.E, 153
to west till the two given stars coincide with the given
altitude on the graduated edge of the quadrant; the
hours passed over by the index will be the time from
noon when the two stars have that altitude.
ExAMPLEs. 1. At what hour at London, on the 2d
of September, will Markab in Pegasus, and 2 in the
head of Andromeda, have each 30 deg. of altitude 7
Answer. At a quarter past eight in the evening.
2. At what hour at London, on the 5th of January,
will 2, Menkar, in the Whale's jaw, and 2, Aldebaran,
in Taurus, have each 35 deg. of altitude 7
3. At what hour at Edinburgh, on the 10th of No-
vember, will 2, Altair, in the body of the Eagle, and z,
in the tail of the Eagle, have each 35 deg. of altitude :
4. At what hour at Dublin, on the 15th of May,
will n, Benetnach, in the Great Bear's tail, and 2-, in the
shoulder of Boötes, have 56 deg. of altitude 7
PROBLEM LXXXIII.
The altitudes of two stars having the same azimuth,
and that azimuth being given, to find the latitude of
the place.
RULE. Place the graduated edge of the quadrant of
altitude over the two stars, so that each star may be
exactly under its given altitude on the quadrant; hold
the quadrant in this position, and elevate or depress the
pole till the division marked o, on the lower end of the
quadrant, coincides with the given azimuth on the ho-
rizon: when this is effected, the elevation of the pole
will be the latitude.
154 PROBLEMs PERFORMED witH
ExAMPLEs. 1. The altitude of Arcturus was obs
served to be 40 deg. and that of Cor. Caroli 68 deg.
their common azimuth at the same time was 71 deg.
from the south towards the east; required the latitude 7
Answer. 51# deg. north.
2. The altitude of s in Castor was observed to be 40
deg., and that of 3 in Procyon 20 deg. ; their common
azimuth at the same time was 73% deg. from the south
towards the east; required the latitude 7
3. The altitude of 2, Dubhe, was observed to be 40
deg., and that of x in the back of the Great Bear 29%
deg., their common azimuth at the same time was 30
deg. from the north towards the east; required the la-
titude 7
4. The altitude of Vega, or 2 in Lyra, was observed
to be 70 deg., and that of , in the head of Hercules
39% deg., their common azimuth at the same time was
60 deg. from the south towards the west; required the
latitude 7
PROBLEM LXXXIV.
The day of the month being given, and the hour when
any known star rises or sets, to find the latitude of
the place.
RULE. Find the sun's place in the ecliptic, bring
it to the brass meridian, and set the index of the hour-
circle to 12; then, if the given time be before noon,
turn the globe eastward till the index has passed over
as many hours as the time wants of noon; but, if the
given time be past noon, turn the globe westward till
the index has passed over as many hours as the time
THE CELESTIAL, GLOBE, 155
is past noon; elevate or depress the pole till the cen-
tre of the given star coincides with the horizon; then
the elevation of the pole will show the latitude.
ExAMPLEs. 1. In what latitude does s, Mirach, in
Boötes, rise at half past twelve o'clock at night, on the
tenth of December 7
Answer. 51# deg. north.
2. In what latitude does Cor Leonis, or Regulus,
rise at ten o'clock at night, on the 21st of January'ſ
3. In what latitude does 3, Rigel in Orion, set at
four o'clock in the morning, on the 21st of December?
4. In what latitude does 3, Capricornus, set at eleven
o'clock at night, on the 10th of October 1 .
PROBLEM LXXXV.
To find on what day of the year any given star passes
the meridian at any given hour.
RULE. Bring the given star to the brass meridian,
and set the index to 12; then, if the given time be
before noon, turn the globe westward till the index has
passed over as many hours as the time wants of noon;
but, if the given time be past noon, turn the globe
eastward till the index has passed over as many hours
as the time is past noon; observe that degree of the
ecliptic which is intersected by the graduated edge of
the brass meridian, and the day of the month answering
thereto, on the horizon, will be the day required.
ExAMPLEs. 1. On what day of the month does Pro-
cyon come to the meridian of London at three o'clock
in the morning?
Answer. Here the time is nine hours before noon, the globe must
156 PROBLEMS PERFORMED WITH
therefore be turned nine hours towards the west, the point of the eclip
tic intersected by the brass meridian will then be the ninth of 1, an
swering nearly to the first of December.
2. On what day of the month, and in what month
does 2, Alderamin, in Cepheus, come to the meridian of
Edinburgh at ten o’clock at night?
Answer. Here the time is ten hours after noon; the globe must
therefore be turned ten hours towards the east, the point of the ecliptic
intersected by the brass meridian will then be the 17th of ITQ, answering
to the ninth of September.
3. On what day of the month, and in what month,
does 8, Deneb, in the Lion's tail, come to the meri-
dian of Dublin at nine o'clock at night !
4. On what day of the month, and in what month,
does Arcturus in Boötes come to the meridian of Lon-
don at noon 7
5. On what day of the month, and in what month,
does 3 in the Great Bear come to the meridian of Lon-
don at midnight?
6. On what day of the month, and in what month,
does Aldebaran come to the meridian of Philadelphia
at five o'clock in the morning at London ?
PROBLEM LXXXVI.
The day of the month being given, to find at what hour
any given star comes to the meridian.
RULE. Find the sun's place in the ecliptic, bring
it to the brass meridian, and set the index of the hour-
circle to 12; turn the globe westward on its axis till
the given star comes to the brass meridian, and the
hours passed over by the index will be the time from
noon when the star culminates.
THE CELESTIAL, GLOBE, I57
OR, witHouT THE GLOBE.
Subtract the right ascension of the sun for the given
day from the right ascension of the star, and the remain-
der will be the time of the star's culminating nearly.
If the sun’s right ascension exceeds the star's add 24
hours to the star's before you subtract.
ExAMPLEs. 1. At what hour does Cor Leonis, or
Regulus, come to the meridian of London on the 23d
of September 7
Answer. The index will pass over 213 hours; hence this star cul-
minates or comes to the meridian 213 hours after moon, or at three
quarters past nine o'clock in the morning.
2. At what hour does Arcturus come to the meri-
dian of London on the 9th of February 7
Answer. The index will pass over 16; hours; hence Arcturus cut
minates 164 hours after noon, or at half past four o'clock in the morn-
3. Required the hours at which the following stars
come to the meridian of London on the respective days
annexed:
Bellatrix, January 9th. 3 Mirach, October 5th.
Menkar, May 18th. Aldebaran, Feb. 12th.
• Draco, Sept. 22d. 8 Aries, November 5th.
* Dubhe, Dec. 20th. • Taurus, January 24th
4. At what time will Sirius come to the meridian of
Greenwich on the 18th of December, 1827, his right
ascension being 99° 15' 26", and the sun's right as-
cension 265°29' 0".
O 2 C.
158 PROBLEMIS PERFORMED WITH
PROBLEM LXXXVII.
Given the azimuth of a known star, the latitude, and the
hour, to find the star's altitude and the day of the
month.
RULE. Bring the pole so many degrees above the
horizon as are equal to the latitude of the given place,
screw the quadrant of altitude upon the brass meridian
over that latitude, bring the division marked o on the
lower end of the quadrant to the given azimuth on the
horizon, turn the globe till the star coincides with the
graduated edge of the quadrant, and set the index of
the hour-circle to 12; then if the given time be before
noon, turn the globe westward till the index has passed
over as many hours as the time wants of noon ; if the
given time be past noon, turn the globe eastward till
the index has passed over as many hours as the time is
past noon ; observe that degree of the ecliptic which
is intersected by the graduated edge of the brass meri-
dian, and the day of the month answering thereto, on
the horizon, will be the day required.
ExAMPLEs. 1. At London, at ten o'clock at night,
the azimuth of Spica Virginis was observed to be 40
deg. from the south towards the west; required its alti-
tude, and the day of the month 7
Answer. The star's altitude is 20 deg. and the day is the 18th of
June. The time being ten hours past noon, the globe must be turned
ten hours towards the east.
2. At London, at four o'clock in the morning, the
THE CELESTIAL, GLOBE. 159
azimuth of Arcturus was 70 deg. from the south to-
wards the west; required its altitude, and the day of
the month
Answer. Here the time wants eight hours of noon, therefore the
globe must be turned eight hours westward; the altitude of the stan
will be found to be 40 deg., and the day the 12th of April.
3. At Edinburgh, at 11 o’clock at night, the azimuth
of a Serpentarius, or Ras Alhagus, was 60 deg. from
the South towards the east; required its altitude, and
the day of the month 7
4. At Dublin, at two o'clock in the morning, the
azimuth of 3 Pegasus, or Scheat, was 70 deg. from
the north towards the east; required its altitude, and
the day of the month 7
PROBLEM LXXXVIII.
The altitudes of two stars being given, to find the lati-
tude of the place.
RULE. Subtract each star's altitude from 90 de-
grees; take successively the extent of the number of
degrees, contained in each of the remainders, fiom the
equinoctial, with a pair of compasses; with the com-
passes thus extended, place one foot successively in the
centre of each star, and describe arcs on the globe with
a black-lead pencil; these arcs will cross each other in
the zenith; bring the point of intersection to that part
of the brass meridian which is numbered from the
equinoctial towards the poles, and the degree above it
will be the latitude.
ExAMPLEs. 1. At sea, in north latitude, I observed
160 PROBLEMIS PERFORMED WITH
the altitude of Capella to be 30 deg., and that of Alde-
baran 35 deg. ; what latitude was I in 7
Answer. With an extent of 60 deg. (=900–300) taken from the
equinoctial, and one foot of the compasses in the centre of Capella, de-
scribe an arc towards the north; then with 55 deg. (=900—350) taken
In a similar manner, and one foot of the compasses in the centre of Al-
debaran, describe another arc, crossing the former; the point of inter-
section brought to the brass meridian will show the latitude to be 20;
deg. north.
2. The altitude of Markab in Pegasus was 30 deg.,
and that of Altair in the Eagle, at the same time, was
65 deg. ; what was the latitude, supposing it to be
north 7
3. In north latitude the altitude of Arcturus was ob-
served to be 60 deg., and that of 8 or Deneb, in the
Lion's tail, at the same time, was 70 deg. ; what was
the latitude 7
4. In north latitude, the altitude of Procyon was
observed to be 50 deg. and that of Betelgeux in Orion,
at the same time, was 58 deg. ; required the latitude
of the place of observation ?
PROBLEM LXXXIX.
The meridian altitude of a known star being given at
any place in north latitude, to find the latitude.
RULE. Bring the given star to that part of the brass
meridian which is numbered from the equinoctial to-
wards the poles; count the number of degrees in the
given altitude on the brass meridian from the star to-
wards the south part of the horizon, and mark where
the reckoning ends; elevate or depress the pole till this
mark coincides with the south point of the horizon,
THE CELESTIAL, GLOBE, 161
and the elevation of the north pole above the north
point of the horizon will show the latitude.
ExAMPLEs. 1. In what degree of north latitude is
the meridian altitude of Aldebaran 52% deg. 7
Answer. 53 deg. 36 min. north.
2. In what degree of north latitude is the meridian
altitude of 3, one of the pointers in Ursa Major, 90 deg. 1
3. In what degree of north latitude is 2, in the head
of Draco, vertical when it culminates?
4. In what degree of north latitude is the meridian
altitude of , or Mirach in Boötes, 68 deg. 1
PROBLEM XC.
The latitude of a place, day of the month, and hour of
the day, being given, to find the NoNAGESIMAL DE-
GREE* of the ecliptic, its altitude and azimuth, and
the MEDIUM. COELI.
RULE. Elevate the north pole to the latitude of the
given place, and screw the quadrant of altitude upon
the brass meridian over that latitude ; find the sun’s
place in the ecliptic, bring it to the brass meridian,
and set the index of the hour-circle to 12; then, if the
given time be before noon, turn the globe eastward till
the index has passed over as many hours as the time
wants of noon; but, if the given time be past noon,
*The nonagesimal degree of the ecliptic is that point which is the
most elevated above the horizon, and is measured by the angle which
the ecliptic makes with the horizon at any elevation of the pole; or, it is
the distance beneath the zenith of the place and the pole of the echip-
tic. This angle is frequently used in the calculation of solar eclipses.
The medium coeli, or mid-heaven, is that point of the ecliptic whium is
upon the meridian.
o 2 2 c 2
162 PROBLEMIS PERFORMED WITH
turn the globe westward till the index has past over
as many hours as the time is past noon, and fix the
globe in this position; count 90 deg. upon the ecliptic
from the horizon, (either eastward or westward) and
mark where the reckoning ends, for that point of the
ecliptic will be the nonagesimal degree, and the degree
of the ecliptic cut by the brass meridian will be the
medium coeli: bring the graduated edge of the qua-
drant of altitude to coincide with the nonagesimal de-
gree of the ecliptic thus found, and the number of de-
grees on the quadrant, counted from the horizon, will
be the altitude of the nonagesimal degree; the azimuth
will be seen on the horizon.
ExAMPLEs. 1. On the 21st of June, at forty-five
minutes past three o’clock in the afternoon at London,
required the point of the ecliptic which is the nonage-
simal degree, its altitude and azimuth, the longitude
of the medium coeli, and its altitude, &c.
Answer. The nonagesimal degree is 10 deg. in Leo, its altitude is
54 deg., and its azimuth 22 deg. from the south towards the west, or
nearly S. S. W. The mid-heaven, or point of the ecliptic under the
brass meridian, is 24 deg. in Leo, and its altitude above the horizon, is
52 deg. The degree of the equinoctial cut by the brass meridian reck-
oning from the point Aries, is the right ascension of the mid-heaven,
which in this example is 146 deg. The rising point of the ecliptic will
be found to be'10 deg, in Scorpio, and the setting point 10 deg. in Tau-
rus. If the graduated edge of the quadrant be brought to coincide with
the sun's place, the sun's altitude will be found to be 39 deg. and his
azimuth 78% deg. from the south towards the west, or nearly W. by S.
2. At London, on the 24th of April, at nine o'clock
in the morning; required the point of the ecliptic which
is the nonagesimal degree, its altitude and azimuth, the
point of the ecliptic which is the mid-heaven, &c. &c."
THE CELESTIAT, GLOBE. 163
3. At Limerick, in 52 deg. 22 min. north latitude, .
on the 15th of October, at five o'clock in the afternoon ,
required the point of the ecliptic which is the nonage-
simal degree, its altitude and azimuth, the point of the
ecliptic which is the mid-heaven, &c. &c."
4. At Dublin, in latitude 53 deg. 21 min. north, on
the 15th of January, at two o'clock in the afternoon :
required the longitude, altitude, and azimuth, of the
nonagesimal degree; and the longitude and altitude of
the medium coeli, &c. &c. 4
PROBLEM XCI.
The latitude of a place, day of the month, and the hour,
together with the altitude and azimuth of a star, being
given, to find the star.
RULE. Elevate the pole so many degrees above the
horizon as are equal to the latitude of the place, and
screw the quadrant of altitude on the brass meridian
over that latitude; find the sun's place in the ecliptic,
bring it to the brass meridian, and set the index of
the hour-circle to 12; then, if the given time be before
noon, turn the globe eastward till the index has passed
over as many hours as the time wants of noon, but, if
the time be past noon, turn the globe westward till the
index has passed over as many hours as the time is past
noon; let the globe rest in this position, and bring the
division marked O on the quadrant to the given azi-
muth on the horizon; then, immediately under the
given altitude on the graduated edge of the quadrant,
wou will find the star.
ExAMPLEs. 1. At London, on the 21st of Decem:
164 PROBLEMS PERFORMED WITH
ber, at four o’clock in the morning, the altitude of a
star was 50 deg., and its azimuth was 37 deg. from the
south towards the east; required the name of the star 7
Answer. Deneb, or 8 in the Lion's tail.
2. The altitude of a star was 27 deg., its azimuth
76% deg. from the south towards the west, at eleven
o'clock in the evening at London, on the 11th of May;
what star was it !
3. At London, on the 21st of December, at four
o'clock in the morning, the altitude of a star was 8 deg.,
and its azimuth 51 deg. from the south towards the
west; required the name of the star 7
4. At London, on the 1st of September, at nine
o'clock in the evening, the altitude of a star was 47
deg., and its azimuth 73 deg. from the south towards
the east; required the name of the star 7
PROBLEM XCII.
To find the time of the moon’s southing, or coming to
the meridian of any place, on any given day of the
month.
RULE. Elevate the pole so many degrees above the
horizon as are equal to the latitude of the given place;
find the moon's latitude and longitude, or her right as-
cension and declination, from an ephemeris, and mark
her place on the globe; bring the sun's place to the
brass meridian, and set the index of the hour-circle to
12; turn the globe westward till the moon’s place
comes to the meridian, and the hours passed over by
the index will show the time from noon when the moon
will be upon the meridian.
THE CELESTIAL, GLOBE. 165
OR, witHouT THE GLOBE.
Find the moon’s age, which multiply by 81, and cut
off two figures from the right hand of the product, the
left hand figures will be the hours; the right hand
figures must be multiplied by 60, for minutes.
OR, CORRECTLY, THUs:
Take the difference between the sun's and moon’s
right ascension in 24 hours; then, as 24 hours dimi-
nished by this difference is to 24 hours, so is the moon’s
right ascension at noon, diminished by the sun's, to the
time of the moon’s transit.
ExAMPLEs. 1. At what hour, on the 10th of April,
1827, will the moon pass over the meridian of Green-
wich The moon’s right ascension at midnight being
185 deg. 28 min., and her declination 5 deg. 49 min.
South.
Answer. By the Globe.—The moon comes to the meridian about
midnight.
By using the Nautical Almanac.
Sun's right ascension at noon 10th April = 1 h. 13' 15" 7
Ditto . . . . 11th April = 1 16 55 5
Increase of motion in 24 hours tº 0 3 39 8
Moon's right ascension at noon 10th April = 1789.47° 32"
Ditto . . . . 11th April = 1929 16’ 45"
Increase in 24 hours . . . . 130 29, 13" equal
to 53'56"; hence 59'56" diminished by 3' 39", leaves 50. 17” the moon's
amotion exceeds the Sun's in 24 hours.
166 PROBLEMS PERFORMED WITH
Moon's right ascension 178947' x 4 = *11h. 55' 8"
Sun's right ascension . = 1 13 15.7
10 41 52.3
24h --50' 17" ; 24h. : : 100 41' : 11h. 4, the true time of the moon's pas-
sage over the meridian in the morning, agreeing within one minute of
the Nautical Almanac.
2. At what hour, on the 1st of January, 1827, will
the moon pass over the meridian of Greenwich, the
moon's right ascension at noon being 328 deg. 43 min.,
and declination 7 deg. 15 min. south.
3. At what hour, on the 12th of March, 1827, will
the moon pass over the meridian at Greenwich, the
moon's right ascension at midnight being 164 deg. 41
min., and declination 1 deg. 43 min. north 7
4. At what hour, on the 17th of October, 1827, will
the moon pass over the meridian of Greenwich, the
moon's right ascension at noon being 163 deg. 28 min.,
and declination 2 deg. 33 min. north'ſ
* PROBLEM XCIII.
The day of the month, latitude of the place, and time
of high water at the full and change of the moon be-
ing given, to find the time of high water on the given
day.
RULE. Find the time at which the moon comes to
the meridian of the given place by the preceding pro-
blem, to which add the time of high water at the given
place at the full and change of the moon, and the sum
will show the time of high water in the afternoon. If
*When the sun's right ascensionis greater than the moon's, 24hours
must be added to the moon's right ascension before you subtract.
THE CELESTIAL, GLOBE. 167
the sum exceed 12 hours, subtract 12 hours and 24
minutes from it, and the remainder will show the time
of high water in the morning; but if the sum exceed
24 hours, subtract 24 hours and 48 minutes from it,
and the remainder will show the time of high water in
the afternoon.
ExAMPLEs. 1. Required the time of high water at
London Bridge on the 2d of April, 1827, the moon's
right ascension at that time being 78 deg. 23 min, and
her declination 20 deg. 4 min. north 7
Answer, By the Globe—The moon comes to the meridian at 4h 39.
Time of high water at the full and change at London - 3 0
Time of high water in the morning - - - - 7 39
2. Required the time of high water at Hull, on the
25th of May, 1827, the moon’s right ascension at noon
being 58 deg. 34 min., and her declination 18 deg. 50
min. north 7 s &
3. Required the time of high water at Liverpool, on
the 22d of June, 1827, the moon’s right ascension at
noon being 68 deg. 2 min., and her declination 19 deg
39 min. north'ſ
4. Required the time of high water at Limerick, on
the 19th of August, 1827, the moon’s right ascension
at noon being 111 deg. 20 min., and her declination 17
deg. 10 min. north?
5. Required the time of high water at Bristol, on
the 9th of September, 1827, the moon’s right ascension
at noon being 31 deg. 51 min., and her declination 13
deg. 6 min. north ?
6. Required the time of high water at Dublin, on
168 PROBLEMIS PERFORMED WITH
the 12th of October, 1827, the moon’s right ascension
at noon being 102 degrees 57 min., and her declination.
18 deg. 3 min. north'ſ
PROBLEM XCIV.
To describe the apparent path of any planet, or of a
comet, amongst the fixed stars, &c.
RULE. Draw a straight line o, o, to represent the
ecliptic, and divide it into any convenient number of
equal parts. Set off eight of those equal parts north-
ward and southward of the ecliptic at each end thereof;
and draw lines, as in the figure Plate W.; these will re-
present the zodiac. Find the planet's geocentric lati-
tude and longitude in an ephemeris, or in the Nautical
Almanac, and mark its place for every month, or for
several days in each month, beginning at the right
hand of the ecliptic line, and proceeding towards the
left.*
Find the latitudes and longitudes f of the principal
stars in the several constellations near which the planet
passes, and set them off in a similar manner from the
right hand towards the left; you will thus have a com-
plete picture of any part of the heavens, with the posi-
*The young student will recollect, that the stars appear in a con-
trary order in the heavens to what they do on the surface of a globe
In the heavens we see the concave part, on the globe the convex.
This manner of delineating the stars will be found extremely useful,
and will enable the student to know their names and places sooner than
by the globe.
t'The places of the stars may likewise belaid down by their righ.
ascensions and declinations, by drawing a portion of the equinoctial
instead of the ecliptic.
THE CELESTIAL, GLOBE. 169
tions of the several stars, &c. as they appear to a spec-
tator on the earth.
ExAMPLE. Delineate the path of the planet Jupiter
for the year 1811; the latitudes and longitudes being
as follow :*
Longitudes. Latitudes.| Longitudes. Latitudes.
Jan. 1st. 121° 45' 0°57'S. July 25th 2.25° 1' 0°24'S.
Feb. 7th 122 11 047 S. Aug. 7th 227 36 0 23 S.
25th 1 23 58 043 S. 19th 2 29 48 0 22 S.
March 1st 1 24 29 0.42 S. 25th 3 0 48 0 22 S.
25th 128 16 0 37 S. Sept. 7th 3 245 021 S.
April 1st 129 35 0.36 S. 25th 3 4 50 0 21 S.
25th 2 4 30 0 32 S.[Oct. 7th 3 544 0 20 S.
May 1st 2 5 49 031 S. 25th 3 615 0 19 S.
13th 2 8 31 0 30 S.INov. 1st 3 610 0 18 S.
25th 2 11 17 0 29 S. 19th 3 512 0 17 S
June 1st 212 54 0 28 S. 25th 3 4 40 0 16 S.
25th 2 1827 0 26 S. Dec. 13th 3 2 34 0 14 S.
July 7th 22149 0.25 S. 25th 3 () 57 0 12 S.
Jupiter's path, when delineated, will be south of the
ecliptic in the order A, B, C, D, E, F, G, H. Thus,
he will appear at A on the 1st of January, at B on the
1st of March, at C on the 1st of April, at D on the 1st
of May, at E on the 1st of June, at F on the 7th of
July, at G on the 25th of August, and at H on the 25th
of October. On the 25th of August, when Jupiter ap-
pears at G, he will be a little to the right hand of the
star marked n in Gemini; when he arrives at H, which
will happen on the 25th of October, he will apparently
return again to G, a small matter above his former path,
*As Jupiter performs his revolution round the sun in 11 years 315
days, he will have nearly the same longitude in the years 1823 and 1835,
consequently he will pass through the same constellations as are deli-
nested in Plate V.
p 2 D
170 PROBLEMs PERFORMED, &c.
where he will be situated on the 25th of December.
Jupiter will not be visible during the whole of his ap-
parent progress from A to H, being too near to the sun
during the months of May and June.
In the same manner the places and situations of the
stars may be delineated; thus, Aldebaran, the princi-
pal star in the Hyades, will be found by the globe, (or
a proper table) to be situated in 7° of II and in 54° of
south latitude; Betelgeux in ORION's right shoulder,
in about 26° of II and 16° of south latitude, and its
place may be laid down on a map by extending the line
of its longitude, as from L, till it meets a straight line
passing through 16, 16, on the sides of the map. In
the same manner any other star's situation may be de-
scribed ; thus the Hyades will appear at Q, the Pleia-
des at P, &c. and Bellatrix, &c. as in the figure.
The constellation ORION, here described, is a very
conspicuous object in the heavens in the months of
January and February, about 9 or 10 o'clock in the
evening, and will be an excellent guide for determining
the positions of several other constellations, particularly
Canis Major, Canis Minor, Auriga, &c.
QUESTIONS
FOR EXAMINATION OF PUPILS.
CHAPTER I.
What is the terrestrial globe?—the celestial?
What is the axis of the earth?
How is it represented
What are the poles of the earth?—the celestial poles?
What is the brazen meridian 7
How is it divided?—marked 2
What are great circles?—small circles?—meridians? When is it
noon What is the first meridian 7—the equator?
How are the latitudes of places reckoned?—the longitudes?
What is the equinoctial
How are declinations and right ascensions reckoned?
What is the ecliptic f—the zodiac! How are the ecliptic and zodiac
divided? Name the spring signs—summer—autumnal—winter.
Which are the ascending signs?—the descending signs?
What are the colures?
How do they divide the ecliptic ;
What is meant by declination ?
When has the sun no declination?
When is his declination north?—when south?—when greatest?
What is the greatest declination of a star?—a planet?
What are the tropics? Of what are they the limits?
What are the polar circles?
What are parallels of latitude :
Is their number limited 2
What is the hour-circle on the artificial globe How is it divided
What is its use?
What is the horizon?—the sensible horizon?—the rational horizont—
the wooden horizon of the artificial globe 2 *
What is marked on its first circle?—the second—third—fourth—fifth
—sixth-geventh—eighth 2 º
171
172 .# QUESTIONS FOR EXAMINATION,
&
What are the cardinal points of the horizon?—of the heavens?—of
the ecliptic?
What is the zenith ?—the nadir'
What is the pole of any circle? Give examples.
What are the equinoctial points?—the solstitial 7
What happens when the sun is one of the equinoctial points?—the
solstitial 2
What is an hemisphere 7
What hemisphere does the horizon divide?—the equator?—the brass
meridian 2
What is the Mariner's eompass?
Describe it.
What is the variation of the compass?
When is the variation east?—when west?
What is the variation in England?
What is the latitude of a place?—how reckoned?—The latitude of
a star or planet?—how reckoned? What is the greatest possible au-
tude of a star?—a planet 2—of the sun ?
What is the quadrant of altitude?
What is the use of the upper division?—the lower?
What is the longitude of a place —how reckoned? What is the
greatest possible longitude of a place?
What is the longitude of a star or planet!—of the Sun ?
What are almacanters?
Are they drawn on the globe” How are they described ?
What are parallels of celestial latitude?—parallels of declination?--
Azimuth or vertical circles?
What are measured on them?
How are they represented?
What is the prime vertical?
What is the altitude of any object in the heavens?
When is it called meridian altitude :
What is the zenith distance of a celestial object?—when is it called
meridian zenith distance?
What is the polar distance of any celestial object?
What is the amplitude of an object in the heavens ! For what is it
used ? When has the sun north amplitude?—when south? When has
it none?
What is the azimuth of a celestial object 3
What are hour-circles? =
QUESTIONS FOR EXAMINATION. 173
f
What is meant by a right sphere?—a parallel sphere?—an oblique
sphere? 4.
What is meant by climate?
What is a zone How many are there? How many climates are
there 7 What is the torrid zone? What opinion was entertained by
the ancients? What are the temperate zones—the frigid zones? What
.s meant by amphiscii ?—ascii?—heteroscii?—periscii?—antoecif—pe-
rioeci?—antipodes?—right ascension?—oblique ascension?—oblique
descension?—ascensional or descensional difference t—crepusculum ?
—the angle of position?
What method of describing the stars is now used ? Who invented
it? How has it been further enlarged ? How are double stars desig-
rated ?—how discovered 7
Repeat the Greek alphabet {
What is meant by the diurnal arcſ—the noctural arcſ—aberration?
THE END.

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THE HARVEST MOON, 91
The moon goes round the ecliptic in 27 days, 8 hours
but not from change to change in less than 29 days, 12
hours; so that she must be once in every sign, and
twice in some one sign every lunation.
If the earth had no annual motion, every new moon would fall in
the same sign and degree of the ecliptic; and every full moon in the
opposite : for the moon would go exactly round the Nº. from change
to change. So that if she were once full in any sign, Sūppose in Pisces
or Aries, she would always be full there.
But in the time the moon goes round the ecliptic from any conjunc-
tion or opposition, the earth goes 27# degrees, that is, almost a signior-
ward; so that the moon must go 27# degrees more than round, before
she can be in conjunction with or opposite to the sun again. Hence,
if she were in her conjunction at the first degree of Aries, she would, in
one lunation, not only return to the same point, but repass it, and go
twice over Aries to the 27; degree.
To the inhabitants at the equator the north and south
poles appear in the horizon; and therefore the ecliptic
makes the same angle southward with the horizon when
Aries rises, as it does northward when Libra rises; con-
sequently she rises and sets not only at nearly equal
angles with the horizon, but at the equal distance in
time of about 50 minutes, all the year round: and hence
there can be no particular harvest moon about the
equator.
The farther any place is from the equator, if it be
not beyond the polar circles, the angle which the eclip.
tic and the horizon make gradually diminishes wher.
Pisces and Aries rise.
This the globe itself will fully illustrate; for the more the north
pole is elevated, the more nearly does the ecliptic coincide with the
horizon; that is, the angle is diminished.
Though in northern latitudes the autumnal full
moons are in Pisces and Aries; yet in southern lati-
92 LEAP-YEAR.
tudes it is just the reverse, because the seasons are the
contrary: for Virgo and Libra rise at as small angles
with the horizon in southern latitudes, as Pisces and
Aries do in the northern : and therefore the harvest
moons are just as regular on one side of the equator as
on the other. -
In this illustration of the harvestmoon, we have supposed the moon
to move in the ecliptic, from which the sun never deviates; but the
orbit in which the moon really moves (as was noticed under the article
Eclipses) is different from the ecliptic; one half being elevated 53 de-
grees above it, and the other half as much depressed below it. And
this oblique motion causes some small difference in the time of her
rising and setting from what has been above mentioned.
At the polar circles, the full moon neither rises in
summer, nor sets in winter. For the winter full moon
being as high in the ecliptic as the summer sun, she
must therefore continue, while passing through the
northern signs, above the horizon; and the summer
full moon being as low in the ecliptic as the winter sun,
can no more rise, when passing through the southern
signs, than he does.
CHAPTER XXXIV.
OF LEAPYEAR.
THE time our earth takes to make one complete re
volution, in its orbit round the sun, we call a year. To
complete this with great exactness is a work of consi-
derable difficulty. It has mostly been divided into
twelve months of 30 days.
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LEAP-YEAR. 93
The ancient Hebrew months consisted of 30 days each, except the
last, which contained 35. Thus the year contained 365 days. An in-
tercalary month at the end of 120 years supplied the difference.
The Athenian months consisted of 30 and 29 days alternately, ac-
cording to the regulation of Solon. This calculation produced a year
of 354 days, and a little more than one-third. But as a solar month
contains 30 days, 10 hours, 29 minutes, Meton, to reconcile the differ-
ence between the solar and lunar year, added several embolismic, or
intercalary months, during a cycle, or revolution of 19 years.
The Roman months, in the time of Romulus, were only ten of 30
and 31 days. Numa Pompilius, sensible of the great deficiency of this
computation, added two more months, and made a year of 355 days.
The Egyptians had fixed the length of their year to 365 days.
Julius Caesar, who was well acquainted with the
learning of the Egyptians, was the first who attained to .
any accuracy on the subject. Finding the year esta-
blished by Numa ten days shorter than the solar year,
he supplied the difference, fixed the length of the year
to be 365 days, 6 hours, and regulated the months ac-
cording to the present measure. To allow for the six
odd hours, he added an intercalary day every fourth
year to the month of February, reckoning the 24th of
that month twice, which year must of course consist of
366 days, and is called Leap-year. From him it was
denominated the Julian year.
This year is also called Bissea:tile in the Almanacs,
and the day added is termed the intercalary day.
The Romans, as has been observed, inserted the intercalary day, by
reckoning the 24th twice, and because the 24th of February in their
calendar was called sexta calendas Martii, the sixth of the calends of
March, the intercalary day was called bis seata calendas Martii, the
second sixth of the calends of March, and hence the year of intercalation
had the appellation of Bissertile. We introduce in leap-year a new
day in the same month, namely, the 29th.
To ascertain at any time what year is leap-year
I 2
94 LEAP-YEAR
divide the date of the year by 4, if thcre is no remain
der it is leap-year. Thus 1824 was leap-year. But
1825 divided by 4, leaves a remainder of 1, showing
that it was the first year after leap-year; and as 1829,
divided by 4, leaves 1, it will be the first after leap-
year.
But the true solar year does not contain exactly 365
days, 6 hours, but 365 days, 5 hours, 48 minutes, and
49 seconds; which to calculate for correctly, requires
an additional mode of proceeding: 365 days, 6 hours,
exceeds the true time by 11 minutes, 11 seconds, every
year, amounting to a whole day in a little less than 130
years.
Notwithstanding this, the Julian year continued in
general use till the year 1582, when Pope Gregory
XIII, reformed the calendar, by cutting off ten days be-
tween the 4th and 15th of October in that year, and
calling the 5th day of that month the 15th. This al-
teration of the style was gradually adopted through the
greater part of Europe, and the year was afterwards
called the Gregorian year, or New style.
In this country, the method of reckoning according to
the New style was not admitted into our calendars until
the year 1752, when the error amounted to nearly 11
days, which were taken from the month of September,
by calling the 3d of that month the 14th.
The error amounting to one whole day in about 130
years (by making every fourth year leap-year,) it is settled
by an act of parliament that the year 1800, and the year
1900, which, according to the rule above given, are
leap-years, shall be computed as common years, having
THE TIDES, 95
only 365 days in each; and that every four hundredth
year afterwards shall be a common year also.
If this method be adhered to, the present mode of reckoning will not
vary a single day from true time in less than 5,000 years:
The beginning of the year was also changed, by the
same act of parliament, from the 25th of March to the
1st of January. So that the succeeding months of Ja-
nuary, February, and March, up to the 24th day, which
would, by the Old style, have been reckoned part of
the year 1752, were accounted as the first three months
of the year 1753. Hence we see such a date as this,
January 1, 1757-8, or February 3, 1764-5; that is, ac-
cording to the Old style it was 1764, but according to
the New, 1765, because now the year begins in Janua-
ry instead of March. t
CHAPTER XXXV.
THE TIDEs.
THE oceans, which cover more than one half of the
globe, are in continual motion; they ebb and flow per-
petually, and these alternate elevations and depressions
are called the tides, or the flux and reflux of the sea.
The ancients considered the ebbing and flowing of the tides as one
of the greatest mysteries in nature, and were utterly at a loss to ac-
count for it. Galileo and Descartes, and particularly Kepler, made
some successful advances towards ascertaining the cause; but Sir Isaac
Newton was the first who clearly pointed out the phenomenon, and
showed what were the chief agents in producing these motions.
The tides are not only known to be dependent upon
some fixed and determinate laws; but the true cause
96 - THE TEDES.
of their agitation is demonstrated to be the attraction
of the sun and moon, particularly the latter; for as she
is so much nearer the earth than the sun, she attracts
with much greater force than he does, and consequently
raises the water much higher; which, being a fluid,
loses, as it were, its gravitating power, and yields to
their superior force.
That the tides are dependant upon some known and determinate
laws, is evident from the exact time of high water being previously
given in every ephemeris, and in many of the common almanacs.
The moon comes every day later to the meridian than on the day
preceding, and her exact time is known by calculation; and the tides
In any and every place, will be found to follow the same rule; hap-
pening exactly so much later every day as the moon comes later to the
meridian. From this exact conformity to the motions of the moon, we
are induced to look to her as the cause; and to infer that those phe-
nomena are occasioned principally by the moon's attraction.
If the earth were at rest, and there were no influence
from either sun or moon, it is obvious from the princi-
ples of gravitation, that the waters in the ocean would
be truly spherical, as plate XVI. fig. 1; but daily expe-
rience proves that they are in a state of continual agi-
tation.
If the earth and moon were without motion, and the
earth covered all over with water, the attraction of the
moon would raise it up in a heap in that part of the
ocean to which the moon is vertical, and there it would,
probably, always continue, as plate XVI. fig. 2; but
by the rotation of the earth upon its axis, each part of
its surface to which the moon is vertical is presented
to the action of the moon, and thus are produced two
floods, and two ebbs.
In this supposition we have omitted to take notice of the sun's ir
fluence. -
THE TIDES. 97
The attractive power of the sun is to that of the moon
as three to ten ; hence, when the moon is at change,
the sun and moon being in conjunction, or on the same
side of the earth, the action of both bodies is on the
same ocean of waters; the moon raising it ten parts,
and the sun three, the sum of which is thirteen parts,
represented by plate XVI. fig. 4. Now it is evident
that if thirteen parts be added to the attractive power
of these bodies, the same number of parts must be drawn
off from some other parts, as at C and D. It will now
be high water under the moon at A, and low water at
C and D.
The attractive power of the sun, according to some authorities, is to
that of the moon as two to ten, or one-fifth, and according to others as
one-third.
Those parts of the earth where the moon appears in
the horizon, as at C and D, will have low water; for
as the waters in the zenith and nadir (A and B) rise at
the same time, the waters adjacent will press towards
those places to maintain the equilibrium; and to sup-
ply the place of those, others will move the same way,
and so on; hence at the places 90° distant (C and D)
the waters will be lowest.
It is evident that, the quantity of water being the same, a rise cannot
take place at A and B, without the parts C and D being at the same
time depressed; and in this situation the waters may be considered as
partaking of an oval form.
98 THE TIDEs.
CHAPTER XXXVI.
THE TIDES, CONTINUED.
IT has been already shown, under the article gravi
tation, that the power of gravity diminishes as the square
of the distance increases; therefore not only those parts
of the sea immediately below the moon must be attract-
ed towards it, and occasion the flowing of the tides
there, as at A, fig. 4; but a similar reason occasions
the flowing of the tides in the nadir, or that part of the
earth diametrically opposite to it, as at B, for in the
hemisphere farthest from the moon, the parts being
less attracted than those which are nearer, gravitate
less towards the earth's centre, and consequently must
be higher than the rest; and as every portion of the
earth will pass twice through the elevated, and twice
through the depressed parts, two tides will be produced
each day.
It has been otherwise thus explained: All bodies moving in circles
have a tendency to fly off from their centres; now as the earth and
moon move round the centre of gravity, that part of the earth which is
at any time turned from the moon, would have a greater centrifugal
force than the side next her. At the earth's centre, the centrifugal
force will balance the attractive force; therefore as much water is
thrown off by the centrifugal force on the side which is turned from
the moon, as is raised on the side next her by her attraction.
If the tide be at high water mark in any point or har-
bour that lies open to the ocean, it will presently sub-
side and flow back for about six hours, and then return
in the same time to its former situation, rising and fall-
ing nearly twice a day, or in the space of somewhat
more than twenty-four hours. -
The interval, however, between its flux and reflux
THE TIDEs. 99
is not precisely six hours, but about 12 minutes and #
more, so that the time of high water does not happen
at the same hour, but is above # of an hour later every
day for about 30 days, when it again recurs as before.
If the moon were stationary, there would be two tides
every twenty-four hours, but as that body is daily pro-
ceeding from west to east in her orbit above 12°, the
earth must make more than a complete revolution on
its axis, before the same meridian is in conjunction
with the moon. And hence, every succeeding day the
time of high water will be above # of an hour later
than on the preceding. g
For example: If it be high water to day at noon, it will be low wa-
ter at 12 and # minutes after six in the evening; and, consequently,
after two changes more, the time of high water the next day will be
above # of an hour after noon: the day following above + past one;—
the day after that above + past two, and so on.
Again: Suppose at any place it be high water at three in the after-
noon upon the day of the new moon, the following day it will be high
water about 3 after three;—the day after about 3 past four, and so on
till the next new moon.
Not only when the sun and moon are in conjunction,
or at the change, but when in opposition, at the full,
the tides are at the highest, as in fig. 6. For when the
moon is at full, ten parts of water are raised from that
side of the earth next her, by her attractions; and as
the side which is next her is opposite to the sun, three
parts must be thrown off by his centrifugal force, the
sum of which will be thirteen parts next the moon.—
Again, from the side opposite to the moon and under
the sun, ten parts are thrown off by her centrifugal force,
and three raised by his attraction, making thirteen, the
same as before,
100 THE TIDES.
If there were no moon, the sun, by his attraction, would raise a
small tide on the side of the earth next him; and it is evident that the
tides on the opposite side would be raised as high by the centrifugal
force; for the sun and earth, as well as the earth and moon move round
their centres of gravity.
The highest tides happen when the sun and moon
are either in conjunction (fig. 4.) or opposition (fig. 6,)
and these are called Spring Tides; but when the moon
is in her quarters (as fig. 5,) the influences of the sun
and moon counteract each other; that is, they act in
different directions; the attraction of the one raising
the waters, while that of the other depresses them. The
moon of herself would raise the water ten parts under
her, but the sun, being then in a line with low water,
his influence keeps the tides from falling so low there,
and consequently from rising so high under and oppo-
site the moon. His power, therefore, on the low water
being three parts, leaves only seven parts for the high
water, under and opposite the moon. These are called
Neap Tides.
CHAPTER, XXXVII.
THE TIDES, CONTINUED.
THE tides are known to rise higher at some seasons
than at others: for the moon goes round the earthin an
elliptic orbit, and therefore she approaches nearer to
the earth in some parts of her orbit than at others.
When she is nearest, the attraction is the strongest,
and consequently it raises the tides most; and when
THE TIDES, 101
she is farthest from the earth, her attraction is the least,
and the tides are the lowest.
From the above theory, it may be supposed that the
tides are at the highest when the moon is on the meri-
dian, or due north and south. But we find that in open
seas, where the water flows freely, the moon has gene-
rally passed the north or south meridian about three
hours, when it is high water. For even if the moon's
attractions were to cease when she had passed the meri-
dian, the motion of ascent communicated to the water
before that time, would make it continue to rise for
some time after. O
Much more must it do so when the attraction is not withdrawn, but
only diminished: as a little impulse given to a moving ball will cause
it to move still farther than it otherwise could have done. And expe-
rience shows that the heat of the day is greater at three o'clock in the
afternoon than it is at twelve; and it is hotter in July and August than
in June, because of the increase made to the heat already imparted.
The tides, however, answer not always to the same
distance of the moon from the meridian, at the same
place; but are variously affected by the action of the
sun, which brings them on sooner, when the moon is in
her first and third quarters; and keeps them back later,
when she is in her second and fourth. Because in the
former case the tide raised by the sun alone would be
earlier than the tide raised by the moon, and in the
latter case later.
The greatest spring tide will happen when the moon
is in perigee, if other things are the same; and the suc-
ceeding spring tide when the moon is in apogee will
be the least. But as the effect of a luminary is greater
the nearer it approaches to the plane of the equator,
102 THE TIDEs.
and as the earth is nearer the sun in winter than in
summer, and still nearer in February and October than
in March and September; the greatest tides happen not
till some time after the autumnal equinox, and return a
little before the vernal.
In open seas the tides rise but to very small heights,
in proportion to what they do in wide-mouthed rivers
opening in the direction of the stream of tide. For in
channels growing gradually narrower, the water is ac-
cumulated by the contracting banks. At the mouth
of the Indus, the water rises and falls full thirty feet,
and in the bay of Fundy seventy feet.
The tide in the above instance has been compared to a moderate
wind, which, though not much felt in an open plain, may yet appear
with a strong and brisk current in a street, and become still more pow-
erful as the more confined.
Though the tides in open seas are at the highest about
three hours after the moon has passed the meridian,
yet the waters, in their passage through shoals and
channels, and by striking against capes and head lands,
are so retarded that, to different places, the tides hap.
pen at all distances of the moon from the meridian,
consequently at all hours of the lunar day.
The tide raised by the moon in the German Ocean, when she is
three hours past the meridian, takes twelve hours to come thence to
London bridge, where it arrives by the time that a new tide is raised
in the ocean.
There are no tides in lakes, because they are gene-
rally so small that, when the moon is vertical, she at-
tracts every part of them alike, and by rendering all
the waters equally light, no part of them can be raised
THE TIDES, 103
higher than another. The Mediterranean and Baltic
seas have very small elevations, because the inlets by
which they communicate with the ocean are so narrow,
that they cannot, in so short a time, either receive or
discharge enough, sensibly to raise or sink their sur-
faces.
Air being lighter than water, it cannot be doubted that the moon
raises much higher tides in the air than in the sea.
Although it has been stated that the highest tides
are produced by the conjunction and opposition of the
sun and moon, yet their effects are not immediate; the
highest tides happen not on the days of the full and
change, neither do the lowest tides happen on the days
of their quadratures. But on account of the continua-
tion of motion these effects are greatest and least,
some time after their forces are. So that the greatest
spring tides commonly happen two days after the new
and full moons; and the least neap tides two days.
after the first and third quarters.
For if the greatest elevation immediately under the moon, points to
one side of the equator, the opposite greatest elevation points as much
to the other side. And those places which are on the same side of the
equator with the luminary, approach nearest to the greatest elevation
when she is above the horizon, than to the greatest opposite elevation
when she is below the horizon.
This inequality is greatest when the sun and moon
have the greatest declination. It is also greatest in
places most remote from the equator. The nearer the
place approaches to the poles, the farther it is removed
from the greatest elevation on the opposite side of the
104 THE PRECESSION OF THE EQUINOX.
equator. Thus the less tide is continually diminishing,
till at last it entirely vanishes, and leaves only one tide
in the day.
Hence it is found by observation, that there is only
one tide in twenty-four hours, in all places in the polar
regions in which the moon is either always above or
always below the horizon, during the whole rotation
of the earth about its axis
CHAPTER XXXVIII.
THE PRECESSION OF THE Equinox.
It has been already observed, that the form of the
earth is that of an oblate spheroid; for by the earth's mo-
tion on its axis there is more matter accumulated all
around the equatorial parts than any where else on the
earth.
The sun and moon by attracting this redundancy of
matter bring the equator sooner under them, in every
return towards it, than if there were no such accumula-.
tion. Therefore if the sun sets out from any star, or
other fixed point in the heavens, the moment when he
is departing from the equinoctial (or from either tropic)
he will come to the same equinox (or tropic) again 20
minutes, 17% seconds of time (or which is equal to 50"
of a degree) before he arrives at the same fixed star ol
point from which he set out. For the equinoctial
points recede 50" of a degree westward every year
contrary to the sun's annual progressive motion.
THE PRECESSION OF THE EQUINOX. 105
To prove that 20 minutes 17; seconds of time are equal to 50" of a
degree, it must be recollected that the sun goes through the whole
ecliptic of 360°, in 365 days, which is not quite one degree each day,
but 59'8", (or 52" less than a degree.) Therefore, if by the rule of pro-
portion we say, as 59'8": 24 hours: : 50", the result will be 20 minutes
17# seconds, nearly. That the sun has a daily apparent motion in the
ecliptic from west to east is evident from comparing the sun's right
ascension every day with that of the fixed stars lying near him. For
the sun is found constantly to recede from those on the west, and ap-
proach those on the east; hence his apparent annual motion is found to
be from west to east.
When the sun arrives at the same equinoctial or sol-
stitial point, he finishes what is called the tropical
year; which, according to some authorities, is found to
contain 365 days, 5 hours, 48 minutes, 48 seconds (see
page 4,) and when he arrives at the same star again,
as seen from the earth, he completes the sidereal year,
which contains 365 days, 6 hours, 9 minutes, 14% se-
conds. The sidereal year is therefore 20 minutes, 17%
seconds longer than the solar or tropical year, and 9
minutes, 14% seconds longer than the Julian or civil
year, which is 365 days, 6 hours. So that the civil
year is almost a mean between the sidereal and tropical.
According to Professor Vince, a sidereal year is 365 days, 6 hours, 9
minutes, 11 seconds, .5; and a tropical year 365 days, 5 hours, 48 mi
nutes, 48 seconds.
As the sun describes the whole ecliptic, or 360° in
a tropical year, he moves 59'8" of a degree every day
at a mean rate; which is equal to 50 seconds of a de-
gree in 20 minutes 17% seconds of time: therefore he
will arrive at the same equinox or solstice when he is
50" of a degree short of the same star or fixed point in
the heavens, from which he set out the year before. Sc
that, with respect to the fixed stars, the sun and equi-
K 2
a 06 THE PRECESSION OF THE EQUINOX.
noctial points fall back (as it were) 30° in 2,160 years.
This will make the stars appear to have gone 30° for-
ward, with respect to the signs in the ecliptic in that
time: for it must be observed, that the same signs al-
ways keep in the same points of the ecliptic, without re-
gard to the place of the constellations.
50" short in one year are = 10 short in 72 years. For in a degree
are (60 × 60) 3,600", which divided by 50", will give 72–And 10 less
in 72 years = 300 or one whole sign in 2,160 years. To explain this by
a figure; suppose the sun (plate XVII, fig, 1st,) to have been in con-
junction with a fixed star at S, on the first degree of Taurus, 342 years
beſore the birth of Christ, or about the 15th year of Alexander the
Great; then making 2,160 revolutions through the ecliptic, he will
still be found at the end of so many sidereal years, again at S: but at
the end of so many Julian years, he will be found at J, and at the end
of so many tropical years, at T. in the 1st degree of Aries, which has
receded back from S to T in that time, by the precession of the equi-
noctial points op and --. The arc S T will be equal to the amount of
the precession of the equinox in 2,160 years, at the rate of 50" of a de-
gree, or 20 minutes 17; seconds of time annually, as above calculated
From the shifting of the equinoctial points, and with
them all the signs of the ecliptic, it follows that the
longitude of the stars must continually increase. Hence
those stars which, in the infancy of astronomy, were in
Aries, are now got into Taurus; those of Taurus into
Gemini, as may be seen by inspecting the celestial
globe. Hence likewise it is that the star which rose
or set at any particular time of the year, in the times
of Hesiod, Eudoacus, Virgil, Pliny, &c. by no means
answers at this time to their descriptions.
By comparing the longitude of the same stars, at different times, the
motion of the equinoctial points, or the precession of the equinoxes may
be found.
Hipparchus was the first person who observed this motion, by cont-
paring his own observations with those which Timocharis made 155
page 106 - Plate 15
- - - -

PRECESSION OF THE EQUINOX. 107
years before. From this he judged the motion to be about 19 in about
100 years; but he doubted whether the observations of Timocharis
were sufficiently accurate.—In the year 128 before Christ he ſound the
longitude of Virgin's Spike to be 5 signs 249, and in the year 1750 its
longitude was found to be 6 s. 20° 21'. In the same year he found the
longitude of the Lion's Heart to be 3 s. 290 50', and in 1750, it was 4 s.
26° 21'. The mean of these gives 507.4 in a year for the precession.
By comparing the observations of Albategmius, in the year 878, with .
those made in 1738, the precession appears to be 51" 9".--From a com-
parison of fifteen observations of Tycho, with as many made by M. de
la Caille, the precession was found to be about 50" 20".
By proceeding to shift a whole degree every 72 years,
and a whole sign every 2160 years, the equinoctial
points will fall back through the whole of the 12
signs, and return to the same points again in 25,920
years; which number of years completes the grand ce-
lestial period.
From the creation to the year 1819, supposing it to be (4004-H 1819)
~ 5823 years, the equinoctial points have receded 2 s.200 51' 54".
CHAPTER XXXIX.
THE PRECESSION OF THE EQUINOX, CONTINUED.
HAVING thus noticed the cause of the precession of
the equinoctial points, which occasions a slow deviation
of the earth's axis from its parallelism, and thereby a
change of the declination of the stars from the equator
together with a slow apparent motion of the stars for.
ward, with respect to the signs of the ecliptic, the
phaenomena may be explained by a diagram.
Let S O N A (fig 3, plate XVII.) be the axis of the
earth produced to the starry heavens, and terminating
in A, the present north pole in the heavens; E O Q
108 PRECESSION OF THE EQUINOX, 2’
is
the equator; T go Z the tropic of Cancer, and VTV3
the tropic of Capricorn; V O Z the ecliptic, and B O
its axis, both which are immoveable among the stars.
But as the equinoctial points recede in the ecliptic,
the earth's axis S O N is in motion upon the earth's
centre O, in such a manner as to describe the cone N
O n, and S O s, round the axis of the ecliptic B O,
in the time the equinoctial points move round the
ecliptic, which is 25,920 years.
In that length of time the north pole of the earth's
axis produced, describes the circle A B C D A in the
heavens, round the pole of the ecliptic, which keeps
immoveable in the centre of that circle. The earth's
axis being 23}* inclined to the axis of the ecliptic,
the circle A B C D A, described by the north pole of
the earth's axis, produced to A, is 47° in diameter, or
double the inclination of the earth's axis.
In consequence of this motion, the point A, which
is at present the north pole of the heavens, and near to
a star of the second magnitude in the tail of the con-
stellation called the Little Bear, must be deserted by
the earth's axis. And this axis moving backward a
degree every 72 years, will be directed towards the
star or point B in 6,480 years from this time: and in
twice that time, or 12,960 years, it will be directed
towards the star or point C, which will then be the
north pole of the heavens; although it is at present 8%.”
south of the zenith of London, L.
Then the present positions of the equator and the
tropics represented by the black lines, will be changed
to those represented by the dotted lines. And the sun
oBLIQUITY OF THE ECLIPTIC, Etc. 109
which in the diagram is over Capricorn, and makes the
shortest days and longest nights to the northern hemi-
sphere, will then be over Cancer, and make the days
longest and nights shortest. *
It will then require 12,960 years more (or 25,920
from this time) to bring the north pole back quite round
to the present point: and then, and not till then, will
the same stars which now describe the equator, tropics,
polar circles, &c. describe them again.
CHAPTER XL.
THE OBLIQUITY OF THE ECLIPTIC, ETC.
IT may not be amiss to mention the method used by
astronomers to determine the obliquity of the ecliptic ;
which is, by taking half the difference of the greatest
and least meridian altitudes of the sun.
Eratosthenes, 230 years before Christ, found o
the obliquity to be 23 51 20
Ptolemy, 140 years after Christ 23 51 10
Copernicus, in 1500 23 28 24
M. De la Lande, in 1768 23 28 0
Not to mention many others; and from all these united observations,
it is manifest that the obliquity of the ecliptic continually decreases.
Comparing the numerous observations that have been
made to ascertain the true obliquity, the mean of the
several results gives about 50” in a century. “We
may therefore state,” says Professor Vince, “The
secular diminution of the obliquity of the ecliptic, at
this time, to be 50”, as determined from the most ac-
curate observations; and this result agrees very well
with that deduced from theory.”
110 MAGNITUDES OF THE PLANETs.
CHAPTER XLI.
TO FIND THE PROPORTIONATE MAGNITUDES OF THE
PLANETS.
To find the proportion that any planet bears to the
earth, or that one globe bears to another, the diameter
of each must be cubed, and the greater number divided
by the less: the quotient will show the proportion that
one bears to another: for all spheres or globes are in
oroportion to one another as the cubes of their diame-
ters.
The cube of any number is the product of that number multiplied
twice into itself. Thus, the cube of 2 is 8; for 2 multiplied by 2 makes
4, and 4 multiplied again by 2 makes 8–So the cube of 3 is 27; for
3 × 3 × 3–27. -
If the diameter of the sun, as some assert, be 893,522
miles: and of the earth 7,920 miles; then the cube of
893,522 is 713371492260872648, and of 7,920 is
496793088000, and the greater number divided by the
less will give 1435952, and so many times is the bulk
of the sun greater than that of the earth.
To FIND THE PLANETs' DISTANCE FROM THE SUN.
By the transits of Venus (already explained, page
101,) the distance of the earth from the sun has been
found to be about 95,000,000 of miles; and by know-
ing the earth's distance, the distances of the other pla
nets are calculated. -
Repler, a great astronomer, discovered that all the
planets are subject to one general law, which is, that
the squares of their periodical times are proportional
to the cubes of their distances from the sun. And this
law was fully demonstrated by Sir Isaac Newton.
DISTANCES OF THE PLANETS.
By their periodical times is meant the time they take in revolving
round the sun: thus the periodical time of the earth is 365 days; that
ºf Venus, about 224 days; that of Mercury nearly 88 days.
Therefore, if we would find the distance of Mercury
from the sun, we say, as the square of 365 days is to
the cube of 95,000,000, so is the square of 88 days to
a fourth number, which will be the cube of its distance.
And if the cube root of this number be extracted, the
answer will be nearly 37,000,000 of miles
Thus the square of 365=133225; the cube of 95=857375; and the
square of 88=7744. Therefore, as 133225 is to 857375, so is 7744 to
49836, the cube of the mean distance of Mercury. And if the root of
49836 be extracted, it will be more than 363,-the mean distance of
Mercury from the sun in millions of miles.
QUESTIONS
FOR EXAMINATION IN ASTRONOMY.
CHAPTER I.
WHAT is Astronomy?—Of how many parts does it consist, and what
are they?—What does descriptive Astronomy treat of!—And what
does physical ?—What is a circle 1
What is the circumference sometimes termed !
What is the radius?—What the diameter of a circle?
Name the proportion between the diameter and radius.
What is an arc of a circle?—What is a chord of a circle – Does a
chord necessarily divide a circle into two unequal or equal parts?—
What is a semicircle :
By what other name is a semicircle sometimes called?
What is a quadrant?
What is the quarter of the periphery of a circle sometimes termed?
Into how many parts are all circles supposed to be divided?—How
are degrees marked f-How minutes and seconds?—Mention the num-
ber of degrees in a semicircle and in a quadrant—What is an angle f
—Which is the angular point?—Which are the legs of a right-angled
triangle —What is a right angle —What is the measure of a right
angle —What is an acute, what an obtuse angle —Define what are pa-
rallel lines—What is a globe or sphere?—What is a spheroid?—What
is a great circle of a sphere f—What is a small circle of a sphere —
What is the diameter of a sphere to any great circle termed?—What are
the extremities of the diameter called !
What distance is the pole of a great circle from every part of the dia- &
meter ? and for what reason —Into what parts, and whether equal os
not, do two great circles divide each other? and why?
What is the axis of the earth?
CHAPTER II.
FULLY define the science of Astronomy. 3, .
What is the general opinion of Astronomers with respect tº the dif.
ferent systems of the universe?
*
L 113
114 QUESTIONS FOR EXAMINATION.
What are the sun and moon termed 1–How are stars distinguished?
—Whence do the planets receive their light?—What attendants have
they?—Is there any other order?—What are the names of the planets,
and which are the Asteroids?—What are these called, and how many
moons are there —To what planets do they belong?
The Sun.
What is the Sun?—What his form, diameter, and circumference?
What is the sun's diameter equal to ?
What is his distance from the earth; and how much larger?
What was the sun formerly thought to be?
What does Dr. Herschel suppose the sun to be?
What can be seen on the sun's surface?
What is meant by maculae and faculae :
What new opinion is formed respecting it?
How many motions has the sun, and what are they?—What does the
sun's motion about its axis render it?
CHAPTER III.-Mercury.
NAME the smallest and nearest planet to the sun?—What is his dia-
meter, and in what time does he revolve about the sun ?—At what dis-
tance, and at what rate does he move in his orbit?
What proportion do the mean distances of Mercury and the earth from
the sun bear to each other?
What appearance has Mercury
How will the sun's diameter appear, if viewed from Mercury, and
how much greater is the light and heat he receives than that of the
earth?
In what manner does he change his phases?
How does this planet appear to us?—How is it known that he does
not shine by his own light?
When the orbit of this planet is between that of the earth and the
sun, what is it denominated
When did the last transit of this planet happen, and when will the
next?
Venus.
What is the next nearest planet to the sun, and how is she distin-
guished?—What is her distance from the sun?–In what time does she
complete her annual revolution; and in what her rotation about her
axis?
QUESTIONS FOR EXAMINATION. 115
What do astronomers make a complete rotation to be 2
What is her magnitude; what her diameter, and at what rate does
she move in her orbit?—Is her quantity of light and heat greater than
that of the earth?—What is her appearance as seen by the naked eye;
and what, when viewed through a telescope —What is Venus deno-
minated when seen by us westward of the sun; and what when east-
ward?—Is there any difference in her seasons, and why?
Does she always appear of the same size, and what do her variations
demonstrate 2
Are there any transits of Venus, and how often do they occur?
When was the last seen, and when will the next happen?—What
have astronomers ascertained by this phenomena?—Who was the first
person that predicted the transit of Venus and Mercury —When was
the first time Venus was ever seen upon the sun, and by whom?
CHAPTER IV.-The Earth.
WHICH is the third planet from the sun, what its mean distance, its
diameter, and its circumference 2
What would be the appearance of the Earth from the planet Venus?
What are the Earth's motions 7–At what rate does it move in its or-
bit?—In what time does it perform an entire revolution, and what does
a complete rotation form 2
What is the more exact time of its annual motion?—By what is time
divided?—On what does the former, and on what does the latter de-
pend ?
What is the true form of the Earth?
What form was the Earth formerly supposed to be? and what since
proved to be
Of what service is the earth to the moon, and of what size does she
appear, viewed from the moon?
The Moon.
To what planet is the Moon a satellite –In what time does it re.
volve in its orbit?—What is the mean distance of the Moon from the
earth, and at what rate does she move in her orbit?—What is her dia.
meter, and bulk —In what time is her rotation on her axis performed,
and what the length of her day and night?—How often does she re-
volve round the earth in a year?—What is the length of her year?—
What are the phases of the Moon?—Whence does the Moon receive
her light?—What enlightens that part of the Moon which is turned
II6 QUESTIONS FOR EXAMINATION.
from the sun ?—Has the Moon any diversity of seasons?—What do the
shades which appear on the face of the Moon result from ?
What were the former opinions respecting the mountains of the
Moon?—What are the present —What else is observed in it t—When
can the irregularity of the Moon's surface be most distinctly seen?
When is the Moon invisible to us? and what is her first appearance
called !
Which hemisphere of the Moon is never completely dark, and why?
—How long is the other hemisphere enlightened?
Is the moon thought to be inhabited?—What is supposed concerning
seas in the Moon, or her atmosphere?
CHAPTER V.—Mars.
WHICH is the next planet to the earth, and how is he known in the
heavens ?—What is his distance from the sun, and what the length of
his year?
Has the cause of his dusky red colour been ascertained?—At what
rate does he move in his orbit?—In what time is the diurnal motion of
this planet performed?—What is his diameter?—What portion of light
does he enjoy 7
What is the mean distance of Mars from the sun, in regard to our
earth? How is the diurnal motion of Mars ascertained ?—Who first dis-
covered them, and what has been since determined from them?
How does Mars appear when viewed through a telescope —Has he
any satellites?
How does he appear when opposite the sun? and what does it prove?
—Is the earth or sun in the centre of his motion?
Asteroids.
Have any planets been discovered between the orbits of Mars and
Jupiter?—What are their names?—Which is the nearest to Mars?—
What is its mean distance from the sum ?—How soon is its revolution
through its orbit performed?—How many degrees does it incline to the
ecliptic 7
By whom was Vesta discovered, and when?
What is the mean distance of Ceres from the sun ?—What its time of
revolution, its diameter, and its inclimation to the eclipticº
By whom was Ceres discovered, and when?
What is the mean distance of Pallas from the sun ?—What is the time
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QUESTIONS FOR EXAMINATION. IIT
of its revolution?—What its diurnal motion?—How great is its inclina-
tion to the ecliptic —What is its diameter?
By whom was Pallas discovered, and when
What is the mean distance of Juno from the sun, and what is its size
-In what time is its revolution round the sun performed ?—What its
diameter?—What is the inclination of its axis to the eclipticº and what
does it appear like
By whom was it discovered 2
CHAPTER VI.-Jupiter.
Between what planets does the orbit of Jupiter lie?—What his mag-
nitude 7 and how is he distinguished ?—What is the distance of Jupiter
from the sun ?—What his mean distance from the sun ?–How much
farther than the earth, and what proportion of light and heat does he
receive?—What is the diameter of Jupiter, and how much larger is he
than the earth?—What proportion does his year bear to ours?—In what
time does he make his revolution round the sun, and at what rate does
he move in his orbit?—In what time does Jupiter revolve on his axis 2
—Does his equatorial exceed his polar diameter?—Does his axis incline
to his orbit 2—What difference in his seasons? and what variation in
his days and nights?—What is the length of his day and night?—What
appearance has he viewed through a telescope?
To what variations are his zones or belts subject, and what are they
supposed to be 7–Are they supposed to adhere to the body of the
planet?
Jupiter's Satellites.
How many satellites has this planet?—In what time does the nearest
make a revolution?—What the most distant?—By whom were they
first discovered?—What were they first taken to be?—What are the
periodical times of the first, second, third, and fourth 7–To what pur-
pose have their eclipses been applied ?
CHAPTER VII.-Saturn.
What was Saturn formerly thought to be 2–What is his appearance?
—What his mean distance from the sun ?—What light and heat has
he in proportion to the earth?—What proportion does his light bear to
that of our full moon?—What is the diameter and magnitude of Sa
turn?—In what time does he perform his revolution in his orbit?--
L 2
118 QUESTIONS FOR EXAMINATION,
How many miles does he travel in an hour?—In what time does he -
revolve about his axis 7–Who ascertained it?
Satellites of Saturn.
How many Satellites or moons is Saturn encompassed with ?–Of
what use are they supposed to be?—What distance is the nearest, and
what is its breadth 7–Of what breadth is the outer ring —What is the
space between them?—What is it conjectured they are composed of?—
In what time does the ring revolve about the planet?
CHAPTER VIII.—Uranus.
Which is the most remote planet yet discovered ?—What appearance
has he to the naked eye?
When can it be best perceived ?–Who discovered this planet, and
when —Why is it named the Georgium Sidus –What is it called by
astronomers ?—What other names does it bear?
What is the distance of this planet from the sun ?
What is the distance given by some authors?—What light and heat
does he receive, compared with the earth?
In what time does he perform his annual revolution, and at what
rate does he travel ?—What is his diameter?
The Herschel's Satellites.
How many Satellites has Herschel ?
In what time does the nearest perform his revolution? and in what
the most remote %
Of what use are they supposed to be
The Proportional Magnitude and Distance of Planets.
How much larger is the Earth than Mercury, Venus, Mars, or Pal-
las?—How much larger than the Earth is Jupiter, Saturn, and Her-
schel ?—How do astronomers express the mean distances of the planets?
—What distance from the sun may the different planets be estimated
at?—How are the distances calculated ?
CHAPTER IX.-Comets.
What are Comets thought to be 7 and what direction do their orbits
take # *
Are they supposed to be adapted to the habitation of animated be
QUESTIONS FOR EXAMINATION. 119
ings?—Whence is the name of Comet derived ?—What are their tails
supposed to be —When could it happen that the tail of a Comet could
come near our atmosphere ?—Of how many Comets were the periods
thought to be distinctly known —When did the first appear? when
the second 2 and when the third 7–What is the greatest distance of
this Comet from the Sun ? and what the least distance from the sun's
centre —At what rate does it travel ?
How many miles in diameter was the head of the Comet of 1807 as
certained to be, and what that of 1811 ?—Of what nature are Comets?
—What did Sir Isaac Newton estimate the head of that Comet to be,
seen by him in 1680 !
Whence are we authorized to conclude that Comets receive their
light?
Of what do comets consist?—What is the nucleus, what the head-
and what the coma 7–How long was the tail of the Comet of 1807 as-
certained to be, and how long that of 1811 ?—What its distance from
the sun, and what from the earth 2
CHAPTER X. —The Fiaced Stars.
What are the heavenly bodies beyond our system called?
What is it probable they are ?
By what light do the fixed stars shine?
How much nearer are we to some stars at one time, than at another.
What is the distance of Sirius, or the Dog-star, from us?—In what
time would a cannon ball reach us from that star 7
How much farther from us than the sun is the nearest fixed star?—
Have any been observed to revolve on their axis?
What is it probable the fixed stars are?—Into how many magnitudes
are they usually classed ?—What are the largest called !—What the
smallest?—How many are visible to the naked eye at one time?
What is the occasion of the stars appearing to us innumerable 7
Do not some of the fixed stars, when viewed through a telescope.
appear double or treble?—What are clusters of stars called !—Which is
the most remarkable of the clusters called nebulae –What has Dr
Herschel remarked concerning the Milky Way ?
What is observed of the Magellanic clouds !—Have not a greater
number of stars been observed since the use of telescopes?
How are planets distinguished from fixed stars?
120 QUESTIONS FOR EXAMINATION,
What is thought to occasion the twinkling of the fixed stars?
Are all stars that were known to the ancients, now to be seen?—
And are not some now seen that were not noticed by them?
By whom is the most ancient observation of a new star?—Which
the first we have any accurate account of? s
Have not some stars alternately appeared and disappeared? What
have other stars been subject to?
What star was discovered in 1600?—What were its different appear-
ances?—What was discovered respecting 3 Lyrae!
What appearance has the heavens to a spectator in any part of the
universe ?—What proof have we of this?—If transplanted to a planet
belonging to Sirius, how would that star and our sun appear to us?
What is the vulgar error respecting the stars?
CHAPTER XI.—Constellations.
Into what did the ancients form the stars?
For what purpose were the constellations formed !
What was the ancient, and what the present number of the constel-
lations?—By what are the heavens usually distinguished?—What is
the number of the constellations in the northern hemisphere ?—What
in the southern ? and what in the zodiac 2–What are the stars called
not comprehended in these.—Name the northern constellations, and
the southerm.—Repeat the zodiacal constellations. How are some par-
ticular stars distinguished?—How are others denoted
CHAPTER XII.-Different Systems.
What is the system called which has been described t—By whom
was it formerly taught?—By whom revived ?—What did Ptolemy sup-
pose 2
What are epicycloids?
What system did the Egyptians receive?—Who at length adopted
the Pythagorean?--How did Copernicus place the sun and planets?—
What system did Tycho Brahe endeavour to establish —By whom was
the solar system first taught?—By whom revived?—By whom con-
firmed ?–And who at length fully established it?
QUESTIONS FOR EXAMINATION. 121
CHAPTER XIII.-On the Motions of the Planets.
How would the planets appear to move if seen from the sun ?—How
do they appear to move as seen from the earth?
Give some illustration of the motions of the planets.
When is their motion direct?—When retrograde —When sta-
tionary 7
Inferior and Superior Conjunctions of the Planets.
What is a planet in its inferior conjunction?—When in its superior?
—What planets have alternately a conjunction and an opposition?—
And when 2–In which case do they rise and set nearly with the sum ?
—When is it the reverse ?—Does the appearance of a planet vary if
viewed through a telescope —When is Venus seen with nearly a full
face?—When only half enlightened -
When can Mercury and Venus be seen in their inferior conjunction?
What planets do these appearances refer to?
CHATTER XIV.-The Plane of an Orbit, Planets,
Nodes, &c.
What circle does the earth describe as seen from the sun ?
In what different signs do the earth and sun appear?
What is understood by the plane of a circle?
Give some illustration.
In what do the orbit of the earth and the ecliptic vary?
Give some illustration.
Do the orbits of the planets vary from the ecliptic?—What is meant
by the obliquity of their orbits?—Demonstrate it by the figure.—What
is meant by the line of the nodes —What by the ascending, and what
by the descending node?—What is really meant by the terms plane
and orbit 2
Transits of Mercury and Venus.
Define by plate VIII. fig. 1, and by plate XIV. fig. 6, the transits of
Venus or Mercury.—Are there great variations in the magnitude of
Venus, as seen from the earth?—Demonstrate this by the figure, plate
VII. fig. 1–What is the least distance of Venus from the earth?-
What the greatest ?
Explain the phases of Venus, in her orbit, by the figure.
122 QUESTIONS FOR EXAMINATION,
CHAPTER XV-The Ecliptic, Zodiac, Equator, &c.
What is the ecliptic?—Name the most conspicuous stars near the
ecliptic. ..
From what stars is the moon's distance calculated ?—Why is the
ecliptic so called ?
Whence arises the obliquity of the ecliptic —What are the points of
intersection called !—What are the times of intersection called?—What
is the zodiac 2
Whence is the term zodiac derived ?
Give the names and characters of the twelve signs?—Which are the
northern signs?—Which the southern?—Which are called the as-
cending?—Which, descending —To what do the signs correspond?—
How much of the ecliptic does the earth pass over each day ?—How
much each month?—How many degrees in a sign —And why?—
What is the terrestrial equator?—What is its distance from the poles?
—How does it separate the globe –What is the celestial equator?
Of the Ephemeris.
What does the first column of the Ephemeris show !—What the sec-
ond'!—What the third 2 -
If you know the time of the sun's rising, how do you know the time
of its setting, and vice versa £
What does the fourth column show 2
What and when is the sun's greatest declination?—When will he
have no declination ?—What is meant by declination?
When does an astronomical day begin?—What do the three next
columns contain?—What is meant by southing?—How often and when
does the moon come to the meridian with the sun ?
How much later, one day with another, does the moon culminate 7
What does the eighth column show 7–What is the adjusting of time
called !
How often and at what times are the clock and dials together?
How are the clocks, &c. regulated ?—What does the first short col-
umn !—What the second short column?—What the five following col-
umns?—What is meant by the heliocentric longitude 7–And what by
the geocentric?
Define the heliocentrie and geocentric longitudes by the figure—
Which longitude is given in page 9 of the Ephemeris? +
Explain the column for daylight.—What is meant by the latitude
of a planet!—And what columns show the latitude 7–How is the lon-
QUESTIONS FOR EXAMINATICN. 123
gitude of a heavenly body usually expressed ?–Which of the columns
speak of the rising or setting of a planet!—Why not of both }
CHAPTER XVI.
What is a degree?—What is the measure of an angle 2
Explain this by fig. 3, plate IX.
What are the poles —What parts of the heavens appear motionless?
—And what part appears to have the greatest motion?—What are the
tropics?—What their distances from the equator?—What are the polar
circles —What their distance from the poles 7
Why is the distance of the polar circles fixed at that number of de-
grees from the poles?
Why are the meridians so called ?—How many meridians are
usually drawn on the globes, and why?—Are these all that can be re-
presented ?
Explain this by fig. 3, plate IX.
What is meant by longitude —Through what place does the first
meridian pass?—How many degrees are equal to an hour?—What
places are before London, in time, and what after?—How do you re-
duce longitude to time?
Give the reason why 15 degrees are equal to an hour; and 30 de-
grees to two hours, &c.—If 12 o'clock at London, what are the times at
Barbadoes, at St. Petersburgh, and at Calcutta.
How is time turned into longitude —What is meant by the latitude
of a place —What by the latitude of a heavenly body?—What are the
colures?—How many zones are there, and what are they?—What are
the solstitial points? And why so called ?—What are the equinoctial
points? And why so called?
CHAPTER XVII.-Planets' orbits Elliptical.
What are the orbits of the planets termed?—Illustrate this by figures
2, 3, and 5, of plate VIII.--When is a planet said to bein its perihelion,
and when in its aphelion ?—And when at its middle or mean distance 1
—What is termed the eccentricity of its orbit?
Attraction of Gravitation.
What is meant by attraction?
What is attraction of magnetism?—What attraction of electricity?—
What of cohesion?
124 QUESTIONS FOR EXAMINATION.
What is attraction of gravitation? In what proportion is this attrac-
tion?—By what kind of attraction does the sun affect the earth, and the
earth the moon?
Upon what principle does the stone fall to the earth—and the waters
of the ocean gravitate, &c.
Repeat one of the laws of attraction.—Illustrate this by the figures 4
and 5 of plate X-What is the second law of gravity?—Do equal mag.
nitudes imply equal quantities of matter?—With what proportion does
the sun attract the earth? And why?—Explain this otherwise, by boats
of equal bulk.
CHAPTER XVIII.-Of Attractive and Projectile
Forces.
What power counteracts that of attraction?—What would be the ef.
fect of rectilineal motion?—Of what are the planets' motions come
pounded ?
Explain this by some projectile force.—What, if a ball be thrown from
the hand?
What united forces retain the planets in their orbits?
Explain the difference of a circular motion and a straightline—Give
a further explanation by the figure 4, plate VIII.
What results from the two ſorces being equal?
What would result if either power were to cease acting?
By what laws are the secondary planets governed ?—Why are the
planets' orbits not true circles?
Explain by the figure, what is meant by equal portions in equal times,
—And by unequal portions in equal times.
What power will a double velocity balance?—Demonstrate this by
the figure—What is meant by equal areas in equal times?—What re
sults from the comets' orbits being so very elliptical?
Suppose a body to receive two different impulses, what would be its
direction?—Epxlain this by the figure. -
CHAPTER XIX-The Centre of Gravity.
What is the centre of gravity?—Explain this by figure 6, plate X.
If the earth were the only attendant on the sun, what motion would
the sun have 2
What, if all the planets were on the same side of him?—Are the se.
QUESTIONS FOR EXAMINATION. 125
condaries governed by the same laws?—What is supposed of every
system in the universe?
The Horizon.
What is the horizon?—To what does the rational horizon apply?—
Explain this by fig. 2, plate IV.
How is this horizon represented on the artificial globe 7
What does the sensible horizon respect?—How Is its extent varied?
Refer to the figure.-What is the extent of view, to an eye elevated
five feet? And to one elevated twenty feet?—How do you mark the
difference of the two horizons?
Why do persons on the sensible horizon see the heavenly bodies when
on the rational? -
What proportion does the earth's semi-diameter bear to the sun's dis-
tance?—And what is the result?—What proportion does the earth's
semi-diameter bear to the moon's distance.
CHAPTER XX.-Day and Night.
What is the cause of the succession of day and night?—Illustrate
this by fig. 2, plate IV.-How much of a sphere does the sun illumine
at one time?—How much of the heavens can a spectator behold at one
time !
Explain the apparent motion of the heavenly bodies, by some fami-
liar motions on our earth.
How are the apparent motions of the whole starry firmament ac
counted for?
What results from the earth's motion to persons in the latitude of
London?—What, to those on the equator?
What points in the heavenskeep the same positions?—Why are stars
not seen by day?—How many revolutions on its axis does the earth
make in a year?—Why are we not sensible of the earth's daily motion?
What proof have we of other motion not being perceptible?
CHAPTER. XXI.-The Atmosphere.
What is the atmosphere?—What does it possess?—Where is it most
uense? And where more rare :
What does the whole mass of atmosphere contain?
M
126 QUESTIONS FOR EXAMINATION.
To what purposes does it serve?—Ofwhat appearanceslsit the cause
What do experiments on the air-pump prove?
Without an atmosphere how would the sky appear?—To what height
does the atmosphere extend?—At what height does it cease to reflect
the rays of light?—What results from the sun's rays falling upon the
atmosphere before he rises? And after he sets?
When does twilight begin?—When does it end?
CHAPTER XXII.-Refraction.
When do the rays of light deviate from a rectilineal course?—From
this cause what results?—What is the apparent elevation called?
Demonstrate this by fig, 1, plate XI.
What is the consequence of this refraction?—How much longer does
the sun appear by this refraction?—Explain this by the figure.
How can you show the effects of refraction?—Have you not another
way of demonstrating it?
CHAPTER XXIII.-Parallar.
What is the parallax of the sun or moon?
Which is called its apparent, and which its true place?
When is the parallax the greatest?—And what is that parallaxcalled?
What is the sun's mean parallax? Why seldom made use of And
for what purpose ?—Have the fixed stars any parallax?
Does the parallax of the sun or moon depress or elevate them? How
must their true altitudes be obtained ?–Illustrate this by fig. 2, plate
XI.-Does distance cause the parallax to be greater or less?—Where
has any object its greatest and where its least parallax? —When is the
parallax nothing?—Explain this by the figure.
CHAPTER XXIV.-Equation of Time.
How much longer is the summer than the winter half year?—By
what occasioned?—Of what is this inequality the cause ?—What keeps
true time?—And what apparent time?—What is the difference of these
termed
Equal time, how measured?—and apparent time, how?
Upon what does this difference depend?—What motion is the most
f
QUESTIONS FOR EXAMINATION. 127
equable in nature?—In what time is the earth's rotation completed?
What is this space called? And why?
If the earth had only a diurnal motion, what would be the length of
the day?
What is a solar or natural day?—By what is this difference oc-
casioned?
Will the hands of a clock convey any idea of this?
How often are the ecliptic and zodiac coincident?—And when?—
Why do they differ at other times? 3
Explain this by the globe.—Refer also to figure 2.—What do the
marks on the ecliptic represent?—And what those on the equator?
In what quarters will the sun be faster, and in what slower than the
clocks? And why?—Will not the elliptic form of the earth's orbit oc-
casion a variation?
What, if the differences depended solely on the inclination of the
earth's axis?—Refer to an Ephemeris for the times of the clock and
dials coinciding, and say on what days.
If the earth's motions in its orbit were uniform, what would result?—
What is the earth's daily course in winter, what in summer?—From
this cause, what variations are there in the natural day? And why?—
What then are the combined causes of the inequalities of time?
CHAPTER XXV.-The Seasons.
What is the inclination of the axis of the earth?—Explain this by the
clate.—What is observed of the axis of the earth?
Illustrate the earth's parallelism.
What is the diameter of the earth's orbit?—To what does the axis of
the earth always point, and how do you account for it?
Can you illustrate this by something familiar?
What proof is deduced from this?
How is the earth's course round the sun proved 2
Can these observations be made in the day?
Upon what does the variety of the seasons depend?—What, if the
axis of the earth were, as in the figure, perpendicular to the sun's rays?
Why must the poles be excepted?
What would result from such a position?
On what does the proportion of heat materially depend?
Explain it by the figure. &
Represent by figure 2, plate X, the position of the earth in our sum-
7.627° S&S07.
128 QUESTIONS FOR EXAMINATION.
Whāt is evident from the circle in the latitude of London?—What is
then the appearance at each pole?
What is observed of places inequal latitudes, the one north, the other
south Ž
CHAPTER XXVI.-Seasons, continued.
What is represented by fig. 2, plate XII.
How much nearer are we to the sun in December than in June?—
What is the sun's apparent diameter in winter?—What in summer ?
What is the time we denominate our summer?—How much longer
than our winter half-year?—What inference is consequent?
Whence does the coldness of our winters arise ?—When are the hot-
test and when the coldest seasons?
In June, what pole inclines to the sun ? And what results there-
from?—In December what pole inclines to the sun? And where is it
then winter?—In March and September what position has the axis –
What length are the days and nights?
In March, what is the real place of the earth?—In what sign will the
sun then appear?—On the 21st of June, where is the sun vertical ?—
Where in September 7–Where in December?
What causes produce the increase and decrease of days and nights?
—To what parts is the sun vertical, from 20th March to 21st June 8–
And from June to September?
To what parts is the sun vertical from 23d September to 21st De-
cember?—And from December to March?—How often is the sun ver-
tical to every part, between the tropics?
CHAPTER XXVII.-The Moon's Months, Phases.
What kind of months are they?—And what is the length of each?—
Whence arises the difference 2
Explain this by the figure.—Is the moon's orbit a circle, or an el-
lipsis?
How much of the moon is at one time enlightened?—Do we always
see the whole enlightened side :
Refer again to the figure.
What is the moon's position at change?—What, at full moon?—What,
when changed? And what is the moon then said to be in?—What,
whet three-fourths are seen?—What, when wholly enlightened?
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QUESTIONS FOR EXAMINATION. 129
Žn what directions are the horns just after the change 2–What, after
the full moon?—Represent the moon's phases by a ball, or small globe.
What is the moon's apparent motion?—What the real motion?
By what may the moon's real motion be known?
CHAPTER XXVIII.-Eclipses—First, of the *n.
What does the term eclipse imply?—By what is an eclipse of the
moon occasioned?—When must an eclipse of the moon happen?—Re-
fer to the plate.—What would resultif the moon's orbit coincided with
the ecliptic?
How much does the orbit of the moon vary from the ecliptic
What is the greatest distance from the node, at which an eclipse of
the moon can happen?—When an eclipse happens full in the node,
what is it called?—What is the duration of an eclipse —Of what shape
is the earth's shadowſ—Does not the moon's distance from the earth
vary 7
How does the moon's being either nearer or more distant, affect the
length of an eclipse?
On which side of the moon does an eclipse begin, and on which side
end ?
How may this be clearly conceived?
How are eclipses calculated 2
Of what form is the earth's shadow —What does that demonstrate?
—How is the sun proved to be larger than the earth?—If the two bodies
were equal, of what shape would be the shadow?—And if the earth
were the larger body, of what shape would be the shadow?
Eclipse of the Sun.
When does an eclipse of the sun happen?—Explain it by the figure.
Illustrate it by a suspended ball or globe.
If the whole of the sun be obscured, what is the eclipse termed?—
What, if only a part 2
What does the word digit mean?
When, only, can the moon cover the sun's whole disc?—Within how
many degrees of the node can an eclipse happen?—At all other new
moons, how does she pass?—And how at all other full moons f—If an
eclipse of the moon be central, what results?—And what, if an eclipse
of the sun be central?—What are annular eclipses?—By what occa-
sioned?—When only can an eclipse of the sun be total?—How long
M 2
130 QUESTIONS FOR EXAMINATION.
may total darkness last?—How many solar eclipses in a year mus.
there be?—What is the least number there may be?—What is the least,
and what the greatest number of lunar eclipses?—How many eclipses
may happen in a year?—In this case, how many of each —What is the
mean number of eclipses?—Why are there more solar than lunar
eclipses?—And in what proportion?—Why, then, are more lunar than
solarčelipses seen?
CHAPTER XXIX.-Polar Day and Night.
How are the long days and nights around the poles accounted for?—
How, when the sun is on the equator?—How, when vertical to the
tropic of Cancer?—What is the extent of the sun's rays?—What the
length of each day and night?–And why?
What benefit have the polar regions from the twilight?—How long
does the moon continue in their horizon?—Explain the reason.—What
third benefit do they receive?—How does the moon's track vary from
the sun's course? --
When the sun is in the equator, in what point does he rise?—How,
during the summer half-year?—How during the winter half-year?
Whence arises a small variation between the rising and setting?.
Explain this by the globe.
CHAPTER XXX.-Umbra and Penumbra.
Explain the meaning of Umbra and Penumbra by the figure? Which
parts will suffer a total eclipse, and which a partial 2–How does the
umbra fall in an annular eclipse?—And what will then be its appear-
ance t—Which parts of the earth will have a partial eclipse!—And to
what parts no eclipse.
How long can the annular appearance remain —What is the moon's
mean motion?—How many miles does it answer to ?—What will be
the relative velocity of the moon's shadow –What affects the length
of a solar eclipse?
Explain the different eclipses by the figure, in the 1st, 2d, and 3d po
sitions.
What were the effects of a total eclipse of the sun according to Cap-
tain Stannyan?—What is Dr. Scheuchzer's account 7–Relate Dr. Hal-
ley's description.
QUESTIONS FOR EXAMINATION. 131
CHAPTER XXXI.-Transits of Venus.
Illustrate a transit of Venus, by the figure.—During which conjunc-
tion does the transit take place?—What is the principal use to which
astronomers apply the transits of Venus
To what other purposes are the transits applied ?—Which take place
the oftener, the transits of Mercury or Venus?—And which are of the
greater utility ?
What is meant by the occultation of the fixed stars ?—By what me-
thods are occultations ascertained ?—What has Cassini remarked with
respect to them?
What is meant by conjunction?—What by latitude?
What computations are needful to determine when an occultation
will happen? -
Will the appearance be different at different places upon the earth?—
From what cause will the difference result?—To what extent may the
moon's parallax affect the obscuration?
CHAPTER XXXII.-The Harvest Moon.
How much later does the moon often rise, one day than another?—
Is there any difference in different latitudes?—What is her difference
in rising about the time of harvest?
What is the difference to those who live in the latitude of London?
How does the autumnal full moon rise in considerable latitudes?—
Why called the Harvest Moon 2
By whom were these first observed?—And to what ascribed ?–At
what intervals of time does the moon rise about the equator?—When,
at the polar circles?—How long does the moon shine within the polar
circles without setting —To what are these phenomena owing 7–
What is remarked of the signs Pisces and Aries 2—What difference is
there in the moon's rising when in these signs?—How do those signs
of the ecliptic set, which rise with the smallest angles?
Illustrate this by the figure—demonstrate it by the globe.
What part of the ecliptic makes the smallest angles, in northern lat-
tudes?—What, the greatest?—What angle is made by Pisces and Arves
wnen rising !—What angle, when setting?—What is the moon's differ-
ence of rising when in Libra?
Demonstrate these phaenomena on the globe.
**
132 QUESTIONS FOR EXAMINATION.
Why is the moon at the full when in Pisces and Aries only in our
autumnal months?—What are the two autumnal full moons called?
CHAPTER XXXIII.-Harpest Moon continued.
How often does it happen that the moon rises, for a week together,
so nearly in point of time?
What time of the day do Pisces and Aries rise in winter?—And what
is then the moon's age?—How do these signs rise in spring 2—And
what then the moon's age?—When do Pisces and Aries rise in summer?
—What is then the moon's age 7–Why is her rising then so unob-
served ?
In what time does the moon go through the ecliptic —What is the
time from change to change?—What results therefrom?
If the earth had no annual motion, how would every new and full
moon fall ?—And why?—How many degrees does the earth move du-
ring one lunation?—How does this affect the moon's conjunction, &c.?
—If in any conjunction she were in at the first degree of Aries, where
would her next conjunction be 2–Why is the moon twice in some one
degree every lunation?
How must the north and south poles appear to the inhabitants on the
equator?—-What angle does the ecliptic make to such 7–And what re-
sults therefrom ?—Why have they no Harvest Moon at the equator?—
What effect has distance from the equator upon the rising of Pisces and
Aries?
Illustrate this by the globe.
In what signs do the autumnal full moons happen to those in southern
latitudes?—With what angles do Virgo and Libra rise ?—What, with
respect to halvest moons in southern latitudes?
What circumstance may cause some small difference in the time of
the moon's rising or setting?—How much does the moon, at times, vary
from the ecliptic :
To what part of the earth does the full moon not rise in summer?——
To what part does she not set in winter?—Explain the cause of this
satisfactorily.
CHAPTER XXXIV-Leap Year.
What is the time we call a year?—What has been the usual division?
What were the ancient Hebrew months?—What the extent of their
QUESTIONS FOR EXAMINATION. 133
year?—Of how many days did the Athenian months consist? and by
whom regulated ?–How did Meton attempt to reconcile the difference?
—How many months composed the year in the time of Romulus?--
What addition was made to them by Numa Pompilius —What was the
length of the Egyptian year?
Who first attained to tolerable accuracy?—How did Julius Caesar
regulate the months?—How allow for the six odd hours?—What was
every fourth year denominated ?–And what is it now called ?
What day did the Romans reckon twice?—And what was such in-
tercalary day called !—What day do we now add in leap-year?
How is it ascertained what years are, and what are not leap-years?—
Mention what year will and what will not be leap-years.-What is the
length of the true solar year?—How much does 365 days 6 hours ex-
ceed the true solar year?—In how many years does it amount to a
whole day?—How long did the Julian year continue in use?—Who
reformed the calendar? And how?—How denominated?—In what year
did we adopt the new style into our calendars?—And by what change
In the days?—Why were the years 1800 and 1900 computed as com-
mon years?—And why, every four hundredth year afterwards?
What will result from this method of reckoning 2
From what day was the beginning of the year changed?—How, for
a time, did it affect the dates?
CHAPTER XXXV.-The Tides.
Describe the fluctuations of the ocean.
What were the ancients' ideas of the tides?—Who made some suo-
cessful advances?—And who clearly pointed out the cause?
What is the true cause of the flowing of the tides?
. How is the moon proved to be the cause of the tides 7
What would be the appearance, if there were no influence from the
sun or moon?—What, if the earth and moon were without motion?—
What proportion does the sun's attraction bear to that of the moon?—
When the moon is at change, how many parts are raised?—If it be high
water at A, fig. 4, plate XVI. what effect will it produce at C and Dž
What is the attractive power of the sun and moon according to some
authorities?
Explain the cause of low water at C and D.
Of what form will the waters partake at full and change?
i
H34 QUESTIONS FOR EXAMINATION.
CHAPTER XXXVI.—The Tides, continued.
In what proportion does the power of gravity diminish?—When
there is a tide, as at A, fig. 4, plate XVI. what occasions a similar tide
at B?—From what cause will two tides be produced each day?
How has it been otherwise explained ?
How often does the tide ebb and flow in twenty-four hours?—What
is the interval between the flux and reflux?—What is the daily varia-
tion as to the time of high water?
Give an example or two.
How are the tides affected at the full of the moon?—Explain this by
fig. 6, plate XVI.
If there were no moon, how would the sun affect the tides?—When
do the highest tides happen?—What are such tides called?—When the
moon is in her quarters, what are the influences of the sun and moon?
—What are such tides called {
CHAPTER XXXVII.—The Tides, continued.
Why are the tides higher at some seasons than at others?—How long
is it, in open seas, after the moon passes the meridian, that the tides are
at the highest?—And why?
Illustrate this by an impulse given to a moving ball—and by the
time of the greatest heat of the day—and by the increasing heatin July
and August.
Why do not the tides always answer to the moon's unstance from the
meridian —When will the greatest spring-tide happen? And why?—
Why do the tides rise higher in channels and rivers?
To what may the tides, in the mouths of rivers, be compared ?
What retards the tides in shoals and channels?—And how much are
they retarded ?
How long does the tide take to come to London bridge 2
Have lakes any tides?—What seas have but small elevations?-,
Give me the reason.
Are there tides in the air?
How long after the new and full moons do the greatest spring-tides
happen?—And how long after the first and third quarters do the least
meap-tides happen?—Are the tides unequal at places remote from the
equator? Whereisthisinequality observed?—What has been remarked
of the morning and the evening tides?
QUESTIONS FOR EXAMINATION. 135
What results, when the moon's greatest elevation points to one side
of the equator?
When and where is the inequality the greatest ?—What is observed
of the moon when she has declimation?
CHAPTER XXXVIII.-The Precession of the Equinor.
What results from the earth's motion on its axis 7–What arises from
the attraction of the sun and moon?—If the sun sets out from any star,
in what time will he return to it?—And why?
How do you prove that 20 minutes, 17; seconds of time are equal to
50" of a degree ?—What is the sun's apparent annual motion?
When does the sun finish the tropical year?—And what does a tro-
pical year contain?—When does he complete his sidereal year?—And
what does it contain?—How much longer is the sidereal year than the
solar or tropical?—And than the Julian or civil year?
Are the lengths of the sidereal and solar years the same as given by
another author?
What is the sun's daily mean rate in a tropical year?—When will he
arrive at the same equinox?—How long will the sun and equinoctial
points be in falling back 300?—What will be the apparent effect upon
the fixed stars?
How do you prove that 50" short in one year, are equal to a whole
sign in 2160 years?—Explain it by fig. 1, plate XVII.
What results from the shifting of the equinoctial points?—What
change has taken place since the infancy of astronomy?
How is the motion of the equinoctial points, or the precession of the
equinoxes, found?—Who first observed this motion?—And by wha
means?—With whom did Hipparchus compare his observations !
How many years is the equinox in shifting a whole degree?—How
long for a whole sign?—What number of years completes the grand
celestial period?
How much have the equinoctial points receded since the creation?
CHAPTERs XXXIX AND XL-Precession of the Equi-
nor, continued.
Explain the phaenomena by fig. 3, plate XVII.
JHow do astronomers determine the obliquity of the ecliptic?
136 QUESTIONS FOR EXAMINATION,
What did Eratosthenes, Ptolemy, Copernicus, and M. De la Lande
find the obliquity to be?—From these observations what is deduced ;
What is the secular diminution of the ecliptic at this time?
Give a full illustration of the precession of the equinox by the ſou
small spheres, plate XVII.--What does the sphere marked 1 exhibit?-
What, the sphere 27—What, the sphere 3?—What, the sphere 4?
CHAPTER XLI.-Proportionate Magnitudes of the
Planets.
How is the proportion that one planet bears to another found?—Re.
peat the general law, All spheres, &c.
What is the cube of any number?—Demonstrate this by the cubes of
2 and 3.
Cube the numbers 893522, and 7920–Divide the greater by the less.
To find the Planets' Distances from the Sun.
How is the earth's distance from the sun found?—What is its dis-
tance?—What other calculations can be made from it?—What genera’
law did Kepler discover?—By whom was this law fully demonstrated?
What is meant by their periodical times?—Give instances of two or
three.
How do we find the distance of Mercury from the sun?—Square
365–Cube 95,000,000–Square 88–State the question, and perform
the operation.
NEW TREATISE
ON THE
USE OF THE GLOBEs,
I DºSIGNED FOR
THE INSTRUCTION OF YOUTH,
ABRIDGED FROM THE * WORK OF
THOMAS KEIT H.
ADWERTISEMENT.
THE present Abridgement of Keith on the Globes, has
been prepared in order to meet a demand which has fre-
quently been made by those teachers who are desirous to
give their pupils a thorough course of Problems on the
Globes, and who are, nevertheless, of opinion, that the larger
work of Keith contains a great deal more than is necessary
for this purpose. It is intended as a companion for Guy's
Astronomy, a popular treatise, issuing simultaneously from
the same press. It comprises,
I. The extensive and clear definitions of Keith, including
every thing which is necessary for a thorough knowledge
of the structure, design, and uses of the globes.
II. Nearly all Keith's Problems; none being omitted
which are of any practical utility for the general student.
The portions of Keith's larger work, which have been
omitted, belong properly to a treatise of Astronomy, and are
superseded by the treatise which this abridgment is intended
to accompany.
3
CONTENTS.
CHAPTER L.
Lines on the Artificial Globes, Astronomical Definitions, &c. 5
CHAPTER II.
Problems performed with the Terrestrial Globe . . . 24
CHAPTER III
Problems performed with the Celestial Globe 28
A
NEW TREATISE
ON
THE USE OF THE GLOBES.
CHAPTER I.
Erplanation of the lines on the Artificial Globes, in-
cluding Geographical and Astronomical Definitions,
with a few Geographical Theorems.
1. THE TERRESTRIAL GLoBE is an artificial repre-
sentation of the earth. On this globe the four quar-
ters of the world, the different empires, kingdoms and
countries; the chief cities, seas, rivers, &c. are truly
represented, according to their relative situation on the
real globe of the earth. The diurnal motion of this
globe is from west to east.
2. The CELESTIAL GLOBE is an artificial represen-
tation of the heavens, on which the stars are laid down
in their natural situations. The diurnal motion of
this globe is from east to west, and represents the ap-
parent diurnal motion of the sun, moon and stars. In
using this globe, the student is supposed to be situated
in the centre of it, and viewing the stars in the con-
cave surface.
A 2 N 2 5
.6 DEFINITIONS, &c.
3. The Axis of THE EARTH is an imaginary line
passing through the centre of it, upon which it is sup-
posed to turn, and about which all the heavenly bodies
appear to have a diurnal revolution. This line is rep-
resented by the wire which passes from north to south,
through the middle of the artificial globe.
4. The Poles of THE EARTH are the two extremities
of the axis, where it is supposed to cut the surface of
the earth, one of which is called the north, or arctic
pole; the other the south or antarctic pole. The ce-
lestial poles are two imaginary points in the heavens,
exactly above the terrestrial poles.
5. The BRAZEN MERIDIAN is the circle in which
the artificial globe turns, and is divided into 360 equal
parts, called degrees. In the upper semicircle of the
brass 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 lower semi-
circle of the brass meridian they are numbered from
0 to 90, from the poles towards the equator, and are
ased in the elevation of the poles.
6. GREAT CIRCLEs divide the globe into two equal
parts, as the equator, ecliptic, and the colures.
7. SMALL CIRCLEs divide the globe into two unequal
parts, as the tropics, polar circles, parallels of latitude,
&c.
8. MERIDIANs, or Lines of Longitude, are semicir-
cles, extending from the north to the south pole, and
cutting the equator at right angles. Every place upon.
the globe is supposed to have a meridian passing through
it, though there be only 24 drawn upon the terrestrial
DEFINITIONs, &c. rº
globe ; the deficiency is supplied by the brass meri-
dian. When the sun comes to the meridian of any
place (not within the polar circles,) it is noon or mid-
day at that place.
9. The FIRST MERIDIAN is that from which geogra-
phers begin to count the longitudes of places. In Eng-
lish maps and globes the first meridian is a semicircle
supposed to pass through London, or the royal obser-
vatory at Greenwich. -
10. The EquaTor is a great circle of the earth, equi-
distant from the poles, and divides the globe into two
hemispheres, northern and southern. The latitudes of
places are counted from the equator, northward and
Southward, and the longitude of places are reckoned
upon it, eastward and westward.
The equator, when referred to the heavens, is called
the equinoctial; because when the sun appears in it,
the days and nights are equal all over the world, viz.
12 hours each. The declinations of the sun, stars and
planets, are counted from the equinoctial northward
and southward, and their right ascensions are reckoned
wpon it eastward round the celestial globe from 0 to
360 degrees.
11. The ECLIPTIC is a 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,
and cuts the equinoctial in an angle of 23°28'; the
points of intersection are called the equinocial points.
The ecliptic is situated in the middle of the zodiac.
12. The ZoDIAC, on the celestial globe, is a space
which extends about eight degrees on each side of the
6 DEFINITIONs, &c.
ecliptic, like a belt or girdle, within which the motion
of all the planets* are performed. -
13. SIGNs of THE ZoDIAC. The ecliptic and zo-
diac are divided into 12 equal parts, called signs, each
containing 30 degrees. The sun makes his apparent
annual progress through the ecliptic, at the rate of
nearly a degree in a day. The names of the signs,
and the days on which the sun enters them, are as ſol-
low:
SPRING SIGNs. SUMMER SIGNs.
‘P Aries, the Ram, 21st gö Cancer, the Crab, 21st
of March. of June.
8 Taurus, the Bull, 19th Śl Leo, the Lion, 22d of
of April. July. -
II Gemini, the Twins, iſ, Virgo, the Virgin, 22d
20th of May. - of August. -
These are called northern signs, being north of the
equinoctial.
AUTUMNAL SIGNs. WINTER SIGNs.
* Libra, the Balance, V5 Capricornus, the Goat,
23d of September. 21st December.
ml Scorpio, the Scor- % Aquarius, the Water-
º pion, 23d of October. bearer, 20th of January,
1 Sagittarius, the Ar- }é Pisces, the Fishes, 19th
cher, 22d of No- February. r
vember.
These are called southern signs.
The spring and winter signs are called ascending
signs; because when the sun is in any of these, he
* Except the new discovered planets, or asteroids, Ceres, Pallas,and
Juno. 4.
DEFINITIONs, &c. 9
is ascending towards our pole. The summer and au-
tumn signs are called descending signs, because when
the sun is in any of these, he is descending or rece-
ding from our pole.
14. The ColuREs are two great circles passing
through the poles of the world; one of them passes
through the equinoctial points, Aries and Libra; the
other through the solstitial points, Cancer and Capri-
corn; hence they are called the equinoctial and solsti-
tial colures. They divide the ecliptic into four equal
parts, and mark the four seasons of the year.
15. DECLINATION of the sun, of a star, or planet, is
its distance from the equinoctial, northward or south-
ward. When the sun is in the equinoctial he has no
declination, and enlightens half the globe from pole to
pole. As he increases in north declination he gradu-
ally shines farther over the north pole, and leaves the
south pole in darkness: in a similar manner, when he
has south declination, he shines over the south pole,
and leaves the north pole in darkness. The greatest
declination the sun can have is 23°28': the greatest
declination a star can have is 90°, and that of a planet
30° 28% north or south.
16. The TROPICs are two small circles, parallel to
the equator (or equinoctial,) at the distance of 23° 28′
3m it; the northern is called the tropic of Cancer,
..he southern the tropic of Capricorn. The tropics are
the limits of the torrid zone, northward and southward.
17. The Polar CIRCLEs are two small circles, paral
* Except the planets, or asteroids, Ceres, Pallas, and Juno, which
are nearly at the same distance from the sun; the former, in April 1802,
was out of the zodiac, its latitude being 150 20 N.
10 DEFINITIONs, &c.
lel to the equator (or equinoctial,) at the distance of
66° 32' from it, and 23° 28' from the poles. The
northern is called the arctic, the southern the antarctic
circle.
18. PARALLELs of LATITUDE are small circles drawn
through every ten degrees of latitude, on the terres-
trial globe, parallel to the equator. Every place on the
globe is supposed to have a parallel of latitude drawn
through it, though there are generally only sia:teen
parallels of latitude drawn on the terrestrial globe.
19. The Hour CIRCLE on the artificial globes is a
small circle of brass, with an index or pointer fixed to
the north pole; it is divided into 24 equal parts, cor-
responding to the hours of the day, and these are again
subdivided into halves and quarters. The hour circle
when placed under the brass meridian, is moveable
round the axis of the globe, and the brass meridian, in
this case, answers the purpose of an index.
20. 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. Horizon, when applied to
the earth, is either sensible or rational.
21. The SENSIBLE, or visible horizon, is the circle
which bounds our view, where the sky appears to touch
the earth or sea.
22. The RATIONAL, or true horizon, is an imaginary
line passing through the centre of the earth parallel to
the sensible horizon. It determines the rising and
setting of the sun, stars, and planets.
23. The WooDEN HoRIzoN, circumscribing the ar-
DEFINITIONs, &c. 11
tificial globe, represents the rational horizon on the real
globe. This horizon is divided into several concentric
circles, which on Bardin's New British Globes are ar
ranged in the following order:
The First is marked amplitude, and is numbered
from the east towards the north and south, from 0 to
90 degrees, and from the west towards the north and
south in the same manner.
The Second is marked azimuth, and is numbe ‘ed
from the north point of the horizon towards the east
and west, from 0 to 90 degrees: and from the south
point of the horizon towards the east and west in the
Saliſle Iſlam I16 T.
The Third contains the 32 points of the compass,
divided into half and quarter points. The degrees in
each point are to be found in the amplitude circle.
The Fourth contains the twelve signs of the zodiac,
with the figure and character of each sign.
The Fifth contains the degrees of the signs, each
sign comprehending 30 degrees.
The Siacth contains the days of the month answering
to each degree of the sun's place in the ecliptic.
The Seventh contains the equation of time, or differ-
ance 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, is followed by the sign + ; when the clock
or watch ought to be slower, the number of minutes in
the difference is followed by the sign —.
The Eighth contains the twelvo calendar months.
12 DEFINITIONs, &c.
24. The CARDINAL PoinTs of the horizon are east,
west, north, and south.
25. The CARDINAL PoſNTs in the heavens are the
zenith, the nadir, and the points where the sun rises
and sets.
26. The CARDINAL Points of the ecliptic are the
equinoctial and solstitial points, which mark out the
four seasons of the year; and the Cardinal Signs are
‘p Aries, g: Cancer, as Libra, and V5 Capricorn.
27. The ZENITH is a point in the heavens exactly
over our heads, and is the elevated pole of our horizon
28. The NADIR is a point in the heavens exactly
under our feet, being the depressed pole of our horizon,
and the zenith, or elevated pole, of the horizon of our
antipodes.
29. The Pole of any 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. Thus the poles of the
earth are 90 degrees from every part of the equator;
the poles of the ecliptic (on the celestial globe) are 90
degrees from every part of the ecliptic, and 23°28'
from the poles of the equinoctial; consequently they
are situated in the arctic and antarctic circles. Every
circle on the globe, whether real or imaginary, has two
poles diametrically opposite to each other.
30. The EquinocTIAL PoſNTs are Aries and Libra,
where the ecliptic cuts the equinoctial. The point
Aries is called the vernal equinox, and the point Libra
the autumnal equinox. When the sun is in either of
these points, the days and nights on every part of the
globe are equal to each other.
81. The SoLSTITIAL PoſNTs are Cancer and Capri
DEFINITIONs, &c. 1.3
corn. When the sun is in, or near, these points, the
variation in his greatest altitude is scarcely perceptible
for several days; because the ecliptic near these points
is almost parallel to the equinoctial, and therefore the
sun has nearly the same declination for several days.
When the sun enters Cancer, it is the longest day to
all the inhabitants on the north side of the equator, and
the shortest day to those on the south side. When the
sun enters Capricorn it is the shortest day to those who
live in north latitude, and the longest day to those who
live in south latitude.
32. An HEMISPHERE is half the surface of the globe;
avery great circle divides the globe into two hemi-
spheres. The horizon divides the upper from the lower
hemisphere in the heavens; the equator separates the
northern from the southern on the earth; and the brass
meridian, standing over any place on the terrestrial
globe, divides the eastern from the western hemi-
sphere.
33. The MARINER's CoMPAss is a representation of
the holizon, and is used by seamen to direct and as-
certain the course of their ships. It consists of a cir
cular brass box, which contains a paper card, divided
into 32 equal parts, and fixed on a magnetical needle
that always turns towards the north. Each point of
the compass contains 11° 15' or 11+ degrees, being
the 32d part of 360 degrees.
34. The VARIATION of THE CoMPAss is the devia-
tion of its points from the corresponding points in the
heavens. When the north point of the compassis to
the east of the true north point of the horizon, the va-
b
14 DEFINITIONs, &c.
riation is east: if it be to the west, the variation is
West.
The learner is to understand, that the compass does not always point
directly north, but is subject to a small (irregular) annual variation.
At present, 1830, in England, the needle points about 24% degrees to
the westward of the north.
The compassis used for setting the artificial globe north and south;
but care must be taken to make a proper allowance for the variation.
35. LATITUDE OF A PLACE, on the terrestrial globe,
is its distance from the equator in degrees, minutes, or
geographical miles, &c. and is reckoned on the brass
meridian, from the equator towards the north or south
pole.
36. LATITUDE OF A STAR OR PLANET, on the celes-
tial globe, is its distance from the ecliptic, northward
or southward, counted towards the pole of the ecliptic,
on the quadrant of altitude. The greatest latitude a
star can have is 90 degrees, and the greatest latitude of
a planet is nearly 8 degrees.* The sun being always
in the ecliptic, has no latitude.
37. The QUADRANT of ALTITUDE is a thin flexi-
ble piece of brass divided upwards from 0 to 90 degrees
and downwards from 0 to 18 degrees, and when used is
generally 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.
38. LoNGITUDE of A PLACE, on the terrestrial globe,
is the distance of the meridian of that place from the
first meridian, reckoned in degrees and parts of a de-
*The newly-discovered planets, or Asteroids, Ceres and Pallas, &c.
do not appear to be confined within this limit.
DEFINITIONs, &c. 15
gree on the equator. Longitude is either eastward or
westward, according as the place is eastward or west-
ward of the first meridian. The greatest longitude
that a place can have is 180 degrees, or half the cir-
cumference of the globe.
39. LoNGITUDE of A STAR, or PLANET, is reckoned
on the ecliptic from the point Aries, eastward, round
the celestial globe. The longitude of the sun is what
is called the sun's place on the terrestrial globe.
40. ALMACANTARs, or parallels of latitude, are ima-
ginary circles parallel to the horizon, and serve to show
the height of the sun, moon, or stars. These circles
are not drawn on the globe, but they may be described
for any latitude by the quadrant of altitude.
41. PARALLELs of CELESTIAL LATITUDE are small
circles drawn on the celestial globe parallel to the
ecliptic. - . . .
42. PARALLELs of DECLINATION are small circles
parallel to the equinoctial on the celestial globe, and
are similar to the parallels of latitude on the terrestrial
globe. -
43. Azimuth, or VERTICAL CIRCLEs, are imaginary
great circles passing through the zenith and the nadir,
cutting the horizon at right angles. The altitudes of
the heavenly bodies are measured on these circles,
which circles may be represented by screwing the quad.
rant of altitude on the zenith of any place, and making
the other end move along the wooden horizon of the
globe. . - -
44. The PRIME VERTICAL is that azimuth circle
which passes through the east and west points of the .
16 DEFINITIONs, &c.
horizon, and is always at right angles to the brass me-
ridian, which may be considered as another vertical
circle passing through the north and south points of
the horizon.
45. The ALTITUDE 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 upon
the meridian, this are is called the meridian altitude.
46. The ZENITH DISTANCE of any celestial object
is the 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
object is on the meridian, this arc is called the meri-
dian zenith distance.
57. 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.
48. 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.
When the sun has north declination, it rises to coun-
tries in north latitudes, to the north of the east, and
sets to the north of the west; and when it has south
declination, it rises to the south of the east, and sets
to the south of the west. At the time of the equinoxes,
when the sum has no declination, viz. on the 21st of
March, and on the 23d of September, it rises exactly
in the east, and sets exactly in the west.
DEFINITIONs, &c. 17
49. The Azim UTH of any object in the heavens is
an arc of the horizon, contained between a vertical cir-
cle passing through the object, and the north or south
points of the horizon. The azimuth of the sun, at any
particular hour, is used at sea for finding the variation
of the compass.
50. Hour CIRCLEs, or HoRARY CIRCLEs, are the
same as the meridians. They are drawn through every
15 degrees” of the equator, each answering to an hour
—consequently every degree of longitude answers to
four minutes of time, every half degree to two minutes,
and every quarter of a degree to one minute.
On the globes these circles are supplied by the brass
meridian, the hour circle, and its index.
51. Positions of THE SPHERE are three : right,
parallel, and oblique.
52. A RIGHT SPHERE is that position of the earth
where the equinoctial passes through the zenith and
the nadir, the poles being in the rational horizon. The
inhabitants who have this position of the sphere, live at
the equator: it is called a right sphere, because the
parallels of latitude cut the horizon at right angles. In
a right sphere the parallels of latitude are divided into
two equal parts by the horizon, and the days and nights
are of equal length.
53. A PARALLEL SPHERE is that position the earth
has when the rational horizon coincides with the equa-
tor, the poles being in the zenith and nadir. The in-
habitants who have this position of the sphere (if there
* On Cary's large Globes the meridians are drawn through every 10
degrees, as on a Map. -
b 2 O 2
18 DEFINITIONs, &c.
be any such inhabitants) live at the poles; it is called
a parallel sphere, because all the parallels of latitude
are parallel to the horizon. In a parallel sphere the
Sun appears above the horizon for six months together,
and he is below the horizon for the same length of
time.
54. AN OBLIQUE SPHERE is that position the earth
has when the rational horizon cuts the equator oblique-
ly, and hence it derives its name. All inhabitants on
the face of the earth (except those who live exactly at
the poles or at the equator) have this position of the
sphere. The days and nights are of unequal lengths,
the parallels of latitude being divided into unequai
parts by the rational horizon.
55. CLIMATE is a part of the surface of the earth
contained between two small circles parallel to the
equator, and of such a breadth, that the longest day in
the parallel nearest the pole, exceeds the longest day
in the parallel of latitude nearest the equator, by half
an hour, in the torrid and temperate zones, or by a
month in the frigid zones; so that there are 24 climates
between the equator and each polar circle, and six cli-
mates between each polar circle and its pole.
56. A ZonE is a portion of the surface of the earth
contained between two small circles parallel to the
equator, and is similar to the term climate, for pointing
out the situations of places on the earth, but less exact;
as there are only five zones, which have been distin-
guished by particular names; whereas there are 60
climates.
57. The Torrid ZonE extends from the tropic of
DEFINITIONS, &c. 19
Uancer to the tropic of Capricorn, and is 46° 56' broad.
This zone was thought by the ancients to be uninhabit-
ed, because it is continually exposed to the direct rays
of the sun ; and such parts of the torrid zone as were
known to them were sandy deserts, as the middle of
Africa, Arabia, &c.; and these sandy deserts extend be-
yond the left bank of the Indus, toward Agimere.
58. The Two TEMPERATE Zones. The north tem-
perate 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. These
zones are each 43°4' broad, and were called temper-
ate by the ancients, because meeting the sun's rays
obliquely, they enjoy a moderate degree of heat.
59. The Two FRIGID Zones. The north frigid
zone, or rather segment of the sphere, is bounded by
the arctic circle. The north pole, which is 23°28'
from the arctic circle, is situated in the centre of this
zone. The south frigid zone is bounded by the antarc-
tic circle, distant 23°28' from the south pole, which
is situated in the centre of this zone.
60. AMPHISCII are the inhabitants of the torrid zone;
so called, because their shadows fall north or south at
different times of the year; the sun being sometimes
to the south of them at noon, 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 AscHII, or shadowless.
61. HETERoscII is a name given to the inhabitants
of the temperate zones, because their shadows at noon
fall only one way. Thus, the shadow of an inhabitant
20 DEFINITIONs, &c.
of the north temperate zone always falls to the north
at noon, because the sun is then due south; and the
shadow of an inhabitant of the south temperate zone
falls towards the south at noon, because the sun is due
north at that time.
62. PERISCII are those people who inhabit the frigid
zones, so called, because their shadows, during a revo-
lution of the earth on its axis, are directed towards
every point of the compass. In the frigid zones the
sun does not set during several revolutions of the earth
on its axis.
63. ANTOECI are those who live in the same degree
of longitude, and in equal degrees of latitude, but the
one in north and the other in south latitude. They
have noon at the same time, but contrary seasons of
the year; consequently, the length of the days to the
one, is equal to the length of the nights to the other.
Those who live at the equator can have no Antocci.
64. PERIOECI are those who live in the same latitude,
but in opposite longitudes; when it is noon with the
one, it is midnight with the other; they have the same
length of days, and the same seasons of the year. The
inhabitants of the poles can have no Periopci.
65. ANTIPODEs are those inhabitants of the earth
who live diametrically opposite to each other, and con-
sequently walk feet to feet; their latitudes, longitudes,
seasons of the year, days and nights, are all contrary to
each other.
66. The RIGHT AscENSION of the sun, or of a star,
is that degree of the equinoctial which rises with the
DEFINITIONs, &c. 21
S.
sun, or star, in a right sphere, and is reckoned from the
equinoctial point Aries eastward round the globe.
67. OBLIQUE AscENSION of the sun or of a star, is
that degree of the equinoctial which rises with the sun
or star, in an oblique sphere, and is likewise counted
from the point Aries eastward round the globe.
68. OBLIQUE DESCENSION of the sun, or of a star, is
that degree of the equinoctial which sets with the sun
or star in an oblique sphere.
69. The AscENSIONAL or DEscENSIONAL DIFFER-
ENCE is the difference between the right and oblique
ascension, or the difference between the right and
oblique descension, and, with respect to the sun, it is
the time he rises before 6 in the spring and summer, or
sets before 6 in the autumn and winter.
70. The CREPUSCULUM, or TwilighT, is that faint
light which we perceive before the sun rises, and after
he sets. It is produced by the rays of light being re-
fracted in their passage through the earth's atmosphere,
and reflected from the different particles thereof. The
twilight is supposed to end in the evening when the
sun is 18 degrees below the horizon, or when stars of
the sixth magnitude (the smallest that are visible to
the naked eye) begin to appear; and the twilight is
said to begin in the morning, or it is day-break, when
the sun is again within 18 degrees of the horizon. The
twilight is the shortest at the equator, and longest at
the poles; here the sun is near two months before he
retreats 18 degrees below the horizon, or to the point
where his rays are first admitted into the atmosphere ;
22 DEFINITIONs, &c.
and he is only two months more before he arrives at
the same parallel of latitude.
71. ANGLE of PosLTION between two places on the
terrestrial globe, is an angle at the zenith of one of the
places, formed by the meridian of that place, and a
vertical circle passing through the other place, being
measured on the horizon from the elevated pole towards
the vertical circle:
THE ANGLE or Position of A STAR, is an angle formed by two
great circles intersecting each other in the place of the star, the one pas-
sing through the pole of the equinoctial, the other through the pole of
the ecliptic.
72. BAYER's CHARACTERs. John Bayer, of Augs-
burg in Swabia, published in 1603 an excellent work,
entitled Uranometria, being a complete atlas of all the
constellations, with the useful invention of denoting the
stars in every constellation by the letters of the Greek
and Roman Alphabets; setting the first Greek letter a
to the principal star in each constellation, 8 to the
second in magnitude, x to the third, and so on, and when
the Greek alphabet was finished, he began a, b, c, &c.
of the Roman. This useful method of describing the
stars has been adopted by all succeeding astronomers,
who have farther enlarged it by adding the numbers,
1, 2, 3, &c. in the same regular succession, when any
constellation contains more stars than can be marked
by the two alphabets. The figures are, however, some-
times placed above the Greek letter, especially where
double stars occur; for though many stars may appear
single to the naked eye, yet when viewed through a
telescope of considerable magnifying power they ap-
pear double, triple, &c. Thus, in Dr. Zach's Tabulae
DEFINITIONs, &c. 24
Motuum Solis, we meet with f Tauri, 8 Tauri, r Tauri,
st Tauri, 32 Tauri, &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 seldom used in the catalogues of stars, but are here given for the
sake of regularity.
JWame. Sound. JName. Sound.
A cº Alpha 8, N v Nu Iſl
B & 6 Beta b # & Xi X
r 5 ſ Gamma g O o Omicron o short
A 3. Delta d II ºr ºr Pi p
E s Epsilon e Short P 6 p Rho r
Z & & Zeta 2 X, a s C Sigma §
H iſ Eta e long T ºr 7 Tau t
& S 6 Theta th T u Upsilon ū
I à Iota I & q' Phi th
K x. Kappa k X 2. Chi ch
A 2. Lambda I Y \, Psi ps
M. As Mul Iºl Q co Omega o long
73. DIURNAL ARC is the arc described by the sun,
moon, or stars, from their rising to their setting. The
sun's semi-diurnal arc is the arc described in half the
length of the day.
74. NocturnAL ARC is the arc described by the
Sun, moon, or stars, from their setting to their rising.
75. ABERRATION is an apparent motion of the ce-
lestial bodies, occasioned by the earth's annual motion
in its orbit, combined with the progressive motion of
light.
24 PROBLEMIS PERFORMED WITH
CHAPTER II.
PROBLEMS PERFORMED WITH THE TERRESTRIAL GLOBE.
PROBLEM I.
To find the latitude of any given place.
RULE. Bring the given place to that part of the
brass meridian which is numbered from the equator
towards the poles; the degree above the place is the
latitude. If the place be on the north side of the equa-
tor, the latitude is north; if it be on the south side the
.atitude is south.
On small globes the latitude of a place cannot be found nearer than
to about a quarter of a degree. Each degree of the brass meridian on
the largest globes is generally divided into three equal parts, each part
containing twenty geographical miles; on such globes the latitude
may be found to 10'.
ExAMPLEs.-What is the latitude of Edinburgh?
Answer.—560 north.
2. Required the latitudes of the following places:
Amsterdam Florence Philadelphia
Archangel Gibraltar Quebec
Barcelona Hamburgh Rio Janeiro
Batavia Ispahan Stockholm
Bencoolen Lausanne Turin
Berlin Lisbon Vienna
Cadiz Madras Warsaw
Canton Madrid Washington
Dantzic Naples Wilna
Drontheim Paris York
THE TERRESTRIAL, GLOBE, 25
3. Find all the places on the globe which have no
latitude.
4. What is the greatest latitude a place can have 7
PROBLEM II.
To find all those places which have the same latitude as
any given place.
RULE. Bring the given place to that part of the
brass meridian which is numbered from the equator
towards the poles, and observe its latitude; turn the
globe round, and all places passing under the observed
latitude are those required.
All places in the same latitude have the same length of day and
night, and the same seasons of the year, though from local circumstan-
ces, they may not have the same atmospherical temperature.
ExAMPLEs. 1. What places have the same, or near-
'y the same latitude as Madrid'ſ
Answer. Minorca, Naples, Constantinople, Samarcand, Philadel-
phia, Pekin, &c.
2. What inhabitants of the earth have the same
length of days as the inhabitants of Edinburgh 3
3. What places have nearly the same latitude as
London 7
4. What inhabitants of the earth have the same sea-
sons of the year as those of Ispahan 7
5. Find all the places of the earth which have the
longest day the same length as at Port Royal in Ja-
maica.
PROBLEM III.
To find the Longitude of any place.
RULE. Bring the given place to the brass meridian,
the number of degrees on the equator, reckoning from
C P
26 PROBLEMS PERFORMED WITH
the meridian passing through London to the brass me-
ridian is the longitude. If the place lie to the right
hand of the meridian passing through London, the lon-
gitude is east; if to the left hand, the longitude is
West.
On Adams' and Cary's globes there are two rows of figures above
the equator. When the place lies to the right hand of the meridian of
London, the longitudes must be counted on the upper line; when it
ties to the left hand it must be counted on the lower line. Bardin's
New British Globes have also two rows of figures above the equator,
but the lowerline is always used in reckoning the longitude.
ExAMPLEs. 1. What is the longitude of Peters-
Surg?
Answer. 3040 east.
2. What is the longitude of Philadelphia?
Answer. 7540 west.
3. Required the longitudes of the following places:
Aberdeen Civita Vecchia Lisbon
Alexandria Constantinople Madras
Barbadoes Copenhagen Masulipatam
Bombay Drontheim Mecca
Botany Bay Ephesus Nankin
Canton Gibraltar Palermo
Carlscrona Leghorn Pondicherry
Cayenne Liverpool Queda.
3. What is the greatest longitude a place can have?
PROBLEM IV.
To find all those places that have the same longitude as
* a given place.
RULE. Bring the given place to the brass meridian,
TIIE TERRESTRIAL, GLOBE, 27
then all places under the same edge of the meridian
from pole to pole have the same longitude.
All people situated under the same meridian from 66°28 north lati.
tude to 66° 28 south latitude, have noon at the same time; or, if it be
one, two, three, or any number of hours before or after moon with one
particular place, it will be the same hour with every other place situa-
ted under the same meridian.
ExAMPLEs. 1. What places have the same, or nearly
the same longitude as Stockholm ?
Answer. Dantzie, Presburg, Tarento, the Cape of Good Hope, &c.
2. What places have the same longitude as Alexan-
dria 7
3. When it is ten o’clock in the evening at London,
what inhabitants of the earth have the same hour?
4. What inhabitants of the earth have midnight when
the inhabitants of Jamaica have midnight?
5. What places of the earth have the same longitude
as the following places? º
London Quebec The Sandwich islands
Pekin Dublin Pelew islands.
PROBLEM V.
To find the latitude and longitude of any place.
RULE. Bring the given place to that part of the
brass meridian which is numbered from the equator to-
wards the poles; the degree above the place is the lati-
tude, and the degree on the equator, cut by the brass
meridian, is the longitude.
This problem is only an exercise of the first and third.
ExAMPLEs. 1. What are the latitude and longitude
of Petersburg!
Answer. Latitude 60° N. longitude 30}o E.
28 PROBLEMS PERFORMED WITH
2. Required the latitudes and longitudes of the fol-
lowing places:
Acapulco Cusco Lima
Aleppo Copenhagen Lizard
Algiers Durazzo Lubec
Archangel Elsinore Malacca
Belfast Flushing Manilla
Bergen Cape Guardafui Medina
Buenos Ayres Hamburgh Mexico
Calcutta Jeddo Mocha
Candy Jaffa Moscow
Corinth Ivica Oporto.
PROBLEM WI.
To find any place on the globe having the latitude and
longitude of that place given.
RULE. Find the longitude of the given place on
the equator, and bring it to that part of the brass me-
ridian which is numbered from the equator towards
the poles; then under the given latitude, on the brass
meridian, you will find the place required.
ExAMPLEs. 1. What place has 151}^east longitude,
and 34° south latitude 7
Answer. Botany Bay.
2. What places have the following latitudes and lon-
gitudes 7
Latitudes. Longitude. Latitude. Longitude.
50° 6' N. 5° 54" W. I99 26' N. 100° 6' W
48 12 N. 16 16 E. 59 56 N. 30 19 E.
55 58 N. 3 12 W. 0 13 S. 77 55 W.
52 22 N. 4 51 E. 46 55 N. 69 53 W
31 13 N. 29 55 E. 59 21 N. 18 4 E.
THE TERRESTRIAL GILOBE, 29
64° 34' N. 38° 58' E. 8° 32' N. 81° 11" E.
34 29 S. 18 23 E. 5 9 S. 119 49 E.
3 49 S. 102 10 E. 22 54 S. 42 44 W.
34 35 S. 58 31 W. 36 5 N. 5 22 W
32 25 N. 52 50 E. 32 38 N. 17 6 W.
PROBLEM VII.
To find the difference of latitude between any two places.
RULE. Bring one of the places to that half of the
brass meridian which is numbered from the equator
towards the poles, and mark the degree above it; then
bring the other place to the meridian, and the number
of degrees between it and the above mark will be the
difference of latitude.
OR, Find the latitudes of both the places (by Prob.
1.) then, if the latitudes be both north or both south,
subtract the less latitude from the greater, and the re-
mainder will be the difference of latitude; but, if the
latitudes be one north and the other south, add them
together, and their sum will be the difference of lati-
tude.
ExAMPLEs. 1. What is the difference of latitude
between Philadelphia and Petersburgh
Answer. 20 degrees.
2. What is the difference of latitude between Mad.
rid and Buenos Ayres 7
Answer, 75 degrees.
3. Required the difference of latitude between the
following places?
London and Rome Alexandria and 'he Cape
Dolhi and Cape Comorin of Good Hop
c 2 P 2
30 PROBLEMIS PERFORMED WITH
Vera Cruz and Cape Horn Pekin and Lima
Mexico and Botany Bay St. Salvador and Surinam
Astracan and Bombay Washington and Quebec
St. Helena and Manilla Porto Bello and the Straits
Copenhagen and Toulon of Magellan
Brest and Inverness Trinidad I. and Trincomalé
Cadiz and Sierra Leone Bencoolen and Calcutta.
4. What two places on the globe have the greatest
difference of latitude 7
PROBLEMI VIII.
To find the difference of longitude between any two
places.
RULE. Bring one of the given places to the brass
meridan, and mark its longitude on the equator; then
bring the other place to the brass meridian, and the
number of degrees between its longitude and the above
mark, counted on the equator, the nearest way round
the globe, will show the difference of longitude.
OR, Find the longitudes of both the places (by Prob.
III.) then, if the longitudes be both east or both west,
subtract the less longitude from the greater, and the
remainder will be the difference of longitude: but, if
the longitude be one east and the other west, add them
together, and their sum will be the difference of lon-
gitude. t–
When this sum exceeds 180 degrees, take it from
360, and the remainder will be the difference of lon-
gitude.
ExAMPLEs. 1. What is the difference of longitude
between Barbadoes and Cape Verd?
THE TERRESTRIAL GI.O.B.E. 31
Answer. 430 42.
2. What is the difference of longitude between
Buenos Ayres and the Cape of Good Hope?
Answer. 760 54'
3. What is the difference of longitude between
Botany Bay and O'why'ee 7
Answer. 52°45', or 523 degrees.
4. Required the difference of longitude between the
following places:
Vera Cruz and Canton Constantinople and Batavia
Bergen and Bombay Bermudas I. and I. of Rhodes
Columbo and Mexico Port Patrick and Berne
Juan Fernandes I. and Mount Heckla and Mount
Manilla Vesuvius
Pelew I. and Ispahan Mount AEtna and Teneriffe
Boston in Amer. and North Cape and Gibraltar.
Berlin
5. What is the greatest difference of longitude com-
prehended between two places?
PROBLEM IX.
To find the distance between any two places.
RULE. The shortest distance between any two
places on the earth, is an arc of a great circle contained
between the two places. Therefore, lay the graduated
edge of the quadrant of altitude over the two places, so
that the division marked 0 may be on one of the places,
the degrees on the quadrant comprehended between
the two places will give their distance; and if these
degrees be multiplied by 60, the product will give the
distance in geographical miles; or multiply the de-
32 PROBLEMS PERFORMED WITH
grees by 69%, and the product will give the distance in
English miles.
OR, Take the distance between the two places with
a pair of compasses, and apply that distance to the equa.
tor, which will show how many degrees it contains.
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 ex-
tent of thread between these marks, applied to the
equator, from the meridian of London, will show the
number of degrees between the two places.
ExAMPLEs. 1. What is the nearest distance be-
tween the Lizard and the island of Bermudas?
45% distance in degrees. 45% distance in degrees.
60 69;
2700 22;
30 405
15 270
tºmºmºsº * : 34%
2745 geographical miles. 17#
3176# English miles.
2. What is the nearest distance between the island
of Bermudas and St. Helena'!
# distance in degrees. 73; distance in degrees.
#
4380 36;
30 657
ººmsºmº 438
4410 geographical miles. 34%
5108} English miles.
3. What is the nearest distance between London
and Botany Bay.
THE TERRIESTRIAL GLOBEe 33
154 distance in degrees. 154 distance in degrees.
60 69;
9240 geographical miles. 77
1386
924
10703 English miles.
4. What is the direct distance between London and
Jamaica, in geographical and English miles?
5. What is the extent of Europe in English miles.
from Cape Matopan in the Morea, to the North Cape
in Lapland 7
6. What is the extent of Africa from Cape Verd to
Cape Guardafui ?
7. What is the extent of south America from Cape
Blanco in the west to Cape St. Roque in the east !
8. Suppose the track of a ship to Madras be from
the Lizard to St. Anthony, one of the Cape Verd is-
lands, thence to St. Helena, thence to the Cape of Good
Hope, thence to the east of the Mauritius, thence a
little to the south-east of Ceylon, and thence to Madras;
how many English miles is the Land's End from Mad-
ras?
PROBLEM X.
A place being given on the globe, to find all places,
which are situated at the same distance from it as
any other given place.
RULE. Lay the graduated edge of the quadrant of
altitude over the two places, so that the division marked
0 may be on one of the places, then observe what de-
gree of the quadrant stands over the other place; move
the quadrant entirely round, keeping the division mark-
34 PROBLEMIS PERFORMED WITH
ed 0 in its first situation, and all places which pass
under the same degree which was observed to stand
over the other place, will be those sought.
OR, Place one foot of a pair of compasses in one of
the given places, and extend the other foot to the other
given place : a circle described from the first place as
a centre, with this extent, will pass through all the pla-
ces sought.
If the distance 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, as in the preceding problem.
ExAMPLEs. 1. It is required to find all the places on
the globe which are situated at the same distance from
London as Warsaw is 7
Answer. Koningsburg, Buda, Posega, Alicant, &c.
2. What places are at the same distance from Lon-
don as Petersburg is ?
3. What places are at the same distance from Lon-
tion as Constantinople is 7
4. What places are at the same distance from Rome
as Madrid is 7
PROBLEM XI.
Given the latitude of a place and its distance from a
given place, to find that place whereof the latitude is
given.
RULE. If the distance be given in English or geo-
graphical miles, turn them into degrees by dividing by
69% for English miles, or 60 for geographical miles,
then put that part of the graduated edge of the quad-
rant of altitude which is marked 0 upon the given place,
and move the other end eastward or westward (accord-
ing as the required place lies to the east or west of
THE TERRESTRIAL, GLOBE, 35
the given place,) till the degrees of distance cut the
given parallel of latitude : under the point of intersec-
tion you will find the place sought.
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 compass in
the given place, as a centre, and his extent of degrees,
describe a circle on the globe; turn the globe till this
circle falls under the given latitude on the brass meri-
dian, and you will find the place required.
ExAMPLEs. 1. A place in latitude 60°N. is 1320%
English miles from London, and it is situated in E.
longitude; required the place 7
Answer. Divide 13203 miles by 69% miles, or which is the same
thing, 2641 half-miles by 139 half-miles, the quotient will give 19 de-
grees; hence the required place is Potersburgh.
2. A place in latitude 32}* N. is 1350 geographical
miles from London, and it is situated in W. longitude;
required the place 7
Answer. Divide 1350 by 60, the quotient is 22° 30', or 22% degrees;
hence the required place is the west point of the island of Madeira.
3. What place in E. longitude and 41° N. latitude,
is 1529 English miles from London 7
4. What place in W. longitude and 13° N. latitude,
is 3660 geographical miles from London?
PROBLEM XII.
Given the longitude of a place and its distance from a
given place, to find that place whereof the longitude
is given.
RULE. If the distance be given in English or geo-
graphical miles, turn them into degrees by dividing by
36 PROBLEMs PERFoRMED" witH
69% for English miles, or 60 for geographical miles,
then put that part of the graduated edge of the quad-
rant 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 intersec-
tion you will find the place sought.
OR, Having reduced the miles into degrees, take
he same number of degrees from the equator with a
pair of compasses, and with one foot of the compasses
in the given place, as a centre, and this extent of de-
grees, describe a circle on the globe; bring the given
longitude to the brass meridian, and you will find the
place, upon the circle, under the brass meridian.
ExAMPLEs. 1. A place in north latitude, and in 60
degrees west longitude, is 4239% English miles from
London; required the place
Answer. Divide 4239; miles by 69% miles, or, which is the same
thing, 8479 half-miles by 139 half-miles, the quotient will give 61 de-
grees; hence the required place is the island of Barbadoes.
2. A place in north latitude, and in 75% degrees
west longitude, is 3120 geographical miles from Lon-
don; what place is it?
3. A place in 31% degrees east longitude, and situ-
ated southward of London, is 2224 English miles from
it; required the place 1
4. A place in 29 degrees east longitude, and situa-
ted southward of London, is 1529 English miles from
it, required the place 1
THE TERRESTRIAL, GLOBE, • 37
PROBLEM XIII.
To find how many miles make a deg. of longitude in any
given parallel of latitude.
RULE. Lay the quadrant of altitude parallel to the
equator, between any two meridians in the given lati-
tude, which differ in longitude 15 degrees; the num
ber of degrees intercepted between them multiplied by
4, will give the length of a degree in geographical
miles. The geographical miles may be brought into
English miles by multiplying by 116, and cutting off
two figures from the right-hand of the product.
OR, Take the distance between two meridians, which
differ in longitude 15 degrees in the given parallel of
latitude, with a pair of compasses; apply this distance
to the equator, and observe how many degrees it makes:
with which proceed as above.
Since the quadrant of altitude will measure no arc truly but that of
a great circle; and a pair of compasses will only measure the chord of
an arc, not the arc itself; it follows that the preceding rule cannot be
mathematically true, though sufficiently correct for practical purposes.
When great exactness is required, recourse must be had to calculation.
The above rule is founded on a supposition that the number of de-
grees contained between any two meridians, reckoned on the equator
is to the number of degrees contained between the same meridians, on
any parallel of latitude, as the number of geographical miles contained
in one degree of the equator, is to the number of geographical miles
contained in one degree on the given parallel of latitude. Thus in the
iatitude of London, two places which differ 15 degrees in longitude are
9} degrees distant by the rule. Hence,
150 : 9} :: 60m. : 37m.; or 150 : 60m. :: 94 : 37m.; but 15 is to 60 as 1
is to 4, therefore, 1:4::9; : 37 geographical miles contained in one de-
gree. Now, any number of geographical miles inay be brought into
English miles by multiplying by 69; and dividing by 60; or by multi-
plying by 1.16; for 60: 69; ; ; 1.16 nearly.
d Q
38 PROBLEMIS PERFORMED WITH
ExAMPLEs. 1. How many geographical and English
miles make a degree in the latitude of Pekin?
Answer. The latitude of Pekin is 400 north : the distance between
*wo meridians in that latitude (which differ in longitude 15 degrees) is
11% degrees. Now, 11% degrees multiplied by 4, produces 46 geogra-
phical miles for the length of a degree of longitude, in the latitude of
Pekin; and if 46 be multiplied by 116, the product will be 5336; cut
off the two right hand-hand figures, and the length of a degree in Eng-
lish miles will be 53. OR, by the rule of three, 150 : 69%m. : : 1149 :
53 miles.
2. How many miles make a degree in the parallels
of latitude wherein the following places are situated?
Surinam Washington Spitzbergen
Barbadoes Quebec Cape Verd
Havana Skalholt Alexandria
Bermudas I. North Cape Paris.
PROBLEM XIV.
To find the bearing of one place from another.
RULE. If both the places be situated on the same
parallel of latitude, their bearing is either east or west
from each other; if they be situated on the same me-
ridian, they bear north and south from each other; if
they be situated on the same rhumb-line, that rhumb-
line is their bearing: if they be not situated on the
same rhumb-line, lay the quadrant of altitude over the
two places, and that rhumb-line which is the nearest of
being parallel to the quadrant will be their bearing.
OR, If the globe have no rhumb-lines drawn on it,
make a small mariner's compass (such as in Plate I.
fig. 4.) 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 bearings
of all the circumjacent places, to the distance of up-
THE TERRESTRIAL, GLOBE, 39
wards of a thousand miles, if the centrical place be not
far distant from the equator.
ExAMPLEs. 1. Which way must a ship steer from
the Lizard to the island of Bermudas?
Answer. W. S. W.
2. Which way must a ship steer from the Lizard to
the island of Madeira'ſ
Answer. S. S. W.
3. Required the bearing between London and the
following places?
Amsterdam Copenhagen Petersburg
Athens Dublin Prague
Bergen Edinburgh Rome
Berlin Lisbon Stockholm
Berne Madrid Vienna
Brussels Naples Warsaw.
Buda Paris
PROBLEM XV.
To find the angle of position between two places.
RULE. Elevate the north or south pole, according
as the latitude is north or south, so many degrees
above the horizon as are equal to the latitude of one of
the given places; bring that place to the brass meri-
dian, and screw the quadrant of altitude upon the de-
gree over it; next move the quadrant till its graduated
edge falls upon the other place; then the number of
degrees on the wooden horizon, between the graduated
edge of the quadrant and the brass meridian, reckoning
towards the elevated pole, is the angle of position be-
tween the two places.
40 PROBLEMS PERFORMED WITH
ExAMPLEs. 1. What is the angle of position between
London and Prague 1
Answer. 90 degrees from the north towards the east: the quadrant
of altitude will fall upon the east point of the horizon, and pass over
or near the following places, viz. Rotterdam, Frankſort, Cracow, Ock-
zakov, Caffa, south part of the Caspian Sea, Guzerat in India, Madras,
and part of the island of Ceylon. Hence all these places have the
same angle of position from London.
2. What is the angle of position between London
and Port Royal in Jamaica'!
Answer. 90 degrees from the north towards the west; the quadrant
of altitude will fall upon the west point of the horizon.
3. What is the angle of position between Philadel-
phia and Madrid'ſ
Answer. 65 degrees from the north towards the east; the quadrant
of altitude will fall between the E. N. E. and N. E. by E. points of the
horizon.
4. Required the angles of position between London
and the following places?
Amsterdam Copenhagen Rome
Berlin Cairo Stockholm
Berne Lisbon Petersburg
Constantinople Madras Quebec.
PROBLEM XVI.
To find the Antaeci, Periocci, and Antipodes to the
inhabitants of any place.
RULE. Place the two poles of the globe in the hori-
zon, and bring the given place to the eastern part of
the horizon; then, if the given place be in north lati-
tude, observe how many degrees it is to the northward
of the east point of the horizon; the same number of
legrees to the southward of the east point will show
THE TERRESTRIAL GIOBE, 41
the Antocci; an equal number of degrees, counted from
the west point of the horizon towards the north, will
show the Perioci; and the same number of degrees,
counted towards the south of 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
contrary.
OR THUs:
For the Antaeci. Bring the given place to the brass
meridian and observe its latitude; then in the opposite
hemisphere, under the same degree of latitude, you
will find the Antoºci.
For the Periaci. Bring the given place to the brass
meridian, 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 latitude of the given place
you will find the Periosci.
For the Antipodes. Bring the given place to the
brass meridian, 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 latitude
with the given place, but in the opposite hemisphere,
wou will find the Antipodes. *
ExAMPLEs. 1. Required the Antoeci, Periocci, and
Antipodes, to the inhabitants of the island of Bermu-
das?
Answer. Their Antoeci are situated in Paraguay, a little N.W. of
Buenos Ayres; their Perioeci in China, N W of Nankin; and their
Antipodes in the S.W. part of New Holland.
2. Required the Antopci, Periopci, and Antipodes to
the inhabitants of the Cape of Good Hope 2
d 2 Q 2
42 PROBLEMS PERFORMED WITH
3. Captain Cook, in one of his voyages, was in 50
degrees south latitude and 180 degrees of longitude;
in what part of Europe were his Antipodes?
4. Required the Antoeci to the inhabitants of the
Falkland islands?
5. Required the Periosci to the inhabitants of the
Philippine islands !
6. What inhabitants of the earth are Antipodes to
those of Buenos Ayres'
To find at what rate per hour the inhabitants of any
given place are carried, from west to east, by the re-
volution of the earth on its aris.
RULE. Find how many miles make a degree of
longitude in the latitude of the given place (by Proh-
lem XIII.) which multiply by 15 for the answer.
OR, look for the latitude of the given place in the
table, Problem IX., against which you will find the
number of miles contained in one degree ; multiply
these miles by 15, and reject two figures from the right
hand of the product; the result will be the answer.
ExAMPLEs. 1. At what rate per hour are the in-
habitants of Madrid carried from west to east by the
revolution of the earth on its axis'
Answer. The latitude of Madrid is about 400 N. where a degree of
longitude measures 46 geographical, or 53 English miles (see Example
1. Prob. XIII) Now 46 multiplied by 15 produces 690; and 53 multi-
plied by 15 produces 795; hence the inhabitants of Madrid are carried
690 geographical, or 795 English miles per hour.
By the Table. Against the latitude 40 you will find 45.96 geogra-
phical miles, and 52.85 English miles: Hence,
44.95 × 15–68940 and 52.85 × 15–792.75, by rejecting the tworight.
hand figures from each product, the result will be 689 geographical
miles, and 792 English miles, agreeing nearly with the above.
THE TERRESTRIAL, GLOBE, 43
2. At what rate per hour are the inhabitants of the
following places carried from west to east by the revo-
lution of the earth on its axis 7
Skalholt Philadelphia Cape of Good Hope
Spitzbergen Cairo Calcutta
Petersburgh Barbadoes Delhi
London Quito Batavia.
PROBLEM XVIII.
A particular place, and the hour of the day at that
place being given, to find what hour it is at 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 12; turn the globe till the other place comes
to the meridian, and the hours passed over by the in-
dex will be the difference of time between the two
places. If the place where the hour is sought lie to
the east of that wherein the time is given, count the
difference of time forward from the given hour; if it
ie to the west, reckon the difference of time backward.
OR, witHouT THE HOUR CIRCLE.
Find the difference of longitude between the two
places (by Problem VIII.) and turn it into time by al-
lowing 15 degrees to an hour, or four minutes of time
to one degree. The difference of longitude in time
will be the difference of time between the two places,
with which proceed as above. Degrees of longitude
may be turned into time by multiplying by 4; observ-
ing that minutes or miles of longitude, when multiplied
44 PROBLEMS PERFORMED WITH
by 4, produce seconds of time; and degrees of longi
tude, when multiplied by 4, produce minutes of time.
Some globes have two rows of figures on the hour circle, others but
one : this difference frequently occasions confusion; and the manner
in which authors in general direct a learner to solve those problems
wherein the hour circle is used, serves only to increase that confusion.
In this, and in all the succeeding problems, great care has been taken
to render the rules general for any hour circle whatsoever.
ExAMPLEs. 1. When it is ten o'clock in the morn-
ing at London, what hour is it at Petersburgh?
Answer. The difference of time is two hours; and, as Petersburg is
eastward of London, this difference must be counted forward, so that
utis 12 o'clock at noon at Petersburg.
OR, the difference of longitude between Petersburgh and London is
300 25, which multiplied by 4 produces two hours 1 min. 40 sec. the
difference of time shown by the clocks of London and Petersburgh.
hence as Petersburgh lies to the east of London; when it is ten o'clock
in the morning at London, it is one minute and 40 seconds past 12 at
Petersburgh.
2. When it is two o'clock in the afternoon at Alex
andria in Egypt, what hour is it at Philadelphia?
Answer. The difference of time is seven hours; and because Phila-
delphia lies to the westward of Alexandria, this difference must be
reckoned backward, so that it is seven o'clock in the morning at Phila.
phia.
Or, The longitude of Alexandria is 30o 16 E.
The longitude of Philadelphia is 75 11 W.
Difference of longitude 105 27
4
Difference of longitude in time 7 h. 1 m.48 sec.:
the clocks at Philadelphia are slower than those of Alexandria; hence
when it is two o'clock in the aſternoon at Alexandria, it is 58 m. 12 sec.
past six in the morning at Philadelphia.
3. When it is noon at London, what hour is it at Cal-
cutta?
THE TERRESTRIAL, GLOBE, 45
4. When it is ten o'clock in the morning at London,
what hour is it at Washington?
5. When it is nine o'clock in the morning at Jamai.
ca, what o'clock is it at Madras?
6. My watch was well regulated at London, and
when I arrived at Madras, which was after a five
months' voyage, it was four hours and fifty minutes
slower than the clocks there. Had it gained or lost
during the voyage 7 and how much
PROBLEM XIX.
A particular place and the hour of the day being given,
to find all places on the globe where it is then noon,
or any other given hour.
RULE. Bring the given place to the brass meridian,
and set the index of the hour circle to 12; then, as the
difference of time between the given and required
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 brass meridian.
OR, witHouT THE Hour CIRCLE.
Reduce the difference of time between the given
place and the required places into minutes; these mi-
46 PROBLEMS PERFORMED WITH
nutes, divided by 4, will give degrees of longitude; if
there be a remainder after dividing by 4, multiply it by
60, and divide the product by four, the quotient will
be minutes or miles of longitude. The difference of
longitude between the given place and the required
places being thus determined, if the hour at the re-
quired places be earlier than the hour at the given
place, the required places lie so many degrees to the
westward of the given place as are equal to the differ-
ence of longitude; if the hour at the required places
be later than the hour at the given place, the required
places lie so many degrees to the eastward of the given
place as are equal to the difference of longitude.
ExAMPLEs. 1. When it is noon at London, at what
places is it half past eight o'clock in the morning 7
Answer. The difference of time between London, the given place,
and the required places, is 3; hours, and the time at the required places
is earlier than that at London; therefore the required places lie 34 hours
westward of London; consequently, by bringing London to the brass
meridian, setting the index to 12, and turning the globe eastward till the
index has passed over 3; hours, all the required places will be under
Jhe brassmeridian, as the eastern coast of Newfoundland, Cayenne, part
of Paraguay, &c.
OR, The difference of time between London, the given place, and the
required places, is 3 hours 30 min.
3 h. 30 m. The difference of longitude between the
60 given place and the required places is 52030
*mºme The hour at the required places being earlier
4)120 m. than that at the given place, they lie 520 30'
westward of the given place. Hence, all
520–2 places situated in 52° 30' west longitude from
60 London, are the places sought, and will be
* - found to be Cayenne, &c, as above.
4)120
».
º º 30 m.
THE TERRESTRIAL, GLOBE, 47
2. When it is two o'clock in the afternoon at Lon-
don, at what places is it # past five in the afternoon?
Answer. Here the difference of time between London, the given
place, and the required places, is 33 hours; but the time at the required
places is later than at London. The operation will be the same as in
example 1, only the globe must be turned 3; hours towards the west,
because the required places will be in east longitude, or eastward of the
given place. The places sought are the Caspian Sea, western part of
Nova Zembla, the island of Socotra, eastern part of Madagascar, &c.
3. When it is # past four in the afternoon at Paris,
where is it noon?
4. When it is # past seven in the morning at Ispa-
han, where is it noon 7
5. When it is noon at Madras, where it is # past six
o'clock in the morning'ſ
6. At sea in latitude 40° north, when it was ten
o'clock in the morning by the time-piece which shows
the hour at London, it was exactly 9 o'clock in the
morning at the ship, by a correct celestial observation.
In what part of the ocean was the ship !
7. When it is noon at London, what inhabitants of
the earth have midnight?
8. When it is ten o’clock in the morning at London,
where is it ten o'clock in the evening 3
PROBLEM XX.
To find the sun's longitude (commonly called the sun's
place in the ecliptic) and his declination.
RULE. Look for the given day in the circle of
months on the horizon, against which, in the circle of
signs, are the sign and degree in which the sun is for
that day. Find the same sign and degree in the eclip-
48 PROBLEMS PERFORMED WITH
tic on the surface of the globe; bring the degree of
the ecliptic, thus found, to that part of the brass méri-
dian which is numbered from the equator towards the
poles; its distance from the equator reckoned on the
brass meridian, is the sun's declination.
This problem may be performed by the celestial globe,
using the same rule.
OR, BY THE ANALEMMA.
Bring the analemma to that part of the brass meri-
dian which is numbered from the equator towards the
poles, and the degree on the brass meridian, exactly
above the day of the month, is the sun's declination.
Turn the globe till a point of the ecliptic, correspond-
ing to the day of the month, passes under the degree of
the sun's declination, that point will be the sun's lon-
gitude or place for the given day. If the sun's declina-
tion be north, and increasing, the sun's longitude will
be somewhere between Aries and Cancer. If the de-
clination be decreasing, the longitude will be between
Cancer and Libra. If the sun's declination be south,
and increasing, the sun's longitude will be between
Libra and Capricorn; if the declination be decreasing,
the longitude will be between Capricorn and Aries.
The sun's longitude and declination are given in the second page of
every month, in the Nautical Almanac for every day in that month;
they are likewise given in White's Ephemeris, for every day in the
year.
ExAMPLEs. 1...What is the sun's longitude and de-
clination on the 15th of April?
Answer. The sun's place is 269 in p, declination 10° N.
THE TERRESTRIAL, GLOBE, 49
2. Required the sun's place and declination for the
following days?
January 21. May 18 September 9.
February 7. June 11 October 16.
March 16. July 11 November 17.
April 8. August 1. December 1.
ProBLEM XXI.
To place the globe in the same situation witH RE-
SPECT TO THE SUN, as our earth is at the EQUI-
NoxEs, at the sum MER solSTICE, and at the wintER
solsTICE, and thereby to show the comparative lengths
of the longest and shortest days.”
1. For THE ExuinoxEs. Place the two poles of the
globe in the horizon: for at this time the sun has no
declination, being in the equinoctial in the heavens,
which is an imaginary line standing vertically over the
equator on the earth. Now, if we suppose the sun to
be fixed, at a considerable distance from the globe, ver-
tically over that point of the brass meridian which is
marked 0, it is evident that the wooden horizon will be
the boundary of light and darkness on the globe, and
that the upper hemisphere will be enlightened from
pole to pole.
*In this problem, as in all others where the pole is elevated to the
sun's declination, the sun is supposed to be fixed, and the earth to
move on its axis from west to east. The author of this work has a
little brass ball made to represent the sun; this ball is fixed upon a
strong wire, and when used, slides out of a socket like an acromatic
telescope. The socket is made to screw to the brass meridian (of any
globe) over the sun's declination, and the little brass ball representing
the sun, stands over the declination, at a considerable distance from the
globe.
(2 R
50 PROBLEMIS PERFORMED WITH
Meridians, or lines of longitude, being generally
drawn on the globe through every 15 degrees of the
equator, the sun will apparently pass from one meri-
dian to another in an hour. If you bring the point
Aries on the equator to the eastern part of the horizon,
the point Libra will be in the western part thereof;
and the sun will appear to be setting to the inhabitants
of London * and to all places under the same meridian :
let the globe be now turned gently 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 comes to the western edge of the horizon; the
moment it emerges above the horizon, the sun will ap-
pear to be rising in the east. If the motion of the
globe on its axis be continued eastward, the sun will
appear to rise higher and higher, and to move towards
the west; when London comes to the brass meridian,
the sun will appear at its greatest height; and after
London has passed the brass meridian, he will continue
his apparent motion westward, and gradually diminish
in altitude till London comes to the eastern part of the
horizon, when he will again be setting. During this
revolution 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; con-
sequently the days and nights are equal all over the
world; for all the parallels of latitude are divided into
*The meridian of London is nere supposed to pass through the
equinoctial point Aries, as on the best modern globes. -
&
THE TERRESTRIAL, GLOBE, 51
two equal parts by the horizon, and in every degree of
latitude there are six meridians between the eastern
part of the horizon and the brass meridian; each of
these meridians answers to one hour, hence half the
length of the day is six hours, and the whole length
twelve hours.
lf any place be brought to the brass meridian, the
number of degrees between that place and the horizon
(reckoned the nearest way) will be the sun's meridian
altitude. Thus, if London be brought to the meridian,
the sun will then appear exactly south, and its altitude
will be 38% degrees; the sun's meridian altitude at
Philadelphia will be 50 degrees; his meridian altitude at
Quito 90 degrees; and here, as in every place on the
equator, as the globe turns on its axis, the sun will be
vertical. At the Cape of Good Hope the sun will ap-
pear due north at noon, and his altitude will be 55%
degrees.
2. For THE SUMMER SOLSTICE.-The summer sol-
stice, to the inhabitants of north latitude, happens on
the 21st of June, when the sun enters Cancer, at which
time his declination is 23° 28′ north. Elevate the
north pole 23% degrees above the northern point of the
horizon, bring the sign of Cancer in the ecliptic to the
brass meridian, and over that degree of the brass meri-
dian under which this sign stands, let the sun be sup-
posed to be fixed at a considerab's 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, the equinoctial point Aries being in the western
52 PROBLEMIS PERFORMED WITH
part of the horizon, and the opposite point Libra in the
eastern part, and between the horizon and the brass
meridian (counting on the equator) there are six meri-
dians, each fifteen degrees, or an hour apart; conse-
quently the day at the equator is twelve hours long.
From the equator northward as far as the arctic circle,
the diurnal arcs will exceed the nocturnal arcs;
that is, more than one half of any of the parallels of
latitude will be above the horizon, and of course less
than one half will be below, so that the days are longer
than the nights. All the parallels of latitude within
the Arctic circle will be wholly above the horizon, con-
sequently those inhabitants will have no night. From
the equator southward, as far as the Antarctic circle,
the nocturnal arcs will exceed the diurnal arcs ; that
is, more than one half of any one of the parallels of lati-
tude will be below the horizon, and consequently less
than one half will be above. All the parallels of lati-
tude within the Antarctic circle, will be wholly below
the horizon, and the inhabitants, if any, will have
twilight or dark 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 parallels 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 inhabitants of north
latitude have the longest day, those in south latitude
have the longest night. It will likewise appear, that
the arcs of those parallels which are above the horizon,
south of the equator, are exactly of the same length w
THE TERRESTRIAL GE, OBE, 53
those below the horizon, north of the equator; there-
fore, when the inhabitants who are situated south of
the equator have the shortest day, those who live north
of the equator have the shortest night.
By counting the number of meridians, (supposing
them to be drawn through every fifteen degrees of the
equator) between the horizon and the brass meridian,
on any parallel of latitude, half the length of the day
will be determined in that latitude, the double of which
is the length of the day.
1. In the parallel of 20 degrees north latitude, there
are six meridians and two thirds more, hence the lon-
gest day is 13 hours and 20 minutes; and in the paral-
lel of 20 degrees south latitude there are five meri-
dians and one third, hence the shortest day in that lati-
tude is ten hours and forty minutes.
2. In the parallel of 30 degrees north latitude, there
are seven meridians between the horizon and the brass
meridian, hence the longest day is 14 hours; and in the
same degree of south latitude there are only five meri-
dians, hence the shortest day in that latitude is ten
hours.
3. In the parallel of 50 degrees north latitude there
are eight meridians between the horizon and the brass
meridian ; the longest day is therefore sixteen hours;
and in the same degree of south latitude there are only
four meridians; hence the shortest day is eight hours.
4. In the parallel of 60 degrees north latitude,
there are 94 meridians from the horizon to the brass
meridian, hence the longest day is 184 hours; and in
the same degree of south latitude, there are only 23 me-
e 2 R 2
‘j4 PROBLEMIS PERFORMED WITH
ridians, the length of the shortest day is therefore 5}
hours.
By turning the globe gently round on its axis from
west to east, we shall readily perceive that the sun will
be vertical to all the inhabitants under the tropic
of Cancer, as the places successively pass the brass
meridian.
If any place be brought to the brass meridian, the
number of degrees between that place and the horizon
(reckoning the nearest way) will show the sun's meri-
dian altitude. Thus, at London, the sun's meridian al-
titude will be found to be about 62 degrees; at Pe-
tersburgh 54% degrees, at Madrid 73 degrees, &c.
To the inhabitants of these places the sun appears due
Juth at noon. At Madras the sun's meridian altitude
will be 79% degrees, at the Cape of Good Hope 32 de-
grees, at Cape Horn 10% degrees, &c. The sun will
appear due north to the inhabitants of these places at
noon. If the southern extremity of Spitzbergen, in
latitude 76% north, be brought to that part of the blass
meridian which is numbered from the equator towards
the poles, the sun's meridian altitude will be 37 de-
grees, which is its greatest altitude; and if the globe
be turned eastwards twelve hours, or till Spitzbergen
comes to that part of the brass meridian which is num-
bered from the pole towards the equator, the sun's al-
titude will be ten degrees, which is its least altitude for
the day given in the problem. It was shown, in the
foregoing part of the problem, that, when the sun is
vertically over the equator in the vernal equinox, the
north pole begins to be enlightened; consequently the
THE TERRESTRIAL GLOBE. 55
farther the sun apparently proceeds in its course north-
ward, the more day-light will be diffused over the north
polar regions, and the sun will appear gradually to in-
crease in altitude at the north pole, till the 21st of
June, when his greatest height is 23% degrees; he will
then gradually diminish in height till the 23d of Sep-
tember, the time of the autumnal equinox, when he
will leave the north pole, and proceed towards the
South ; consequently the sun has been visible at the
north pole for six months.
3. For THE WINTER SoLSTICE.-The winter sol-
stice, to the inhabitants of north latitude, happens on
the 21st of December, when the sun enters Capricorn,
at which time his declination is 23°28' south. Elevate
the south pole 23% degrees above the southern point of
the horizon, bring the sign of Capricorn in the ecliptic
to the brass meridian, and over that degree of the brass
meridian under which this sign stands, let the sun be
supposed to be fixed at a considerable distance from
the globe.
Here, as at the summer solstice, the days at the equa-
tor will be twelve hours long, but the equinoctial point
Aries will be in the eastern part of the horizon, and
Libra in the western. From the equator southward,
as far as the Antarctic circle, the diurnal arcs will ex-
ceed the nocturnal arcs. All the parallels of latitude
within the Antarctic circle will be wholly above the
horizon. From the equator northward, the nocturnal
arcs will exceed the diurnal arcs. All the parallels of
Iatitude within the Arctic circle will be wholly below
the horizon. The inhabitants south of the equator
56 PROBLEMS PERFORMED WITH
will now have their longest day, while those on the
north of the equator will have their shortest day.
As the globe turns on its axis from west to east, the
sun will be vertical successively to all the inhabitants
under the tropic of Capricorn. By bringing any place
to the brass meridian, and finding the sun's meridian
altitude (as in the foregoing part of the problem,) the
greatest altitudes will be in south latitude, and the
least in the north; contrary to what they were before.
Thus, at London, the sun's greatest altitude will be only
15 degrees, instead of 62; and its greatest altitude at
Cape Horn will now be 57% degrees, instead of 10}, as
at the summer solstice; hence it appears, that the dif-
ference between the sun's greatest and least meridian
altitude at any place in the temperate zone, is equal to
the breadth of the torrid zone, viz. 47 degrees, or more
correctly 46° 56'. On the 23d of September, when the
sun enters Libra, that is, at the time of the autumnal
equinox, the south pole begins to be enlightened, and,
as the sun's declination increases southward, he will
shine farther over the south pole, and gradually increase
in altitude at the pole; for, at all times, his altitude at
either pole is equal to his declination. On the 21st of
December, the sun will have the greatest south declina-
tion, after which his altitude at the south pole will
gradually diminish as his declination diminishes; and
on the 21st of March, when the sun's declination is
nothing, he will appear to skim along the horizon at
the south pole, and likewise at the north pole ; the sun
has therefore been visible at the south pole for six
months.
THE TERRESTRIAL GI, OBE. 57
PROBLEM XXII.
To place the globe in the same situation, witH RESPECT
To THE POLAR STAR in the heavens, as our earth is
to the inhabitants of the equator, &c. viz. to illustrate
the three positions of the sphere, RIGHT, PARALLEL
and obliquE, so as to show the comparative length
of the longest and shortest days.
1. For THE RIGHT SPHERE. The inhabitants who
live upon the equator have a right sphere, and the north
polar star appears always in (or very near) the horizon.
Place the two poles of the globe in the horizon, then
the north pole will correspond with the north polar star,
and 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, so that the stars
will be visible for twelve hours, and invisible for the
same space of time; and, in the course of 6 months, an
inhabitant upon the equator may see all the stars in the
heavens. The ecliptic being drawn on the terrestrial
globe, young students are often led to imagine that the
sun apparently moves daily round the earth in the same
oblique manner. To correct this false idea, we must
suppose the ecliptic to be transferred to the heavens,
where it properly points out the sun's apparent annual
path amongst the fixed stars. The sun's diurnal path
is either over the equator, as at the time of the equi-
noxes, or in lines nearly parallel to the equator; this
may be correctly illustrated by fastening one end of a
58 PROBLEMS PERFORMED WITH
piece of packthread upon the point Aries on the equa-
tor, and winding the packthread round the globe towards
the right hand, so that one fold may touch another, till
you come to the tropic of Cancer : thus you will have
a correct view of the sun's apparent diurnal path from
the vernal equinox to the summer solstice; for, after
a diurnal revolution, the sun does not come to the same
point of the parallel whence it departed, but, according
as it approaches to or recedes from the tropic, is a little
above or below that point. When the sun is in the
equinoctial, he will be vertical to all the inhabitants
upon the equator, and his apparent diurnal path will
be over that line: when the sun has ten degrees of
north declination, his apparent diurnal path will be
from east to west nearly along that parallel. When the
Sun has arrived at the tropic of Cancer, his diurnal path
in the heavens will be along that line, and he will be
vertical to all the inhabitants on the earth in latitude 23°
28' north. The inhabitants upon the equator will always
have twelve hours day and twelve hours night, notwith-
standing the variation of the sun’s declination from north
to south, or from south to north; because the parallel of
latitude which the sun apparently describes for any day,
will always be cut into two equal parts by the horizon.
The greatest meridian altitude of the sun will be 90°,
and the least 66° 32'. During one half of the year, an
inhabitant on the equator will see the sun full north at
noon, and during the other half it will be full south.
2. For THE PARALLEL SPHERE. The inhabitants,
(if any) who live at the north pole have a parallel sphere,
and the north polar star in the heavens appears exactly
THE TERRESTRIAL, GLOBE, 59
(or very nearly) over their heads. Elevate the north
pole ninety degrees above the horizon, then the equa-
tor will coincide with the horizon, and all the parallels
of latitude will be parallel thereto. In the summer
half-year, that is, from the vernal to the autumnal
equinox, the sun will appear above the horizon, con-
sequently the stars and planets will be invisible during
that period. When the sun enters Aries, on the 21st
March, he will be seen by the inhabitants of the north
pole (if there be any inhabitants) to skim just along the
edge of the horizon: and as he increases in declination,
he will increase in altitude, forming a kind of spiral
course, as before deseribed, by wrapping a thread round
the globe. The sun's altitude at any particular hour
is always equal to his declination. The greatest alti-
tude the sun can have is 23°28', at which time he has
arrived at the tropic of Cancer; after which he will
gradually decrease in altitude as his declination de-
creases. When the sun arrives at the sign Libra, he
will again appear to skim along the edge of the horizon,
after which he will totally disappear, having been above
the horizon for six months. Though the inhabitants
at the north pole will lose sight of the sun a short time
after the autumnal equinox, yet the twilight will con-
tinue for nearly two months; for the sun will not be
18° below the horizon till he enters the 20th of Scorpio,
as may be seen by the globe.
After the sun has descended 18° 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
60 PROBLEMS PERFORMED WITH
when he was above the horizon. These stars will
never set; and the planets, when they are in any of
the northern signs, will be visible. The inhabitants
under the north polar star have the moon constantly
above their horizon during fourteen revolutions of
the earth on its axis; and at every full moon which
happens from the 23d of September to the 21st of
March, the moon is in some of the northern signs,
and consequently visible at the north pole; for the
sun being below the horizon at that time, the moon
must be above the horizon, because she is always in
that sign which is diametrically opposite to the sun at
the time of full 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: FULL 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 be-
ginning of Libra in her THIRD QUARTER ; having been
visible for fourteen revolutions of the earth on its axis,
viz. 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 inhabitants 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.
3. For THE OBLIQUE SPHERE. Whenever the ter-
restrial globe is placed in a proper situation with res-
THE TERRESTRIAL, GLOBE, 61
pect to the fixed stars, the pole must be elevated as
many degrees above the horizon as are equal to the
latitude of the given place, and the north pole of the
globe must point to the north polar star in the heavens;
for in sailing, or travelling from the equator northward,
the north polar star appears to rise higher and higher.
On the equator it will appear in the horizon; in 10 de-
grees of north latitude it will be ten degrees above the
horizon; in twenty degrees of north latitude it will be
twenty degrees above the horizon; and so on, always
increasing in altitude as the latitude increases. Every
inhabitant of the earth, except those who live upon the
equator, or exactly under the north polar star, has an
oblique sphere, viz. the equator cuts the horizon
obliquely. By elevating and depressing the poles, in
several problems, a young student is sometimes led to
imagine that the earth's axis moves northward and south-
ward just as the pole is raised or depressed: this is a
mistake, the earth's axis has no such motion.* In tra-
velling from the equator northward, our horizon varies;
thus, when we are on the equator, the northern point
of our horizon is in a line with the north polar star;
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 ter-
restrial 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
*The earth's axis has a kind of librating motion, called the nutation.
but this cannot be represented by elevating or depressing the pole,
S
f
62 PROBLEMS PERFORMED WITH
below the pole, the appearance will be exactly the
$30,162,
The latitude of London is about 514° north ; if Lon-
don be brought to the brass meridian, and the north pole
be elevated 514° above the north point of the wooden
horizon, then the wooden horizon will be the true
horizon of London; and, if the artificial globe be
placed exactly north and south by a mariner's compass,
or by a meridian line, it will have exactly the position
which the real globe has. Now, if we imagine lines
to be drawn through every degree within the torridzone,
parallel to the equator, they will nearly represent the
sun's diurnal path on any given day. By comparing
these diurnal paths with each other, they will be found
to increase in length from the equator northward, and
to decrease in length from the equator southward ;
consequently, when the sun is going north from the
equator, the days are increasing in length to us; and
when going from the equator, the days are decreas-
ing. The sun's meridian altitude, for any day, may be
found by counting the number of degrees from the
parallel in which the sun is on that day, towards the
horizon, upon the brass meridian ; thus, when the sun
is in that parallel of latitude which is ten degrees north
of the equator, his meridian altitude will be 484°.
Though the wooden horizon be the true horizon of the
given place, yet it does not separate the enlightened
hemisphere of the globe from the dark hemisphere,
when the pole is thus elevated. For instance, when the
sun is in Aries, and London at themeridian, all the places
on the globe above the horizon beyond those meridians
THE TERRESTRIAL, GLOBE, 63
which pass through the east and west points thereof,
reckoning towards the north, are in darkness, notwith-
standing they are above the horizon : and all places
below the horizon, between those same meridians and
the southern point of the horizon, have day-light, not-
withstanding they are below the horizon of London.
PROBLEM XXIII.
The month and day of the month being given, to find all
places of the earth where the sun is vertical on that
day, those places where the sun does not set, and
those places where he does not rise on the given day.
RULE. Find the sun's declination (by Problem XX.)
for the given day, and mark it on the brass meridian;
turn the globe round on its axis from west to east, and
all the places which pass under this mark will have the
sun vertical on that day.
Secondly. Elevate the north or south pole, accord-
ing as the sun's declination is north or south, so many
degrees above the horizon as are equal to the sun’s de-
clination: turn the globe on its axis from west to east;
then, to those places which do not descend below the
horizon, in that frigid zone near the elevated pole, the
sun does not set on the given day: and to those places
which do not ascend above the horizon, in that frigid
zone adjoining to the depressed pole, the sun does not
rise on the given day.
OR, BY THE ANALEMMA.
Bring the analemma to that part of the brass meri-
dian which is numbered from the equator towards the
64 PROBLEMS PERFORMEB WITH
poles, the degree directly above the day of the month.
on the brass meridian, is the sun’s declination. Ele-
vate the north or south pole, according as the sun's de-
clination is north or south, so many degrees above the
horizon as are equal to the sun's declination; turn the
globe on its axis from west to east, then to those places
which pass under the sun's declination, on the brass
meridian the sun will be vertical; to those places (in
that frigid zone near the elevated pole) which do not
go below the horizon, the sun does not set; and to
those places (in that frigid zone near the depressed
pole) which do not come above the horizon, the sun
does not rise on the given day.
ExAMPLEs. 1. Find all places of the earth where
the sun is vertical on the 11th of May, those places in
the north frigid zone where the sun does not set, and
those places in the south frigid zone where he does not
T1862,
Answer. The sun is vertical at St. Anthony, one of the Cape Verd
islands, the Virgin islands, south of St. Domingo, Jamaica, Golconda,
&c. All the places within eighteen degrees of the north pole will have
constant day; and those (if any) within eighteen degrees of the south
pole will have constant night.
2. Whether does the sun shine over the north or
south pole on the 27th of October, to what places will
he be vertical at noon, what inhabitants of the earth
will have the sun below their horizon during severai
revolutions, and to what part of the globe will the sun
never set on that day !
3. Find all the places of the earth where the in-
habitants have no shadow when the sun is on their
meridian on the first of June.
THE TERRESTRIAL, GLOBE, 65
4. What inhabitants of the earth have their shadows
directed to every point of the compass during a revo.
lution of the earth on its axis on the 15th of July 7
5. How far does the sun shine over the south pole
on the 14th of November, what places in the north
frigid zone are in perpetual darkness, and to what
places is the sun vertical ?
6. Find all places of the earth where the moon
will be vertical on the 3d of June 1827.
PROBLEM XXIV.
A 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 that part of the brass
meridian which is numbered from the equator towards
the poles, 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 against
them, in the circle of months stand the days required.
OR, BY THE ANALEMMA.
Find the latitude of the given place (by Problem I.)
and mark it on the brass meridian; bring the analem-
ma to the brass 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 at Madras 7
Answer On the 25th of April and on the 18th of August.
f2 s 2 -
66 PROBLEMS PERFORMED WITH
2. On what two days of the year is the sun vertica
at the following places? *
O'why'hee St. Helena Sierra Leone
Friendly Isles Rio Janeiro Vera Cruz
Straits of Alass Quito Manilla
Penang Barbadoes Tinian Isle
Trincomalé Porto Bello Pelew Islands.
PROBLEM XXV.
The month and the day of the month being given (at any
place not in the frigid 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 Problem XX.) bring it to the brass me,
ridian, and observe the degree above it; turn the globe
on its axis till some other point of the ecliptic falls un-
der the same degree of the meridian : find this point
of the ecliptic on the horizon, and directly against it
you will find the day of the month required.
This Problem may be performed by the celestial globe in the same
??0.717107°.
OR, BY THE ANALEMMA.
Look for the given day of the month on the analem.
ma, and adjoining to it you will find the required day
of the month. tº
OR, witHouTA 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, whatevér number of days the
THE TERRESTRIAL, GLOBE, 67
given day is before the longest or shortest day, just so
many days will the required day be after the longest or
shortest day, et contra.
ExAMPLEs. 1. What day of the year is of the same
length as the 25th of April 7 *
Answer. The 18th of August.
2. What day of the year is of the same length as the
25th of May ?
3. If the sun rise at four o'clock in the morning at
London on the 17th of July, on what other day of the
year will it rise at the same hour !
4. If the sun set at seven o'clock in the evening at
London on the 24th of August, on what other day of
the year will it set at the same hour?
5. If the sun’s meridian altitude be 90° at Trinco-
malé, in the island of Ceylon, on the 12th of April,
on what other day of the year will the meridian alti-
tude be the same 7
6. If the sun's meridian altitude at London on the
25th of April be 51° 35', on what other day of the year
will the meridian altitude be the same 1
7. If the sun be vertical at any place on the 15th
of April, how many days will elapse before he is verti-
cal a second time at that place {
8. If the sun be vertical at any place on the 20th of
August, how many days will elapse before he is vertical
a second time at that place {
68 PROBLEMs PERFORMED with
PROBLEM XXVI.
The month, day, and hour of the day being given, to find
- where the sun is vertical at that instant.
RULE. Find the sun's declination (by Problem XX.)
and mark it on the brass meridian ; bring the given
place to the brass 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 noon,
turn the globe eastward as many hours as the time is
past noon; the place exactly under the degree of the
sun's declination will be that sought.
ExAMPLEs. I. When it is forty minutes past six
o'clock in the morning at London on the 25th of April,
where is the sun vertical? :
Answer. Here the given time is five hours twenty minutes before
noon; hence the globe must be turned towards the west till the index
has passed over five hours twenty minutes, and under the sun's decli
nation on the brass meridian you will find Madras, the place required.
2. When it is four o'clock in the afternoon at Lon.
don on the 18th of August, where is the sun vertical?
Answer. Here the given time is ſour hours past noon; hence the
globe must be turned towards the east, till the index has passed
over four hours, then, under the sun's declination, you will find Bar-
badoes, the place required.
3. When it is three o'clock in the afternoon at Lon-
don on the 4th of January, where is the sun vertical ?
4. When it is three o'clock in the morning at London
on the 11th of April, where is the sun vertical ?
5. When it is thirty-seven minutes past one o'clock
THE TERRESTRIAL, GLOBE. 69
º
in the afternoon at the Cape of Good Hope on the 5th
of February, where is the sun vertical ?
6. When it is eleven minutes past one o'clock in the
afternoon at London on the 29th of April, where is the
sun vertical ?
7. When it is twenty minutes past five o'clock in the
afternoon at Philadelphia on the 18th of May, where is
the sun vertical ?
8. When it is nine o'clock in the morning at Cal-
cutta on the 11th of April, where is the sun vertical ?
PROBLEM XXVII.
The month, day, and hour of the day 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 morn-
ing twilight, those places that have evening twilight,
and those places that have midnight.
RULE. Find the sun's declination (by Problem XX.)
and mark it on the brass meridian ; elevate the north
or south pole, according as the sun's declination is
north or south, so many degrees above the horizon as
are equal to the sun's declination; bring the given place
to the brass 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 noon, 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 edge of the horizon have the sun rising;
70 PROBLEMS PERFORMED WITH
those places along the eastern edge have the sun set
ting; those under the brass meridian above the horl
zon, have noon; that particular place which stands
under the sun’s declination on the brass meridian, has
the sun vertical; all places below the western edge of
the horizon, within eighteen degrees, have morning
twilight; those places which are below the eastern
edge of the horizon, within eighteen degrees, have
evening twilight; all places under the brass meridian
below the horizon, have midnight; all the places above
the horizon have day, and those below it have night or
twilight.
ExAMPLEs. 1. When it is fifty-two minutes past four
o'clock in the morning at London on the fifth of March,
find all places of the earth where the sun is rising, set-
ting, &c. &c.
Answer. The sun's declination will be found to be 64° south; there-
fore, elevate the south pole 640 above the horizon. The given time be-
ing seven hours eight minutes before noon (=12 h.-4 h. 52 m.) the
globe must be turned towards the west, till the index has passed over
seven hours eight minutes. Let the globe be fixed in this position;
then,
The sun is rising at the western part of the White Sea, Petersburgh,
the Morea in Turkey, &c.
Setting at the eastern coast of Kamtschatka, Jesus island, Palmerston
island, &c. between the Friendly and Society islands.
Noon at the lake Baikalin Irkoutsk, Cochin China, Cambodia, Sunda
islands, &c.
Vertical at Batavia.
Morning twilight at Sweden, part of Germany, the southern part of
Italy, Sicily, the western coast of Africa along the AEthiopian Ocean
&c.
Evening twilight at the north-west extremity of North America, the
Sandwich islands, Society islands, &c.
Midnight at Labrador, New-York, western part of St. Domingo, Chili,
and the western coast of South America.
THE TERRESTRIAL GILOBE, 71
Day at the eastern part of Russia in Europe, Turkey Egypt, the Cape
of Good Hope, and all the eastern part of Africa, almost the whole of
Asia, &c.
Night at the whole of North and South America, the western part of
Africa, the British isles, France, Spain, Portugal, &c.
2. When it is four o'clock in the afternoon at Lon-
don on the 25th of April, where is the sun rising, set-
ting, &c. &c. 7
Answer. The sun's declination being 130 north, the north pole must
be elevated 13° above the horizon; and as the given time is four o'clock
m the afternoon, the globe must be turned four hours towards the east,
then the sun will be rising at O'why'hee, &c. setting at the Cape of
Good Hope, &c.; it will be noon at Buenos Ayres, &c. the sun will be
vertical at Barbadoes, and following the directions in the Problem, all
the other places are readily found.
3. When it is ten o'clock in the morning at London
on the longest day, to what countries is the sun rising,
setting, &c. &c. 7
4. When it is ten o’clock in the afternoon at Botany
Bay on the 15th of October, where is the sun rising,
setting, &c. &c.?
5. When it is seven o’clock in the morning at Wash-
ington on the 17th of February, where is the sun rising,
setting, &c. &c. 7
6. When it is midnight at the Cape of Good Hope
on the 27th of July, where is the sun rising, setting,
&c. &c. 7
PROBLEM XXVIII.
To find the time of the sun's rising, and setting, and
length of the day and night, at any place not in the
frigid zones.
RULE. Find the sun's declination (by Problem XX.)
and elevate the north or south pole, according as the
72 PROBLEMS PERFORMED WITH
declination is north or south, so many degrees above
the horizon as are equal to the sun's declination; bring
the given place to the brass meridian, and set the in.
dex of the hour-circle to twelve ; turn the globe east.
ward till the given place comes to the eastern semi-
circle of the horizon, and the number of hours passed
over by the index will be the time of the sun's setting :
deduct these hours from twelve, and you have the time
of the sun's rising; because the sun rises as many
hours before twelve as it sets after twekwe. Double
the time of the sun's setting gives the length of the
day, and double the time of rising gives the length of
the night.
By the same rule, the length of the longest day, at all places not in
the frigid zones, may be readily found; for the longest day at all places
in north latitude is on the 21st of June, or when the sun enters Cancer;
and the longest day at all places in south latitude is on the 21st of De-
cember, or when the sun enters the sign Capricorn.
OR,
Find the latitude of the given place, and elevate the
north or south pole, according as the latitude is north
or south, so many degrees above the horizon as are equat
to the latitude; find the sun's place in the ecliptic (by
Problem XX.) bring it to the brass meridian, and set
the index of the hour circle to twelve; turn the globe
westward till the sun's place come to the western
semicircle of the horizon, and the number of hours
passed over by the index will be the time of the sun's
setting; and these hours taken from twelve will give
the time of rising; then, as before, double the time of
setting gives the length of the day, and double the time
of rising gives the length of the night,
*.
THE TERRESTRIAL, GLOBE, 73
OR, BY THE ANALEMMA.
Find the latitude of the given place, and elevate the
north or south pole, according as the latitude is north
or south, the same number of degrees above the hori-
zon; bring the middle of the analemma to the brass
meridian, and 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 semicircle of the
horizon, and the number of hours passed over by the in-
dex will be the time of the sun's setting, &c. as above.
ExAMPLEs. 1. What time does the sun rise and set
at London on the 1st of June, and what is the length
of the day and night?
Answer. The sun sets at 8 min, past 8, and rises at 52 min. past 3,
the length of the day is 16 hours 16 minutes, and the length of the night
7 hours 44 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 found 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 found; if the length of the night be given, the
length of the day and the time the sunrises and sets are easily known.
2. At what time does the sun rise and set at the
following places, on the respective days mentioned, and
what is the length of the day and night?
London, 17th of May Cape of Good Hope, 7th
Gibraltar, 22d July December
Edinburgh, 29th January iCape Horn, 29th January
Botany Bay, 20th Febru-|Washington, 15th Decem-
ary Petersburgh, 24th October
Pekin, 20th April |Commiſſiºn.
3. Find the time the sun rises and sets at every
place on the surface of the globe on the 21st of March,
and likewise on the 23d of September,
§ T ~sº
74 PROBLEMS PERFORMED WITH
4. Required the length of the longest day and short-
est night at the following places:
London Paris Pekin
Petersburg Vienna Cape Horn
Aberdeen Berlin Washington
Dublin Buenos Ayres Cape of Good Hope
Glasgow Botany Bay Copenhagen.
5. Required the length of the shortest day and longest
night at the following places:
London Lima Paris
Archangel Mexico O'why'hee
O Taheitee St. Helena Lisbon
Quebec Alexandria Falkland islands.
6. How much longer is the 21st of June at Peters-
burg than at Alexandria 7
7. How much longer is the 21st of December at
Alexandria than at Petersburgh?
8. At what time does the sun rise and set at Spitz-
bergen on the 5th of April.
PROBLEM XXIX.
The length of the day at any place, not in the frigid
zones, being given, to find the sun's declination and
the day of the month.
RULE, Bring the given place to the brass meridian
and set the index 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; keep the globe
from revolving on its axis, and elevate or depress one
of the poles till the given place exactly coincides with
the eastern semicircle of the horizon; the distance of
#,
ts
THE TERRESTRIAL GLOBE, 75
the elevated pole from the horizon will be the sun’s
declination : mark the sun's declination, thus found,
on the brass meridian: turn the globe on its axis, and
observe what two points of the ecliptic pass under this
mark; seek those points in the circle of signs on
the horizon, and exactly against them, in the circle of
months, stand the days of the months required.
OR,
Bring the meridian passing through Libra to coincide
with the brass meridian, elevate the pole to the latitude
of the place, 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 mark where the meridian pass-
ing through Libra is cut by the eastern semicircle of
the horizon; bring this mark to the brass meridian, and
tne degree above it is the sun’s declination; with which
proceed as above.
OR, BY THE ANALEMMA. *
Bring the middle of the analemma to the brass meri-
dian, elevate the pole to the latitude of the place, 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; the
two days, on the analemma, which are cut by the east-
ern semicircle of the horizon, will be the days required;
and, by bringing the analemma to the brass meridian,
the sun's declination will stand exactly above these
days.
76 PROBLEMS PERFORMED WITH
ExAMPLEs. 1. What two days in the year are each
sixteen hours long at London, and what is the sun's
declination ?
Answer. The 24th of May and the 17th of July. The sun's declina-
tion is about 210 north.
2. What two days of the year are each fourteen hours
long at London 1
3. On what two days of the year does the sun set at
half-past seven o'clock at Edinburgh?
4. On what two days of the year does the sun rise
at four o'clock at Petersburg'ſ
5. What two nights of the year are each ten hours
long at Copenhagen :
6. What day of the year at London is sixteen hours
and a half long?
PROBLEM XXX.
To find the length of the longest day at any place in
the north frigid zone.
RULE. Bring the given place to the northern point
of the horizon (by elevating or depressing the pole,)
and observe its distance from the north pole on the brass
meridian; count the same number of degrees on the
brass meridian from the equator, towards the north pole,
and mark the place where the reckoning ends; turn
the globe on its axis, and observe what two points of
the ecliptic pass under the above mark; find those
points of the ecliptic in the circle of signs on the hori-
zon, and exactly against them, in the circle of months,
you will find the days on which the longest day begins
and ends. The day preceding the 21st of June is
THE TERRESTRIAL GIOBE, 77
that on which the longest day begins at the given place,
and the day following the 21st of June is that on which
the longest day ends: the time between these days is
the length of the longest day.
OR, BY THE ANALEMMA.
Bring the given place to that part of the brass meri-
dian which is numbered from the north pole towards
the equator, and observe its distance in degrees from
the pole; count the same number of degrees on the
brass meridian from the equator towards the north pole,
and mark where the reckoning ends; bring the ana-
lemma to the brass meridian, and the two days which
stand under the above mark will point out the begin-
ning and end of the longest day.
ExAMPLEs. 1. What is the length of the longest
day at the North Cape, in the island of Maggeroe, in
latitude 71°30' north 7
Answer. The place is 1839 from the pole; the longest day begins
on the 14th of May, and ends on the 30th of July; the day is therefore
seventy-seven days long, that is, the sun does not set during seventy-
seven revolutions of the earth on its axis.
2. What is the length of the longest day in the
north of Spitzbergen, and on what days does it begin
and end ?
3. What is the length of the longest day at the
northern extremity of Nova Zembla?
4. What is the length of the longest day at the north
pole, and on what days does it begin and end?
g 2 T 2
78 PROBLEMS PERFORMED WITH
PROBLEM XXXI.
To find the length of the longest night at any place in
the north frigid zone.
RULE. Bring the given place to the northern point
of the horizon (by elevating or depressing the pole,)
and observe its distance from the north pole on the brass
meridian; count the same number of degrees on the
brass meridian from the equator towards the south pole,
and mark the place where the reckoning ends; turn
the globe on its axis, and observe what two points of
the ecliptic pass under the above mark; find those
points of the ecliptic in the circle of signs on the hori-
zon, and exactly against them in the circle of months,
you will find the days on which the longest night be-
gins and ends. The day preceding the 21st of De-
cember is that on which the longest night begins at the
given place, and the day following the 21st of Decem-
ber is that on which the longest night ends : the time
between these days is the length of the longest night.
OR, BY THE ANALEMMA.
Bring the given place to that part of the brass meri
dian which is numbered from the north pole towards
the equator, and observe its distance in degrees from
the pole ; count the same number of degrees on the
brass meridian from the equator towards the south pole,
and mark where the reckoning ends; bring the ana-
lemma to the brass meridian, and the two days which
stand under the above mark will point out the begin.
nung and end of the longest night.
THE TERRESTRIAL GLOBE, 79
ExAMPLEs. 1. What is the length of the longest
night at the North Cape, in the island of Maggeroe, in
latitude 71°30' north 7
Answer. The place is 1839 from the pole; the longest night begins
on the 16th of November, and ends on the 27th of January: the night
is therefore seventy-three days long, that is, the sun does not rise during
seventy-three revolutions of the earth on its axis.
2. What is the length of the longest night at the
north of Spitzbergen!
3. The Dutch wintered in Nova Zembla, latitude 76
degrees north, in the year 1596; on what day of the
month did they lose sight of the sun; on what day of
the month did he appear again ; and how many days
were they deprived of his appearance, setting aside the
effect of refraction ?
4. For how many days are the inhabitants of the
northernmost extremity of Russia deprived of a sight
of the sun ?
PROBLEM XXXII.
To find the number of days which the sun rises and sets
at any place in the north *frigid zone.
RULE. Bring the given place to the northern point
of the horizon, (by elevating or depressing the pole,)
and observe its distance from the north pole on the
brass meridian ; count the same number of degrees on
the brass meridian from the equator towards the poles
northward and Southward, and make marks where the
reckoning ends; observe what two points of the eclip-
*The same might be found for a place in the south frigid zone, were
that zone inhabited.
80 PROBLEMIS PERFORMED WITH
tic nearest to Aries pass under the above marks; these
points will show (upon the horizon) the end of the lon-
gest night and the beginning of the longest day; dur-
ing the time between these days the sun will rise and
set every twenty-four hours; next observe what two
points of the ecliptic, nearest to Libra, pass under the
marks on the brass meridian ; find these points, as be-
fore, in the circle of signs, and against them you will
find the day on which the longest day ends at the given
place, and the day on which the longest night begins;
during the time between these days the sun will rise
and set every twenty-four hours.
OR,
Find the length of the longest day at the given place
(by Prob. XXX.) and the length of the longest night
(by Prob. XXXI.) add these together, and subtract the
sum from 365 days, the length of the year, the remain-
der will show the number of days which the sun rises
and sets at that place.
OR, BY THE ANALEMMA.
Find how many degrees the given place is from the
north pole, and mark those degrees upon the brass
meridian on both sides of the equator; observe what
four days on the analemma stand under the marks on
the brass meridian ; the time between those two days
on the left hand part of the analemma (reckoning to-
wards the north pole) will be the number of days on
which the sun rises and sets, between the end of the
Yongest night and the beginning of the longest day
**
THE TERRESTRIAL GLOBE. 81'
and the time between the two days on the right-hand
part of the analemma (reckoning towards the south
pole) will be the number of days on which the sun rises
and sets, between the end of the longest day and the
beginning of the longest night. .
ExAMPLEs. 1. How many days in the year does the
sun rise and set at the North Cape, in the island of
Maggeroe, in latitude 71°30' north 7
Answer. The place is 18}o ſrom the pole, the two points in the
ecliptic, nearest to Aries, which pass under 1840 on the brass meridian,
are 89 in ºt, answering to the 27th of January, and 249 in 8, answering
to the 14th of May. Hence the sun rises and sets for 107 days, viz.
from the end of the longest night, which happens on the 27th of Janu-
ary, to the beginning of the longest day, which happens on the 14th of
May. Secondly, the two points in the ecliptic, nearest to Libra, which
pass under 1839 on the brass meridian, are 8C in Q, answering to the
30th of July, and 249 in 111, answering to the 15th of November. Hence
the sun rises and sets for 108 days, viz. from the end of the longest
day, which happens on the 30th of July, to the beginning of the longest
night, which happens on the 15th of November; so that the whole
time of the sun's rising and setting is 215 days.
OR, THUS :
The length of the longest day. by Example 1st, Prob. XXX, is 77
days; the length of the longest night by Example 1st, Prob. XXXI. is
73 days; the sum of these is 150, which, deducted from 365, leaves 215
days as above.
2. How many days in the year does the sun rise and
set at the north of Spitzbergen 7
3. How many days does the sun rise and set at Green-
land, in latitude 75° north
4. How many days does the sun rise and set at the
northern extremity of Russia in Asia?
82 PROBLEMIS PERFORMED WITH
PROBLEM XXXIII.
To find in what degree of north latitude, on any day
between the 21st of March and the 21st of June, or
in what degree of south latitude, on any day between
the 23d of September and the 21st of December, the
sun begins to shine constantly without setting ; and
also in what latitude in the opposite hemisphere he
begins to be totally absent.
RULE. Find the sun's declination (by Prob. XX.)
and count the same number of degrees from the north
pole towards the equator, if the declination be north,
or from the south pole, if it be south, and mark the
point 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 all the places where
twilight or total darkness begins.
ExAMPLEs. 1. In what latitude north, and at what
places, does the sun begin to shine without setting dur-
ing several revolutions of the earth on its axis, on the
14th of May ?
Answer. The sun's declination is 18;o north, therefore all places in
latitude 713° north will be the places sought, viz. the North Cape in
Lapland, the southern part of Nova Zembla, Icy Cape, &c.
2. In what latitude south does the sun begin to shine
without setting on the 18th of October, and in what
latitude north does he begin to be totally absent?
Answer. The sun's declination is 10° south, therefore he begins to
shine constantly in latitude 800 south, where there are no inhabitants
THE TERRESTRIAL, GLOBE, 83
known, and to be totally absent in latitude 800 north, viz. at Spitz.
bergen.
3. In what latitude does the sun begin to shine with-
out setting on the 20th of April 7
4. In what latitude north does the sun begin to shine
without setting on the 1st of June, and in what degree
of south latitude does he begin to be totally absent?
PROBLEM XXXIV.
Any number of days, not exceeding 186, being given,
to find the parallel of north latitude in which the sun
does not set for that time.
RULE. Count half the number of days from the 21st
of June on the horizon, eastward or westward, and op-
posite to the last day you will find the sun's place in
the circle of signs: look for the sign and degree on the
ecliptic, which bring to the brass meridian, and observe
the sun's declination; reckon the same number of de-
grees from the north pole (on that part of the brass me-
ridian which is numbered from the equator towards
the poles) and you will have the latitude sought.
ExAMPLEs. 1. In what degree of north latitude,
and at what places, does the sun continue above the
horizon for seventy-seven days?
Answer. Half the number of days is 38%, and if reckoned backward
or towards the east, from the 21st of June, will answer to the 14th of
May; and if counted forward, or towards the west, will answer to the
30th of July; on either of which days the sun's declination is 18; de-
grees north, consequently the places sought are 18; degrees from the
north pole, or in latitude 713 degrees north; answering to the North
Cape in Lapland, the south part of Nova Zembla, Icy Cape, &c.
2. In what degree of north latitude is the longest
day 134 days, or 3216 hours in length 7
84 PROBLEMIS PERFORMED WITH
3. In what degree of north latitude does the sun
continue above the horizon for 2160 hours?
4. In what degree of north latitude does the sun con,
tinue above the horizon for 1152 hours ?
PROBLEM XXXV.
To find the beginning, end, and duration of twilight at
any given place on any given day.
RULE. Find the sun's declination for the given day
(by Problem XX.) and elevate the north or south pole,
according as the declination is north or south, so many
degrees above the horizon as are equal to the sun's de-
clination; screw the quadrant of altitude on the brass
meridian, over the degree of the sun's declination;
bring the given place to the brass 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 hours passed over by the
index, from 12, will show when evening twilight ends.
The time when evening twilight ends, subtracted from
12, will show the beginning of morning twilight.
OR, THUs:
Elevate the north or south pole, according as the la-
titude of the given place is north or south, so many
degrees above the horizon as are equal to the latitude;
find the sun's place in the ecliptic, bring it to the brass
THE TERRESTRIAL, GLOBE, 85
meridian, set the index of the hour-circle to twelve,
and screw the quadrant of altitude upon the brass me-
ridian over the given latitude : 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; continue the motion of
the globe westward till the sun's place coincides with
18° on the quadrant of altitude below the horizon, the
time passed over by the index of the hour-circle, from
the time of the sun's setting, will show the duration of
evening twilight.
OR, BY THE ANALEMMA.
Elevate the pole to the latitude of the place, as above,
and screw the quadrant of altitude upon the brass me-
ridian over the degree of latitude; bring the middle
of the analemma to the brass meridian, and set the in-
dex of the hour-circle to twelve; turn the globe west-
ward till the given day of the month, on the analemma,
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:
continue the motion of the globe westward till the
given day of the month coincides with 18° on the
quadrant below the horizon, the time passed over by
the index, from the time of the sun's setting, will show
the duration of evening twilight.
ExAMPLEs. 1. Required the beginning, end, and
duration of morning and evening twilight at London on
the 19th of April?
k U
86 PROBLEMS PERFORMED WITH
Answer. The sun sets at two minutes past seven, and evening twi-
light ends at nineteen minutes past nine; consequently morning twi-
light begins at (12 n. —9 h. 19 m. =) 2 h. 41 m. and ends at (12h. —7 h
2 m. =) 4h. 58 m.; the duration of twilight is 2 h. and 17 minutes.
2. What is the duration of twilight at London on the
23d of September, what time does dark night begin,
and at what time does day break in the morning?
Answer. The sun sets at six o'clock, and the duration of twilight is
two hours; consequently the evening twilight ends at eight o'clock, and
the morning twilight begins at four.
3. Required the beginning, end, and duration of
morning and evening twilight at London on the 25th
of August?
4. Required the beginning, end, and duration of
morning and evening twilight at Edinburgh on the 20th
of February 7
5. Required the beginning, end, and duration of
morning and evening twilight at Cape Horn on the 20th
of February 1
~. 6. Required the beginning, end, and duration of
morning and evening twilight at Madras on the 15th
of June 7
PROBLEM XXXVI.
To find the beginning, end, and duration of constant
day or twilight at any place.
RULE. Find the latitude of the given place, and
add 18° to that latitude; count the number of degrees
correspondent to the sum, on that part of the brass me-
ridian which is numbered from the pole towards the
equator, mark where the reckoning ends, and observe
what two points of the ecliptic pass under the mark;
THE TERRESTRIAL, GLOBE. 87
that point wherein the sun's declination is increasing
will show on the horizon the beginning of constant
twilight; and that point wherein the sun's declination is
decreasing, will show the end of constant twilight.
ExAMPLEs. 1. When do we begin to have constant
day or twilight at London, and how long does it con-
tinue !
Answer. The latitude of London is 51% degrees north, to which
add 18 degrees, the sum is 69%, the two points of the ecliptic which pass
under 69% are two degrees in II, answering to the 22d of May, and 29
degrees in gå, answering to the 21st of July; so that, from the 22d of
May to the 21st of July the sun never descends 18 degrees below the
horizon of London.
2. When do the inhabitants of the Shetland islands
cease to have constant day or twilight?
3. Can twilight ever continue from sun-set to sun-
rise at Madrid 7
4. When does constant day or twilight begin at
Spitzbergen!
5. What is the duration of constant day or twilight
at the North Cape in Lapland, and on what day, after
their long winter's night, do the Sun's rays first enter
the atmosphere 7 -
PROBLEM XXXVII.
To find the duration of twilight at the north pole.
RULE. Elevate the north pole so that the equator
may coincide with the horizon; observe what point of
the ecliptic nearest to Libra passes under 18° below
the horizon, reckoned on the brass meridian, and find
the day of the month correspondent thereto, the time
elapsed from the 23d of September to this time will be
88 PROBLEMIS PERFORMED WITH
the duration of evening twilight. Secondly, observe
what point of the ecliptic, nearest to Aries, passes
under 18° below the horizon, reckoned on the brass
meridian, and find the day of the month correspondent
thereto ; the time elapsed from that day to the 21st of
March will be the duration of morning twilight.
ExAMPLE. What is the duration of twilight at the
north pole, and what is the duration of dark night
there 7
Answer. The point of the ecliptic nearest to Libra which passes
under 18 degrees below the horizon, is 22 degrees in 11, answering to
the 13th of November; hence the evening twilight continues from the
23d of September (the end of the longest day) to the 13th of Novem-
ber, (the beginning of dark might) being 51 days. The point of the
ecliptic nearest to Aries which passes under 18 degrees below the hori-
zon is 9 degrees in X, answering to the 29th of January; hence the
morning twilight continues from the 29th of January to the 21st of
March (the beginning of the longest day) being 51 days. From the 23d
of September to the 21st of March are 179 days, from which deduct
102 (= 51 × 2) the remainder is 77 days, the duration of total dark-
ness at the north pole; but, even during this short period, the moon and
the Aurora Borealis shine with uncommon splendour.
PROBLEM XXXVIII.
To find in what climate any given place on the globe is
situated.
RULE. 1. If the place be not in the frigid zone,
find the length of the longest day at that place (by
Problem XXVIII.) and subtract twelve hours there-
from ; the number of half hours in the remainder will
show the climate.
2. If the place be in the frigid zone,” find the length
*The climates hetween the polar circles and the poles were un-
known to the ancient geographers; they reckoned only seven climates
THE TERRESTRIAL, GLOBE, 89
i
of the longest day at that place (by Problem XXX.)
and if that be less than thirty days, the place is in the
twenty-fifth climate, or the first within 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 climate, or the third within the
polar circle, &c.
JExAMPLEs. 1. In what climate is London, and
what other remarkable places are situated in the sarbe
climate 7
Answer. The longest day in London is 16; hours, if we deduct 12
therefrom, the remainder will be 44 hours, or nine half hours; hence
London is in the ninth climate north of the equator; and as all places
in or near the same latitude are in the same climate, we shall find
Amsterdam, Dresden, Warsaw, Irkoutsk, the southern part of the pe-
ninsula of Kamtschatka, Nootka Sound, the south of Hudson's Bay, the
north of Newfoundland, &c. to be in the same climate as London.
2. In what climate is the North Cape in the island
of Maggeroe, latitude 71°30' north?
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 Rome or the Hellespont; the sixth through the mouth
of the Borysthenes or Dnieper; and the seventh through the Riphhaean
mountains, supposed to be situated near the source of the Tanais or Don
river. The southern parts of the earth being in a great measure un:
known, 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 Antidiameroes, or the opposite
climate to Meroe; Antidiasyenes was the opposite climate to Syenes,
&c.
h 2 U 2
90 PROBLEMS PERFORMED WITH
Answer. The length of the longest day is 77 days; these days di-
vided by 30, give two months for the quotient, and a remainder of 17
days; hence the place is in the third climate within the polar circle, or
the 27th climate reckoning from the equator. The southern part of
Nova Zembla, the northern part of Siberia, James' Island, Baffin's Bay
the northern part of Greenland, &c. are in the same climate.
3. In what climate is Edinburgh, and what other
places are situated in the same climate 7
4. In what climate is the north of Spitzbergen :
5. In what climate is Cape Horn ?
6. In what climate is Botany Bay, and what other
places are situated in the same climate 7
PROBLEM XXXIX.
To find the breadths of the several climates between the
equator and the polar circles.
RULE. For the northern climates. Elevate the north
pole 23%% above the northern point of the horizon;
bring the sign Cancer to the meridian, and set the in-
dex to twelve ; turn the globe eastward on its axis till
the index has passed over a quarter of an hour; observe
that particular point of the meridian passing through
Libra, which is cut by the horizon, and at the point of
intersection make a mark with a pencil; continue the
motion of the globe eastward till the index has passed
over another quarter of an hour, and make a second
mark: proceed thus till the meridian passing through
Libra” will no longer cut the horizon; the several
*On Adams' and Cary's globes, the meridian passing through Libra
is divided into degrees, in the same manner as the brass meridian is di-
vided; the horizon will, therefore, cut this meridian in the several de-
grees answering to the end of each climate, without the trouble of bring:
ing it to the brass meridian, or marking the globe.
THE TERRESTRIAL GIOBE, 91
marks brought to the brass meridian will point out the
latitude where each climate ends.
ExAMPLEs. 1. What is the breadth of the ninth north
climate, and what places are situated within it?
Answer. The breadth of the 9th climate is 2957; it begins in lati-
tude 4902 north, and ends in latitude 510 59' north, and all places situ.
ated within this space are in the same climate. The places will be
nearly the same as those enumerated in the first example to the preced-
ing problem.
2. What is the breadth of the second climate, and
in what latitude does it begin and end ?
3. Required the beginning, end, and breadth of the
fifth climate?
4. What is the breadth of the seventh climate north
of the equator, in what latitude does it begin and end,
and what places are situated within it !
5. What is the breadth of the climate in which Pe-
tersburg is situated ?
6. What is the breadth of the climate in which
Mount Heckla is situated 7
PROBLEM XL.
To find that part of the equation of time which depends
on the obliquity of the ecliptic.
RULE. Find the sun's place in the ecliptic, and bring
it to the brass meridian; count the number of degrees
from Aries to the brass meridian, on the equator and
on the ecliptic ; the difference, reckoning four minutes
of time to a degree, is the equation of time. If the
number of the degrees on the ecliptic exceed those on
the equator, the sun is faster than the clock; but if the
92
PROBLEMIS PERFORMED WITH
number of degrees on the equator exceed those on the
ecliptic, the sun is slower than the clock.

Note. The equation of time, or differ-
ence between the timeshown by a well-
regulated clock, and a true sun-dial, de-
pends upon two causes, viz. the obliquity
of the ecliptic, and the unequal motion
of the earth in its orbit. The former of
these causes may be explained by the
above Problem. If two suns were to set
off at the same time from the point Aries,
and move over equal spaces in equal
time, the one on the ecliptic, the other on
the equator, it is evident they would
never come to the meridian together, ex-
cept at the time of the equinoxes, and on
the longest and shortest days. The an-
nexed table shows how much the sun is
faster or slower than the clock ought to
be, so far as the variation depends on the
obliquity of the ecliptic only. The signs
of the first and third quadrants of the
ecliptic are at the top of the table, and the
degrees in these signs on the left hand;
in any of these signs the sun is faster than
the clock. The signs of the second and
third quadrants are at the bottom of the
table, and the degrees in these signs at
the right hand; in any of these signs the
sun is lower than the clock.
Thus, when the sun is in 20 degrees
of 8 or ſí, it is 9 minutes 50 seconds
faster than the clock, and, when the sun
is in 18 degrees of gº or V5, it is 6 mi-
nutes 2 seconds slower than the clock.
|sus faster than the CLock in
Q
É. Op || 8 * {3.
# 2, m| f |38.
M. S. M. S. M. S.
0 0 08 248 46. 30
1 |0 208 35|8 36; 29
2 |0 408 45|8 25, 28
3 |1 018 54|8 14, 27
4 || 199 3|8 || 26
5 || 39|9 11||7 49 25
6 |1 59|9 187 35i 24
7 |2 189 24 7 21| 23
8 |2 379 31||7 6. 22
9 2 569 36||6 51] 21
10 3 16|9 416 35 20
11 |3 349 4516 19| 19
12 13 539 496 2. 18
13 |4 11|9 515 45, 17
14 |4 299 535 27, 16
15 4 ſº 54|5 9. 15
16 5 49 55|4 50 14
17 § 219 85 4 3il 13
18 |5 389 544 12 12
19 |5 549 523 52 11
20 ||6 10 9 50 3 32 10
21 6 269 47|3 12 9
22 6 419 432 51 8
23 (6 359 38|2 30| 7
24 |7 9.9 33 2 9| 6
25 || 23g ºli 4s. 5
26 Z 36.9 201 27| 4
27 7 499 13.1 5 3
28 |8 1.9 50 43| 2
29 § 1335|Q 22 I
30 s 248460 0 o
29 u iſ | Q. gā #
4Qu] × & y? | 5
|son slower than the CLocK in
g=-& *
THE TERRESTRIAL GLOBE, 93
ExAMPLEs. 1. What is the equation of time on the
17th of July 1
Answer. The degrees on the equator exceed the degrees on the
ecliptic by two; hence the sun is eight minutes slower than the clock.
2. On what four days of the year is the equation of
time nothing 1
3. What is the equation of time dependant on the
obliquity of the ecliptic on the 27th of October 1
4. When the sun is in 18° of Aries, what is the
equation of time !
PROBLEM XLI.
To find the sun's meridian altitude at any time of the
$year at any given place.
RULE. Find the sun's declination, and elevate the
pole to that declination ; bring the given place to the
brass meridian, and count the number of degrees on
the brass meridian (the nearest) to the horizon; these
degrees will show the sun's meridian altitude.
NotE. The sun's altitude may be found at any particular hour, tr.
the following manner.
Find the sun's declination, and elevate the pole to that declination;
bring the given place to the brass meridian and set the index to 12:
then, if the given time be before noon, turn the globe westward as
many hours as the time wants of noon; if the given time be past noon,
turn the globe eastward as many hours as the time is past noon. Keep
the globe fixed in this position, and screw the quadrant of altitude on
the brass meridian over the sun's declination; bring the graduated
edge of the quadrant to coincide with the given place, and the number
of degrees between that place and the horizon will show the sun's al
titude.
OR,
Elevate the pole so many degrees above the horizon
t
94 PROBLEMS PERFORMED WITH
as are equal to the latitude of the place; find the sun’s
place in the ecliptic, and bring it to that part of the
brass meridian which is numbered from the equator to-
wards the poles; count the number of degrees con-
tained on the brass meridian between the sun's place
and the horizon, and they will show the altitude.
To find the sun's altitude at any hour, see Problem XLIV.
OR, BY THE ANALEMMA.
Elevate the pole so many degrees above the horizon
as are equal to the latitude of the place; find the day
of the month on the analemma, and bring it to that part
of the brass meridian which is numbered from the
equator towards the poles; count the number of degrees
contained on the brass meridian between the given day
of the month and the horizon, and they will show the
altitude.
To find the sun's altitude at any hour, see Problem XLIV.
ExAMPLEs. 1. What is the sun's meridian altitude
at London on the 21st of June 7
Answer. 62 degrees.
2. What is the sun's meridian altitude at London on
the 21st of March 1
3. What is the sun’s least meridian altitude at Lon-
don'ſ
4. What is the sun's greatest meridian altitude at
Cape Horn ?
5. What is the sun's meridian altitude at Madras on
the 20th of June 7
6. What is the sun's meridian altitude at Bencoolen
on the 15th of January "
THE TERRESTRIAL, GLOBE, 95
ExAMPLEs to the note.
1. What is the sun's altitude at Madrid on the 24th
of August, at 11 o'clock in the morning?
Answer. The sun's declination is 113 degrees north; by elevating
the north pole 114 degrees above the horizon, and turning the globe so
that Madrid may be one hour westward of the meridian, the sun's alt-
tude will be ſound to be 574 degrees.
2. What is the sun's altitude at London at 3 o'clock
in the afternoon on the 25th of April 7
3. What is the sun’s altitude at Rome on the 16th
of January at 10 o'clock in the morning?
4. Required the sun's altitude at Buenos Ayres on
the 21st of December at two o'clock in the afternoon?
PROBLEM XLII.
When it is midnight at any place in the temperate or
torrid 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. Find the sun's declination for the given day
and elevate the pole to that declination; bring the place
(in the frigid zone) to that part of the brass meridian
which is numbered from the north pole towards the
equator, and the number of degrees between it and the
herizon will be the sun's altitude.
OR,
Elevate the north pole so many degrees above the
horizon as are equal to the latitude of the place in the
96 PROBLEMIS PERFORMED WITH
frigid zone; bring the sun's place in the ecliptic to the
brass 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 be-
tween the sun's place and the horizon, counted on the
brass 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 Alexan-
dria in Egypt on the 21st of June 7
Answer. 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°
north
3. What is the sun's altitude at the north-east of
Nova Zembla, when it is midnight at Tobolsk, on the
15th of July 1
4. What is the sun's altitude at the north of Baffin's
Bay, when it is midnight at Buenos Ayres, on the 28th
of May ?
PROBLEM XLIII.
To find the sun's amplitude at any place.
Elevate the pole so many degrees above the horizon
as are equal to the latitude of the given place; find the
sun's place in the ecliptic, and bring it to the eastern
semicircle of the horizon; the number of degrees from
the sun's place to the east point of the horizon will be
the rising amplitude; bring the sun's place to the west-

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