:
ARTES
18371
SCIENTIA
LIBRARY
VERITAS
OF THE
UNIVERSITY OF MICHIGAN
PLURIBUS UNUM
TUEBOR
QUERIS PENINSULAMPAMORAM
CIRCUMSPICE
FROM THE LIBRARY OF
PROFESSOR W. W. BEMAN
AB,,1870; AM.1873
TEACHER OF MATHEMATICS
|| 1871-1922
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1782
GEORGE R.
1
GⓇ
EORGE the Second, by the Grace of God, King
of Great-Britain, France and Ireland, Defender of
the Faith, &c. To all to whom theſe Preſents fhall come,
Greeting. Whereas James Buckland, James Waugh, John
Ward, Thomas Longman, and Edward Dilly, Citizens and
Bookfellers of our City of London, have by their Petition
humbly reprefented unto Us, that they have purchaſed the
Copy-Right of the WHOLE WORKS of the late DOCTOR
ISAAC WATTS, and that they are now printing and prepar-
ing for the Profs new Editions with Improvements of feve-
ral of the feparate Picces of the faid Doctor Ifaac Watts.
They have therefore moft humbly prayed Us, that We would
be graciously pleaſed to grant them our Royal Licence and
Protection for the fole printing, publiſhing, and vending the
faid Works, in as ample Manner and Forin as has been done
in Cafes of the like Nature; We being willing to give all
due Encouragement to Works of this Nature, which may
be of publick Ufe and Benefit, are graciously pleaſed to
condefcend to their Requeft, and do therefore by theſe Pre-
fents, as far as may be agreeable to the Statute in that Be-
half made and provided, grant unto them, the faid James
Buckland, James Waugh, John Ward, Thomas Longman, and
Edward Dilly, their Executors, Adminiſtrators, and Affigns,
our Royal Privilege and Licence, for the fole printing, pub-
liſhing, and vending the faid Works for the Term of four-
teen Years, to be computed from the Date hereof; ftrictly
fc. bidding and prohibiting all our Subjects within our King-
doms and Dominions, to reprint, abridge, or tranflate the
fame, either in the like, or any other Volume or Volumes
whatſoever, or to import, buy, vend, utter, or diſtribute any
Copies thereof reprinted beyond the Seas, during the afore-
faid Term of fourteen Years, without the Conſent and Ap-
probation of the faid James Buckland, James Waugh, John
Ward, Thomas Longman, and Edward Dilly, their Execu-
tors, Adminiftrators and Affigns, by Writing under their
Hands and Seals firft had and obtained, as they and every
of them offending herein, will anfwer the contrary at their
Peril. Whereof the Commiffioners and other Officers of our
Cuſtoms, the Mafter, Wardens, and Company of Stationers
of our City of London, and all other our Officers and Mini-
fters, wh m it may concern, are to take Notice, that due
Obedience be rendered to our Pleaſure herein fignified,
Given at our Court at St. James's the 21ft Day of March,
1758, in the 31st Year of our Reign.
By his Majefty's Command,
W. PIT T.
J
The Knowledge of the HEAVENS and the
EARTH made easy:
OR, THE
FIRST PRINCIPLES
O F
ASTRONOMY
AND
GEOGRAPHY
Explained by the Ufe of GLOBES and MAPS,
1
WITH
Solution of the Common PROBLEMS by a Plain
Scale and Compaſſes, as well as by the Globe.
WRITTEN feveral Years fince for the USE of
LEARNER s.
By IWATTS, D. 5.18
D.
The EIGHTH EDITION, Corrected.
Pfal. viii. 3.-I confider thy Heavens, the Work of thy Fingers,
the Moon and Stars which thou haft ordained.
LONDON:
Printed for J. BUCKLAND, J. F. and C. RIVINGTON, T,
LONGMAN, T. FIELD, C. DILLY, and S. BLADON.
M,DCC,LXXXII,
W. W. Bemans
at.
5-131-1923
To my LEARNED FRIEND
Mr. JOHN EAMES,
Fellow of the ROYAL SOCIETY.
DEAR SIR,
T would be mere trifling to fay any Thing
to you of the Excellency and great Ad-
vantage of thoſe Sciences whofe firſt Rudi-
ments I have here drawn up. Your large
Acquaintance with theſe Matters hath given
you a juft Reliſh of the Pleaſure of them,
and well informed you of their ſolid Ufe, But,
perhaps, it is neceffary to excufe myſelf to
the World, if I publiſk ſome of the Fruits
of my former Studies on fuch Subjects as
A 3
theſe.
426285
{
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[ vi }
1
?
thefe. I would therefore willingly have the
unlearned Part of Mankind apprized of the
Neceffity and general Uſe of this Sort of
Learning, and that not only to Civil, but to
Sacred Purpoſes.
If you, Sir, would pleaſe to take upon you
this Service, you would make it
appear with
rich Advantage, how far the Knowledge of
Things Human and Divine are influenced
and improved by theſe Studies.
You can tell the World, that it is the
Knowledge of this Globe of Earth on which
we tread, and of thofe Heavenly Bodies which
feem to roll around us, that hath been
wrought up into theſe two kindred Sciences,
Geography and Aftronomy. And there is not
a Son or Daughter of Adam but has fome
Concern in both of them, though they may
not know it in a learned Way.
This Earth is given us for an Habitation:
It is the Place of preſent Refidence for all
our Fellow-mortals: Nor is it poffible that
there ſhould be any Commerce maintained
with thoſe who dwell at a Diftance, without
fome Acquaintance with the different Tracts
of Land, and the Rivers or Seas that divide
the Regions of the Earth.
The
[vii]
The Heavenly Bodies, which are high over
our Heads, meaſure out our Days and Years,
our Life and Time, by their various Revolu-
tions. Now Life and Time are fome of the
deareſt Things we have, and it is of impor-
tant Concern to diftinguiſh the Hours as they
pafs away, that proper Seaſons may be cho-
fen and adapted for every Bufinefs.
>
You know, Sir, that thofe neceffary and
uſeful Inftruments, Clocks, Watches, and Di-
als, owe their Origin to the Obfervations of
the Heavens: The Computation of Months
and Years had been for ever impracticable,
without fome careful Notice of the various
Situations and Appearances of thoſe ſhining
Worlds above us.
I ſhall be told, perhaps, that theſe are not
my ſpecial Province. It is the Knowledge
of God, the Advancement of Religion, and
Converſe with the Scriptures, are the peculiar
Studies which Providence has affigned me.
I know it, and I adore the Divine Favour.
But I am free and zealous to declare, that
without commencing fome Acquaintance
with theſe Mathematical Sciences, I could
never arrive at fo clear a Conception of ma-
ny Things delivered in the Scriptures; nor
could I raiſe my Ideas of God the Creator to
A 4
fo
•
[ viii]
ſo high a Pitch: And I am-well affured, that
many of the facred Function will join with
me, and ſupport this Affertion from their
own Experience.
If we look down to the Earth, it is the
Theatre on which all the grand Affairs re
corded in the Bible have been tranfacted.
How is it poffible that we ſhould trace the
Wandrings of Abraham, that great Patriarch,
and the various Toils and Travels of Jacob,
and the Seed of Ifrael in fucceffive Ages, with-
out ſome Geographical Knowledge of thofe
Countries? How can our Meditations follow
the Bleffed Apoftles in their laborious Jour-
nies through Europe and Afia, their Voyages,
their Perils, their Shipwrecks, and the Fa-
tigues they endured for the Sake of the Göf-
pel; unleſs we are inftructed by Maps and
Tables, wherein thofe Regions are copied out
in a narrow Compaſs, and exhibited in one
View to the Eye?
If we look upward with David to the
Worlds above us, we confider the Heavens as
the Work of the Finger of God, and the Moon
and the Stars which he hath ordained. What
amazing Glories diſcover themſelves to our
Sight! What Wonders of Wiſdom are ſeen
in the exact Regularity of their Revolutions!
Nor
[ix]
Nor was there ever any thing that has con-
tributed to enlarge my Apprehenfions of
the immenfe Power of God, the Magnifi-
cence of his Creation, and his own tranfcen-
dent Grandeur, fo much as that little Portion
of Aftronomy which I have been able to attain.
And I would not only recommend it to young
Students, for the fame Purpoſes, but I would
perfuade all Mankind, if it were poffible, to
gain fome Degree of Acquaintance with the
Vaftneſs, the Diſtances, and the Motions of
the Planetary Worlds, on the fame Account.
It gives an unknown Enlargement to the Un-
derſtanding, and affords a divine Entertain-
ment to the Soul and its better Powers. With
what Pleaſure and rich Profit would Men
furvey thofe aftoniſhing Spaces in which the
Planets revolve, the Hugenefs of their Bulk,
and the almoft incredible Swiftnefs of their
Motions! And yet all theſe governed and ad-
juſted by fuch unerring Rules, that they ne-
ver miſtake their Way, nor loſe a Minute of
their Time, nor change their appointed Cir-
cuits in feveral thoufands of Years! When
we mufe on theſe Things we may lofe our-
felves in holy Wonder, and cry out with the
Pfalmift, Lord! what is Man that thou art
mindful of him, and the Son of Man that thou
Shouldeft vifit him?
It was chiefly in the younger Part of my
Life indeed that theſe Studies were my En-
tertainment;
3
[ x ]
*
tertainment; and being defired both at that
time, as well as fince, upon fome Occafions,
to lead fome young Friends into the Know-
ledge of the firſt Principles of Geography and
Aftronomy, I found no Treatife on thofe Sub-
jects written in fo very plain and compre-
henfive a Manner as to anſwer my Wiſhes
Upon this Account I drew up the following
Papers, and fet every thing in that Light in
which it appeared moft obvious and eaſy
to me.
I have joined the general Part of theſe two
Sciences together: What belongs particularly
to each of them is caft into diftinct Sections:
And I wiſh, Sir, you would preſent the
World with the ſpecial Part of Aftronomy,
drawn up for the Uſe of Learners, in the moſt
plain and eafy Method, to render this Work
more complete:
Moſt of the Authors, which I peruſed in
thofe Days when I wrote many Parts of this
Book, were of older Date: And therefore
the Calculations and Numbers which I bor-
rowed from their Aftronomical Tables, cannot
be fo exact as thofe with which fome later
Writers have furniſhed us: For this Reafon
the Account of the Sun's Place in the Eclip-
tick, the Declination and Right Afcenfion of
the Sun and the Stars in fome Parts of the
Book, eſpecially in the Solution of fome of
the
[xi]
the Problems in the twentieth Section, may
perhaps need a little Correction; though I
hope the Theorems will appear true in Spe-
culation, and the Problems fo regular and
fucceſsful in the Practice, as is fufficient for
a Learner. However, to apply fome Remedy
to this Inconvenience, there are added at the
End of the Book fome later Tables, which
are formed according to the celebrated Mr.
Flamstead's Obfervations.
I have exhibited near Forty Problems to be
practiſed on the Globe, and Thirty-five more
of various Kinds, to be performed by manual
Operation, with the Aid of fome Geometrical
Practices. Theſe were very fenfible Allure-
ments to my younger Inquiries into theſe
Subjects, and I hope they may attain the
fame Effect upon ſome of my Readers,
It was my Opinion, that it would be a very
delightful Way of learning the Doctrine and
Uses of the Sphere, to have them explained by
a Variety of Figures or Diagrams; this is
certainly much wanting in moſt Authors that
I have perufed. I have therefore drawn
Thirty Figures with my own Hand, in or-
der to render the Defcription of every thing
more intelligible.
I have endeavoured to entertain younger
Minds, and entice them to theſe Studies, by
all
را
[ xii
B
}
all thofe eafy and agreeable Operations relat-
ing both to the Earthand the Heavens, which
probably may tempt them on to the higher
Speculations of the great Sir Ifaac Newton,
and his Followers, on this Subject.
Yet there fhould be a due Limit fet to
theſe Inquiries too, according to the different
Employments of Life to which we are called:
For it is poffible a Genius of active Curiofity
may waſte too many Hours in the more ab-
frufe Parts of thefe Subjects, which God and
his Country demand to be applied to the Stu-
dies of the Law, Phyfic, or Divinity; to
Merchandize, or Mechanical Operations.
If I had followed the Conduct of mere In-
clination, perhaps I ſhould have laid out more
of my ferene Hours in Speculations which
are fo alluring: And then indeed I might
have performed what I have here attempted
in a Manner more anſwerable to my Defign,
and left lefs for the Criticks to cenfure, and
my Friends to forgive. But fuch as it is, I
put it entirely, Sir, into your Hands, to re-
view and alter whatſoever you pleaſe, and
make it anſwerable to that Idea which I have
formed of your Skill. Then if
you ſhall
think fit to preſent it to the World, I per-
fuade myſelf I ſhall not be utterly difappoint-
ed in the Views I had in putting theſe Papers
together,
[ xiii ]
together, many of which have lain by me in
Silence, above twenty Years.
Farewel, dear Sir, and forgive the Trou-
ble that you have partly devolved on yourſelf,
by the too favourable Opinion you have con-
ceived both of thefe Sheets, and of the Wri-
ter of them, who takes a Pleaſure to tell the
World that he is, with great Sincerity,
Theobalds, in
Hertfordshire,
June 11, 1725.
SIR,
Your most obedient Servant,
I. WATTS.
TO
TO THE
REA DE R,
I Think myself obliged, in Juftice to the in-
genious Author, as well as the Publick, to
affure them, that the Alterations I have ven-'
tured to make in the Revifal of this Work, are
but few and ſmall. The fame Perfpicuity of
Thought, and Eafe of Expreffion, which diftin-
guifh his other Works, running through the
whole of this: I do not question but the Worla
will meet with equal Pleafure and Satisfac
tion in the Perufal.
Auguft zo,
1725.
JOHN EAMES,
J
A
A BL E
TA
OF TH E
CONTE
NT S
SECTION I.
F the Spheres or Globes of the Heaven and
Earth,
OF
Page I
Maps are Imitations of the Earthly Globe, 2
Sect. II. The four great Circles; namely, the
Horizon, the Meridian, the Equator, and
the Ecliptick,
3
The Horizon, Sun-rife, Sun-fet, and Twi-
light,
The Horizon fenfible and rational,
The Parallax of the Planets,
The Meridian, Noon and Midnight,
The Equator, Summer and Winter,
The Ecliptick and the Twelve Signs,
The Sun's daily and yearly Motion,
Leap-Year, New-Stile, and Old,
The Zodiack,
4
ibid.
6
6, 7
8
ibid.
IO
II
12
Sect. III. The four leffer Circles; namely, the two
Tropicks, and the two Polar Circles, 13
Sect. IV. The more remarkable Points of the
Globe, namely, the two Poles, the Ze-
nith, Nadir, &c.
15
The thirty-two Points of the Compafs, 16.
The Solftitial and Equinoctial Points, 16,17
Of
xvi
CONTENT S.
The
1
Of the Preceffion of the Equinox, Page 18
The Poles of the Ecliptick and the two
Colures,
The Repreſentation of the Sphere in ſtraight,
Lines on the Analemma,
19
20
Sect. V. Longitude and Latitude on the Earthly
Globe,
21
The Elevation of the Pole always equal to
the Latitude,
23.
25
Parallels of Latitude and Climates,
Sect. VI. Right Afcenfion and Hour Circles, 27
Degrees, Hours, Minutes, Seconds, 28, 29.
The Dial Plate and Index or Pointer, 29
Declination of Sunor Star, North or South, 30
It alters much lower than the Sun's Place, 31
Of the different Increaſe and Decreaſe of the
Days at the Solſtices and at the Equinox, 33
Sect. VII. Longitude and Latitude on the Hea-
venly Globe,
ibid.
The Orbits of Planets, their Nodes and
36
Sect. VIII. Altitude and Azimuth of the Sun
Eclipfes,
and Stars,
Parallels of Altitude,
Vertical Circles,
The Sun or Stars Amplitude,
38, 39
39
40
41
How the Sun's Hour differs from his Azi-
muth,
43
Stars rifing or ſetting Heliacally, &c. ibia.
Sect. IX. The Inhabitants of the Earth diftin-
guished by the Sphere,
44
Right,
The CONTENT S. xvii
Right, Parallel and Oblique Pofitions of
the Sphere,
Right and Oblique Afcenfion,
The five Zones,
Page 45, &c.
48
50
The Pericci, Antœci, and Antipodes, 53
Sect. X. The natural Deſcription of the Earth
and Waters,
54
An Ifland, a Continent, a Peninfula, Ifth-
mus, &c.
}
Ocean, Lake, Gulf, Bay, &c.
55
56, &c.
How all theſe are defcribed on Globes or
Maps,
Sect. XI. Of Maps and Sea Charts,
59
61
The various Projections of the Sphere, 63
Maps of the whole World,
Maps of particular Countries,
64
65
Difference between Maps and Sea Charts, 67.
Sect. XII. The political Divifions of the Earth, 69
Sect. XIII. Europe, with its Countries and King-
doms,
71
Sect. XIV. Afia, with its Countries and King-
doms,
79
Sect. XV. Africa, with its various Divifions, 82
Sect. XVI. America, and its Divifions,
Sect. XVII. The fixt Stars on the Heavenly Globe,
84
88
Difference between Planets and fixt Stars, 89
The Northern and Southern Conſtellations,
90
The Milky Way,
95
Sect. XVIII. Planets and Comets,
ibid.
a
Con-
xviii The CONTENT S.
Conclufion of the fpeculative Part of this
Difcourfe, or the Spherical Doctrine of
Geography and Aftronomy, Page 98
The fecond or fpecial Part of Geography,
what it contains,
Sect. XIX. Problems relating to Geography and
Aftronomy to be performed by the Globe,
99
104
The chief Deitions in the fpherical Doc-
trine rehearfed,
105
Prob. 1. To find the Longitude and Latitude of
any Place on the Earthly Globe, 107
Prob. 2. The Longitude and Latitude of any
Place being given, how to find that Place
on a Globe or Map,
108
Prob. 3. To find the Diſtance of any two Places
on the Earthly Globe, or two Stars on the
Heavenly Globe,
ibid.
Prob. 4. To find the Antoci, Perioci, and An-
tipodes of any Place given (fuppofe Lon-
I10
III
don)
Prob. 5. Any Place being given, to find all thoſe
Places which have the fame Hour of the
Day with that in the given Place,
Prob. 6. Any Place being given, (fuppofe Paris)
to find all thofe Places in the World,
which have the fame Latitude, and confe-
quently have their Days and Nights of
the fame Length,
II2
Prob. 7. To rectify the Globe according to the
Latitude of any Place required, ibid.
Prob. 8. The Hour being given in any Place,
(as at London) to find what Hour it is in
any other Part of the World,
113
The CONTENT S.. Xix
Prob. 9. To rectify the Globe for the Zenith,
Page 114
Prob. 10. Any two Places being given, to find
ibid.
the Bearing from one to the other; that
is, at what Point of the Compaſs the one
lies in reſpect to the other,
Prob. 11. Having the Day of the Month given,
to find the Sun's Place in the Ecliptick,
120
Prob. 12. The Day of the Month being given,
to find thofe Places of the Globe, where
the Sun will be vertical, or in the Zenith
that Day,
ibid.
Prob. 13. The Day and Hour of the Day at one
Place being given, to find at what other
Place the Sun is vertical at that Hour, 121
Prob. 14. The Day and Hour being given, to
find all thofe Places of the Earth, where
the Sun is then Rifing, Setting, or on the
Meridian; alſo where it is Daylight, Twi-
light, or Dark Night,
ibid.
Prob. 15. A Place being given in the Torrid
Zone, to find thoſe Days in which the Sun
fhall be vertical there,
122
Prob. 16. A Place being given in one of the
Frigid Zones, fuppofe the North, to find
when the Sun begins to depart from, or
to appear on that Place, how long he is
abfent, and how long he ſhines conſtant-
ly on it,
a 2
ibid.
Prob.
XX
The CONTENTS.
Prob. 17. To find the Sun's Declination and
Right Afcenfion any Day in the Year,
fuppofe the 10th of May, Page 124
Prob. 18. To rectify the Globe for the Sun's
Place any Day in the Year, and thus to
repreſent the Face of the Heavens for that
Day,
ibid.
Prob. 19. The Place and Day being given, namely,
the 10th of May at London, to find at
what Hour the Sun rifes or fets, his Af-
cenfional Difference, his Amplitude, the
Length of Day and Night,
125
Prob. 20. The Place and Day being given, to
find the Altitude of the Sun at any given
126
Hour,
Prob. 21. The Place and Day being given, to
find the Azimuth of the Sun at any given
Hour,
Prob. 22. The Sun's Altitude being given, to
find the Hour of the Day, and alſo his
127
ibid.
Azimuth,
Prob. 23. When the Sun is due Eaft or Weft in
the Summer, how to find the Hour and
128
his Altitude,
Prob. 24. To find the Degree of the Depreffion
of the Sun below the Horizon, or its Azi-
muth at any given Hour of the Night, 129
Prob. 25. To find how long the Twilight con-
tinues in any given Place and given Day,
fuppofe the 10th of May at London, both
at Morning and Evening,
129
Prob. 26. To know by the Globe the Length of
the Longest and Shorteft Days and Nights
in any Place of the World,
130
I
The CONTENT S.
xxi
"
Prob. 27. The Declination and Meridian Altitude
of the Sun, or of any Star being given,
to find the Latitude of the Place,
ibid.
Prob. 28. The Latitude of a Place being given,
to find the Hour of the Day in the Sum-
mer when the Sun fhines,
131
Prob. 29. To find the Sun's Altitude when it
fhines, by the Globe,
132
Prob. 30. The Latitude and Day of the Month
being given, to find the Hour of the Day
when the Sun fhines,
ibid.
Prob. 31. The Place being given to find what
Stars never rife or never fet in that Place,
133
Prob. 32. The Place and Day of the Month being
given, to repreſent the Face or Appear-
ance of the Heavens, and fhew the Situa-
tion of all the fixt Stars at any Hour of
the Night,
ibid.
Prob. 33. Any Star on the Meridian being given,
to find the Hour of the Night, 134
Prob. 34. The Azimuth of any known Star being
given, to find the Time of Night, 136
Prob. 35. The Altitude of a Star being given,
to find the Hour of the Night, ibid.
Prob. 36. To find the Longitude and Latitude,
Right Afcenfion and Declination of any
Star,
137
Prob. 37. How to find at what Hour any Planet,
ſuppoſe Jupiter, will rife or fet, or will
be on the Meridian any given Day in the
Year,
139
аз
xxii
CONTENT S.
The
1
Prob. 38. The Day and Hour of a folar Eclipfe
being known, to find all thofe Places im
which that Eclipfe will be vifible, Page 141
Prob. 39. The Day and Hour of a lunar Eclipfe
being known, to find by the Globe all
thofe Places in which the fame will be
viſible,
ibid.
Sect. XX. Problems relating to Geography and
Aftronomy to be performed by the Ufe of
the plain Scale and Compaffes, 142
Prob. 1. How to fix a Needle perpendicular on
a Plane, or to raiſe a perpendicular Style
or Pointer, in order to make Obfervations
of a Shade,
143
Prob. 2. How to take the Altitude of the Sun by
a Needle fixt on a Horizontal Plane, or
any perpendicular Style,
147
Prob. 3. How to take the Altitude of the Sun
by a Style on a perpendicular or upright
Plane,
149
Prob. 4. To find the Sun's or any Star's Alti-
tude by a plain Board, Thread and Plum-
met,
150
Prob. 5. To obferve the Meridian Altitude of the
Sun, or the Height at Noon: And by
the fame Method to find any Star's Me-
ridian Altitude,
153
Prob. 6. How to find out the Declination of the
Sun, or of any large or known Star, ibid.
Prob. 7. To find the Latitude of any Place by
the Meridian Altitude and Declination of
the Sun any Day in the Year,
155
The CONTENT S. xxiii
Prob. 8. To find the Meridian Altitude of the
Sun any Day of the Year, the Latitude of
the Place being given,
Prob.
Page 159
9. To find the Declination of the Sun, its
Meridian Altitude, and the Latitude of
the Place being given,
ibid.
Prob. 10. To find the Latitude of a Place by the
Meridian Altitude of a Star, when it is on
the South Meridian,
160
Prob. 11. By what Methods is the Longitude of
Places to be found,
ibid.
Prob. 12. To find the Value of a Degree of a
greater Circle upon the Earth, or how
much it contains in Engliſh Meaſure, 163
Frob. 13. To find the Circumference, the Di-
ameter, the Surface, and Solid Contents
of the Earth,
164
Prob. 14. To find the Value of a Degree of a
leffer Circle on the Earth, that is, the Va-
lue of a Degree of Longitude on the lef
fer Parallels of Latitude,
165
Prob. 15. To erect the Analemma, or repreſent
the Sphere in ftraight Lines, particularly
for the Latitude of London 51 Degrees,
167
Prob. 16. How to repreſent any Parallel of Decli-
nation on the Analemma, or to defcribe
the Path of the Sun any Day in the
Year,
171
Prob. 17. How to repreſent any Parallel of Alti-
tude, either of the Sun or Star, on the
Analemma,
ibid.
xxiv
The CONTENT S.
Prob. 18. The Day of the Month and the Sun's
Altitude being given, how to find the
Hour or Azimuth of the Sun by the
Page 172
Analemma,
Prob. 19. How to meaſure the Number of De-
grees on any of the ftraight Lines in the
Analemma,
174
Prob. 20. To find the Sun's Place in the Eclip-
tick any Day in the Year,
178
Prob. 21. The Day of the Month being given,
to draw the Parallel of Declination for
that Day, without any Tables or Scales.
of the Sun's Declination,
184
Prob, 22. How to draw a Meridian Line, or a
Line directly pointing to North and South
on a Horizontal Plane, by the Altitude or
Azimuth of the Sun being given,
188
Prob. 23. To draw a Meridian Line on a Ho-
rizontal Plane by a perpendicular Style,
189
Prob. 24. To draw a Meridian Line on a Ho-
rizontal Plane by a Style or Needle ſet up
at random,
191
Prob. 25. To draw a Meridian Line on an Equi-
noctial Dial,
193
Prob. 26. To draw a Meridian Line by a Point
of Shadow at Noon,
193
Prob. 27. To draw a Meridian Line by a Ho-
rizontal Dial,
194
Prob. 28. How to transfer a Meridian Line from
one Place to another,
•
ibid.
Prob. 29. How to draw a Line of Eaſt and Weſt
on a Horizontal Plane,
Prob. 30. How to uſe a Meridian Line,
195
197
་
4
The CONTENT S.
XXV
Prob. 31. How to know the chief Stars, and to
find the North Pole,
Page 199
Prob. 32. To find the Latitude by any Star that
is on the North Meridian,
201
Prob. 33. To find the Hour of the Night by the
Stars on the Meridian,
202
Prob. 34. To find at what Hour of any Day a
known Star will come upon the Meridian,
203
Prob. 35. Having the Altitude of any Star given,
to find the Hour,
The Ufe of feveral Aftronomical
Sect. XXI.
Tables,
205
206
Tables of the Sun's Declination for the Years
1753, 1754, 1755, 1756,
212-214
A Table of the Declination and Right Af-
cenfion of feveral fixt Stars for the Year
1754,
Tables of the Sun's Right Afcenfion, 222
220
THE
"
J
I
To the Bookbinder,
Obſerve to place the Tables at the End of the
Book, and the Plates after them.
****
***
*
I
THE FIRST
PRINCIPLES
OF
Geography and Aſtronomy.
SECT. I.
Of the Spheres or Globes of the Heavens
and Earth.
T
HERE is nothing gives us a more
eafy or ſpeedy Acquaintance with
the Earth and the visible Heavens,
than the Repreſentation of them on a Globe
or Sphere; becauſe hereby we have the
moſt natural Image of them fet before our
Eyes.
The Terreftrial Globe reprefents the Earth
with its feveral Lands, Seas, Rivers, Iflands,
&c. The Celestial Sphere, or Globe, repre-
fents the Heavens and Stars.
Several Points and Circles are either mark-
ed or deſcribed on theſe Spheres or Globes,
or are repreſented by the Brafs and Wooden
Work
2
Sect. I.
The first Principles of
Work about them, to exhibit the Places and
the Motions of the Sun, Moon, or Stars, the
Situation of the feveral Parts of the Earth,
together with the Relation that all theſe bear
to each other.
The Earthly Globe, with the Lines and
Signs and Points that are uſually marked up-
on it, is fufficient to inform the Reader of
almoſt every Thing that I fhall mention
here, even with regard to the Heavens, the
Sun and the Planets; unleſs hè has a Mind
to be particularly acquainted with the fixed
Stars, and the feveral Ufes of them; then
indeed a Celestial Globe is moſt convenient to
be added to it.
Note 1ft, Half the Globe is called a He-
mifphere; and thus the whole Globe, or
Sphere of the Heavens, or of the Earth, may
be repreſented on a Flat or Plane in two He-
mifpheres, as in the common Maps of the
Earth, or in Draughts or Deſcriptions of the
Heavens and Stars.
Becauſe Globes are not always at Hand, the
feveral Points and Circles, together with their
Properties, ſhall be ſo deſcribed in this Diſ-
courſe, as to lead the Reader into fome ge-
neral and imperfect Knowledge of thefe
Things (as far as it may be done by a Map of
the World, which is nothing elſe but a Re-
prefentation of the Globe of Earth and Waters
on two flat or plain Surfaces;) or at leaſt I ſhall
3
fo
Sect. 2. Geography and Aftronomy.
3
fo expreſs theſe Matters, that a Map will affift
him to keep them in Remembrance, if he
has been firſt a little acquainted with the
Globe itſelf.
Note 2d, Though the lateſt and beſt Aſtro-
nomers have found that the Sun is fixt in
or near the Centre of our World, and that
the Earth moves round its own Axis once in
twenty-four Hours with a Circular Motion,
and round the Sun once in a Year with a
Progreffive Motion; yet to make theſe Things
more eafy and intelligible to thofe that are
unſkilful, we ſhall here fuppofe the Sun to
move round the Earth, both with a daily
and yearly Motion, as it appears to our Senſes;
namely, daily going round the Earth, and
yet every Day changing its Place a little in
the Heavens, till in a Year's Time it returns
to the fame Place again.
1
SECT. II.
Of the greater Circles.
THE Greater Circles are fuch as divide
the Globe into two equal Parts, and
are theſe four; namely, the Horizon, the Me-
ridian, the Equator, and the Ecliptick.
I. The Horizon is a broad flat Circle, or
the Wooden Frame in which the Globe
B
ftands.
4
Sect. 2.
The first Principles of
ftands. Its upper Edge divides the Globe into
the upper and lower Halves or Hemifpheres,
and repreſents the Line or Circle which di-
vides between the upper and the lower Parts
of the Earth and Heavens, and which is
called the Horizon. This Circle determines
the Rifing or Setting of Sun or Stars, and dif-
tinguiſhes Day and Night.
*
When the Sun is in the Eaft Part of the
Horizon, it is Rifing. When in the Weſt
Part it is Setting. When it is above the Ho-
rizon, it is Day. When below, it is Night.
Yet till the Sun be 18 Degres below the
Horizon, it is uſually called Twilight; be-
cauſe the Sun-Beams fhooting upward are
reflected down to us by the Atmoſphere af-
ter Sun-fet, or before Sun-rife: And it is up-
on this Account that in our Horizon at Lon-
don, there is no perfect Night in the very.
Middle of Summer for two Months together,
becauſe the Sun is not 18 Degrees below the
Horizon.
The Horizon is diftinguiſhed into the Sen-
fible and the Rational.
See Fig. 1.
The Senfible Horizon fuppofes, the Specta-
tor placed on s the Surface of the Earth or Wa-
ter, and it reaches as far as the Eye can fee.
But the Rational or True Horizon, fuppofes
the Spectator placed in the Centre of the Earth
c, and thus divides the Globes both of the
Heavens and the Earth into Halves.
3
Sup-
1
Sect. 2. Geography and Aftronomy.
Ś
Suppofe in Figure 1. the Circle s dpeis
the Earth, u b b nr g the Heavens, b s ģ g
the Line making the Senfible Horizon, br
the Rational Horizon.
за
The Senfible Horizon on the Earth or Sea
includes a so, and it reaches but a very few
Miles; for if a Man of fix Feet high ftood
on a large Plain, or on the Surface of the Sea;
at s, he could not ſee the Sea itſelf, or the
Land, farther than three Miles round.
Thus it appears that the Senfible Horizon
on the Earth or Sea as o, differs very much
from the Extent of the Real or Rational Ho-
rizon, dse. But as to the Heavens where the
fixt Stars are, the Senfible Horizon, bu g ſcarce
differs at all from the Rational Horizon, bur:
For the Eye placed in the Centre of the Earth
c, or on the Surface of, it s, would find no
evident Difference in the Horizon of the fixt
Stars, becauſe they are at fo immenſe a Dif-
tance, that in compariſon thereof half the
Diameter of the Earth, that is, sc or g r,
the Diſtance between the Surface and the
Centre is of no Confideration.
{
But let it be obſerved here, that the Pla-
nets are much nearer to the Earth than the
Fixt Stars are: And therefore half the
Diameter of the Earth, that is, sc org r, is
of fome Confideration in the Horizon of the
Planets.
B 2
It
6
Sect. z.
The first Principles of
1
}
1
It may not therefore be improper to note
in this Place, that ſuppoſe a Planet to be at
g, if the Eye of the Spectator were on the
Surface of the Earth at s, he would behold it
as level with the Horizon: But if his Eye
were at the Centre of the Earth at c, he
would behold it raifed feveral Degrees or Mi-
nutes above the Horizon, even the Quan-
tity of the Angleg cr, or (which is all one)
sgc.
L
Now the Difference between the Place
where a Planet appears to a Spectator, placed
on the Centre of the Earth, and to a Specta-
tor placed on the Surface, is called the Pa-
rallax of that Planet at that Time; and
therefore the Difference between thoſe two
Places g and r, or rather the Quantity of
the Angle gcr, or s g c, is called its Hori-
zontal Parallax. And this is of
And this is of great ufe
to adjust the real Diſtances, and confequent-
ly the real Magnitudes of the feveral Planets,
But this Doctrine of Parallaxes belongs
rather to the ſecond or Special Part of Aftro-
nomy.
·
II. The Meridian is a great Brazen Cir-
cle in which the Globe moves; it croffes
the Horizon at right Angles, and divides
the Globe into the Eaftern and Weftern
Hemifpheres. It reprefents that Line or
Circle in the Heaven which paffes juft
over our Head, and cutting the Horizon
6
in
Sect. 2. Geography and Aftronomy.
7
in the North and South Points of it, comes
juft under our Feet on the oppofite Side of
the Globe.
This Circle fhews when the Sun or Stars
are juſt at North or South, and determines
Noon or Midnight.
When the Sun is on the Meridian and
above the Horizon to us in Great-Britain, it
is juft in the South, and it is Noon. When
it is on the Meridian, and under the Horizon,
it is juſt in the North, and it is Midnight.
Note, Whenfoever we move on the Earth,
whether Eaft, Weft, North, or South, we
change our Horizon both Senfible and Ratio-
nal; for every Motion or Change of Place
gives us a Hemifphere of Sky or Heaven
over our Head a little different from what it
was; and we can fee lefs on one Side of the
Globe of the Earth, and more on the other
Side,
1
Whenfoever we move toward the Eaft or
Weft, we change our Meridian: But we do
not change our Meridian if we move directly
to the North or South.
Upon this Account the Horizon and Meri-
dian are called Changeable Circles, and the
Globe is made moveable within thefe Circles,
to repreſent this Changeableness; whereby
every Place on the Earth may be brought un-
der its proper Meridian, and be furrounded
with its proper Horizon.
B 3
III. The
"
?
8
Sect. 2.
The first Principles of
t
III. The Equator, or Equinoctial Line,
croffes the Meridian at right Angles, and di-
vides the Globe into the Northern and South-
ern Hemiſpheres; and diftinguiſhes the Sun's
yearly Path into the Summer and Winter
Half-Years. It reprefents in the Heavens
that every Line or Circle which is the Path
of the Sun in thoſe two Days in Spring and
Autumn, when the Days and Nights are of
equal Length.
Among all the Circles of the Globe, this
is fometimes eminently called The Line; and
paffing over it at Sea, is called by Sailors,
Croffing the Line.
Note, The Sun, Moon and Stars, with all
the Frame of the Heavens, are ſuppoſed to
be whirled round from Eaft to Weft every
twenty-four Hours upon the Axis of the
Equator, or (which is all one) in their ſeveral
Paths parallel to the Equator. This is call-
ed their Diurnal, or Daily Motion.
2
IV. The Ecliptick Line is the Sun's An
nual or Yearly Path, cutting the Equinoc-
tial into oppofite Points obliquely at the
Angles of 23 Degrees. On it are figured
the Marks of the 12 Signs, through which
the Sun paffes, namely, Aries the Ram v,
Taurus the Bull, Gemini the Twins п,
Cancer the Crab, Leo the Lion a, Virgo,
the Virgin m, Libra the Balance, Scor-
pio the Scorpion m, Sagittarius the Archer,
Capri-
Sect. 2. Geography and Aftronomy.
9
Capricornus the Sea-Goats, Aquarius
the Waterer, Pifces the Fishes x.
Theſe Signs are certain Conftellations, or
Numbers of Stars, which are reduced by the
Fancy of Men for Diftinction Sake into the
Form of twelve Animals, and for the Uſe of
the Engliſh Reader may be deſcribed thus.
The Ram, the Bull, the heavenly Twins,
And next the Crab the Lion fhines,
The Virgin, and the Scales:
The Scorpion, Archer, and Sea-Goat,
The Man that holds the Water-pot,
And Fiſh with glittering Tails.
Among theſe Signs Aries, Taurus, Ge-
mini, Cancer, Leo, Virgo, are called North-
ern. But Libra, Scorpio, Sagittarius, Ca-
pricornus, Aquarius, Pifces, are Southern.
Capricorn, Aquarius, Pifces, Aries, Taurus,
Gemini, are Afcending Signs, becauſe they
ſtand in Succeffion Nothward, or rifing grå-
dually higher in our European Hemiſphere:
But Cancer, Leo, Virgo, Libra, Scorpio, Sa-
gittarius, are Defcending Signs, for their Suc-
ceffion tends lower toward our Horizon, or
rather toward the Southern Hemiſphere.
Each of theſe Signs has 30 Degrees of the
Ecliptick allotted to it. The Sun, or any
Planet, is faid to be in fuch a-Sign, when he
is between our Eye and that Sign, or when
B 4
he
1
ΙΟ
The first Principles of Sec, 2,
1
he appears in that Part of the Heavens where
thofe Stars are of which the Sign is com-
pofed.
If it be inquired, How we can know the
Place of the Sun among the Stars, fince all
the Stars near it are loft in the Sun-Beams?
It is anfwered, That we can fee plainly what
Conftellation, or what Stars are upon the Me-
ridian at Midnight, and we know the Stars
which are exactly oppofite to them, and theſe
muſt be upon the Meridian (very nearly) the
fame Day at Noon; and thereby we know
that the Sun at Noon is in the Midft of them.
So that when you have a Globe at hand on
which the Stars are delineated, you find on
what Degree of any Sign the Sun is in on a
given Day, and fee the Stars around it.
The Sun is reckoned to go through almoft
one Sign every Month, or 30 Days, and thus
to finish the Year in 365 Days, 5 Hours, and
49 Minutes, that is, near fix Hours: So that
the Sun may be fuppofed to move flowly as
a Snail through almoft one Degree of the
Ecliptick Line every Day from the Weft to the
Eaft, while it is whirled round together
with the whole Frame of the Heavens from
Eaft to Weft, in a Line parallel to the Equa-
tor in the Time of 24 Hours.
Note, We vulgarly call the Sun's diurnal,
or daily Path, a Parallel to the Equator,
though
}
Sect. 2. Geography and Aftronomy.
II
though properly it is a Spiral Line, which
the Sun is ever making all the Year long,
gaining one Degree on the Ecliptick daily.
From what has been now faid it appears
plainly, that the Equinoctial Line, or Equator
itſelf, is a diurnal Path of the Sun about the
20th or 21ft of March, and the 23d of Sep-
tember, which are two oppofite Points
where the Ecliptick, or Yearly Path of the
Sun, cuts the Equator.
And theſe two Days are called the Equi-
noctial Days, when the Sun rifes and fets at
fix o'clock all the World over, (that is, where
it riſes and ſets at all that Day;) and the Day
and Night are every where of equal Length:
And indeed, this is the true Reaſon, why this
Line is called the Equator or the Equinoctial.
It may not be improper in this Place to re-
mark, that thoſe 5 Hours and 49 Minutes,
which the Sun's Annual Revolution requires
above 365 Days, will in four Year's Time
amount to near a whole Day: Therefore
every fourth Year has 366 Days in it, and is
called the Leap-rear. Note, The fuper-added
Day in that Year is the 29th of February in
Great-Britain.
It may be farther remarked alfo, that the
odd 11 Minutes, which in this Account are
wanting yearly to make up a complete Day
of 24
Hours, are accounted for in the New
Style, by leaving out a whole Day once in
133
12
The firft Principles of Sect. 2.
4
133 or 134 Years*. And it is the Neglect of
accounting for theſe odd Minutes in the Old
Style above a thouſand Years backwards, that
has made the Difference between the Old Style
and the New to be at preſent Eleven Days.
Note, The Zodiack is fancied as a broad
Belt ſpreading about 7 or 8 Degrees on each
Side of the Ecliptick, fo wide as to contain
moſt of thoſe Stars that make up the 12 Con-
ftellations, or Signs.
Note, The inner Edge of the wooden Hori-
zon, is divided into 360 Degrees, or 12 times
30, allowing 30 Degrees to every Sign or
Conftellation, the Figures of which are ufu-
ally drawn there.
The next Circle to thefe on the Horizon,
contains an Almanack of the Old Style, which
begins the Year eleven Days later; and the
next Circle is an Almanack of the New Style,
which begins fo much fooner; and theſe
ſhew in what Sign the Sun is, and in what
Degree of that Sign he is every Day in the
Year, whether you count by the Old Style or
Note,
the New.
* This was contrived to be done by Pope Gregory, in
the Year 1582, in this manner.
Since three times 133
Years make near 400 Years, he ordered the additional
Day to be omitted at the End of three Centuries fuccef-
fively, and to be retained at the 400th Year, or 4th Cen-
tury. But in this Reformation of the Kalendar, he look-
ed back no farther than the Council of Nice. This Order
almoſt all foreign Nations obſerved: Great-Britain did
not obſerve it till the Year 1752, when it was introduced
and eſtabliſhed by Act of Parliament.
Se&t. 3. Geography and Aftronomy.
13
}
Note, One Side or Edge of the brazen Me-
ridian is alſo divided into 360 Degrees, or
4 times
90; on the
Semicircle where-
upper
of the Numbers uſually begin to be counted
from the Equator both Ways toward the Poles:
On the under Semicircle they begin to be
counted from the Poles both Ways toward the
Equator for ſpecial Ufes, as will afterward ap-
pear. And it fhould be remembered, that it
is this Edge of the Brafs Circle, which is
gratuated, or divided into Degrees, that is
properly the Meridian Line.
Note, The Equator and the Ecliptick are
called Unchangeable Circles, becauſe wherefo-
ever we travel or change our, Place on the
Earth, theſe Circles are ſtill the fame.
SECT. III.
Of the Leffer Circles.
THE Leffer Circles divide the Globe
into two unequal Parts, and are theſe
four, all parallel to the Equator, namely, the
two Tropics, and the two Polar Circles.
2
I. The Tropic of Cancer just touches the
North Part of the Ecliptick, and deſcribes
the Sun's Path for the longeſt Day in Sum-
mer: It is drawn at 23 Degrees Diſtance
from the Equator toward the North. And it
is called the Tropic of Cancer, becauſe the
Sun enters into that Sign the 21ft of June,
the longeſt Day in the Year.
II. The
14
Sect. 3.
The firft Principles of
1
1
t
༡
II. The Tropic of Capricorn juſt touches
the South Part of the Ecliptick, and deſcribes
the Sun's Path for the ſhorteſt Day in the
Winter: It is drawn at 23 Degrees Diſtance
from the Equator toward the South. And
it is called the Tropic of Capricorn, becauſę
the Sun enters into that Sign the 21 ft of De-
cember, the ſhorteſt Day in the Year.
Note, What I ſpeak of the fhorteſt and
longeft Days, relates only to us who dwell on
the North Side of the Globe: Thofe who
dwell on the South Side, have their longeft
Day when the Sun is in Capricorn, and their
fhorteft in Cancer.
I
III, and IV. The North and South Polar
Circles are drawn at 23 Degrees of Diftançe
from each Pole, or which is all one, at go
Degrees Diſtance from the contrary Tropic;
becauſe the Inhabitants under the Polar
Circles, juft lofe the Sun under the Horizon
one whole Day at their Mid-winter, or when
it is in the utmoft Part of the contrary Side
of the Ecliptick; and they keep it one whole
Day, or 24 Hours, above their Horizon at
their Mid-fummer, or when it is in the near-
eft Part of their Side of the Ecliptick.
The North Polar Circle is called the Arc-
tick Circle, and the South is the Antarctick.
Here I might mention the Five Zones by
which the Ancients divided the Earth, for
they are a fort of broad Circles; But per-
haps
Sect. 4. Geography and Aftronomy.
15
1
haps thefe may be as well referred to the fol-
lowing Part of this Book.
THE
SECT. IV.
Of the Points.
HE moft remarkable Points in the Hea-
vens are theſe twelve or fourteen.
I, and II, are the two Poles of the Earth,
or Heavens, namely, the North and the South,
which are ever ftedfaſt, and round which
the Earth or the Heavens are ſuppoſed to
turn daily, as the Globe does upon theſe Iron
Poles. Theſe are alfo the Poles of the Equator,
for they are at 90 Degrees Diſtance from it.
From one of theſe Poles to the other, a
fuppofed Line runs through the Centre of the
Globe of the Earth and Heavens, and is called
the Axis or Axle of the World.
III, and IV, are the Zenith, or Point juſt
over our Head; and the Nadir, or the Point
juſt under our Feet, which may be properly
called the two Poles of the Horizon, for they
are 90 Degrees diftant from it every Way.
V, VI, VII, and VIII, are the four Cardi-
nal Points of Eaſt, West, North, and South:
Theſe four Points are in the Horizon, which
divide it into four equal Parts.
Note, For the Ufes of Navigation, or Sail-
ing, each of theſe Quarters of the Heavens,
Eaft, Weft, North, and South, are fubdivided
into eight Points, which are called Rhumbs;
fo
1
1
}
16
Sect. 4.
The firft Principles of
}
fo that there are 32 Rhumbs or Points in the
whole, each containing 11 Degrees. Thefe
are defcribed on the utmoſt Circle of the
wooden Horizon.
From the NORTH towards the Eaft theſe
Points are named, North and by Eaft, North
North-Eaft, North-Eaſt and by North,
North-Eaft; North-Eaſt and by Eaſt, Eaſt-
North-Eaft, Eaft and by North, East, &c.
Then from the Eaft toward the South it
proceeds much in the fame manner.
The whole Circle of 360 Degrees divided
in this manner is called the Mariner's Compass,
by which they count from what Point of the
Heavens the Wind blows, and toward what
Point of the Earth they direct their Sailing,
which they call Steering their Course. See
Figure 11.
譬
​IX, and X, are the two Solftitial Points:
Theſe are the Beginning of the Signs Cancer
and Capricorn in the Ecliptick Line, where
the Ecliptick juft touches thoſe two Tropics.
Theſe Points fhew the Sun's Place the longeſt
and ſhorteſt Days, namely, the 21st of June,
and the 21st of December.
Note, Theſe two Days are called the Sum-
mer and Winter Solftices, becauſe theSun feems
to ſtand ſtill, that is, to make the Length of
Days neither increaſe nor decreaſe ſenſibly for
twenty Days together.
XI, and XII, are Aries and Libra, or the
two Equinoctial Points, where the Ecliptick
1
cuts
Sect. 4. Geography and Aftronomy.
17
cuts the Equator: When the Sun enters into
theſe two Signs, the Days and Nights are e-
qual all over the World. It enters Aries in
Spring the 21st of March, which is called the
Vernal Equinox, and Libra in Autumn the
23d of September, which is called the Au-
tumnal Equinox.
Theſe four Points, namely, twoEquinoctial
and two Solſtitial divide the Ecliptick into
the four Quarters of the Year.
Here let it be noted, that the twelve Con-
ſtellations, or Signs in the Heavens, obtained
their Names about two thouſand Years ago
or more; and at that time the Stars that make
up
Aries or the Ram, were in the Place where
the Ecliptick afcending cuts the Equator; but
now the Conftellation Aries is moved upward
toward the Place of Cancer near thirty Degrees;
and fo every Conftellation is moved forward
in the Ecliptick from the Weft toward the
Eaſt near thirty Degrees; fo that the Conftel-
lation or Stars that make up the Sign Piſces,
are now in the Place where Aries was, or
where the Ecliptick cuts the Equator in the
Spring: And the Conftellation Virgo is now
where Libra was, or where the Ecliptick
cuts the Equator in Autumn. So Gemini is
in the Summer Solstice where Cancer was;
and Sagittarius in the Winter Solftice where
Capricorn was: And by this means the Sun is
got into the Equinoxes in Pifces and Virgo,
and
}
1
18
Sect. 4.
The firft Principles of
and is arrived at the Solftices in Gemini and
Sagittarius, that is, when it is among thoſe
Stars.
This Alteration is called the Preceffion of
the Equinox, that is, of the Equinoctial Signs
or Stars, which feem to be gone forward,
that is, from Weft to Eaft; but fome call it
the Retroceffion of the Equinox, that is, of
the two Equinoctial Points, which ſeem to be
gone backwards, that is, from East to West.
This comes to paſs by fome ſmall Variation
of the Situation of the Axis of the Earth, with
regard to the Axis of the Ecliptick, round
which it moves by a conical Motion *, and
advances 50 Seconds, or almoſt a Minute of
a Degree every Year, which amounts to one
whole Degree in 72 Years, and will fulfil a
complete Revolution in 25920 Years. This
Period fome have called the Platonical Year,
when ſome of the Antients fancied all things
ſhould return into the fame State in which
they now are.
1
Yet we call theſe Equinoctial and Solfti-
tial Points in the Heavens, and all the Parts
of the Ecliptick by the fame ancient Names
ftill
* The Axis of the Earth is fuppofed to be faſtened at
its Middle in the Centre, while both Ends of it, or each
of the Poles in this Motion deſcribes a Circle round each
Pole of the Ecliptick, which is the Bafe of the Cone.
The Vertexes of each of theſe Cones meet in the Centre
of the Earth; and by this Motion of the Earth, all the
fixt Stars ſeem to be moved from their former Places in
Circles parallel to the Ecliptick.
1
Sect. 4. Geography and Aftronomy.
19
ftill in Aftronomy, and mark them ſtill with
the fame Characters, namely, r, 8, º, I, N,
&c. though the Conftellations themfelves
feem to be removed ſo much forward.
XIII, and XIV. Here it may not be im-
proper, in the laſt Place, to mention the Poles
of the Ecliptick, which are two other Points
marked generally in the Celeſtial Globe.
If there were an Axis thruft through the
Centre of the Globe juft at right Angles
with the Plane of the Ecliptick, its Ends or
Poles would be found in the two Polar Cir-
cles. So that a Quarter of a Circle, or 90 De-
grees, numbered directly or perpendicularly
from the Ecliptick Line, fhew the Poles of the
Ecliptick, and fix theſe two Points through
which the two Polar Circles are drawn.
It is ufual alfo in Books of this kind, to
mention two great Circles called Colures,
drawn fometimes on the Celestial Globe thro'
the Poles of the World, one of which cutting
the Ecliptick in the two Solfticial Points,
is called the Solfticial Colure; the other cut-
ing it in the Equinoctial Points, is called the
Equinoctial Colure; but they are not of much
ufe for any common Purpoſes or Practices
that relate to the Globe.
I think it may not be amifs, before we
proceed farther, to let the Learner ſee a Re-
preſentation of all the foregoing Circles and
Points on the Globe, just as they ftand in our
Horizon at London, and fo far as they can be
C
re-
1
20
Sect. 4.
The first Principles of
!
i
1
1
1
repreſented on a flat Surface, and in ſtraight
Lines.
Let the North Pole be raiſed above the
North Part of the Horizon 51% Degrees,
which are numbered on the brazen Meridian,
then let the Globe be placed at fuch a Dif-
tance as to make the Convexity infenfible,
and appear as a flat or plain Surface, and let
the Eye of the Spectator be juſt level and
op-
pofite to c, which repreſents the East Point
of the Horizon; then the Globe and the
Circles on it will appear nearly as repre-
fented in Figuré III.
The large Circle divided by every five
Degrees repreſents the Meridian, the reft of
the larger and the leffer Circles are there
named, together with the North and South
Poles. z is the Zenith of London, N the
Nadir, H the South Point of the Horizon,
o the North Point, c the East and West
Points, s the Summer Solstice, w the Win-
ter Solstice, a the Ecliptick's North Pole, e
the Ecliptick's South Pole. The two Equi-
noctial Points are reprefented by c, fup-
pofing one to be on this Side, the other on
the oppofite Side of the Globe.
If you would have the two Colures repre-
fented here in this Figure, you muſt fup-
pofe the Meridian to be the Solfticial Colure,
and the Axis of the World to repreſent the
Equinoctial Colure.
'
Note,
!
}
Sect. 5. Geography and Aftronomy.
2 I
1
Note, This Reprefentation, or Projection
of the Sphere in ftraight Lines is uſually
called the Analemma. See how to project
it, or to erect this Scheme, Sect. XX.
Prob. XV. Fig. XXIII.
SECT. V.
Of Longitude and Latitude on the Earthly
Globe, and of different Climates.
THE various Parts of the Earth and
Heavens bear various Relations both
to one another, and to theſe feveral Points
and Circles, which have been defcribed.
First, The Earth ſhall be confidered here.
Every Part of the Earth is fuppofed to
have a Meridian Line paffing over its Zenith
from North to South thro' the Poles of the
World. It is called the Meridian Line of that
Place, becauſe the Sun is on it at Noon.
That Meridian Line which paffes through
Ferro, one of the Canary-Iſlands, has been
uſually agreed upon by Geographers as a firſt
Meridian, from which the reft are counted
by the Number of Degrees on the Equator.
Others have placed their first Meridian in
Teneriff, another of the Canary-Iſlands,
which is two Degrees more to the Eaft, but
all this is Matter of Choice and Cuftom,
not of Neceffity.
C 2
The
7
£2
Sect. 5.
The first Principles of
1
The Longitude of a Place is, its Distance
from the firft Meridian toward the Eaft, mea-
fured by the Degrees upon the Equator. So
the Longitude of London is about to De-
grees, counting the firſt Meridian at Ferro.
Note, In English Globes or Maps, fome-
times the Longitude is computed from the
Meridian of London, in French Maps from
that of Paris, &c. for it being purely arbitrary
where to fix a firft Meridian, Mariners and
Map-makers determine this according to their
Inclination. When only the word Longitude
is mentioned in general, it always means the
Distance Eaſtward; but fometimes we men-
tion the Longitude Weftward as well as Eaſt-
ward, that is, from London, or Paris, &c.
eſpecially in Maps of particular Countries.
By the Meridian Circles on a Map or
Globe, the Eye is directed to the true Lon-
gitude of any Place according to the Degrees
marked on the Equator: And upon this
Account the Meridians are fometimes called
Lines of Longitude.
The Latitude of a Place is, its Diſtance
from the Equator toward the North or South
Pole, meafured by the Degrees on the Meri-
dian. So the Latitude of London is
51 De-
grees, 32 Minutes, that is, about 51.
A Place is faid to have North Latitude, or
South Latitude, according as it lies toward
the North Pole or South Pole in its Diſtance
from the Equator. So London has 51 De-
grees of North Latitude.
The
Sect. 5. Geography and Aftronomy.
23
The Elevation of the Pole in any particular
Place is, the Diſtance of the Pole above the
Horizon of that Place, meafured by the De-
grees on the Meridian; and is exactly equal
to the Latitude of that Place: For the Pole
of the World, or of the Equator, is juſt ſo
far diſtant from the Horizon, as the Zenith
of the Place (which is the Pole of the Ho-
rizon) is diſtant from the Equator. For
which reaſon the Latitude of the Place, or
the Elevation of the Pole, are uſed promif-
cuouſly for the fame Thing.
The Truth of this Obfervation, namely,
that the Latitude of the Place and the Pole's
Elevation are equal, may be proved ſeveral
Ways; I will mention but theſe two.
Fig. IV.
See
Let H Co be the Horizon, z the Zenith,
or the Point over London, Ez the Latitude
of London, 51, P o the Elevation of the
North Pole above the Horizon. Now that
Ez is equal to P o is proved thus:
Demonftration I. The Arch z p added to
E z makes a Quadrant, (for the Pole is always
at 90 Degrees Diſtance from the Equator.)
And the Arch z P added to PO makes a
Quadrant, (for the Zenith is always at 90
Degrees Diſtance from the Horizon.) Now
if the Arch z P added either to Ez or to Po
completes a Quadrant, then Ez muſt be
equal to P o.
C 3
Demon-
$
{
1
24
Sect. 5.
The first Principles of
take
Demonftration II. The Latitude Ez muſt
be the ſame with the Pole's Elevation Po:
For the Complement of the Latitude, or
the Height of the Equator above the Hori-
zon EH is equal to the Complement of the
Pole's Elevation P z. I prove it thus: The
Equator and the Pole ſtanding at right An-
gles, as E CP, they complete a Quadrant,
or include 90 Degrees: Then if you
the Quadrant E CP out of the Semicircle,
there remains Po the elevated Pole, and
E H the Complement of the Latitude, which
complete another Quadrant. Now if the
Complement of the Latitude, added to the
Elevation of the Pole, will make a Quadrant,
then the Complement of the Latitude is
equal to the Complement of the Pole's Ele-
vation, and therefore the Latitude is equal to
the Pole's Elevation; for where the Com-
plements of any two Arches are equal, the
Arches themſelves muft alfo be equal.
As
* Note, The Complement of any Arch or Angle under
go Degrees, denotes fuch a Number of Degrees as is
fufficient to make up 90; as the Complement of 50 De-
grees is 40 Degrees, and the Complement of 51 is 38/
Degrees. And fo the Complement of the Sine or Tan-
gent of any Arch is called the Co-fine, or Co-tangent: So
alfo in Aftronomy and Geography we ufe the Words
Co-latitude, Co-altiti de, Co-declination, &c. for the Com-
plement of the Latitude, Altitude, or Declination, of
which Words there will be more frequent Ufe among
the Problems,
Sect. 5. Geography and Aftronomy.
25
As every Place is ſuppoſed to have its pro-
per Meridian, or Line of Longitude, fo every
Place has its proper Line of Latitude, which
is a Parallel to the Equator. By theſe Paral-
lels the Eye is directed to the Degree of the
Latitude of the Place marked on the Meri-
dian, either on Globes or Maps.
By the Longitude and Latitude being given,
you may find where to fix any Place, or where
to find it in any Globe or Map: For where
thoſe two ſuppoſed Lines, namely, the Line
of Longitude, and Parallel of Latitude, croſs
each other, is the Place inquired. So if
ſeek the Longitude from Ferro, 20 Degrees,
and the Latitude 51 Degrees, they will
fhew the Point where London ftands.
2
you
The Parallels of Latitude which are drawn
at fuch Diſtances from each other near and
nearer to the Poles, as determine the longeſt
Days and longeſt Nights of the Inhabitants
to be half an Hour longer or fhorter, include
fo many diftinct Climates, which are propor-
tionally hotter or colder, according to their
Diſtance from the Equator. Though it
muſt be owned, that we generally uſe the
Word Climate in a more indeterminate Senfe,
to fignify a Country lying nearer or farther
from the Equator, and confequently botter or
colder, without the precife Idea of its longeft
Day being just half an Hour ſhorter or
longer than in the next Country to it.
C 4
The
{
1
26
Sect. 5:
The first Principles of
}
#
The Latitude is never counted beyond 90
Degrees, becauſe that is the Diſtance from
the Equator to the Pole: The Longitude
arifes to any Number of Degrees under 360,
becauſe it is counted all round the Globe.
If you travel never fo far directly towards
Eaft or Weft, your Latitude is ftill the fame,
but the Longitude alters. If directly toward
North or South, your Longitude is the fame,
but the Latitude alters. If you go oblique-
ly, then you change both your Longitude
and Latitude.
The Latitude of a Place, or the Elevation
of the Pole above the Horizon of that Place,
regards only the Distance Northwardor South-
ward, and is very eafy to be determined by
the Sun or Stars with Certainty, as Sect. XX.
Prob. VII, and IX. becauſe, when they are
upon the Meridian, they keep a regular and
known Diſtance from the Horizon, as well
as obferve their certain and regular Diſtances
from the Equator, and from the two Poles, as
fhall be fhewn hereafter: So that either by
the Sun or Stars (when you travel Northward
or Southward) it may be found precifely
how much your Latitude alters.
But it is exceeding difficult to determine
what is the Longitude of a Place, or the Diſ-
tance of any two Places from each other
Eaſtward or Weftward by the Sun or Stars,
becauſe they are always moving round from
Eaft to Weft.
7
The
1
Sect. 6. Geography and Aftronomy.
27
+
The Longitude of a Place has been there-
fore uſually found out and determined by
meaſuring the Diſtance travelled on the Earth
or Sea, from the Weft toward the Eaft, fup-
pofing you know the Longitude of the Place
whence you fet out.
}
SECT. VI.
Of Right Afcenfion, Declination, and Hour
Circles.
HAVING confidered what refpect the
Parts of the Earth bear to theſe arti-
ficial Lines on the Globe, we come, fecondly,
to furvey the feveral Relations that the Parts
of the Heavens, the Sun or the Stars, bear
to theſe ſeveral imaginary Points and artifi-`
cial Lines or Circles.
The Right Afcenfion of the Sun, or any
Star is, its Distance from that Meridian which
pafes through the Point Aries, counted to-
ward the Eaft, and measured on the Equator;
it is the fame Thing with Longitude on the
Earthly Globe.
The Hour of the Sun, or any Star, is
reckoned alſo by the Diviſions of the Equa-
tor; but the Hour differs from the Right
Afcenfion chiefly in this, namely, The Right
Afcenfion is reckoned from that Meridian
which
28
The First Principles of Sect. 6.
!
which paſſes thro' Aries; the Hour is reck-
oned on the Earthly Globe, from that
Meridian which paffes through the Town or
City required; or it is reckoned on the hea-
venly Globe from that Meridian which
paffes thro' the Sun's Place in the Ecliptick,
and which, when it is brought to the Brazen
Meridian, reprefents Noon that Day.
There is alſo this Difference. The Right
Afcenfion is often computed by fingle De-
grees all round the Equator, and proceeds
to 360: The Hour is counted by every 15
Degrees from the Meridian of Noon, or of
Midnight, and proceeds in Number to 12,
and then begins again': Though fometimes
the Right Afcenfion is computed by Hours
alfo inſtead of Degrees, but proceeds to 24.
So the Sun's Right Afcenfion the 10th of
May is 59 Degrees, or as fometimes it is
called three Hours and 56 Minutes.
The fame Lines which are called Lines of
Longitude, or Meridians on the Earth, are
called Hour Circles on the heavenly Globe,
if they be drawn through the Poles of the
World at every 15 Degrees on the Equator,
for then they will divide the 360 Parts or
Degrees into
into 24
Hours.
Note, As 15 Degrees make one Hour, fo
15 Minutes of a Degree make one Minute
in Time, and one whole Degree makes four
Minutes in Time.
Note,
1
Sect. 6. Geography and Aftronomy.
29
Note, Degrees are marked fometimes with
(a) or with a ſmall Circle (°), Minutes of De-
grees with a Daſh (), Seconds of Minutes with
a double Daſh ("), Hours with (¹), Minutes
of Hours fometimes with (m), and fometimes
a Dash: Seconds with a double Dafh.
By theſe Meridians or Hour-Lines croffing
the Equator on the heavenly Globe, the Eye
is directed to the true Hour, or the Degree of
Right Afcenfion on the Equator, though the
Sun or Star may be far from the Equator.
By theſe you may alſo compute on the
Earthly Globe what Hour it is at any Place
in the World, by having the true Hour
given at any other Place, and by changing
the Degrees of their Difference of Longitude
into Hours.
But fince ſeveral Questions or Problems
that relate to the Hour, cannot be fo com-
modiouſly refolved by theſe few Meridians
or Hour-Lines, becauſe every Place on the
Earth hath its proper Meridian where the Sun
is at 12 o'Clock, therefore there is a Braſs
Dial-plate fixed at the North-pole in the
Globe, whofe 24 Hours do exactly anſwer
the 24 Hour Circles which might be drawn
on the Globe: Now the Dial being fixed,
and the Pointer being moveable, this an-
fwers all the Purpoſes of having an infinite
Number of Hour Circles drawn on the
Globe, and fitted to every Spot on the Hea-
vens
1
30
Sect. 6.
The first Principles of
vens or the Earth.
For the Pointer or In-
dex may be fet to 12 o'Clock when the Sun's
true Place in the Heavens, or when any
Place on the Earth is brought to the Braſs-
Meridian, and thus the Globe moving round
with the Index naturally reprefents, and
fhews by the Dial-plate, the 24 Hours of
any Day in the Year, or in any particular
Town or City.
Note, The upper 12 o'Clock is the Hour
of Noon, the lower 12 is the Midnight Hour,
when the Globe is fixed for any particular
Latitude where there are Days and Nights.
The Declination of the Sun or Stars is,
their Diſtance from the Equator toward the
North or South Pole, meafured on the Meri-
dian; and it is the fame Thing with Lati-
tude on the Earthly Globe.
Note, The Sun in the vernal or autumnal
Equinoxes, and the Stars that are juſt on the
Equator, have no Declination.
Parallels of Declination are Lines parallel
to the Equator, the fame as the Parallels of
Latitude on the Earthly Globe. In the Hea-
vens they may be ſuppoſed to be drawn
through each Degree of the Meridian, and
thus fhew the Declination of all the Stars; or
they may be drawn through every Degree of
the Ecliptick, and thus reprefent the Sun's
Path, every Day in the Year. Theſe parallel
Lines alfo would lead the Eye to the Degree
of
1
!
Sect. 6. Geography and Aftronomy.
3I
of the Sun's or any particular Star's Declina-
tion marked on the Meridian.
The Declination is called North or South
Declination, according as the Sun or Star lies
Northward or Southward from the Equator.
Obferve here, That as any Place, Town, or
City on Earth is found determined by the
Parallel of its Latitude croffing its Line of
Longitude; fo the proper Place of the Sun or
Star in the Heavens is found and determined
by the Point where its Parallel of Declina-
tion croffes its Meridian, or Line of Right
Afcenfion; which indeed are but the felf-
fame Things on both the Globes, though
Aftronomers have happened to give them
different Names.
I
2
Note, The Sun's utmoſt Declination North-
ward in our Summer is but 23 Degrees;
and it is juſt fo much Southward in our
Winter; for then he returns again: There
the Tropics are placed which deſcribe the
Path of the Sun when fartheft from the
Equator at Midfummer, or Midwinter:
Theſe two Tropics are his Parallels of De-
clination on the longeſt and fhorteſt Day.
While the Sun gains 90 Degrees on the
Ecliptick, (which is an oblique Circle) în a
Quarter of a Year, it gains but 23' Degrees
of direct Distance from the Equator mea-
fured on the Meridian; this appears evi-
dent on the Globe, and
may be
be reprefented
thus in Figure V.
Let
32
The first Principles of
Sect. 6.
Let the Semicircle v P be the Meri-
dian of the Northern Hemisphere, the Line
C be the Equator or the Sun's Path at
Aries, and Libra the Arch v the Eclip-
tick, the Line TO the Summer Tropic,
the Line ae the Sun's Path when it enters
Gemini and Leo, the Line ns the Sun's Path
when it enters Taurus and Virgo: Then it
will appear that in moving from v to 8 the
Sun gains 30 Degrees in the Ecliptick, in about
a Month, and at the fame time 12 Degrees
of Declination, namely, from v to n. Then
moving from 8 to п in a Month more it gains
30 Degrees on the Ecliptick, and 8 Degrees
of Declination, namely, from n to a. Then
again from п to in a Month more it gains
30 Degrees on the Ecliptick, and but
3 -/-/- De
grees of Declination, namely, from a to T. I
might alſo fhew the fame Difference between
its Declination and its Motion on the Eclip-
tick in its Defcent from to n, m, and .
12
4.
By drawing another Scheme of the fame
Kind below the Line v C we might repre-
fent the Sun's Defcent towards the Winter
Solſtice, and its Return again to the Spring;
and thereby fhew the fame Difference be-
tween the Sun's Declination and its Motion on
the Ecliptick in the Winter Half-Year, as
the preſent Scheme fhews in the Summer
Half-Year.
Hereby it is evident how it comes to paſs,
that the Sun's Declination alters near half a
5
Degree
Sect. 7. Geography and Aftronomy. 33
}
Degree every Day just about the Equinoxes;
but it ſcarce alters fo much in 10 or 12 Days
on each Side of the Solftices: And this fhews
the Reaſon why the Length of Days and
Nights changes fo faft in March and Septem-
ber, and fo exceeding flowly in June and De-
cember: For according to the Increaſe of the
Sun's Declination in Summer, its Semidiur-
nal Arc* will be larger, and confequently
it muſt be ſo much longer before it comes to
its full Height at Noon, and it ſtays ſo much
longer above the Horizon before it ſets.
Thus while the Sun's Declination increaſes
or decreaſes by flow Degrees, the Length of
the Days must increaſe and decreaſe but very
flowly; and when the Sun's Declination in-
creaſes and decreafes fwiftly, fo alfo muft the
Length of the Days: All which are very na-
turally and eaſily reprefented by the Globe.
1
SEC T. VII.
Of Longitude and Latitude on the Heavenly
Globe, and of the Nodes and Eclipfes of
the Planets.
THE Longitude and Latitude in Aftro-
nomy are quite different Things from
Longi-
*The Diurnal Arc is that Part of the Circle or Pa-
rallel of Declination which is above the Horizon, and
the Half of that Part is called the Semidiurnal Arc,
34
Sect. 7.
The first Principles of
1
Longitude and Latitude in Geography, which
is apt to create fome Confufion to Learners.
The Longitude of the Sun or any Star is, its
Distance from the Point Aries Eastward, mea-
fured on the Ecliptick. This is a fhort way of
defcribing it, and agrees perfectly to the Sun:
But in truth a Star's Longitude is its Distance
Eastward from a great Arch drawn perpendi-
cular to the Ecliptick through the Point Aries,
and measured on the Ecliptick.
We do not ſo uſually talk of the Sun's
Longitude, becauſe we call it his Place in the
Ecliptick, reckoning it no farther backward
than from the Beginning of the Sign in
which he is. So the 25th Day of June, we
fay the Sun is in the 14th Degree of Cancer,
and not in the 104th Degree of Longitude.
The Latitude of á Star or Planet is, its
Distance from the Ecliptick, measured by an
Arch, drawn through that Star perpendi-
cular to the Ecliptick.
Longitude and Latitude on the Heavenly
Globe bear exactly the fame Relation to the
Ecliptick, as they do on the Earthly Globe
to the Equator. As the Equator is the Line
from which the Latitude is counted, and.
on which the Longitude is counted on the
Earthly Globe, fo the Ecliptick is the Line
from which the Latitude, and on which the
Longitude are counted on the Heavenly
Globe.
And
Sect. 7. Geography and Aftronomy.
35
And thus the Lines of Latitude in the Hea-
venly Globe are all fuppofed Parallels to the
Ecliptick, and the Lines of Longitude cut the
Ecliptick at right Angles, and all meet in
the Poles of the Ecliptick, bearing the fame
Relation to it as on the Earthly Globe they
do to the Equator.
The Latitude of a Star or Planet is called
Northern or Southern, as it lies on the North
or South Side of the Ecliptick:
The Sun has no Latitude, becauſe it is al-
ways in the Ecliptic: This Relation of La-
titude therefore chiefly concerns the Planets
and Stars:
The Fixt Stars as well as the Planets have
their various Longitudes and Latitudes; and
their particular Place in the Heavens may
be affigned and determined thereby, as well
as by their Right Afcenfion and Declination.
which I mentioned before; and Aftronomers
ufe this Method to fix exactly the Place of a
Star: But I think it is eaſier for a Learner
to find a Star's Place by its Declination, and
D
Right
+Aftronomers know that not only the 12 Conftella-
tions of the Zodiac, but alſo all the Fixt Stars feem to
move from the Weft toward the Eaft about 50" in a Year,
or one Degree in 72 Years, in Circles parallel to the
Ecliptick. Therefore their Declination is a little altered
in 72 Years time, that being meaſured from the Equator:
But their Latitude never alters, that being meaſured from
the Ecliptick. And upon this Account Aftronomers uſe
the Latitude rather than the Declination in their Meaſures,
becauſe it abides the fame for ever.
36
The first Principles of Sect. 7.
Right Afcenfion; and the common Aftrono-
mical Problems feem to be folved more na-
turally and eaſily by this Method.
It may be here mentioned, though it is
before its proper Place, that the ſeveral Planets,
namely, Saturn, Jupiter, Mars, Venus, Mer-
cury, and the Moon, make their Revolutions
at very different Diſtances from the Earth,
from the Sun, and from one another; each
having its diftin&t Orbit or Path nearer or
farther from us. And as each of their Orbits
is at vaſtly different Diſtances, ſo neither are
they perfectly parallel to one another, nor to
the Ecliptick or yearly Path of the Sun.
Thence it follows, that theſe Planets have
fome more, fome lefs Latitude, becauſe their
Orbits or Paths differ fome few Degrees from
the Sun's Path, and interfect or croſs the
Ecliptick at two oppofite Points in certain
fmall Angles of two, three, four or five De-
grees, which Points are called the Nodes.
The Node where any Planet croffes the
Ecliptick afcending to the Northward, is
called the Dragon's Head, and marked thus
a. Where the Planet croffes the Ecliptick
defcending to the Southward, it is called the
Dragon's Tail, and marked thus V..
It is very difficult to reprefent the Lati-
tude of the Planets in their different Orbits,
either upon a Globe, or upon a flat or plain
Surface; the beſt Way that I know is, to take
two fmall Hoops of different Sizes, as in Fi-
2
gure
Sec. 7.
Geography and Aftronomy.
37
gure x1.and thrufta ftraight Wire co through
them both in the two oppofite Parts of their
Circumference: Then turn the innermoſt
Hoop (which may repreſent the Path of the
Moon) fo far afide or obliquely as to make an
Angle of 5 Degrees with the outermoft
Hoop, (which reprefents the Sun's Path.)
Thus the two Points c and o, or a and v,
where the Wire joins the Hoops, are the two
Nodes, or the Points of Interfection.
This Difference of Orbits of the Planets,
and their Interfections or Nodes, may be re-
prefented alfo by two circular Pieces of Pafte-
board, as in Figure X11. When the leſs
(whofe Edge reprefents the Moon's Orbit,) is
put half Way through a Slit AB, that is,
made in the Diameter of the larger (or the
Sun's Orbit,) and then brought up near to a
Parallel or level with the Larger within 5
Degrees. Thus the two Nodes will be re-
preſented by A and B.
If the Moon's Path and the Sun's were pre-
cifely the fame, or parallel Circles in the
fame Plane, then at every New Moon the
Sun would be eclipfed by the Moon's coming
between the Earth and the Sun: And at
every Full Moon the Moon would be eclipfed
by the Earth's coming between the Sun and
the Moon. But fince the Planes of their
Orbits or Paths are different, and make
Angles with each other, there cannot be E-
clipfes but in or near the Place where the
Planes
D 2
J
}
38
Sect. 8.
The firft Principles of
}
Planes of their Orbits or Paths interfect or
crofs each other.
In or very near thefe Nodes, therefore, is
the only Place where the Earth or Moon can
hide the Sun, or any Part of it, from each
other, and cauſe an Eclipfe either total or
partiai: And for thefe Reaſons the Orbit or
Path of the Sun is called the Ecliptick.
The Eclipfes of other Planets, or of any
Part of the Sun by their Interpofition, are
fo very inconfiderable as deferve not our pre-
fent Notice.
SECT. VIII.
Of Altitude, Azimuth, Amplitude, and va-
rious Rifings and Settings of the Sun and
Stars.
THE Altitude of the Sun or Star, is its
Heighth above the Horizon, measured by
the Degrees on the Quadrant of Altitudes.
As the Height of the Sun at Noon is
called its Meridian Altitude, or its Culminat-
ing, fo the Height of the Sun in the Eaſt
or Weft is fometimes called its Vertical Alti-
tude.
The Quadrant of Altitudes is a thin Label
of Brafs, with a Nut and Screw at the End
of it, whereby it is faſtened to the Meridian
at the Zenith of any Place; now by bending
this down to the Horizon, you find the Alti-
tude
Sect. 8.
39
Geography and Aftronomy.
t
tude of any Star or Point in the Heavens, be-
cauſe the Label is divided into 90 Degrees,
counting from the Horizon upward.
Circles parallel to the Horizon, fuppofed to
be drawn round the Globe, through every De-
gree
of the Quadrant of Altitudes lefs and lefs,
till they come to a Point in the Zenith, are
called Parallels of Altitude, or fometimes by
the old Arabick Name Almicanters. Butthefe
can never be actually drawn on the Globe,
becauſe the Horizon and Zenith are infinitely
variable, according to the different Latitudes
of Places. In the vith Figure, fuppoſe z to
be the Zenith, N the Nadir, HR the Horizon,
and the ſtraight Lines a b, fg, km, will re-
preſent the Parallels of Altitude,
Note, The Sun being always higheft on
the Meridian, or at Noon, it defcends in an
Arch towards the Horizon in order to fet,
by the fame Degrees by which it aſcended
from the Horizon after its rifing. Stars and
Planets rife and fet, and come to the Meri-
dian at all different Hours of the Day or Night,
according to the various Seafons of the Year,
or according to the Signs in which the Planets
'are.
As the Word Altitude is uſed to fignify the
Height of the Sun or Star above the Horizon,
fo the Depreffion of the Sun or Star, is its
Diſtance from or below the Horizon.
D 3
The
་
1
{
40
The first Principles of
Sect. 8.
The Azimuth of the Sun or Star is, its
Distance from any of the four Cardinal Points,
Eaft, Weft, North and South, measured by
the Degrees of the Horizon.
Note, When we ſpeak of the Sun's Azimuth
in general, we uſually mean his Diſtance from
the South: But when his Diſtance from the
North, Eaft, or Weft, is intended, we ſay,
his Azimuth from the North, the Eaft, or
the Weft.
Great Circles cutting every Degree of the
Horizon at right Angles, and meeting in
the Zenith and Nadir, are called Azimuthal
or Vertical Circles. They direct the Eye to
the Point of the Sun or Star's Azimuth on the
Horizon, tho' the Sun or Stars may be far
above or below the Horizon.
Note, Vertical Circles are the fame with
regard to the Zenith, Nadir, and the Hori-
zon, as Meridians or Hour Circles are with
regard to the two Poles of the World and the
Equator. But thefe Vertical Circles can ne-
ver be actually drawn on a Globe, becauſe
the Zenith, Nadir, and Horizon, are ever va-
riable. See them reprefented Figure vi. by
the Lines z H N, Za N, e N, Z, &c. fuppof-
ing HR to be the Horizon.
Note, The Quadrant of Altitudes being
moveable, when one End of it is faftened at
the Zenith, the graduated Edge of it may
be laid over the Place of the Sun or Star,
and
Sect. 8. Geography and Aftronomy.
4.I
and brought down to the Horizon; then it
repreſents any Azimuth or Vertical Circle, in
which the Sun or Star is; and thus it fhews
the Degree of its Azimuth on the Horizon.
Note, The Azimuth of the Sun or Star
from the Eaft or Weft Points of the Horizon,
at its rifing or ſetting, is called its Amplitude.
Note, The Sun is always in the South at
Noon, or 12 o'Clock, and in the North at
Midnight, namely, in Europe, and all Places
on this Side the Equator. But it is not at the
Eaſt or Weſt at fix o'Clock any other Day
in the Year befides the two Equinoctial Days,
as will eafily appear in an oblique Pofition of
the Sphere, (of which fee the next Section)
and eſpecially in th laft Section, where the
Analemma fhall be more fully deſcribed.
Yet the Relation which the Parallels of
Allitude bear to the Vertical Circles, and
which theſe Vertical or Azimuthal Circles
bear to the Meridians or Hour Cis cles, may
be repreſented to the Eye in Figure vi, and
VII.
k
m,
In Figure vi. Suppofe the outermoſt Cir-`
cle be the Meridian, H R the Horizon, z the
Zenith, N the Nadir; then db, fg,
will be Parallels of Altitude: And za N,
ZeN, ZON, Z C N, &c. will be Vertical Cir-
cles, or Circles of Azimuth croffing the others
at Right Angles.
Thus z C N is the Vertical Circle of Eaft or
Weft. And in this Scheme sa, or ƒн
D 4
will
42
Sect. 8.
The first Principles of
؟؟
9
will be the Arch of the Altitude of the Star
and н a will be its Azimuth from the Me-
ridian; and c a will be its Azimuth from the
Eaft to Weſt.
But if the Line H R be fuppofed to repre-
fent the Equator, then z and N will be the
two Poles of the World, and then db, fg,
&c. will be Parallels of Latitude on Earth,
or Parallels of Declination in the Heavens.
Then alfo the Arches z н N, za N, ZeN,
ZON, ZC N, will be Meridians or Lines of
Longitude on Earth, and Hour Circles in the
Heavens.
In Figure vII. Let the utmoſt Circle be the
Meridian, HR the Horizon, z the Zenith,
N the Nadir, E Q the Equator, P L the
Axis of the World, or rather the two Poles,
North and South; then z H N, za N, ZeN,
ZCN, will be Circles of Azimuth: PE L,
POL, PUL, PCL, &c. will be Hour Circles.
7
And in this Pofition the Stars will have
Ts, that is, equal to E o for its Hour from
Noon or the Meridian; but its Azimuth from
Noon, or the South, or Meridian, will be He.
Or if you reckon its Azimuth from the Eaft
or Weſt Vertical (which is z c N) it will be
found to be ce, while its Hour reckoned
from P 6 ci, (which is the Six o'Clock
Hour-Line) will be found to be 6 s, or
Co.
Thus it will appear how the Hour of the
Sun differs from its Azimuth, and that both
of
Sect. 8. Geography and Aftronomy.
43
of them are numbered, or counted from the
Meridian P Z E H L N ; yet they do not by any
Means keep equal Pace with one another,
one being numbered along the Equator E Q₂
the other numbered along the Horizon H R.
Thus you fee moft evidently, that if you
ſuppoſe the Suns to be in the Tropic of
Cancer reprefented by the Line T, the
Difference between the Hour and Azimuth
will appear to be very great; and that the
Sun's Azimuth from Noon He increaſes a
great deal fafter than his Hour T s doth in
the Middle of Summer. And if another
Line K were drawn to repreſent the Tra-
pic of Capricorn, the Sun's Azimuth from
Noon will appear to increaſe a great deal
flower than his Hours do in the Middle of
Winter.
I think it should not utterly be omitted
here, what is mentioned in almoſt all Wri-
tings of this Kind, namely, that a Star is faid
to rife or fet Cofmically, when it rifes or ſets
at Sun-rifing.
It is faid to rife or fet Achronically, if it
rife or fet at Sun-fetting.
A Star is faid to rife Heliacally when it
is juft come to fuch a Diſtance from the Sun
as that it is no longer hid by the Sun-Beams.
And it is faid to fet Heliacally when the Sun
approaches fo near to it as that it begins to
difappear from our Sight, being hid by the
Beams of the Sun.
The
{
:
1
1
44
Sect. 9.
The firft Principles of
1
1
The fixt Stars, and the three fuperior
Planets, Mars, Jupiter and Saturn, rife
Heliacally in the Morning, but the Moon
in the Evening; for it is in the Evening
the New Moon firft appears, coming from
her Conjunction with the Sun.
Note, This Sort of Rifing and Setting of
the Stars is alfo called Poetical; becauſe the
ancient Poets frequently mention it.
SECT. IX.
Of the Inhabitants of the Earth according to
the Pofition of the Spheres, the Zones, &c.
IN
1
N order to make the Doctrine of the
Sphere or Globe yet more plain and in-
telligible, let us confider the Inhabitants of
the feveral Parts of the World, who may
be diſtinguiſhed three Ways, (1.) According
to the various Pofitions of the Globe. (2.)
According to the five Zones. (3.) In rela-
tion to one another.
First, Let us confider them according to
the various Pofitions of the Globe or Sphere,
which are either Direct, Parallel, or Oblique.
Theſe three Pofitions of the Sphere are
repreſented in Figure VIII, IX, x, in each
of which the utmoft Circle is the Meridian,
HR is
S
Sect. 9. Geography and Aftronomy.
45
HR is the Horizon, EQ the Equator,
the Ecliptick, s n the Axis of the World,
N the North Pole, s the South, z D the
Vertical Circle of Eaft and Weft, z the
Zenith, D the Nadir, A the Tropic of
Cancer, cw the Tropic of Capricorn. The
various Pofition of thefe Lines or Circles
will appear by the following Defcriptions.
I. A Direct or Right Sphere, Figure vIII.
is when the Poles of the World are in the
Horizon, and the Equator paffes through the
Zenith: This is the Cafe of thoſe who live
directly under the Line or Equator.
Here the Inhabitants have no Latitude, no
Elevation of the Pole: The North or South
Poles being in the Horizon, they may very
nearly fee them both.
All the Stars do once in twenty four
Hours rife and fet with them, and all at
right Angles with the Horizon.
The Sun alfo, in whatfoever Parallel of
Declination he is, rifes and fets at right
Angles with the Horizon; their Days and
Nights therefore are always equal, becauſe
the Horizon exactly cuts the Sun's Diurnal
Circles in Halves.
They have two Summers every Year,
namely, when the Sun is in or near the two
Equinoctial Points, for then he is just over
their Heads at Noon, and darts his ſtrongeſt
Beams. And they have two Winters, name-
ly,
1
I
a
}
Sect. 9.
$6
The first Principles of
}
1
ly, when the Sun is in or near the Tropics
of Cancer and Capricorn; for then the Sun
is fartheft diftant from them, though even
then it is nearer than it is to us in England
at Midfummer.
II. A Parallel Sphere, Figure 1x. is where
the Poles of the World are in the Zenith and
Nadir: And the Equator is in the Horizon.
Now if there were any Inhabitants thus
directly under the North and South Poles,
they would have only one Day of fix Months
long, and one Night of fix Months, in a whole
Year, according as the Sun is on this or the
other Side of the Equator, for the Sun mov-
ing flowly in the Ecliptick on the North Side
of the Equator half a Year, would be all that
Time above the Horizon to the Inhabitants
at the North Pole, though it went round
them daily: And the Sun moving in the
Ecliptick on the South Side of the Equator
half a Year, would be below their Horizon
all that Time. The fame might be faid con-
cerning the Inhabitants of the South Pole.
The two Equinoctial Days, or when the
Sun is in the Points Aries, or Libra, the
Day and Night are equal all the World over;
and this is true in a Senfe to thofe who live
under the Poles; for the Centre of the Sun
is in their Horizon. Thus half the Sun is
above their Horizon, and half below it for
Hours together.
Thus,
2.4
Sect. 9. Geography and Aftronomy.
47
1
Thus, though the Polar Inhabitants begin
to loſe the Sun at the Autumnal Equinox, they
are not in utter Darkneſs all the Time of the
Sun's Abſence: For the Twilight laſts till the
Sun is 18 Degrees below their Horizon, and
that is till he has 18 Degrees of Declination.
The Inhabitants of the North Pole are there-
fore without the Twilight only from the 2d
of November till the 18th of January.
Let it be noted alfo, that the Refraction of
the Rays through the thick Air or Atmoſphere
makes the Sun appear above their Horizon
feveral Days fooner, and difappear feveral
Days later, than otherwiſe it would do. It
may be added in Favour of their Habitations
too, that the Moon when ſhe is brighteſt,
namely, from the firft Quarter to the laſt,
does not fet during their Middle of Winter:
For in that Part of her Month fhe is moſt
oppofite to the Sun, and is therefore in that
Part of the Heavens which is moft diſtant
from the Sun while he never rifes.
The Parallels of the Sun's Declination in
this Pofition of the Sphere, are all parallel to
the Horizon; and are the fame with the
Parallels of his Altitude, and therefore his
highest Altitude with them can never exceed
231 Degrees.
The Stars that they could fee would be
always the fame, making perpetual Revo-
lutions
I
I
1
+1
1
1
1
1
48
The first Principles of
Sect. 9.
lutions round them, and never fet nor rife,
nor be higher or lower. And the Planets
during half their Periods will be above their
Horizon, as Saturn 15 Years, Jupiter 6,
Mars 1, &c.
III. An Oblique Sphere, Fig. x. is where
the Latitude or Elevation of the Pole is at
any Number of Degrees leſs than 90. There-
fore all the Inhabitants of the Earth (except
under the Equator and the Poles) have an
Oblique Sphere.
Here the Equator and all the Parallels
of Declination cut the Horizon obliquely,
therefore the Sun and Stars always rife and
fet at oblique Angles with the Horizon.
As one Pole of the World is always in
their View, and the other is never feen, fo
there are fome Stars which never fet, and
others which never rife in their Horizon.
Their Days and Nights are of very diffe-
rent Lengths, according to the different De-
clination of the Sun in the feveral Seafons
of the Year.
In this Oblique Pofition of the Sphere,
Aftronomers fometimes talk of the Oblique.
Afcenfion of the Sun or Stars; and in order
to obtain a clearer Idea of it, let us again
confider the Right Afcenfion, which is the
Sun or Star's Diſtance from that Meridian,
which paffes through the Point Aries, mea-
Jured on the Equator.
Or
Sect. 9.
49
Geography and Aftronomy.
}
Or it may be expreffed thus: The Right
Afcenfion is that Degree of the Equator which
comes to the Meridian together with the
Sun, or Star, confidered in its Diſtance from
the Point Aries.
But the Oblique Afcenfion is that Degree
of the Equator which in an oblique Sphere
rifes together with the Sun or Stars, confi-
dered in its Diſtance from the Point Aries.
Note, That in a Right or Direct Sphere,
all the heavenly Bodies can only have Right
Afcenfion, and no Oblique Afcenfion; becauſe
the fame Point or Degree of the Equator
that riſes with them, comes alfo to the Me-
ridian with them: But in an Oblique Sphere
there is ſometimes a great deal of Difference
between the Point that rifes with them, and
the Point that comes with them to the Me-
ridian.
Now the Difference between the Right
Afcenfion of the Sun or Star, and its Oblique
Afcenfion, is called the Afcenfional Difference.
Note, Concerning the Stars in the Equa-
tor, that their Right and Oblique Afcenfion
are equal: Therefore the Sun in the Equi-
noxes rifing at Six, and fetting at Six, has
no Afcenfional Difference: But as he
goes on-
ward from the Equator toward the Winter
Solſtice, he rifes after Six; and as he goes
toward the Summer he rifes before Six; and
the
1
2
1
1
to The first Principles of
Sect. 9.
1
the Diſtance of his rifing or fetting from Six
o'Clock, is called the Afcenfional Difference:
And perhaps it is fufficient as well as
much eafier for a Learner to remember that
the Time of the Sun or Star's rifing or ſet-
ting before or after Six o'Clock, is called
by Aftronomers the Afcenfional Difference,
without taking any Notice at all of the Ob-
lique Afcenfion, which is neither ſo eaſy to
be apprehended or remembered.
The ſecond Diſtinction of the Inhabitants
of the Earth may be made according to the
five Zones, which they inhabit; this was an
ancient Divifion of the Globe.
The Zones are broad Circles, five of which
cover or fill up the Globe.
the Globe. There are two
Temperate, two Frigid or cold, and one Tor-
rid or hot.
The Torrid or burning Zone, is all the
Space that lies between the two Tropics; it
was once counted uninhabitable, becauſe of
exceffive Heat, being fo near the Sun; but
later Diſcoveries have found many and great
Nations inhabiting thofe Parts, which con-
tain the greateſt Part of Africa, and of South
America.
The two Frigid or cold Zones, are thoſe
Spaces which are included within the two
Polar Circles, with the Pole in the Centre,
at great Diſtance from the Sun, fcarcely ha-
bitable by reafon of the Cold.
真
​There lies
Greenland
Sect. 9. Geography and Aftronomy.
5¢
?
Greenland and Lapland toward the North
Pole. The South Pole and Polar Regions are
undiſcovered.
The two temperate Zones are thofe Spaces
that lie on either Side of the Globe between
the Tropics and the Polar Circles, where the
Sun gives a moderate Heat, and makes thoſe
Parts moft convenient for the Habitation of
Men. All Europe, and the greateſt Part of
Afia, and North America, lie in the North
temperate Zone.
Note, That the Torrid Zone lying between
the two Tropics, every Place in it has the Sun
in the Zenith, or exactly over their Heads
once or twice in every Year.
Thoſe who live under the Tropic of Can-
cer, have their Winter when the Sun is in
Capricorn. Thoſe who live under the Tro-
pic of Capricorn, have their Winter when the
Sun is in Cancer. Thofe who live under the
Equator have (as I faid before) two Winters
in the Year; though indeed there is fcarce
any Seafon can be called Winter within the
Limits of the Torrid Zone.
Thoſe who live juft within the Borders of
the two Frigid Zones, lofe the Sun for twen-
ty-four Hours together at Midwinter, when
the Sun is in the contrary Tropic: And thoſe
Places that are nearer and nearer to the Poles,
lofe the Sun for two, three, four, five, fix
Days, for whole Weeks or Months together
E
at
&
5.2
Sect. 9.
The first Principles of
(
at their Winter, or when the Sun is near the
contrary Tropic.
What is faid concerning the Lofs of Light
a whole Day, or Week, or Month, at Winter,
in either of the frozen Zones, muſt be alfo
faid concerning the gaining a whole Day or
Week, or Month of Daylight, at their Sum-
mer; and thofe Farts of the Year are all
Darkness in the Northern frigid Zone, which
are all Daylight in the Southern.
་
Thus as you go farther Northward or
Southward, the Continuance of the Sun above
the Horizon grows longer in their Summer;
and the utter Abfence of it below the Hori-
zon grows longer in their Winter, till you
come to thoſe Inhabitants (if any fuch there
be) who live under the Pole, for thefe have
half the Year Night, and half the Year
Day, as I faid before concerning the Parellel
Sphere.
In the two Temperate Zones, (as alſo in
the Torrid Zone) there are never quite 24
Hours either of Day or of Night together;
but when the Sun is in the Equator, all Days
and Nights are equal: Afterwards their Days
gradually increaſe till their longeſt Day in
Summer, and gradually decreafe till their
ſhorteſt Day in Winter: Though thoſe who
live on the Borders of the Polar Circles, or the
Frigid Zones, have their 22d of June, or
longeſt Day in Summer, near 24 Hours; and
their
↑
Sect. 9. 53
>
Geography and Aftronomy.
1
their 22d of December, or ſhorteft Day in
Winter, but juft allows the Sun to peep a
Moment above the Horizon, fo that their
Night is very near 24 Hours long.
Thirdly, The Inhabitants of the Earth may
alſo be divided into three Sorts, in refpect of
their Geographical Relation to one another,
and they are called the Periæci, the Antæci,
and Antipodes.
t
I. The Pericci live under the fame Pa-
rellel of Latitude on the fame Side of the
Globe, but differ in Longitude from Eaſt to
Weft 180 Degrees, or juſt half the Globe.
Theſe have their Summer and Winter at the
fame Times with one another, but Day and
Night juft at contrary Times. Note, Thoſe
who live under the Poles have no Periæci.
II. The Antoci live under the fame Meri-
dian, or Line of Longitude, and have the fame
Degree of Latitude too, but on contrary Sides
of the Equator, one to the North, the other
to the South. Theſe have Day and Night
exactly at the fame Time, but Summer and
Winter contrary to each other. Note, Thofe
who live under the Equator have no Anteci.
III. The Antipodes have (if I may fo ex-
prefs it) the Properties of the Antæci and
Periaci joined together, for they live on con-
trary Sides of the Equator, tho' in the fame
Latitude or Diftance from it; and their
Meridian, or Line of Longitude, is 180 De-
E 2
grees
❤
54 The first Principles of
Sect. 10.
i
grees, or half the Globe different. A Line
paffing through the Centre of the Earth from
the Feet of the one would reach the Feet of
the other. They dwell at the full Diſtance
of half the Globe, and have Day and Night,
Summer and Winter at contrary Times.
In each of the three laft Figures, namely,
VIII. IX. and x. you may fee thefe Diftinc-
tions of the Earth's Inhabitants exactly re-
prefented, A are Periæci, fo are cr.
Butc or AS are Antaci., or A c,
or N 8, or H R, or EQ, are all Antipodes to
each other.
مد
The Amphifcii, Heterofcii, and Afcii,
which are only Greek Names invented to tell
how the Sun cafts the Shadows of the feve--
ral Inhabitants of the World, are not worth
our prefent Notice.
SECT. X.
The Natural Defcription of the Earth and
Waters on the Terreftrial Globe.
THE Earth may be divided into its
Natural or its Political Parts. The
Qr
one Diftinction is made by the God of Na-
ture who created it: The other by Men who
inhabit it.
The Globe or Surface of Earth on which
we dwell, is made up naturally of two Parts,
Land
Sect. 10. Geography and Aftronomy.
55
Land and Water; and therefore it is called
the Terraqueous Globe. Each of theſeElements
have their various Parts of Subdivifions,
which are as variouſly defcribed on artificial
Globes or Maps.
The Land is called either an Iſland, a Con-
tinent, a Peninfula, an Ifthmus, a Promontory,
or a Coast. See the plain Defcription of all
theſe Figure XIII.
An Iſland is a Country or Portion of Land,
compaffed about with Sea or other Water; as
Great Britain, Ireland, in the Britiſh Seas;
Sicily, Crete, Cyprus, &c. in the Mediterra-
nean Sea; the Iſles of Wight, of Angleſea, of
Mann, near England; There are alfo Iflands
in Rivers.
A Continent, properly fo called, is a large
Quantity of Land in which many great Coun-
tries are joined together, and not feparated
from each other by the Sea; fuch are Europe,
Afia Africa. This is fometimes called the
Main-Land.
A
A Peninfula, is a Part of Land almoſt in-
compaffed with Water, or which is almoſt
an Iſland: Such is the Morea which joins to
Greece, fuch is Denmark as joining to Ger-
many, and Taurica Cherfonefus joining to Lit-
tle Tartary near Mufcovy; and indeed Africa
is but a large Peninfula joining to Afia.
An Ifthmus, is a narrow Neck of Land be
tween two Seas, joining a Peninſula to the
E 3
Con-
}
1
56
The firft Principles of Sect. 10.
Continent, as the Ifthmus of Darien, or Pa-
nama, which joins North and South America:
The Ifthmus of Corinth which joins the Morea
to Greece: The Ifthmus of Sues which joins
Africa to Afia.
A Promontory, is a Hill or Point of Land
ftretching out into the Sea: It is often called
a Cape, fuch is the Cape of Good Hope in the
South of Africa; the Land's-End and the
Lizard-Point are two Capes on the Weft of
England; Cape Finisterre on the Weft of
Spain, &c.
A Coaft, or Shore, is all that Land that bor
ders upon the Sea, whether it be in Inlands
or Continents: Whence it comes to paſs, that
failing near the Shore is called Coafting.
The Part of the Land which is far diftant
from the Sea, is called the Inland Country:
Thefe are the Divifions of the Land.
The Water is divided into Rivers or Seas.
A River, is a Stream of Water which has
uſually its Beginning from a ſmall Spring or
Fountain, whence it flows continually without
Intermiffion, and empties itſelf into fome
Sea. But the Word Sea implies a larger
Quantity of Water, and is diftinguiſhed into
Lakes, Gulphs, Bays, Creeks, Straits, or the
Ocean.
The Ocean, or the Main-Sea, is a vaſt
fpreading Collection of Water which is not
divided or feparated by Lands running be-
tween :
Sect. 10. Geography and Aftronomy.
57.
:
tween Such is the Atlantick or Weftern
Ocean between Europe and America: The
Eaftern or the Indian Ocean in the Eaft-In-
dies: The Pacifick Ocean or South-Sea, on
the Weft Side of America, &c.
Note, The various Parts of this Ocean, or
Main-Sea, that borders upon the Land, are
called by the Name of the Lands which lie
next to it: So the British Sea, the Irish Sea,
the Ethiopian Sea, the French and Spanish
Seas.
A Lake, is a large Place of Water inclof
ed all round with Land, and having not any
vifible and open Communication with the
Sea: Such are the Cafpian Sea or Lake in A-
fia; the Lake Zaire in Africa, (as fome
Maps defcribe) and many others there are
in Europe and America, and eſpecially in
Sweden and Finland, and on the Weft of
New England: Such alſo is the Lake or Sea
of Tiberias in the Land of Canaan, and the
Dead Sea there, which we read of in Scrip-
ture.
A Gulf, is a Part of the Sea that is almoſt
incompaffed with Land, or that runs up a
great Way into the Land.
If this be very large, it is rather called an
Inland Sea: Such is the Baltick Sea in Swe-
den, and the Euxine Sea between Europe and
Afia; the Ægean Sea, between Greece and
Leffer Afia; and the Mediterranean Sea be-
E 4
tween
58
Sect, 19.
The first Principles of
tween Europe and Africa, which is often in
the Old Teftament called the Great Sea.
If it be a lefs Part of the Sea thus almoſt
incloſed between Land, then it is more ufu-
ally called a Gulf or Bay: Such is the Gulf
of Venice between Italy and Dalmatia: The
Arabian Gulf, or the Red Sea, between Asia
and Africa: The Perfian Gulf, between A-
rabia and Perfia: The Gulf or Bay of Fin-
land, in the Baltick Sea; and the Bay of Bif-
cay, between France and Spain.
If it be but a very fmall Part, or as it were
an Arm of the Sea that runs but a few Miles
between the Land, it is called a Creek, a Ha-
ven, a Station, or a Road for Ships; as Mil-
ford Haven in Wales; Southampton Haven in
Hampshire, and many more in every Mari-
time Country.
A Strait, is a narrow Part of the Ocean ly-
ing between two Shores, whereby two Seas
are joined together, as the Sound, which is the
Paffage into the Baltick Sea, between Den-
mark and Sweden: The Hellefpont and Bof-
phorus, which are two Paffages into the Eux-
ine Sea, between Romania and the Leffer Afia;
Tie Straits of Dover, between the British
Channel and the German Sea; and the Straits
Gibraltar, between the Atlantick and the
Mediterranean, though the whole Mediter-
ranean Sea is fometimes called the Straits.
If
Se&t. 10. Geography and Aftronomy.
59
If we compare the various Parts of the
Land with thofe of the Water, there is a
pretty Analogy or Refemblance of one to
the other. The Defcription of a Continent
reſembles that of the Ocean, the one is a
vaſt Tract of Land, as the other is of Water.
An Iſland incompaffed with Water reſembles
a Lake incompaffed with Land. A Peninfula
of Land is like a Gulf or Inland Sea. A Pro-
montory or Cape at Land is like a Bay or Creek
at Sea; and an Ifthmus, whereby two Lands
are joined, has the fame Relation to other
Parts of the Earth, as a Strait has to the
Sea or Ocean.
Let us now take Notice by what Figures
the various Parts of Land or Water are de-
ſcribed in a Globe or Map, and in what Man-
ner they are reprefented. See Figure XIII.
Sea is generally left as an empty Space, ex-
cept where there are Rocks, Sands, or Shelves,
Currents of Water or Wind, deſcribed.
Rocks are fometimes made like little point-
ed things ſticking up fharp in the Sea. Sands
or Shelves are denoted by a great Heap of
little Points placed in the Shape of thoſe
Sands, as they have been found to lie in the
Ocean by founding or fathoming the Depths.
Currents of Water are defcribed by feveral
long crooked parallel Strokes imitating a Cur-
rent. The Courfe of Winds is reprefented by
the Heads of Arrows pointing to that Coaſt
towards which the Wind blows.
The
60
The first Principles of Sect. 10.
The Land is divided or diftinguiſhed from
the Sea by a thick Shadow made of ſhort
fmall Strokes to reprefent the Shores or Coafts,,
whether of Iflands or Continents, &c. and
it is uſually filled with Names of Kingdoms,
Provinces, Cities, Towns, Mountains, Fo-
refts, Rivers, &c. which are deſcribed in
this Manner, (viz.)
Y
Kingdoms or Provinces are divided from
one another by a Row of fingle Points, and
they are often painted or ſtained with diſtinc
Colours. Cities or great Towns are made
like little Houſes with a ſmall Circle in the
Middle of them. Leffer Towns or Villages
are marked only by fuch a ſmall Circle.
Mountains are imitated in the Form of little
rifing Hillocks. Forefts are repreſented by a
Collection of little Trees. Small Rivers are
deſcribed by a fingle, crooked, waving Line;
and larger Rivers, by fuch a waving or curl-
ing double Line made ftrong and black.
The Mouths of large Rivers, where they
empty themſelves into the Sea, are repre-
fented fometimes as Currents of Water, by
feveral parallel crooked Lines.
I ſhould add this alfo, That in Terreftrial
Globes you find the Mariner's Compass figured
in feveral Parts, and the Lines of it are
drawn out to a great Length towards all
Parts of the World, on purpoſe to ſhew how
any Part of the Earth or Sea ftands fituated
with
Sect. 11. Geography and Aftronomy.
61
with regard to any other Part; and this is
called its Bearing, by which you may know
what Places bear Eaft, Weft, North, or South,
from the Place where you are, or at what
other immediate Points of the Compaſs they
lie. The North is generally deſcribed by a
Flower-de-luce, and the Eaft frequently by a
Crofs.
Globes are generally fo formed as to have
the North Pole juft ftanding before the Face:
Then the Eaft is at the right Hand, and the
Weft at the Left: And thus ufually the Names
and Words are written to be read from the
Weft to the East. This is alſo obſerved in
large Maps, and it ſhould be the fame in
fmall ones; for when a Map of a Conntry is
drawn in any other Form, fo that the North
does not lie juft before us, and the Eaft to
our right Hand, it gives great Confufion to
the Learner, and fometimes confounds the
Eye and Imagination even of Perſons ſkilled
in Geography.
S E C T. XI
Of Maps and Sea Charts.
1
THough nothing can reprefent the Hea-
vens or the Earth in their natural Ap-
pearance fo exactly as a Globe, yet the two
Hemispheres, either of the Heavens or of
the
62
Sect. 11.
The first Principles of
?
the Earth, may be reprefented upon a flat or
plain Surface, which are generally called
· Projections of the Sphere.
tor.
If you fuppofe a Globe to be cut in Halves
juſt at the Equator, and each Hemiſphere
repreſented on a Plane, it is called a Pro-
jection of the Globe upon the Plane of the Equa-
Then the Equinoctial Line will be the
Circumference, and the two. Poles of the
World will be the Centres of thoſe two Pro-
jections, and all the Meridian Lines will
be ſo many ſtraight Lines or Semidiameters
meeting in the Centre. This is the moſt
common Method of reprefenting the Celestial
Globe and the Stars.
If the Globe be cut aſunder at the Hori-
zon of any particular Place, and thus repre-
fented on a Plane, it is called the Projection
on the Plane of the Horizon. Then the Ze-
nith and Nadir will be the Centres of thoſe
Projections, and the Horizon is the Circum-
ference. The two Poles will be placed at
fuch a Diſtance from the Circumference, as
the Pole of the World is elevated above the
Horizon of that Place; and the Meridian
will be repreſented as curve Lines meeting in
the Pole Point, excepting only that Meridian
that paffes through the Zenith, which is al-
ways a right Line. This is a more uncom-
mon Projection of the Sphere, though it is
much uſed in Dialling.
The
}
Sect. 11. Geography and Aftronomy.
63
t
The moſt uſual Way of defcribing the
Earthly Globe on a Plane, or a Map, is to
ſuppoſe the Globe cut in Halves about the
firft Meridian at the Ifland Fero or Teneriff.
This is a Projection on the Plane of the Meri-
dian: Then the firft Meridian will determine
the Circumference: The Pole Points will ftand
in the upper and lower Parts of that Circle,
and the other Meridians will be curve Lines
meeting in the Pole Points, except that which
paffes through the Centre of the Projection,
which is a right Line.
Here the Equator will be a ſtraight Line,
or Diameter, croffing all the Meridians at
right Angles, and at equal Diſtances from
the two Poles.
Here the two Tropics of Cancer and Ca-
pricorn are drawn at their proper Diſtances
of 23 Degrees from the Equator; and the
two Polar Circles at the fame Diſtance from
the Poles.
In this Projection the Ecliptick is fome-
times aftraightLine cutting the Middle of the
Equator obliquely in each Hemiſphere, and
ending where the two Tropics meet the Me-
ridian: But fometimes the Ecliptick is drawn
as a curve Line, or an Arch beginning where
the Equator meets the Meridian, and carried
upward juſt to touch the Tropic of Cancer in
one Hemiſphere, and downward to touch the
Tropic of Capricorn in the other.
It
1
64
The first Principles of Sect. rr.
It is in this Form the Maps of the World
are generally drawn in two large Hemi-
ſpheres.
Note here, that it is impoffible to repre-
ſent a ſpherical Body exactly in its due Pro-
portion upon a Plane; and therefore the ar-
tificial Meridians, or Lines of Longitude, Pa-
rallels of Latitude, &c. are placed at fuch
different Diſtances by certain Rules of Art,.
and the Degrees. marked on them are often
unequal; but fo drawn as may moſt commo-
diouſly repreſent the Situation of the ſeveral
Parts of the Earth with regard to one ano-
ther.
The Meridian, or Circumference of theſe
Circles, is divided into four Quarters, and
each marked with go Degrees, beginning
from the Equator, and proceeding toward
the Poles. Theſe Figures or Numbers fhew
the Latitude of every Place in the Earth, or
its Diſtance from the Equator; and at every
ten Degrees there is a Parallel of Latitude,
drawn on Purpoſe to guide and direct the Eye
in feeking the Latitude of any Place.
The Equator of each Hemiſphere is divided
into 180 Parts, which makes 360. in the
whole : And the ſeveral Meridians or Lines of
Longitude, cutting the Equator at every ten
Degrees, guide and direct the Eye to find
the Longitude of any Place required.
*
Į
1
As
Sect. 11. Geography and Aftronomy.
6.5
As the Equator, the feveral Lines of Lon-
gitude, of Latitude, &c. cannot be repre-
fented on a Plane exactly as they are on a
Globe; ſo neither can the ſeveral Parts of the
World, Kingdoms, Provinces, Iſlands, and
Seas, be repreſented in a Map exactly in the
fame Proportion as they ftand on a Globe.
But as the Divifions of Degrees in a Map are
bigger or lefs, fo the Parts of the Land and
Sea are repreſented there bigger or leſs, in a
moſt exact Proportion to thofe Lines of Lon-
gitude and Latitude among which they are
placed.
Therefore though the Length or Breadth,
or Diſtance of Places on a Map of the World,
cannot be meaſured by a Pair of Compaffes,
as they may be on a Globe, yet you may
count the Number of Degrees to which fuch
Lengths, Breadths or Diſtances correfpond,
and thereby you may compute their real Di-
menfions; though not always fo well as on
Globe; of which hereafter.
Thus much ſhall fuffice concerning Maps,
that repreſent the Whole World, or the Globe
of Earth and Water. Let us next confider
thoſe Maps which repreſent particular Parts
of the World, Kingdoms or Provinces; theſe
are generally drawn in a large Square, and are
to be confidered as Parts of a Projection on the
Plane of the Meridian.
From the Top to or toward the Bottom of
the
66 The first Principles of
Sect. II.
}
་
the Square are drawn Meridians, or Lines of
Longitude; and the Number of Degrees of
Longitude are divided and marked on the
up-
per and undermoft Line of the Square.
From Side to Side are drawn Parallels of
Latitude, and the Degrees of Latitude are
marked on the two Side Lines.
Thus you may eafily find on a Map what is
the Longitude or Latitude of any Place given,
or you may find the Point where any Town
ſtands or ſhould ſtand, when the true Longi-
tude or Latitude of it are given.
Note, In fuch Maps of particular Countries
the Longitude is not always reckoned from the
firft Meridian, as Fero or Teneriff, but often-
times it is reckoned from the Chief City of
that Kingdom which is defcribed in the Map,
as I have intimated before.
Obferve farther, That though in Globes
and Maps of the whole World the Longitude
is reckoned from the Weft toward the Eaft, yet
in finaller Maps it is often reckoned both
Ways, as Briftol is 2 Degrees Weſtern Longi-
tude from London, Amfterdam has near 5 De-
grees of Eaſtern Longitude.
2
Note alfo, That when a fmall Country
is repreſented in a large Map, the Lines of
Longitude, and Parallels of Latitude, are
drawn not merely at every 10 Degrees, as in
the Globe, but fometimes at every five De-
grees, and fometimes at every fingle Degree.
Let
Sect. 11. Geography and Aftronomy.
67.
Z
Let it be obferved alfo in large Maps, that
defcribe any particular Country or Province,
as a ſingle or double crooked waving Line ſig-
nifies a River when it is made ſtrong and
black; fo a Publick Road is deſcribed by a
fingle or a double Line drawn from Town to
Town, not quite fo curled nor ſo ſtrong as a
River is, but ſtraight or winding, as the Road
itſelf happens. And where the Roads lie thro'
a broad Plain or great Common, without
Houſes or Hedges, they are fometimes de-
fcribed by a double Row of Points.
As Villages and fmaller Towns are deſcribed
by a little Circle or ſmall round o in Maps
of larger Countries, where the Cities are re-
preſented by the Figure of a Houſe or two,
with a Spire or Steeple; fo in Maps of fmal-
ler Countries or Provinces, the little Towns
and Villages are deſcribed by the Figure of a
Houfe or two, and great Towns or Cities are
marked like feveral Buildings put together
in Profpect, or elfe the naked Plan of thoſe
very Towns or Cities is drawn there and
diſtinguiſhed according to their Streets.
I proceed now to confider Sea-Charts.
As Maps are drawn to defcribe particular
Countries by Land, ſo a Deſcription of Coafts
or Shores, and of the Seas for the ufe of Ma-
riners, is called a Sea-Chart, and it differs
from a Map chiefly in theſe Particulars.
I. A Map of the Land is full of Names
and Marks defcribing all the Towns, Coun-
F
tries,
68
Sect. II.
The first Principles of
-
tries, Rivers, Mountains, &c. but in a Sea-
Chart there are feldom any Parts of the Land
marked or defcribed, befides the Coafts or
Shores, and the Sea-Ports, the Towns or
Cities that border upon the Sea, and the
Mouths of Rivers.
II. In a Map the Sea is left as an empty
Space, except where the Lines of Longitude
and Latitude, &c. are placed; But in Sea-
Charts all the Shoals or Sands, and fhallow
Waters, are marked exactly according to
their Shape, as they have been found to lie
in the Sea by founding the Depth in every
Part of them.
III. In Sea-Charts the Meridians are often
drawn in ftraight and parallel Lines, and the
Lines of Latitude are alfo ftraight Parallels
croffing the Meridian at right Angles, This
is called Mercator's Projection; and the
Points of the Compafs are frequently repeat-
ed and extended through the whole Chart in
a Multitude of croffing Lines *, that where-
foever the Mariner is upon the Sea, he may
know toward what Point of the Compaſs he
muſt ſteer, or dire& his Veffel to carry it
toward any particular Port; and that we
may be able to fee with one Caft of an Eye
the various Bearings of any Port, Coaſt,
Inland, Cape, &c. toward each other.
IV. The Sea is alfo filled in Sea-Charts
with various Numbers or Figures which
denote
* See the Marginal Note, Problem X. Sect. XIX,
Sect. 12. Geography and Aftronomy.
69
denote the Depth of Water, and ſhew how
many Fathom deep the Sea is in thofe Places
where the Number ftands. Thefe are called
Soundings.
V. In Sea-Charts there is not fuch Care
taken to place the North Parts of the World
always directly upright and before the Face
of the Reader; but the Coafts and Coun-
tries are uſually deſcribed in fuch a Poſition,
as may afford the fittest Room to bring in
the greateſt Variety of Shores and Seas with-
in the Compaſs of the fame Chart, whether
the Eaft, or Weft, or North, be placed di-
rectly before the Reader.
Here let it be noted, that as Geography,
taken ſtrictly and properly, is a Deſcription
of Land, ſo a Deſcription of Water or Sea
is called Hydrography; and as thoſe who de-
fcribe the Land on Maps are properly called
Geographers, fo. thofe who draw the Sea-
Charts are often called Hydrographers.
1
SE C T. XII.
The Political Divifions of the Earth repre-
fented on the Globe.
THUS we have finiſhed the natural
Divifions of the Surface of the Earth;
we come now to confider how it is divided
Politically by Men who inhabit it.
F 2
In
70
Sect. 12.
The first Principles of
}
In this Senſe it is diſtinguiſhed into Four
Quarters; and into Empires, Kingdoms,
Commonwealths, Principalities,
Dukedoms, Provinces, Counties, Cities,
Towns, Villages, &c.
States,
The Earth is firft divided into four chief
Parts or Quarters, which are called Europe,
Afia, Africa, and America.
Europe is divided from Africa, and bound-
ed on the South Side by the Mediterranean
Sea. On its Eaftern Side it is divided from
Afia by a Line drawn on the Eaſt Side of
Candia, or Crete, paffing up the Ægean Sea,
and through the Propontis into the Euxine
or Black Sea, and from thence through the
Sea of Zabaique, by the River Don or Tanais,
and thence through Muscovy, (as fome will
have it) to the River Oby, rúnning into the
Northern Ocean. It is alfo bounded on the
Weft Side by the Weſtern or Atlantick Ocean.
Afia is alfo bounded on the North by the
Northern frozen Seas: On the South by the
Indian Ocean: On the Eaft it includes Chi-
na, and the Oriental Islands: But on the
North Eaft its Bounds are unknown, for
Travellers have not yet been able to deter-
mine whether thofe Eaftern Parts of Great
Tartary may not be joined to fome un-
known Parts of North America.
Africa is a large Peninſula joining to Afia
by a little Neck of Land at Egypt, bounded
on the North by the Mediterranean Sea:
On
Sect. 13. Geography and Aftronomy.
71
On the Weſt by the Atlantick and Ethiopick
Oceans: On the North Eaſt by the Red Sea;
and on the South and Eaft by the Southern
and Indian Oceans.
America was unknown to the Ancients,
till found out by Christopher Columbus, a
little above two hundred Years ago. It is
called in general the West Indies. It lies al-
moſt three thouſand Leagues to the Weft-
ward from Europe and Africa, on the other
Side of the Atlantick and Ethiopick Seas: It is
made up of two large Continents, divided by
a narrow Neck of Land into two Parts ; the
one is called North America, or Mexicana,
the other South America, or Peruana.
Let us treat briefly of each of theſe in
their Order.
SECT. XIII.
Of EUROPE, and its feveral Countries
and Kingdoms.
ΤΗ
HE chief Countries of which EUROPE
is compofed, may be diſtinguiſhed in-
to the Northern, the Middle, and the South-
ern Parts.
I. The Northern Parts are the British Isles,
Denmark, Norway, Sweden, Mufcovy, and
Lapland.
F 3
The
{
72
The first Principles of
Sect. 13
The British Isles are Great Britain and
Ireland; Great Britain contains the two
Kingdoms of England and Scotland, which
were lately united into one. The chief City
of England is London, and Edinburgh is the
chief in Scotland, as Dublin is in Ireland.
Note, That Wales is reckoned a Part of Eng-
land, though they ſpeak, in general, a diffe-
rent Language.
Denmark is a ſmall Kingdom on the North
of Germany, made up of one Peninſula, and
feveral Iflands in the Baltick Sea; its chief
City is Copenhagen, which fſtands in the
largeft of thoſe Iſlands.
The Kingdom of Norway (which lies all
along bordering on the Weft of Sweden) has
its chief Town Drontheim; this, together
with the Ifle of Iceland, far diftant in the
Northern Sea, is under the Government of
the King of Denmark.
Sweden is one of the Northern Kingdoms
which almoſt encompaffes the Baltick Sea:
Its chief city is Stockholm. That Part of it
that lies on the Eaft Side of the Baltick, is
called Finland, Livonia, &c. and the South-
ern Part on the Weft Side next to Denmark,
is called Gothland.
All the North-Eaft Part of Europe is
Ruffia and Mufcovy, under the Government
of the Czar, whofe capital City is Mofcow.
His Conquefts have lately joined Livonia to
his
Sect. 13.
73
Geography and Aftronomy.
+
11
I
his Dominion, which before belonged to
Sweden, and there he has built the City called
Peterburg.
Lapland is a cold favage Country that lies
on the North of Sweden, and belongs to
three Princes, namely, the Dane, the Swede,
and the Muscovite.
Note, That Norway, Lapland, and Swe-
den, were once all comprized under the ge-
neral Name of Scandinavia.
IÍ. The middle Parts of Europe are France,
Germany, Poland, Hungary, and Little Tar-
iary.
France lies juft Southward of England;
its Northern Coaſt is waſhed by the Engliſh
Channel; its Weſtern Shores by the Atlan
tick Sea; and its Southern by the Mediter-
ranean: Its chief City is Paris.
Before I proceed to Germany, it is proper
to mention a long Row of diftinct Govern-
ments which lie on the Eaft of France, and
divide it from Germany and Italy. Theſe are
the Seven United Provinces, the Ten Spanish
Provinces, the Dukedom of Lorrain, the
Countries of Switzerland, Savoy, and Pied-
mont.
The Seven United Provinces are called by
the Name of Holland, becaufe that is the big-
geft of them. They are a moft confiderable
Commonwealth, and their chief Cities are
Amfterdam, Rotterdam, Leyden, Utrecht, &c.
F 4
South-
1
1
74 The firft Principles of
Sect. 13.
Southward of this lie the Ten Spanish Pro-
vinces, or the Low Countries, or Netherlands,
which are called by the Name of Flanders,
becauſe that is the largest of them: They
have belonged to the Kingdom of Spain for
fome Ages; but they are now under the Em-
peror of Germany; their chief Cities are
Bruffels, Antwerp, Louvain, Mons, Namur,
Ghent, &c.
Lorrain lies to the South of Flanders, and
is governed by a Duke: Its chief Town is
Nancy.
Switzerland is the next: It is a free Repub-
lick divided into thirteen Parts, commonly
called the Swiss Cantons; named, Zurich,
Bern, Bafil, Lucern, &c. Their Allies are
the Grifons, the Valtoline, &c. The Com-
monwealth of Geneva might alſo be men-
tioned here, which is a very ſmall but free
Sovereignty, and maintains its Rights, becauſe
none of its Neighbours will let the others
feize and poffefs it.
The Dukedom of Savoy and Piedmont bor-
ders upon the South of Switzerland, and
reaches to the Mediterranean Sea: Its chief
City is Turin. Its Duke is lately made King
of Sardinia.
I proceed now to Germany, which ſtands
in the very Heart of Europe; it is called an
Empire, and its chief City, where the Em-
peror dwells, is Vienna: But there are in it
many
}
Sect. 13. Geography and Aftronomy.
75
many leffer Governments, fuch as Dukedoms,
Marquifates, Biſhopricks, and feveral free
Towns or Cities that have fome Dependence
upon the Emperor, but yet are little Sove-
reignties within themſelves.
The moſt confiderable of theſe is the Do-
minion of the Archduke of Auſtria, who is
King of Bohemia and Hungary, and is gene-
rally chofen Emperor. The nine Electorates
are next in Honour, which are fo called be-
cauſe their Governors are Electors, by whom
the Emperor of Germany is chofen. Their
Names or Titles are thefe. (1.) The Arch-
bishop of Ment. (2.) The Archbiſhop of
Triers or Treves. (3.) The Archbiſhop of
Cologn. (4.) The King of Bohemia. (5.)
The Duke of Bavaria. (6.) The Duke of
Saxony. (7.) The Marquis of Brandenburgh,
now King of Prufia. (8.) The Prince Pa-
latine of the Rhine. (9.) The Duke of
Brunfwick and Lunenburg, who is alſo King
of Great Britain. Befides all theſe, there are
many ſmall Principalities governed by Secular
or Ecclefiaftical Powers, which are too nu-
merous to be reckoned up here.
Poland is a large Kingdom lying to the
Eaft of Germany: It comprehends alſo the
large Province of Lithuania: The chief Cities
of this Kingdom are Warfaw and Cracow. I
might here mention the Country of Pruſſia,
which fome Years paft has been dignified
with
1
;
76
The first Principles of Sect. 13.
'
with the Name of a Kingdom: It is fituate
Northward between Germany and Poland.
The King refides at Berlin in Brandenburgh.
Hungary is a Kingdom which lies juft South
of Poland, its chief Towns are Prefburg and
Buda: It has been in a great Meaſure under
the Government of the Turks; but it now
belongs to the Emperor of Germany.
Little Tartary, which is alfo called Crim
Tartary, is a ſmall Country lying to the Eaſt
of Poland, and ſtretching along on the North
Side of the Euxine or Black Sea.
III. We go on now to the Southern Parts
of Europe; and theſe are Spain, Italy, and
the European Dominions of the Turk.
Spain is the moſt Southern Kingdom of
Europe, a large Country; its capital City Ma-
drid, ftands in the Midft of it: On the Weft
Side of it lies the Kingdom of Portugal, bor-
dering all along upon it; it was once a Part
of Spain, but now is fubject to a diſtinct
King: Its chief City is Libon.
Italy is a large Peninſula in the Mediterra-
nean Sea, and contains various Governments in
it, namely, Mantua, Modena, Parma, Lucca,
Genoa, &c. but the moſt noted and remarka-
ble are theſe five, Venice, Milan, Florence or
Tuſcany, Naples, and the State of the Church,
which is the Dominion of the Pope, whoſe
chief City is Rome.
In
i
Sect.. 13.
Geography and Aftronomy.
77
In the South-Eaſt Part of Europe lies the
famous Country of Greece, which contains
the ancient Provinces of Macedonia, Theffa-
lia, Achaia, &c. with the Towns of Theſſa-
lonica, Philippi, Athens, Corinth, &c. and
the Peninſula of Peloponnefus, now called the
Morea; but all theſe, together with the more
Northern Provinces of Tranfilvania, Wala-
chia, Bulgaria, Romania, &c. are now al-
moſt intirely under the Dominion of the
Turk, whofe chief City is Conftantinople, fi-
tuate at the Mouth of the Euxine Sea. All
this is called Turky in Europe.
Thus have we gone through the Northern
and Middle, and Southern Countries of Eu-
rope: But it may be proper to mention alfo
fome of the chief Iſlands of this Part of the
World, as well as the Mountains of Europe,
and its Rivers.
Near to Italy, France and Spain, lie ſeve-
ral Iſlands in the Mediterranean Sea; fuch as
Majorca, Minorca, Ivica, Corfica, Sardinia,
Sicily and Malta, which belong to different
Princes.
On the Eaſt Side of Greece is the Ægean
Sea, or Archipelago, in which are many finall
Iſlands, and Crete, a large one: On the Weſt
Side of Greece is the Gulph of Venice, or the
Adriatick Sea, in which alſo there are feveral
fmall Iſlands, as Corfu, Cephalonia, Zant,&c.
Divers
78
Sect. 13.
The firft Principles of
+
1
}
- Divers other Iles there are which are in-
cluded in Europe; as the Isle of Mann, of An-
glefey, of Wight, of Jersey, Guernsey, &c.
which belong to England: The Hebrides on
the Weft of Scotland, the Orcades, and
Schetland Isles on the North: Some in the
Baltick Sea, which belong to Sweden and
Denmark: The Azores or Weſtern Iſlands in
the Atlantick Sea, which are under the King
of Spain. And ſeveral others of lefs Note.
Some of the moſt remarkable Mountains
in Europe are, (1.) The Alps between France
and Italy. (2.) The Apennine Hills in Italy.
(3.) The Pyrenean Hills between France and
Spain. (4.) The Carpathian Mountains in
the South of Poland. (5.) The Peak in Der-
byſhire in England. (6.) Plinlimmon in Wales,
&c. Befides feveral Volcano's, or Burning
Mountains, as Vefuvius and Stromboli in Na-
ples, Mount Etna, now called Mon-Gibel,
in the Iſland of Sicily, and Mount Hecla in
the cold Iſle of Iceland.
The principal Rivers of Note in Europe,
are the Thames and the Severn in England;
the Tay in Scotland; the Shannon in Ireland;
Tagus in Portugal and Spain; the Po and
Tiber in Italy; the Weifel or Viftula in Po-
land. In Germany, the Elbe and the Oder,
the Rhine and the Danube. In France, the
Seine
5
Sect. 14. Geography and Aftronomy.
79.
Seine and the Rhone. In Mofcovy, the Don
and the Volga.
The Danube and the Volga are the largeſt
Rivers in Europe, the Danube runningthrough
all Germany and Turky into the Euxine, or
Black Sea; and the Volga, (which fome Wri-
ters attribute to Afia, becauſe) though it runs
through a great Part of Mofcovy, yet it emp-
ties itſelf into the Cafpian Sea.
SECT. XIV.
Of ASIA, and its feveral Countries and
Kingdoms.
ASIA may be divided into theſe five
Parts, namely, Turky, Perfia, India,
China and Tartary.
The Dominions of the Turks in Aſia con-
tains feveral Countries in it, named Natolia,
Palestine, Arabia, Georgia, &c.
1. Natolia, or Afia Minor, which is a
Peninſula between the Euxine Sea and the
Mediterranean, where lay the antient Coun-
tries of Galatia, Cappadocia, Pontus, Bythi-
nia, Lyconia, Cilicia, Phrygia, Pamphylia,
&c. throughwhich the Apoſtle Paul travelled,
and made many Converts there. Here were
the ſeven famous Churches of Afia, to which
the Epiftles were written in the fecond and
third
80
Sect. 14.
The firft Principles of
third Chapters of the Revelation, namely,
Ephefus, Smyrna, Sardis, &c. Many of them
are now called by different Names: But
Smyrna is one of the chief Cities in the whole
Country.
2. Palestine, or the Holy Land, and all the
adjacent Countries of Syria, Chaldea, Mefo-
potamia, &c. The chief Towns in it now
are Aleppo, Scanderoon, or Alexandretta, Bag-
dat or Babylon, Damafcus, Jerufalem, &c.
3. Arabia, which anciently was divided
into Arabia the Happy, Arabia the Deſert,
and Arabia the Stony, lying all between the
Perfian Gulf, and the Red Sea: The chief
Towns of it are Mecca, Medina, &c.
4. Georgia and Turkomania, formerly call-
ed Armenia Major, are Northern Provinces
belonging to the Turks, that lie between the
Euxine and the Cafpian Sea.
Perfia, a large Empire, lies Eaſtward from
Turky between the Cafpian and Indian Seas :
Its capital City is Ifpahan.
India is divided in two Parts by the River
Ganges. India, on this Side the Ganges, con-
tains the biggeſt Part of the Empire of the
Great Mogul, whoſe chief City is Agra. In
a Peninſula or large Promontory in this Part
of India, are various Settlements of the Eu-
ropean Nations; as at Fort St. George, Tran-
quebar, Goa, &c. Beyond the River Ganges
lies another large Peninſula, which contains
the Countries of Pegu, Siam, Tunquin, Co-
chinchina, &c.
Eaſtward
Sect. 14.
81
Geography and Aftronomy.
'
Eaſtward of all theſe lies the Empire of
China, a large and a polite Nation, whofe
chief City is Pekin. Thefe Countries laft
named are called in general the East Indies.
Great Tartary takes up all the Northern
Part of Afa. That which borders upon
Mofcovy, is often called Mofcovy in Afia:
The whole is a favage, unpoliſhed, and un-
known Country, as to the Parts, as well as
the Inhabitants of it; and how far it reaches
to the North-Eaft, no Man in this Part of
the World can inform us.
There are Multitudes of Iſlands which be-
long to Afia, the chief of which are Japan,
Borneo, Celebes, Java, Sumatra, Ceylon, the
Philippine Iles, the Maldive Ifles, &c. all
thefe in the Eaſtern Ocean, and Cyprus in the
Mediterranean.
The moſt remarkable Rivers are Tigrus
and Euphrates in Turky, Ganges and Indus
in India, whence the whole Country took
its firft Name.
1
The chief Mountains are Imaus, Caucafus,
Ararat, which are but different Parts of the
long Ridge of Hills which runs through
Afia from the Weſt to the Eaſt, and is call-
ed by the ancient general Name of Mount
Taurus,
AS
SECT.
82
Sect. 15.
The first Principles of
0
SE C T. XV.
Of AFRICA, and its Divifions.
AFRICA is the Third Quarter of the
World: It may be divided into the fol-
lowing Territories; Egypt, Barbary, Bildul-
gerid, Zaara, Nigritia, Guinea, Ñubia, A-
byffinia and Ethiopia.
Egypt lies to the North Eaſt, and joins to
Afia; the chief Cities are Grand Cairo and
Alexandria.
Barbary is a long Country, it compre-
hends moft Part of the ancient Mauritania,
or the Country of the Moors; it lies along
the Coaſt of the Mediterranean Sea: Its
chief Towns are Fez, Morocco, Mechanefs,
Sallee, Tangier, Ceuta, Algier, Tunis, Tri-
poli and Barca.
Bidulgerid, or the ancient Numidia, has
its chief Town Dara; it lies South and
South Eaft of Barbary, unleſs it be reckon-
ed a Part of it.
Zaara comes next; it is a Defert Inland
Country, and much unknown. So is Ni-
gritia, or the Land of the Negroes, which
lies to the South of Zaara; as Guinea is fi-
tuated in the South of Nigritia. The Tooth
or Ivory Coaft, and the Quaque Coaft, and
the Gold Coaſt, are ſeveral Divifions of Gui-
nea well known to Mariners.
Nubia
1
Į
Sect. 15. Geography and Aftronomy.
83
1
Nubia lies Southward of Egypt, as Abyf-
finia does to the South of Nubia, both near
the Coaft of the Red Sea.
Ethiopia has been given as a general Name
to all the Countries that compoſe the South-
Eaft and South Part of Africa, at leaft, all
the Maritime Countries or Coafts from Gui-
nea, on the Weſtern Side to Abyffinia, or
Nubia on the Eaft, and fometimes it includes
Abyffinia alfo, which is called the Leffer or
Inner Ethiopia.
In the more Southern Part of Ethiopia,
are the Inland Kingdoms of Monomotapa,
Monoemunga, &c. On the Weſtern Coaſt,
Congo, Loango, Angola: The Eaſtern Coaſt
is Zanguebar and the Mozambique: The
Southermoſt Coaſt is inhabited by the Cafres
and the Hottentots, near the Cape of Good
Hope, who are remarkable for their Stupidity,
living in the moſt brutal and barbarous Man-
ner, as though they had little of human Na-
ture in them befide the Shape.
The chief Ilands near Africa are the
large Ifle Madagascar, called the Ifle of St.
Lawrence, that lies toward the Eaftern Sea;
and on the Weft or North-Weft are the
fmall Iſlands of Cape Verd, the Canary Iſlands,
and the Maderas in the Atlantick Sea, with
others of leffer Note in the Ethiopick Sea.
G
The
1
84
Sect. 16.
The first Principles of
The moſt famous Rivers in Africa are the
Nile and the Niger. The Nile runs through
all the Eaſtern Part of the Country, and emp-
ties itſelf into the Mediterranean Sea by ma-
ny Mouths at the Land of Egypt. The
River Senegal, anciently called Niger, runs
through Negroland into the Atlantick Ocean.
The moſt remarkable Mountains are thefe,
(1.) Mount Atlas, or the Atlantick Hills in
the Weft of Barbary, which were fuppofed.
by the Ancients to be the higheſt in the
World; whence came the Fable of Atlas a
Giant, bearing the Heavens upon his Shoul-
ders. (2.) The Mountains of the Moon,
which lie much more Southward toward Mo-
nomotapa: And (3.) The exceeding high
Hill of Teneriff, which is among the Canary
Iflands.
SECT. XVI.
Of AMERICA, and its Divifions.
MERICA is the Fourth and laſt Quar-
AM
ter of the World, it is divided into the
Northern and Southern Parts by an Ifthmus
or Neck of Land at Darien or Panama.
Northern America includes Canada, the
English Empire, Old Mexico, New Mexico,
Florida, and the Northern Land.
The
Sect. 16. Geography and Aftronomy.
85
The Northern Land contains fome Iſlands
and Settlements of European Nations, in
Hudson's Bay and other Coafts of Groenland,
Greenland, near to the Arctick Circle, but
few of them are much known, frequented,
or inhabited.
As for the North-Weft Part of North-
America, it is utterly unknown whether it
be Iſland or Continent, whether it may not
reach thouſands of Miles farther, and be joined
to the North-Eaft Part of Great Tartary.
Canada, or New France, lies on the North-
Eaſt Side of the River St. Lawrence, its chief
Town is Quebec*.
The English Empire in America lies along
the Eaſtern Coaſt from about thirty to almoſt
fifty Degrees of North Latitude.
New England is the chief Province, of
which Boſton is the principal Town or City.
North of New England lies Acadia, ſometimes
called New Scotland: Its chief Town was
Port Royal, which hath changed its Name to
Annapolis. Southward of New England lie
New York, New Jersey, Pennfilvania and Ma-
ryland, Virginia and Carolina. On the Weſt
and North-Weft Side of thefe Plantations, lie
large Tracts of Land with many great Lakes
in it, where various Nations of Savages inhabit.
Florida comes next in Courſe to be men-
tioned; it borders Eaft or North-Eaſtward
G 2
on
* Ganada was taken from the French, and ceded to
the British Empire at the Peace made in 1763.
1
86
Sect. 16.
The first Principles of
گھر "
}
1
on Carolina, and Weftward it reaches to the
River Miffifippi and beyond it: It is bounded
by the Sea on the South, but there have
been no very great or remarkable Towns or
Settlements formed there by the Spaniards,
who found and named it.
New Mexico, or New Granada, lies Weft
of Florida *, poffeffed alfo by the Spaniards ;
its chief Town is St.Fe, upon the River Nort.
Mexico, or New Spain, lies more South,
it is a large and rich Country, long and un-
even, ftretching from North-Weft to South-
Eaft; and contains many Provinces in it be-
longing to the Spaniards, who have deſtroy-
ed Millions of the Natives there. It has fe-
veral Towns, of which the chief has the
Name of Mexico given it. Florida and Mex-
ico together makes a large Bay, which is call-
ed the Gulf of Florida, or the Gulf of Mexi-
co. This Country reaches down to the ſmall
Neck of Land whereby South America is
joined to it.
On this Neck of Land are Pa-
nama on the South Side, and Porto Bello on
the North.
The Southern Part of America is fome-
thing like a large Triangle lying on the vaſt
Southern Ocean, and almoſt encompaffed by
it: On the Weftern Side this Ocean is called
the Pacifick Sea, becauſe feldom vexed with
Storms.
1
* Ceded alſo to the British Empire in 1763.
This
Sect. 16. Geography and Aftronomy.
87
This Southern Part of America compre-
hends many great Countries, namely, Terra
Firma, Peru, Amazonia, Guinea, Brafil,
Chili, Paraguay, Terra Magellanica, &c. The
Inland Parts are very much unknown, but
the greateſt Part of the Coaſts are poffeffed
by the Inhabitants derived from Spain and
Portugal, who have made various Settle-
ments there.
The chief Iſlands of America in the North
are Newfoundland, which is a Triangle near
Acadia; then Cuba, Hifpaniola, and Ja-
maica, all in the fame Climate with Mexico.
The leffer Iſles are called Lucayes, or Bahama
Ilands, South-Eaſt of Florida; and the Ca-
ribbee Islands Eaftward of Hifpaniola. On
the Weft Side of North America lies a very
large and long Iſland, called California, with
many little ones near it.
The chief fland in South America is Terra
Delfuego, which lies near the main Land,
and thus makes the Straits of Magellan.
There are many others of lefs Extent and
Note, both on the Coaſt, and in the vaſt
South Sea.
The most noted Rivers of North America,
are the great River St Lawrence, that di-
vides Canada from New England; and the
River Miffippi, where the French have
made large Settlements.
G
3
In
!
88
Sect. 17.
The first Principles of
In South America the two great Rivers are
the Amazon with all its Branches, and Rio
de la Plata, or the River of Plate.
The chief Mountains are the Apalachian
Hills in North America, which divide Florida
from the more Northern Countries; and the
Andes in South America; which is a long
Ridge of Mountains running from the South
Part of America toward the North: Travel-
lers ſuppoſe them to be the higheſt in the
World.
Thus I have deſcribed the various Coun-
tries of the Earth in a very brief but imper-
fect manner, ſufficient only to give the young
and ignorant Reader a Taste of Geography,
and to encourage him to purſue the Study
farther in that excellent Manual, Gordon's
Geographical Grammar, or in Volumes of
larger Size.
SE C T. XVII,
Of the Fixed Stars on the heavenly Globe.
As
S the Terreftrial Globe has the various
Countries, Cities, Mountains, Rivers,
and Seas drawn upon it: So on the Celestial
Globe are placed the fixed Stars exactly ac-
cording to their Situation in the Heavens.
Yet there is this Difference between the
Repreſentations made by the Heavenly and
thofe
2
Sect. 17. Geography and Aftronomy.
89
thoſe made by the Earthly Globe, namely,
That the feveral Countries, Rivers and Seas,
are reprefented on the Convex or outward
Surface of the Earthly Globe, juſt as they
lie naturally on the Convex Surface of the
Earth: Whereas the Stars naturally appear
to us in the Concave, or inward hollow Sur-
face of the Heaven, but they are repreſented
on the Heavenly Globe on the Convex Sur-
face of it. Therefore we muſt ſuppoſe our
Eye to be placed in the Centre of the Globe,
in order to have the Stars and Heavens ap-
pear to us in their Concavity and proper Si-
tuation.
Planets and Comets are vulgarly called by
the general Name of Stars; but the fixed
Stars differ from the Planets and the Comets
in this, that they always keep the fame
Place or Diſtance with regard to one ano-
ther; whereas the Planets and Comets are
perpetually changing their Places and Dif- -
tances with regard to one another, and with
regard to the fixed Stars.
They differ alfo in this Reſpect, that the
fixed Stars generally twinkle, except when
near the Zenith, or feen through a Teleſcope;
and they ſhoot ſprightly Beams like the Sun;
which is ufually given as a Proof, that like
the Sun they ſhine with their own Light:
The Planets have a more calm Afpect like
the Moon, and never twinkle, which is
G 4
one
90
Sect. 17.
The first Principles of
}
one Argument among many others that they
derive their Light from the Sun, and fhine
only by Reflection.
For our better Acquaintance with the fix-
ed Stars, Aftronomers have reduced them to
certain Conftellations. This we have fhewn
already in the fecond Section, concerning
thofe Stars that lie in the Zodiack, which are
reduced to 12 Conſtellations, and called the
Twelve Signs, namely, Aries, or the Ram,
Taurus or the Bull, Gemini or the Twins, &c.
The reſt of the Stars are diftinguiſhed into
the Northern and Southern Conſtellations,
as lying North or South of the Zodiack or
Ecliptick.
;
The Northern Conftellations were thus
framed by the Ancients, Urfa Minor, or the
little Bear, in whofe Tail is the Pole Star;
Urfa Major, or the great Bear; Draco, or
the Dragon; Cepheus, whofe Feet are juſt at
the North Pole: Caffiopeia and her Chair
Andromeda, the Northern Triangle, Perfeus
with Medufa's Head, Auriga or the Chario-
teer, Bootes or the Hunter, who is fometimes
called Arcturus, or the Bear-keeper; Corona
Borealis, or the Northern Crown; Egonafi,
or Hercules kneeling; Lyra, or the Harp;
Cygnus, or the Swan; Pegafus, or the great
flying Horfe; Equuleus, or Equiculus, the
little Horfe's Head; Delphinus, or the Dol-
phin; Sagitta, or the Arrow; Aquila, or the
Eagle,
Sect. 17. Geography and Aftronomy.
91'
1
Eagle, which fome call the Vulture; Serpens,
or the Serpent, and Serpentarius the Man
who holds it.
To theſe 21 Northern Conftellations were
afterwards added Antinous at the Equator,
next to the Eagle, Cor Caroli, or King Charles's
Heart, a fingle Star South of the Great Bear's
Tail, and Bernice's Hair, a few fmall Stars
South of Charles's Heart, &c.
The Southern Conftellations known to the
Antients, are, Cetus the Whale, and the Ri-
ver Eridanus; Lepus the Hare; the glorious
Conftellation of Orion with his Girdle, Sword
and Shield; Sirius, or the great Dog; Cani-
cula, or the little Dog; Hydra, or the large Ser-
pent; the Ship Argo, Crater or the two-hand-
ed Cup; Corvus, the Crow, or the Raven;
Centaurus, or the Half-Man, Half-Horfe
Lupus, or the Wolf; Ara, or the Altar; Co-
rona Auftralis, or the Southern Crown; Pifcis
Notius, or the Southern Fiſh.
To thefe 15 there have been added 12
other Conftellations made up of the fixed
Stars toward the South Pole, which are ne-
ver vifible to us in Britain, and therefore I
fhall not mention them.
Aftronomers have framed foine leffer Con-
ftellations which are contained in the greater;
as the Pleiades, or the Seven Stars; and the
Hyades in Taurus, or the Bull; Capella, or
the Goat, in which is a very bright Star
fo
92
The first Principles of Sect. 17.
fo called, in the Arms of Auriga, or the Cha-
rioteer: The Manger and Affes in the Crab,
which indeed is nothing but a bright Spot
compofed of a Multitude of fmall Stars;
Charles's Wain, which are feven bright Stars
in the Rump and Tail of the Great Bear,
three of which in the Tail reſemble the Horſes,
and the other four, c, d, b, r, a Square
Cart: See Figure xxx. The two hindmoſt
Stars in the Cart, namely, b and r, are called
the Pointers, becauſe they point to the
North Pole p.
Befides theſe there are feveral other ſmaller
Stars fcattered up and down in the Heavens,
which are not reduced to any of the Conftel-
lations; though of late Years Hevelius, a
great Aftronomer, has made Conftellations
of them, which are defcribed upon fome
modern Globes.
The fixed Stars are of different Sizes, and
are divided into thofe of the firft, fecond, third,
fourth, fifth, and fixth Magnitudes.
There are but a few Stars of the first and
fecond Magnitude, and many of them have
remarkable Names given to them; as the
Ram's Head; Aldebaran, or the Bull's Eye ;
Capella, or the Goat; the three Stars in Orion's
Girdle; the Lion's Heart; Deneb, or the
Lion's Tail; Regel, the Star in Orion's left
Foot; Spica Virginis, which is an Ear of Corn
in the Virgin's Hand, Hydra's Heart, the
Scor-
1
93
Se&t. 17. Geography and Aftronomy.
Scorpion's Heart; the Eagle or Vulture's
Heart; Ala Pegafi, or the Horfe's Wing;
Fomahant, a large Star in the Southern Fish's
Mouth near Aquarius; the Pole Star in the
Little Bear's Tail, &c. See more in the Ta-
ble of fixed Stars at the End of this Book.
Some remarkable Stars are called by the
Name of the Conſtellation in which they
are, as the Great Dog, the Little Dog, Ly-
ra, or the Harp, Arcturus the Bear-keeper,
Capella the Goat, &c.
As the Globe of the Earth, with all the
Lands and Seas defcribed on a Terreſtrial
Sphere is reprefented on Maps, fo the Ce-
leftial Sphere, with all the fixed Stars, is often
repreſented on two Tables, or Planifpheres,
projected, one on the Plane of the Equator,
with the two Poles of the World in their
Centres; and the other on the Plane of the
Ecliptick, with the Poles of the Ecliptick
in their Centres *
Note, This fort of Projections have ſome-
times been furniſhed with fome little Ap-
pendices which are moveable, and makes an
Inftrument called a Nocturnal, to take the
Hour of the Night, and perform many other
Aftronomical Problems by the Stars.
It is hardly neceffary to fay, that the
Stars are ſuppoſed to keep their conftant
Revo-
* Mr. Senex, at the Globe, over-againſt St. Dunstan's,
in Fleet-ſtreet, printed the beſt that ever were in England,
or perhaps in any other Country.
8
94 The first Principles of ·
1
Sect. 17.
Revolution once in twenty-four Hours by
Day as well as by Night: But the Day-Light
conceals them from our Eyes.
The Sun in its annual Courſe moving from
Weſt to Eaſt through all the Signs of the
Zodiack, hides all thofe Stars from our Sight
which are near its own Light or Place in the
Heavens; and therefore at ſeveral Seaſons of
the Year you fee different Stars or Conftella-
tions rifing or ſetting, or upon the Meridian
at every Hour of the Night: And as the Sun
goes onward daily and monthly toward the
Eaft, the Eaſtern Conftellations come daily
and monthly within the Reach of the Sun-
Beams, and are concealed thereby, which is
called their Setting Heliacally.
Heliacally. And the
Weſtern Conſtellations hereby getting farther
off from the Sun-Beams, are made vifible to
us, which is called Rifing Heliacally.
Thus, as I intimated before, we may
eafily find what Stars will be upon the Me-
ridian every Midnight, by confidering in
what Sign the Sun is, and in what Degree of
that Sign; for the Sun, with the Stars that
are near it, being upon the Meridian at Noon,
the Stars that are directly oppofite to them in
the Heavens will be upon the Meridian that
Day at Midnight. And by the fame Means,
if you obſerve what Stars are upon the Meri-
dian at Midnight, you eafily infer the Sun is in
the oppofite Point of the Heavens at Midnoon.
Here
Sect. 18. Geography and Aftronomy.
95
i
Here it ſhould not be forgotten, that there
is a broad uneven Path incompaffing the Hea-
vens, paffing near the North Pole, which is
brighter than the reft of the Sky, and may
be beſt feen in the darkest Night; this is
called the Milky Way, which later Philofo-
phers have found by their Teleſcopes to be
formed by the mingled Rays of innumerable
finall Stars. It is to the fame Cauſe that
ſome other bright Spots in the Sky (though
not all) are afcribed, which appear to us like
whitish Clouds in Midnight Darkneſs.
SECT. XVIII.
Of the Planets and Comets.
THOUGH the Planets and Comets are
never painted upon the Globe, becauſe
they have no certain Place, yet it is neceſ-
fury here to make fome mention of them;
fince they are Stars much nearer to us than
the fixed Stars are, and we know much more
of them.
The Planets are in themſelves huge dark
Bodies which receive their Light from the
Sun, and reflect it back to us. They are
called Planets from a Greek Word, which
fignifies
1
96
Sect. 18.
The firft Principles of
fignifies Wanderers; because they are always
changing their Places in the Heavens, both
with regard to the fixed Stars, and with re-
gard to one another.
The Planets are placed at very different
Diſtances from the Centre of our World,
(whether that be the Earth or the Sun) and
they make their various Revolutions through
the twelve Signs of the Zodiack in different
Periods of Time..
Saturn
Jupiter
Mars
in 29 Years and 167 Days, i. e. about 24 Weeks.
→ Earth or Sun in
Venus
Mercury
Moon
in II
in
I
314
321
45
46
I
O
in
224
32
in
87
121
in o
27 1/2
4
As the Ecliptick Line is the Orbit or An-
nual Path of the Earth or Sun, fo each Pla-
net has its proper Orbit, whofe Plane differs
fome few Degrees from the Plane of the Or-
bit of the Sun, and to a Spectator's Eye pla-
ced in the Centre would interfect or cut the
Sun's Orbit at two oppofite Points or Nodes.
Now the Diſtance of a Planet from the Eclip-
tick, meaſured by an Arch perpendicular to
the Ecliptick, is the Latitude of that Planet,
as before.
To reprefent this as in Figure x1. you
may imagine as many Hoops as there are Pla-
nets thruſt thro' with feveral ftraight Wires,
and thereby joined in different Places to the
Hoop
1
Sect. 18. Geography and Aftronomy.
97
Hoop that repreſents the Plane of the Ecliptick,
that is, the Sun's or Earth's Orbit; and then
let theſe Hoops be turned more or lefs oblique-
ly from the Plane of the Ecliptick: For all
the feveral Orbits or Paths of the Planets do
not croſs or interfect the Ecliptick or Sun's
Path in the fame Point, nor at the fame An-
gles But their Nodes or Interfections of the
Ecliptick are in different Parts of the Eclip-
tick, and alſo make different Angles with it.
Among the feveral Uſes of obſerving the
Latitude of a Planet, fee one very neceſſary
in Problem XXXVII.
The Comets were by Ariftotle and his Fol-
lowers fuppofed to be a fort of Meteors or
Fires formed in the Sky below the Moon,
continuing for fome Months, and then vaniſh-
ing again. But by later Aftronomers they
have been found to be dark Bodies like the
Planets, moving through the Heavens with-
out any regard to the Ecliptick, but in very
different Orbits, which are ſuppoſed to be
Ellipfes or Ovals of prodigious Length, and
returning at various Periods of feveral fcores
or hundreds of Years. Though it must be
confeffed, thofe Parts of their Orbits which
are within the Reach of our Sight, are fo very
inconfiderable Parts of the vaft Ovals they
are ſaid to deſcribe, that it has been much
doubted, whether the Lines they defcribe
in their Motion be not Parabolical, or fome
other
1
"
98
Sect. 18.
The first Principles of
other infinite Curve; and thus whether the
Comets themſelves are not wandering Stars
that have loft all regular Revolution, and
perhaps have no fettled Periods at all, and
may never return again: But Comets appear
ſo ſeldom, that they have ſcarce given the
nice Enquirers of theſe laft Ages fufficient
Opportunity to obferve or calculate their
Motions with fuch an abfolute Certainty as
could be wifhed.
Thus I have finiſhed the fpeculative Part
of this Difcourfe, which contains the Rudi-
ments, or firft Principles of Aftronomy : It
is called the Spherical Part, becauſe it treats
of the Doctrine and Ufe of the Sphere; and
I have concluded therein the general Part of
Geography, and given a flight Survey of the
particular Divifions of the Earth.
It is indeed the Second or Special Part of
Geography, that treats properly of theſe
par-
ticular Divifions of the Earth, which I have
but flightly run over, and in a much larger
manner enumerates' not only all the King-
doms, States, and Governments of the World,
but alſo gives fome Account of their Man-
ners, Temper, Religion, Traffick, Manu-
factures, Occupations, &c. It alſo deſcribes
the various Towns and Villages, the larger
and leffer Mountains, Rivers, Forefts, the
feveral Products of every Country, the Birds,
Beafts,
Sect. 18. Geography and Aftronomy.
99
Beaſts, Infects, Fiſhes, Plants, Herbs, the
Soil, Minerals, Metals, and all Rarities of
Art and Nature: It relates alfo the various
ancient and modern Names of the Nations,
Cities, Towns, Rivers, Iſlands, &c. What
remarkable Occurrences of Battles, Victories,
Famine, Defolations, Prodigies, &c. has
happened in every Nation, and whatſoever
has rendered it worthy of public Notice in
the World.
There are many Books extant in the World
on this Subject; ſome of leffer Size, ſuch as
Gordon's Geographical Grammar, Chamber-
lain's Geography; and larger, namely, Morden's
Geography Rectified, in Quarto, Thefaurus Geo-
graphicus, Moll's Geography, in Folio, &c.
The Second or Special Part of Aftronomy,
is called the Theory of the Heavens, or the Sun
andPlanets; which will lead us into theKnow-
ledge of a thouſand beautiful and entertaining
Truths concerning the Syftem of the World,
the various Appearances of the Heavenly Bo-
dies, and the Reaſons of thofe Appearances,
namely, a more particular and exact Account
of the Day and Night; and of the ſeveral
Seaſons of the Year, Spring, Summer, Autumn,
and Winter; of the Length and Shortness of
the Days: Why in the Winter the Sun is
nearer to us than it is in the Summer, and
why the Winter Half-Year is feven or eight
H
Days
1
......
100
The first Principles of Sect. 18.
1
Days fhorter than the Summer Half-Year:
Whence come the Eclipfes of the Sun and
Moon, both total and partial; why the Moon
is only eclipfed when ſhe is full, and the Sun
only when ſhe is new: Whence proceed the
different Phaſes of the Moon, as the New or
Horned Moon, the Half-Moon, the Full, &c.
Why the two lower Planets, Mercury and Ve-
nus, always keep near the Sun, and never move
fo far as two whole Signs from it: Why Venus
is horned, halved and full, as the Moon is:
Why the three fuperior Planets, Mars, Jupiter
and Saturn, appear at all Diſtances from the
Sun, and are fometimes quite oppofite to it:
Why both the upper and lower Planets fome-
times appear ſwifter, fometimes flower: Why
they ſeem ſometimes to move directly, or
forward, fometimes retrograde, or backward,
fometimes are ftationary, or feem to ftand
ſtill: Why they are fometimes nearer to the
Earth, which is called their Perigeum, and
fometimes farther from the Earth, which is
called their Apogeum, and by this Means ap-
pear greater or leſs. Why they are nigher to,
or farther from the Sun, which is called their
Perihelion and Aphelion; and in what Part of
their Orbits this Difference falls out: How
it comes to paſs that they ſeem higher in the
Horizon than really they are, by Refraction;
and how again they feem lower than they
really are, by the Parallax.
In
í
|
t
Sect. 18. Geography and Aftronomy.
IOI
In this Part of Aſtronomy it is proper alfo
to fhew the different Schemes or Hypothefes
that have been invented to folve or explain
all theſe Appearances of the Heavenly Bodies.
Here the Ptolemaic or ancient Syſtem ſhould
have the firſt Place, to reprefent how the
Antients placed the Earth in the Centre of
the World, and fuppofed the Sun to move
round it amongſt the other Planets, as it ap-
pears to the vulgar Eye; and what tedious
and bungling Work they made by their Con-
trivance of folid transparent Spheres of dif-
ferent Thickneſs, placed in Eccentric Order,
and affifted by their little Epicycles: What
infinite Embarraffments and Difficulties at-
tend this rude and ill adjuſted Contrivance ;
and how impoffible it is to folve all the Ap-
pearances of Nature by this Hypothefis.
Then the Modern or Copernican Scheme
fhould be repreſented, which makes the Hea-
ven all void, or at least filled only with very
fine Ethereal Matter; which places the Sun
in the Centre of our World, with all the
Planets whirling round it; which makes the
Earth a Planet, turning daily round its own
Axis (which is the Axis of the Equator) to
form Day and Night; and alſo carried yearly
round the Sun in the Ecliptick, between the
Orbits of Venus and Mars, to form Summer
and Winter. This Scheme alfo makes the
Moon a Secondary Planet, rolling monthly round
H 2
the
102 The first Principles of Sect. 18.
}
the Earth, and carried with it in its yearly
Courſe round the Sun, whereby all the Va-
riety of Appearances of the Sun and Moon,
and of all the Planets, as well as the Dif-
ferences of Day and Night, Summer and
Winter, are refolved and explained with the
greateſt Eaſe, and in the moſt natural and
fimple manner.
Here alſo it ſhould be fhewn, that as the
Moon is but a Secondary Planet, becauſe it
moves round the Earth, which is itſelf a
Planet: So Jupiter, which moves round the
Sun, has alfo four Secondary Planets, or Moons,
moving round it, which are ſometimes called
his Satellites, or Life-Guards; Saturn alfo
has five fuch Moons, all which keep their cer-
tain Periodical Revolutions: And befide thefe,
Saturn is incompaffed with a large Flat Ring,
21000 Miles broad, whofe Edges ſtand in-
ward toward the Globe of Saturn, (like a
wooden Horizon round a Globe) at about
21000 Miles Diſtance from it, which is the
moſt amazing Appearance among all the hea-
venly Bodies: But theſe Secondary Planets,
which belong to Jupiter and Saturn, toge-
ther with this admirable Ring, are vifible only
by the Affiſtance of Teleſcopes: And yet Ma-
thematicians are arrived at fo great an Exact-
neſs in adjuſting the Periods and Diſtances of
thefe Secondary Planets, that by the Motions.
and Eclipfes of the Moons of Jupiter, they
find
Sect. 18. Geography and Aftronomy.
103
find not only the true Swiftneſs of the Motion
of Light or Sun-beams, but they find alſo
the Difference of Longitude between two
Places on the Earth.
It may be manifefted here alfo, that fe-
veral of the Planets have their Revolutions
round their own Axis in certain Periods of
Time, as the Earth has in 24 Hours; and
that they are vaſt bulky dark Bodies, fome
of them much bigger than our Earth, and
confequently fitted for the Dwelling of fome
Creatures; ſo that it is probable they are all
Habitable Worlds, furniſhed with rich Variety
of Inhabitants, to the Praiſe of their great
Creator. Nor is there wanting fome Proof
of this from the Scripture itſelf. For when
the Prophet Iſaiah tells us, that God who
formed the Earth, created it not in vain, be-
cauſe be formed it to be inhabited, Ifa. xlv. 18.
He thereby infinuates, that had ſuch a Globe
as the Earth never been inhabited, it had been
created in vain. Now the fame Way of Rea-
ſoning may be applied to the other Planetary
Worlds, fome of which are fo much bigger
than the Earth is, and their Situations and
Motions feem to render them as convenient
Dwellings for Creatures of fome Animal and
Intellectual Kind.
Many of thefe Things have been performed
by ingenious Men with great Exactneſs, for
the Uſe of Perfons learned in the Mathe-
H 3
matics;
104 The First Principles of Sect. 19.
matics; but I know not any ſhort, plain,
and intelligible Account of them fitted for the
Ufe of the unlearned World, except among
Dr Wells's Volumes, intitled, Mathematics for
a young Gentleman: Yet I perfuade myfelf,
that fome Parts of it might be performed
with greater Eafe and Clearnefs, in a more
natural Method, and to much greater Per-
fection, if ſome Perfon of peculiar Skill in
theſe Sciences, and of equal Condefcenfion,
would undertake the Work,
?
7
SE C T. XIX.
Problems relating to Geography and Aftro-
nomy to be performed by the Globe.
AS Theorems in Mathematic Sciences are
certain Propofitions declaring fome Ma-
thematical Truth: So a Problem is a Mathe-
matical Queſtion propofed to be refolved, or
fome Practice to be performed.
Becauſe this Problematic Part will require
the Recollection of a great many Things in
the former Sections, I think it may not be
improper to give a fhort Summary of Defi
nitions of the chief Subjects of Diſcourſe in
the
1
Sect. 19.
Geography and Aftronomy.
105
the Doctrine of the Sphere, and ſet them in
one View.
DEFINITION S.
The Latitude of a Place on the Earthly
Globe, is the Diſtance of the Zenith of that
Place from the Equator toward the North
or South Pole, meaſured by the Degrees of
the Meridian.
The Elevation of the Pole is the Height
of the Pole above the Horizon of that Place,
meafured on the Meridian : And it is always
the fame Number of Degrees as the Lati-
tude.
The Longitude of a Place is the Diſtance
of it toward the Eaft or Weft from fome
firft Meridian, and it is meaſured on the
Equator.
The Declination of the Sun, or any Star or
Planet, is its Diſtance Northward or South-
ward from the Equator, meaſured on the
Meridian. It is the fame Thing as Latitude
on the Earthly Globe.
The Right Afcenfion of the Sun, is its Dif-
tance from that Meridian that cuts the Point
Aries, meaſured Eaſtward on the Equator;
it is much the fame with Longitude on the
Earthly Globe.
The Hour of the Sun, is its Diſtance from
Noon, or the Meridian of the Place meaſured
H 4
on
106
Sect. 19.
The first Principles of
i
1
on the Equator by 15 Degrees, for every 15
Degrees on the Equator make an Hour. Or
it may be reckoned from the oppofite Meri-
dian, or Midnight.
Note, The Right Afcenfion is reckoned ei-
ther in Degrees or in Hours.
The Latitude of a Star or Planet is its Dif-
tance Northward or Southward from the
Ecliptick: Note, The Sun has no Latitude,
becauſe it is always in the Ecliptick.
The Longitude of the Sun, or a Star, is its
Diſtance from the Point Aries Eaſtward, mea-
fured on the Ecliptick. But with regard to
the Sun or a Planet, this is ufually called the
Place of the Sun, or Planet, for any parti-
cular Day, that is, its Place in the Zodiack,
or the Degree of the Sign in which it is at
that Time.
The Altitude or Height of the Sun, or a
Star, is its Diſtance from and above the Ho-
rizon, meaſured on the Quadrant of Alti-
tudes.
The Depreſſion of the Sun or a Star, is its
Diſtance from and below the Horizon.
The Azimuth of the Sun, or a Star, is its
Diſtance from the Cardinal Points of Eaft,
Weft, North or South, meaſured in the Ho-
rizon.
The Sun or Stars Meridian Altitude is its
Altitude or Height when it is on the Meri-
dian, or at the South,
The
1
1
:
Sect. 19. Geography and Aftronomy.
107
The Vertical Altitude of the Sun is uſed by
fome Writers for its Height above the Hori-
zon, when it is in the Azimuth or Vertical
Circle of Eaft or Weft. But the Sun is faid
to be Vertical at any Place, when it is in the
Zenith of that Place at Noon.
The Amplitude of the Sun, or a Star is its
Azimuth or Diſtance from Eaft or Weſt at
rifing or ſetting.
The Afcenfional Difference is the Time of
the Sun or Star's rifing or fetting before or
after Six o'Clock: Or it is the Difference
between the Sun or Star's femidiurnal Arc and
a Quadrant, or 90 Degrees, as fome Perfons
exprefs it, becauſe go Degrees, or a Quadrant,
reaches from 6 o'Clock to 12.
1
1
1
PROBLEM S.
Problem I. To find the Longitude and
Latitude of any Place on the Earthly Globe.
Turn the Globe about till the Place come
juſt under the Side of the brazen Meridian
on which the Figures are, which is called
its Graduated Edge, then the Degree marked
on the Meridian juft over the Place, fhews
the Latitude either North or South: And
the Globe ſo ſtanding, that Degree of the
Equator, which is cut by the Meridian,
ſhews the true Longitude of the Place. So
London
|
108 The firft Principles of Sect. 19.
{
1
2
London will appear to have 51 Degrees of
511
North Latitude, and near 18 Degrees of Lon-
gitude, counting the firſt Meridian at Tene-
riff. So Rome has 412 Degrees of North
Latitude, and about 13 Degrees of Longitude
Eaſtward from London, or almoſt 31 De- .
grees from Teneriff
Problem II. The Longitude or Latitude
of any Place being given, how to find that
Place on a Globe or Map.
If only the Latitude of a Place be given,
the Place itſelf may be eaſily found, by cafting
your Eye Eaſtward and Weftward along that
Parallel of Latitude in that Part of the World
where it lies, and the Place (if it be marked
on the Globe) will foon appear.
着
​If the Longitude only were given, guide
your Eye along that Meridian Northward
or Southward, and you will quickly fee it.
But if both Longitude and Latitude be
given, then the Place is immediately found;
for where the given Line of Longitude, or
Meridian, cuts the given Line of Latitude,
there is the Place required. The two Pro-
blems alſo may be practiſed on a Map as well
as on a Globe.
/
Problem III. To find the Distance of any
two Places of the Earthly Globe, or two Stars
on the Heavenly.
6
Here
Sect. 19. Geography aud Aftronomy.
109
1
Here let it be noted, that a Degree of the
Meridian, or of the Equator, or of any great
Circle on the Earthly Globe, is found by
Meaſure to be 69%, or 70 English Miles:
See Prob. XII. Sect. XX. Though Geo-
graphers many Times count 60 Geographical
Miles to a Degree, making them the fame
with the Minutes of a Degree, for the greater
Eaſe in Computation.
Let it be noted alfo, that all the Degrees
on the Meridians or Lines of Longitude on the
Globe are equal, becauſe all thoſe Lines are
great Circles; but in the Parallels of Lati-
tude, the farther you go from the Equator,
the Circle grows lefs and lefs, and confe-
quently the Degrees of thofe Circles are lefs
alfo: And therefore if two diftant Places are
either both on the Equator, or have the fame
Meridian, the Number of the Degrees of
their Diſtance on the Equator, or on the Me-
ridian, being reduced to Miles, fhews you
their true Diftance: But if the two Places
are not both on the Equator, nor on the fame
Meridian, you must find their true Diftance
by the following Method.
To perform this third Problem, lay the
Quadrant of Altitude from one Place to the
other, and that will fhew the Number of
Degrees of Diſtance, which being multi-
plied by 60 Geographical Miles, or by 70
Engliſh Miles, will give the Diſtance fought.
Or
110
Sect. 19.
The firft Principles of
Or you may take the Diſtance between
the two Places with a Pair of Compaffes,
and meaſure it upon the Equator, which
ſhews the Diſtance in Degrees, and then re-
duce them to Miles.
The Quadrant of Altitudes, or a Pair of
Compaffes, in the fame Manner, will ſhew
the Diſtance of any two Stars on the Hea-
venly Globe, namely, in Degrees, but not in
Miles.
Obferve here, that though theſe Methods
will find the true Diſtance of Places on the
Globe, yet on a Map the fame Methods are
uſeleſs; becauſe in Maps or plain Surfaces
the Degrees of Longitude marked on the
fame Parallel of Latitude are unequal, and
fo the Degrees of Latitude marked on the
fame Meridian are often unequal. (See the
XIth Section concerning Maps.) The only
Way therefore of meaſuring Diſtances on a
Map, is to meaſure the Number of Degrees
on the neareſt correfpondent Line of Longi-
tude or Latitude, and apply that to the Dif
tance required, which after all is but an un-
certain Account.
Problem IV. To find the Antœci, Periœci,
and Antipodes, of any Place given, ſuppoſe
of London.
Bring
Sect. 19. Geography and Aftronomy.
III
Bring London to the Meridian, obſerve its
Latitude Northward, then reckon ſo many
Degrees on the Meridian from the Equator
Southward, and it fhews the Place of the
Antæci.
Keep London under the Meridian, ſet the
Hour Index or Pointer on the Dial at the
Pole to the upper 12 which is 12 o'clock at
Noon, turn the Globe about till the Index
point to 12 at Midnight, and the Place that
will be under the fame Degree of the Me-
ridian where London was, fhews where the
Periaci dwell.
The Globe ſo ſtanding, count the fame
Degrees of Latitude from the Meridian South-
ward, and that will fhew who are the Anti-
podes to London.
Problem V. Any Place being given, to find
all thofe Places which have the fame Hour of
the Day with that in the given Place.
All the Places that have the fame Longi-
tude have the ſame Hour. Bring the given
Place therefore to the Brazen Meridian, and
obferve what Places are then exactly under
the graduated Edge of the Meridian, for
the People in thofe Places have the fame
Hour, and their Habitation has the fame
Longitude.
1
Problem
II2 The first Principles of Sect. 19.
1
Problem VI. Any Place being given (ſup-
pofe Paris) to find all thofe Places in the
World which have the fame Latitude, and
confequently have their Days and Nights of
the fame Length.
Bring Paris to the Meridian, and you find
it near 49 Degrees North Latitude, Turn the
Globe all around, and all thofe Places which
pafs under the 49th Degree of the Meridian,
have the fame Latitude with Paris, and the
Pole is just as much elevated above their
Horizon, namely, 49 Degrees.
Problem VII. To rectify the Globe accord-
to the Latitude of any given Place.
Elevate the proper Pole (whether it be
North or South) fo far above the Horizon as
is the Latitude of the Place propoſed; this is
done by moving the Pole of the Globe up-
ward from the Horizon, counting by the De-
grees of the under Part of the Meridian,
which begin to be numbered from the Pole;
thus for London you muſt raiſe the Pole 51
Degrees above the Horizon.
1/1/1
Then while London ftands under the Me-
ridian, the true and real Situation of it is ex-
actly reprefented on the Globe with its
proper
Horizon: For London is by this Means
placed in the Zenith, or on the very Top of
the Globe, at go Degrees Diſtance from the
Horizon
Sect. 19. 113
1
Geography and Afronomy.
1
Horizon every Way; and thus the Zenith is
as high above the Equator on the South Side,
as the Pole is above the Horizon on the North
Side.
To render this Repreſentation of the Si-
tuation of any Place yet more perfect, it is
a uſeful Thing to have a fmall Mariner's
Compass at hand, with a Needle touched
with a Loadſtone, to fhew which are the
North or South Points of the real Horizon,
and then, as near as you can, fet the Brazen
Meridian of the Globe exactly North and
South.
Thus the wooden Horizon will be a perfect
Parallel to the real Horizon, the brazen Me-
ridian to the real Meridian, the Equator, the
Ecliptick, and all the leffer Circles, and the
Points on the Globe, will reprefent thofe Cir-
cles and Points on the Earth, or in the Hea-
vens, in their proper Pofition.
Problem VIII. The Hour being given in
any Place (as at London) to find what Hour
it is in any other Part of the World.
Rectify the Globe for London, bring the
City of London to the Side of the Meridian
where the Degrees are marked; then fix the
Index of the Dial-plate to the Hour given,
(fuppofe Fouro'Clock in the Afternoon) this
being done, turn the Globe, and bring any
Places fucceffively to the Meridian, then the
Index
114
Sect. 19.
The first Principles of
R
Index or Hour Pointer will fhew the true
Hour at the Place required. Thus when it is
Four o'clock in the Afternoon at London, it
is almoſt Five at Rome, near Six at Conftan-
tinople, it is almoſt half an Hour paft Nine at
Night at Fort St. George in the Eaſt Indies,
it is near Midnight at Pekin in China, it is
Eleven o'clock in the Morning at Jamaica,
and a little paſt Noon at Barbadoes.
Problem IX. To rectify the Globe for the
Zenith.
After the former Rectification for the Lati-
tude of the Place, faſten the Edge of the Nut
of the Quadrant of Altitude on its graduated
Side, at the proper Degree of Latitude on the
graduated Side of the brazen Meridian, and
that will repreſent the Zenith of that Place in
the Heavens.
The Quadrant of Altitude being thus faſt-
ened, ferves to meaſure the Sun or Star's Al-
titude above the Horizon, and the Sun or
Star's Azimuth; and it has been fometimes
(though erroneously) uſed to fhew the Bear-
ing of one Place to another, as in the follow-
ing Problem.
Problem X. Any two Places being given,
to find the Bearing from one to the other; that
is, at what Point of the Compaſs the one
lies in reſpect to the other.
The
1
Sect. 19. Geography and Aftronomy.
115
>
The commonWay whereby feveral Writers
have folved this Problem is this. Rectify
the Globe both for the Latitude and for the
Zenith of one of thofe Places, and bring that
Place to the Zenith. Then bring down the
Edge of the Quadrant of Altitude to the other
Place, and the End of the Quadrant ſhall cut
the Horizon in the true Point of the Com-
paſs, and fhew how the one bears to the
other. So if you rectify the Globe for the
Latitude and Zenith of Barbadoes, you will
find that Cape Finiſterre in Spain, and Azoff
in Muscovy, both lie in a direct Line North-
Eaft from Barbadoes, according to this Prac-
tice.
But here let it be noted, that though ac- -
cording to this fort of meaſuring, they both
lie North-East from Barbadoes, yet they do
not lie North-Eaft of one another; for if
you
rectify the Globe for the Latitude and Zenith
of Cape Finisterre, you will find Azoff lies
near East-North-East from Cape Finiſterre,
or more than two Points of the Compaſs,
that is, more than 22 Degrees different
from the North-Eaft.
I
2
And if a Sailor or Traveller who is at Bar-
badoes, fhould every League or Mile of his
Way, by obſerving the Compaſs, ftill make
toward the North-East, he would come fooner
to the Hebrides, or Weſtern Scots Iflands,
than to Azoff, or even to Cape Finiſterre.
But the Courſe that he muſt really ſteer to
I
come
4
1
}
Sect. 19.
The first Principles of
1
come to Cape Finisterre, is near North-Eaft
and by Eaft: And if he would fail all the Way
clear to Azoff from Barbadoes, he muft fteer
ftill more to the Eastward: All which Things
fhew the Miſtake of folving this Problem in
this Manner.
Perhaps this may be made yet plainer to
a Learner, if we name two Places which lie
under the fame Parallel of Latitude, namely,
Madrid in Spain, and Pekin in China, Lati-
tude 40. Now these muft always bear di-
rectly Eaft and Weft from each other. But if
you bring Madrid to the Zenith, and having
fixed there your Quadrant of Altitude, you
bend it down to the Horizon, it will not fol-
low the Courſe of the 40th Parallel of Lati-
tude, and lead your Eye to Pekin, but to much
more Southern Places very far diftant from
Pekin, and which have a very different Bear-
ing, namely, to the Ifle of Ceylon, &c.
Upon this Account, the beſt Writers call
that the Angle of Pofition between two Places,
which is found by the Quadrant of Altitude
thus fixed at the Zenith of any Place, and
drawn down to the Horizon: But they de-
fcribe the Rhumb or Courfe of Bearing from
one Place to the other in a different Manner,
namely, It is that Point of the Compass, to-
ward which any Perfon must conftantly fail or
travel, in order to arrive at the diftant Place
given. And without all Doubt, this is the
moſt juſt and exact Account of Things.
Now
Sect. 19. Geography and Aftronomy.
117
Now in order to find this, it is fufficient
for a Learner to know, that if any one of
the Lines drawn from the Points of the Ma
riner's Compass marked on the Globe, (which
are called Rhumb Lines) paffes through both
Places, that Line fhews the Courſe or Bear-
ing from one to the other, as the Courſe from
Cape St. Vincent in Portugal, to Cat Iſland,
among the Bahama Iſlands, is Weft and by
South.
If no Rhumb Lines paſs through thoſe
Places, then that Rhumb Line to which thofe
two Places lie moft parallel, fhews their
Bearing: Thus the Courfe from Barbadoes
to Cape Finiſterre, is North-East and by Eaft,
or thereabouts.
If the Learner has a Mind to fee the Rea-
fon, why there muſt be ſuch a Difference be-
twixt the Angle of Pofition between two Places,
and their Courſe of Bearing to each other, I
know not how to reprefent it upon a flat Sur-
face plainer than by Figure xxI.
Suppoſe the four Cardinal Points, North,
South, Eaft, and Weft, are repreſented on the
Globe by the Letters N. S. W. E: Sup-
pofe three diſtant Places are B. Barbadoes,
C. Cape Finisterre, and A. Azoff. If the
Surface of the Earth were not Spherical, but
a Plane, and the Meridian of thefe Places
were all parallel (as in that Reprefentation
or Projection of the Globe, which is called
Mercator's
I 2
118 The first Principles of
Sect. 19.
1
}
Mercator's Chart) then their Angle of Pofition,
and their Courſe of Bearing, would be the
fame: Then as Ns is the Meridian of the
Place B, fo q u would be the Meridian of the
Place c, namely, a ſtraight Line, and parallel
to N s Then the Line B C A would be the
Line or Rhumb of North-East, namely, 45
Degrees diftant from N s; which would re-
prefent both the Angle of Pofition, and the
Courfe of Bearing between all the three Places
B C and A: For the Angle q c A would be
the fame with the Angle N B A; and thus
A would ftill bear North-East from c and
from B*.
But the Earth being of a Spherical Figure,
and the Meridians meeting in the Poles, the
Meridian of B on the Globe being brought
to the Zenith, is N s; the Meridian of c is
the Curve Line N cm; and the Meridian of
A is the Curve Line N A z; all which meet
in N the North Pole. Now though the ftraight
Line B C A fhews the Angle of Poſition be-
tween the three Places B C and A, (as в ftands
on the Globe at the Zenith) yet the Line B C A
does
* And for this Reafon in thoſe Sea Charts where the
Points of the Compaſs or Rhumbs are drawn in ſtraight
Lines quite through the Chart, the Meridians or Lines
of Longitude are all made ftraight and parallel Lines:
For if the Meridians were a little curved, as they are
commonly in, Maps, the Rhumbs could not be drawn
through the Chart in ftraight Lines.
See Sect. XI. Of Sea-Charts,. p. 68,
Sect. 19. Geography and Aftronomy.
119
}
1
does by no means make the fame Angles, or
has the fame Bearing with the Curve Line
N cm (which is the Meridian of c) as it
does with N s, (which is the Meridian of в :)
and it ſtill makes more different Angles with
the Curve Line N A z, (which is the Meri-
dian of A.)
Thence it follows, that all the RhumbLines
muſt be a Sort of Spiral Lines on the Globe,
except the North and South, which is the Me-
ridian, and the Equator with its Parallels of
East and West, which are Circles *.
The North-East Line in this Place muſt be
B Px, ftill gradually inclining toward the fe-
veral Meridians, that fo it may make the
fame Angles with the Meridians N cm and
NA Z, as it does with N B s.
But by this Means you fee, that to ſteer or
travel ſtill to the North-Eaft would bring you
down to P and x, not to c and A.
You fee alfo, that the Courſe you muſt
fteer or travel to come to A, will be repre-
I 3
fented
* All the other Lines of East and Weft befides the
Equator, are Parallels of Latitude, and are leffer Circles.
And though the Line of Eaft and Weft in this Figure, be
for the Eafe of a young Learner reprefented in a ſtraight
Line, becauſe it is a Parallel to the Equator, and if
drawn round the Globe would be a perfect Circle and
run into itſelf, yet it fhould more properly be ſo far
curved, as to cut all the Side-Meridians Nm and NZ
at right Angles, as well as the Meridian of the Place N s.
And thus they are commonly drawn in Maps of the
World, wherein there is no Line of East and Weft drawn
ftraight befides the Equator.
น
"
120
The first Principles of Sect. 19.
fented by the Line B r A, which is much
nearer the Eaſt Point.
But it is fomething too laborious and
painful for every Reader to trouble his
Thoughts with it.
Problem XI. Having the Day of the
Month given, to find the Sun's Place in the
Ecliptick.
Find the Day of the Month in the Calendar
on the Horizon, (either Old Stile or New,
whichſoever is required) lay a flat Rule on
the Day of the Month, and overagainſt it on
the inner Edge of the Horizon, will appear
both the Sign in which the Sun is, and the
Degree of that Sign; as, on the Tenth of May
Old Stile, the Sun is juſt entering into the firſt
Degree of Gemini, which you may find in both
the Globes on the Ecliptick Circle; and there
you may alfo compute the Longitude of the
Sun from the Point Aries, if
you pleaſe.
Problem XII. The Day of the Month be-
ing given, to find thofe Places of the Globe
where the Sun will be Vertical, or in the Ze-
nith that Day.
Find out the Sun's Place in the Ecliptick
Circle; bring it to the Meridian; mark the
Degree over it; then turn the Globe round,
and all thofe Places that paſs under that De-
gree, will have the Sun in their Zenith that
Day.
Problem
+
Sect. 19. Geography and Aftronomy. 121
Problem XIII. The Day and Hour of the
Day at one Place, namely, London, being
given, to find at what other Place the Sun is
Vertical at that Hour.
The Sun's Place for that Day being brought
to the Meridian, and the Degree over it, (that
is, the Declination) being obferved, bring the
firſt Place, that is, London, to the Meridian.
Set the Hour Index to the given Hour; and
turn the Globe till the Index come to the
upper 12, (that is 12 at Noon) then the Place
of the Earth that ftands under the obſerved
Degree of the Meridian, has the Sun at that
Moment in the Zenith.
Problem XIV. The Day and Hour at one
Place, namely, London, being given, to find
all thofe Places of the Earth where the Sun is
then rifing, fetting, or on the Meridian, (which
is called culminating) alfo where it is Day-
light, Twilight, or dark Night.
By the foregoing Problem, find the Place
where the Sun is Vertical at the Hour given:
Rectify the Globe for the Latitude of that
Place; bring that Place to the Meridian.
Then all thofe Places that are in the Weft
Semi-Circle of the Horizon, have the Sun
rifing, for it is 90 Degrees from their Zenith.
Thoſe in the Eaft Semi-Circle of the Ho-
rizon have it ſetting, for it is 90 Degrees paſt
their Zenith.
I 4
To
122
The first Principles of Sect. 19.
To thoſe who live under the fame Line of
Longitude, or upper Meridian, it is Noon, if
they have any Day at that Time.
To thoſe who live under the oppofite Line
of Longitude, or lower Meridian, it is Mid-
night, if they have any Night at that Time.
Thofe Places that are above the Horizon,
have the Sun above the Horizon fo many De-
grees, as the Places themfelves are.
Thoſe Places that are under the Horizon,
but within 18 Degrees, have Twilight.
And with thoſe who are lower than 18
Degrees, it is dark Night.
Problem XV. A Place being given in the
Torrid Zone, to find thofe two Days in which
the Sun fhall be Vertical there.
Bring the Place to the Meridian; mark the
Degree over it, which is its Latitude; move
the Globe round, and obſerve theſe two op-
pofite Points of the Ecliptick, that pafs
through the aforefaid Degree; fearch on the
Wooden Horizon on what two Days the Sun
paffes through thoſe two Points of the Eclip-
tick, for then the Sun at Noon will be in
the Zenith of the Place given.
Problem XVI. A Place being given in one
of the Frigid Zones, (ſuppoſe the North) to
find when the Sun begins to depart from, or to
appear on that Place, how long he is abfent,
and how long he fpines conftantly upon it.
Suppofe
t
Sect. 19. Geography and Aftronomy.
123
Suppoſe the Place given by the North Cape
of Lapland, 71 Degrees of Latitude. Rectify
the Globe for that Place, or elevate the Pole
71 Degrees; then turn the Globe till the de-
fcending Part of the Ecliptick, the Meridian
and South Part of the Horizon meet toge-
ther: Thus the Ecliptick will ſhew, that the
Sun toward the End of Scorpio (that is, a lit-
tle after the Middle of November,) goes be-
low the Horizon intirely, and leaves that
Part of Lapland.
Then turn the Globe a little further, till
the aſcending Part of the Ecliptick meet the
Meridian in the fame South Point of the Ho-
rizon, and it will fhew that about the ninth
or tenth Degree of Aquarius, that is, about
the End of January, the Sun begins to rife
above their Horizon. Thus they are at leaſt
two Months without the Sun in Winter.
In like Manner bring the aſcending Part of
the Ecliptick to meet the Meridian in the
North Point of the Horizon, there you will
find that the Sun begins to be entirely above
their Horizon toward the End of Taurus, or
near the Middle of May; and if you turn the
Globe a little farther, the defcending Eclip-
tick will meet the Meridian and Horizon in
the North at the 8th or 9th Degree of Leo,
or about the Beginning of August: Thus it ap
pears that thofe Laplanders will have the Sun
at least two Months above their Horizon in
Summer, or two Months of compleat Day-
light.
Problem
}
$
124
The firft Principles of Sect. 19.
Problem XVII. To find the Sun's Decli-
nation and Right Afcenfion any Day in the
Year: Suppofe the 21ft of May.
Find out the Sun's Place for that Day, or
the Beginning of the firft Degree of Gemini
on the Ecliptick; bring that Point of the
Ecliptick to the Meridian, and the Degrees
numbered on the Meridian will fhew the.
Sun's Declination, namely, 20 Degrees North-
ward.
At the fame Time the Place where the
Meridian cuts the Equator will fhew the Right
Afcenfion of the Sun, or its Diſtance from the
Point Aries on the Equator, namely, 58 De-
grees. It is marked ufually in Degrees on the
Globe; if you would turn it into Hours, di-
vide it by 15, and it amounts to three Hours
, which is 52 Minutes.
I 3
Note, That any Star's Declination, and
Right Afcenfion, are found the fame Way, by
bringing it to the Meridian.
Remember the Sun's Declination is always
North in our Summer Half-Year from the
21ft of March, and Southward in our Winter
Half-Year from the 23d of September.
Problem XVIII. To rectify the Globe for
the Sun's Place, any Day in the Year, and
thus to reprefent the Face of the Heavens for
that Day:
Bring
"
Sect. ig. Geography and Aftronomy. 125
1
Bring the Sun's Place found on the Eclip-
tick of the Globe to the Meridian; and at
the fame Time fet the Hour-Index, or Pointer
of the Dial, to the upper 12, that is, to
Noon.
Note, When the Globe is thus rectified for
the Latitude of the particular Town or City
by Problem th, and for the Zenith of it by
Problem 9th, and for the Sun's Place in the
Ecliptick that Day by this Problem 18th, it
is then fitted to refolve moft of the following
Problems, for then it moſt exactly reprefents
the real Face and State of the Heaven's for
that Day.
Here let it be obferved, that this Practice
does really repreſent the Face of the Heavens
only for that Day at Noon, (when the Aſtro-
nomers Day begins) and not for all the fol-
lowing Hours of the Day; becauſe the Sun
is every Moment changing his Place a little
in the Ecliptick. But it is cuftomary, and
it is fufficient for Learners, to make this go
for a Repreſentation of the Heavens for all
that Day, to perform any common Opera-
tions.
Problem XIX. The Place and Day being
given, (namely, May 10th at London) to find
at what Hour the Sun rifes or fets, his afcen-
fional Difference, his Amplitude, the Length
of Day and Night.
Rectify
}
126 1
Sect. 19.
The firft Principles of
Rectify for the Latitude, and for the Sun's
Place, then bring the Sun's Place down to
the Eaftern Part of the Horizon, and the In-
dex will fhew the Time of Sun-rife on the
Dial, namely, five Minutes after four in the
Morning. Bring the Sun's Place to the Weſtern
Side of the Horizon, and the Dial will fhew
the Hour of Sun-fetting, namely, five Mi-
nutes before Eight at Night.
Thus his Afcenfional Difference will ap-
pear, that is, how long he rifes or fets be-
fore or after Six o'Clock, which is one Hour
and 55 Minutes,
Thus alſo his Amplitude will appear in the
Horizon to be almost 34 Degrees to the North
of the Eaft.
The Hour of the Sun's rifing doubled gives
the Length of the Night, namely, eight Hours,
and ten Minutes; and the Hour of the Sun's
fetting doubled gives the Length of the Day,
which will be 16Hours wanting 10 Minutes;
that is, 15 Hours Minutes.
Problem XX.
given, to find the
given Hour.
50
The Place and Day being
Altitude of the Sun at any
Rectify for the Latitude, for the Zenith,
and for the Sun's Place: Bring the Quadrant
of Altitude under the Meridian, and it will
meet the Sun's Place in the Meridian Alti-
tude of the Sun that Day, and thus fhew how
high it is at Noon.
Turn
}
Sect. 19. Geography and Aftronomy.
127
1
Turn the Globe till the Index point to any
other given Hour on the Dial, then obſerve
where the Sun's Place is, bring the Quadrant
of Altitude to it, and it will fhew the Sun's
Altitude at that Hour: Thus May 10th at
London, the Sun's Meridian Altitude will be
a little above 58; Degrees, and at 9 o'Clock
in the Morning will be 434.
Problem XXI. The Place and Day being
given, to find the Azimuth of the Sun at any
given Hour.
Rectify the Globe for the Latitude, the
Zenith, and the Sun's Place: Then turn the
Globe till the Index point to the Hour given;
then obferve the Sun's Place; bring the Edge
of the Quadrant of Altitude down upon it,
and it will cut the Horizon in the Azimuth
of the Sun, or fhew what Point of the Com-
paſs the Sun is in. Thus May 10th, at 20
Minutes paft 9 in the Morning, the Sun's
Azimuth will be about 60 Degrees from the
South toward the Eaft, that is, near South-East
and by Eaft.
Problem XXII. The Sun's Altitude being
given at any certain Place and Day, to find
the Hour of the Day, and alſo his Azimuth.
Rectify as before for the Latitude, the
Zenith, and the Sun's Place: Turn the Globe
and move the Quadrant of Altitudes, ſo that
}
the
1
128
Sect. 19.
The firft Principles of
}
1
}
the Sun's Place may meet the Degree of Al-
titude given on the Quadrant, then the Index
will fhew the Hour on the Dial; and the
Quadrant of Altitude will cut the Azimuth
on the Horizon. Thus May 10th in the
Morning, if the Altitude be near 46 Degrees,
the Azimuth from the South will be 60, and
the Hour 26 Minutes paft Nine.
Here note, That to find the Sun's Hour,
or Azimuth, by his Altitude, you fhould ne-
ver ſeek it too near Noon, becauſe then the
Altitude alters fo very little for two Hours
together.
1
Problem XXIII. When the Sun is due Eaft
or Weft in Summer, how to find the Hour,
and his Altitude.
Rectify as before; then bring the Qua-
drant to cut the Eaft or West Point of the
Horizon, and turn the Globe till the Sun's
Place in the Ecliptick meet the Edge of the
Quadrant. Thus the Quadrant will fhew
the Altitude, and the Index will point to the
Hour: Thus May 10th in the Afternoon, the
Sun will be due Weft at about 56 Minutes
paſt 4; and its Altitude will be near 26 De-
grees. This is called the Vertical Altitude
by fome Writers.
Thus if the Place and Day be known, and
either the Hour, the Azimuth, or the Altitude
be given, you may eafily find the other two.
Problem
1
Sect. 19. Geography and Aftronomy. 129
t
Problem XXIV. To find the Degree of the
Depreffion of the Sun below the Horizon, or its
Azimuth, at any given Hour of the Night.
Obſerve the Place of the Sun, fuppoſe May
21ft in the firſt Degree of Gemini, then ſeek
his oppofite Place in the Ecliptick at half a
Year's Diſtance, namely, the firſt Degree of
Sagittary on the 23d of November; this be-
ing done, ſeek the Altitudes, the Azimuths,
and the Hours, juft as you pleaſe for that Day,
and they will ſhew you what are the Sun's
Depreffions, Azimuths, and Hours, on the
21ft of May at Night *.
Problem XXV. To find how long the Twi-
light continues in any given Place and given
Day, fuppofe the 21st of May at London, both
at Morning and Evening.
The Way to anſwer this Queſtion, is to
feek how many Hours or Minutes it will
be after Sun-fet, before the Sun be depreffed
18 Degrees below the Horizon in that Place
on the 21st of May: And fo before Sum
rife for the Morning Twilight. This is beſt
performed
*Note, The Reaſon why we uſe the oppofite Part
of the Globe, to find the Degrees of Depreſſion of the
Sun, is becauſe the Wooden Horizon is fo thick, that we
cannot conveniently fee, obferve, or compute the Dif-
tances of Depreffion from the upper Edge of it, which
Edge is the true Repreſentative of the real Horizon.
+
130
Sect. 19.
The firft Principles of
>
performed by ſeeking how long it will be
after Sun-rife, or before Sun-fet on the 23d
of November, that the Sun will have 18 De-
grees
of Altitude, which is done by the fore-
going Problem.
Note, That from the 26th of May, to the
18th of July, at London, there is no dark
Night, but conftant Twilight: For during
this Space the Sun is never depreffed above 18
Degrees below the Horizon.
Problem XXVI. To know by the Globe the
Length of the longest and shortest Days and
Nights in any Place of the World.
Remember that the Sun enters the firſt
Degree of Cancer on the longeſt Day, at all
Places on the North Side of the Equator, and
the firſt Degree of Capricorn on the South
Side: Alfo remember that he enters the firſt
Degree of Capricorn, the ſhorteſt Day in all
Places of the Northern Hemiſphere, and the
firſt Degree of Cancer in the Southern: Then
rectify the Globe for the Latitude and Sun's
Place, and find the Hour of Sun-rifing,
which doubled fhews the Length of the
Night: And the Hour of the Sun-fetting
doubled, fhews the Length of the Day, as
in Problem XIX.
Problem XXVII. The Declination and
Meridian Altitude of the Sun, or of any
Star,
Sect. 19. Geography and Aftronomy. igi
Star being given, to find the Latitude of the
Place.
Mark the Point of Declination on the Me-
ridian as it is either North or South from the
Equator; then flide the Meridian up and down
in the Notches, till the Point of Declination
be fo far diftant from the Horizon as is the
given Meridian Altitude. Then is the Pole
elevated to the Latitude fought.
2
Thus where the Sun or any Star's Meri-
dian Altitude is 58 Degrees, and its Decli-
nation 20 Degrees Northward, the Latitude
of that Place will be 51 Degrees North.
See more at Problem VII, VIII, IX. Section
XX.
Note, There are ſome few Problems which
relate to the Sun and to the Hour, which
may be performed on the Globe when the
Sun fhines, though not with any great Exact-
nefs, yet fufficient for Demonftration of the
Reaſon of them, as follows.
Problem XXVIII. The Latitude of a Place
being given, to find the Hour of the Day in the
Summer when the Sun fhines.
Set the Frame of the Globe upon a Plane
perfectly Level or Horizontal, and fet the
Meridian due North and South; both which
are difficult to be done exactly; even though
you have a Mariner's Compafs by you: Then
rectify the Globe for the Latitude, and the
K
Iron
}
132
The first Principles of Sect. 19.
1
For
Iron Pin of the Pole will caft a Shadow on
the Dial, and fhew the true Hour.
when the Globe is thus placed, the Dial-
Plate with the Pole in the Centre of it, is a
true Equinoctial Dial for our Summer Half-
Year, when the Sun is on the North Side of
the Equator.
The fame may alſo be done in the Winter
Half-Year, by depreffing the North Pole as
much below the South Part of the Horizon
as is equal to the Latitude of the Place; for
then the Dial-Plate is a proper Equinoctial
Dial for the Winter Half-Year: But this is
not ſo commodiouſly performed, though the
Reaſon of it is the fame as the former.
Problem XXIX. To find the Sun's Alti-
tude, when it fhines, by the Globe.
Set the Frame of the Globe truly Horizon-
tal or Level; turn the North Pole to the Sun;
move the Meridian up and down in the`
Notches till the Axis caft no Shadow; for
then it points exactly to the Sun, and then
the Arch of the Meridian between the Pole
and the Horizon fhews the Sun's Altitude.
Problem XXX. The Latitude and Day of
the Month being given, to find the Hour of the
Day when the Sun fhines.
Let
1
Sect. 19. Geography and Aftronomy.
133
1
Let the Globe ftand on a Level, and the
Meridian due North and South; rectify the
Globe for the Latitude, and for the Sun's
Place; ftick a Needle perpendicular to the
Sun's Place on the Globe; turn the Globe
about till the Needle point directly toward
the Sun, and caft no Shadow; then will the
Index fhew the Hour of the Day.
I proceed now to fhew fome Problems to
be performed by the Stars upon the Heavenly
Globe.
Problem XXXI. The Place being given,
to find what Stars never rife or never fet in
that Place.
Rectify the Globe for the Latitude; turn
it round, and obferve that fuch Stars as do
not go under the Horizon during its whole
Revolution, do never fet in the Place given ;-
and fuch Stars as rife not above the Horizon
of the Globe during its whole Revolution,
they never riſe in the Place given, nor are
ever feen by the Inhabitants thereof: So the
Little Bear, the Dragon, Cepheus, Caffiopea,
and the Great Bear, never fet at London, nd
many of the Southern Conftellations never
rife.
Problem XXXII. The Place and Day of
the Month being given, to repreſent the Face
or Appearance of the Heavens, and fhew the
Situation
K 2
f
1
134
Sect. 19.
The first Principles of
1
1
Situation of all the fixt Stars at any Hour of
the Night.
Set the Globe exactly North and South:
Rectify it for the Latitude, and for the Sun's
Place; then turn the Globe till the Index
points to the given Hour. Thus every Star
on the Globe will exactly anſwer the Appear-
ance of the Stars in the Heavens; and
you
may ſee what Stars are near or on the Meri-
dian, which are rifing or fetting, which are
on the Eaft or Weft Side of the Heavens.
Thus October 13th at 10 o'Clock at Night,
the glorious Conftellation Orion will appear
on the Eaſt Side at London, the Star Regel
in the left Knee (or Foot) of Orion juſt above
the Horizon, the three Stars in his Girdle a
little higher, &c. This reprefents the Face
of the Heavens at Night, as Problem XVIII.
does in the Day.
Note, This Problem is of excellent Uſe to
find out and know the feveral Conftellations,
and the more remarkable Stars in each Con-
ftellation.
Here follows feveral Problems to find the
Hour of the Night by the Stars.
Problem XXXIII. Any Star on the Meri-
dian being given, to find the Hour of the
Night.
In order to find what Stars are upon the
Meridian at any Time, it is good to have
a Me-
Sect. 19. Geography and Aftronomy. 135
}
a Meridian Line drawn both in a North and
in a South Window; that is, a Line pointing
exactly to the North and South: Then fet up
a broad ſmooth Board of 20 or 24 Inches
high, and 8 or 10 Inches broad; place it
perpendicular on the Window with its lower
Edge on, or parallel to the Meridian Line,
and fixing your Eye at the upright neareſt
Edge of the Board, and glancing along the
plain Face of it, you will eafily obferve what
Stars are on the Meridian, either North or
South at that 'Time *.
Having found what Star is on the Meri-
dian, rectify the Globe for the Latitude, and
for the Sun's Place that Day; then bring the
Centre of the Star which is on the Meridian
in the Heavens, to the Edge of the brazen
Meridian of the Globe; and the Index will
fhew the Time of Night on the North Side of
the Dial among the Evening, or Midnight,
or early Morning Hours.
Note, How to draw a Meridian Line, fee
Sect. XX. Problem XXII. &c.
+
K
3
Problem
Note, To fet the Board perpendicular and convenient,
it is fit to have a Foot made to it behind, that it may
ftand firm. And let a ftraight Line be drawn from the
Top to the Bottom of the Board, through the Middle
of it, parallel to the Sides: Fix alſo a Pin in the upper
Part of this Line, near the Top of this upright Board,
on which hang a Thread and Plummet, to play looſe in
a Hole near the Bottom, to keep it perpendicular. Then
the Thread hanging almoſt cloſe to the Board will direct
your Eye to the Stars on the Meridian.
136 The first Principles of
Sect. 19.
1
Problem XXXIV. The Azimuth of any
known Star being given, to find the Time of
Night.
The Method I juſt before propoſed, will
eafily find the Azimuth of any Star. Set this
tall flat Board perpendicular on the Window,
with one End of it upon the Meridian Line
drawn there, ſo as that your Eye may juſt ſee
the Star in the very Edge of the Plane of this
Board; then a Line drawn on the Window by
the Foot of the Board will croſs the Meridian
Line in the true Angle of its Azimuth, or its
Diſtance from North to South.
Having found the Azimuth of the Star, rec-
tify the Globe for the Latitude, and for the
Sun's Place, as before; rectify it alfo for the
Zenith, and bring the Quadrant of Altitude
to the Azimuth of the Star in the Horizon
then turn the Globe till the graduated Edge
of the Quadrant of Altitude cut the Centre of
that Star, and the Index will fhew the Hour
of the Night upon the Dial-Plate.
Note, That if you have a Meridian Line
drawn on a Window, you may find by fuch
Methods as thefe when the Sun is in the Me-
ridian, and what is its Azimuth at any
Time.
Problem XXXV. The Altitude of a Star
being given, to find the Hour of the Night.
Note,
2
Sect. 19. Geography and Aftronomy.
137
!
Note, That the Altitude of the Star muft
be found by a Quadrant, or fome fuch In-
ſtrument: But remember, that if you would
find the Hour by the Altitude of a Star, you
muft never chooſe a Star that is too near the
Meridian; becauſe for almoft two Hours to-
gether, the Altitude varies very little when
it is near the Meridian.
Rectify the Globe as before for Latitude,
Zenith, and Sun's Place; move the Globe and
the Quadrant of Altitude backward or for-
ward, till the Centre of that Star meet the
Quadrant of Altitude in the Degree of Alti-
tude which is given, then the Index will
point to the true Hour.
Note, Theſe three laſt Problems being well
underſtood, will fhew you how to find at
what Hour any Star will rife or fet any Day
of the Year; what Stars are or will be upon
the North or South Meridian at any Hour
given; what Stars are in the Eaft or in the
Weft, or on any Points of Azimuth at any
Time of the Night; and what Altitude they
have at that Hour, or at that Azimuth.
Problem XXXVI. To find the Latitude
and Longitude of any Star : Alſo its Right
Afcenfion and Declination.
Put the Centre of the Quadrant of Alti-
tude on the proper Pole of the Ecliptick,
K 4
whether
138
The first Principles of
Sect. 19:
;
whether it be North or South; bring its gra-
duated Edge to the given Star; then that De-
gree on the Quadrant is the Star's Latitude
and the Degree cut by the Quadrant on the
Ecliptick in the Star's Longitude. Thus the
Latitude of Arc&turus is 31 Degrees North :
Its Longitude is 200 Degrees from the Point
Aries, or 20 Degrees from Libra. The La-
titude of Sirius, or the. Dog Star, is near 40
Degrees of South Latitude, and its Longitude
is about 100 Degrees from Aries, or 10 De-
grees from Cancer.
To find a Star's Right Afcenfion and Decli-
nation, fee Problem XVII. for it is done the
fame Way as that of the Sun; only obferve
this Difference, that the Sun changes both
his Right Afcenfion and his Declination every
Day, whereas the fixt Stars have the fame
Right Afcenfion and Declination all the Days
in the Year.
Remember alſo, that the fixt Stars every
Day in the fame Year, keep the fame Lon-
gitude and Latitude, as well as the fame
Right Afcenfion and Declination *; but the
Planets are ever changing all theſe, and the
Learner
ศ
*The infenfible Change of the Longitude, Right Af-
cenfion, and Declination of the fixt Stars, made by their
flow Motion parallel to the Ecliptick, is not worth No-
tice in this Place.
1
Sect. 19. Geography and Aftronomy.
139
Learner can know none of them but by fome
Almanacks which are called Ephemerides, of
Tables which are calculated on Purpoſe to
fhew the Longitude and Latitude, or the
Place of the feveral Planets among the twelve
Signs of the Zodiack every Day in the
Year.
Problem XXXVII. To find the Place of
any Planet on the Globe: Alfo to find at what
Hour any Planet, (fuppofe Jupiter) will rife
or fet, or will be upon the Meridian any given
Day of the Year.
You muſt firſt find out by fome Ephe-
meris, what Degree of what Sign Jupiter
poffeffes that Day of that Year: Mark that
Point on the Ecliptick either with Chalk or
with a Pencil, or by ſticking on a little black
Patch; and then for that Day and that Night
you may perform any Problem by that Planet
in the fame Manner as you did by a fixt
Star.
But if you would be very exact, you
you muſt
not only feek the Planet's Place in the Sign
for that Day, which is its Longitude, but
you muſt feek its Latitude alfo in the Ephe-
meris, (which indeed in the fuperior Pla-`
nets Jupiter, Saturn, Mars, alters but very
little for whole Months together) and thus
fet your Mark in that Point of Latitude, or
Diſtance from its fuppofed Place in the
Ecliptick,
I
Sect. 19.
140
The firft Principles of
1
1
1
Ecliptick, whether Northward or Southward,
and then go to work your Problem by this
Mark.
On
I fhall give but one Inftance, which will
fufficiently direct to folve all others of the
fame Kind that relate to the Planets.
the third of April, 1723, I find by an Ephe-
meris, that the Sun is about the End of the
23d Degree of Aries, Jupiter enters the 8th
Degree of Capricorn, and (if I would be
very exact) I obſerve alſo that the Latitude
of Jupiter that Day is 15 Minutes, or a Quar-
ter of a Degree to the North: There I make
a Mark, or put on a ſmall black Patch on the
Globe to ftand for Jupiter. Then having
rectified the Globe for the Latitude v. c. of
London, and for the Sun's Place, April the
3d, I turn the Mark which I made for Ju-
piter to the Eaſtern Edge of the Horizon, and
I find Jupiter will rife near the South-Eaſt at
a little paſt One in the Morning: He will
come to the Meridian at a very little paſt
Five: He will fet near the South-Weft, about
Nine in the Morning.
Then if I rectify the Globe for the Zenith,
the Quadrant of Altitude being brought down
to the Horizon, will tell you what is his
Altitude, and what his Azimuth, at any given
Hour of the Morning, by the Help of the
Dial and Index.
Or
1
1
Sect. 19. Geography and Aftronomy. 141
2
Or his Altitude or Azimuth being given,
you may find what it is a Clock.
By this Means you may find the Hour
when the Moon will rife and fet, together
with her Southing, or the Time of her com-
ing to the Meridian. But let it be noted,
that the Moon changes her Place in the Zo-
diack fo fwiftly, that the moves through 13
Degrees of one Sign every Day, or thereabouts;
and therefore you cannot find the precife
Hour and Minute of her rifing, fetting, fouth-
ing, &c. upon the Globe, without much
more Trouble than moſt of the other Planets
will give you, which change their Places in
the Zodiack much more flowly.
Problem XXXVIII. The Day and Hour
of a folar Eclipfe being known, to find all thofe
Places in which that Eclipfe will be vifible.
By the XIIIth Problem find out at what
Place the Sun is vertical at that Hour of the
Day. Bring that Place to the Pole or vertical
Point of the Wooden Horizon, that is, rectify
the Globe for the Latitude of that Place; then
the Globe being in that Situation, obferve
what Places are in the upper Hemiſphere; for
if it be a large Eclipfe, the Sun will be vifi-
bly eclipſed in moſt of them.
Problem XXXIX. The Day and Hour of
a Lunar Eclipfe being known, to find by the
Globe
4
}
142 The first Principles of
Sect. 20.
Globe all thofe Places in which the fame will be
vifible.
By Problem XIII. find as before at what
Place the Sun is vertical at that Hour; then by
Problem IV. find the Antipodes of that Place:
Rectify the Globe for the Latitude of thofe
Antipodes; thus they will be in the Zenitḥ,
or in the Pole of the Horizon; then obſerve
as before what Places are in the upper Hemi-
fphere of the Globe, for in moft of thofe Places
the Moon will be visibly eclipfed.
The Reaſon of rectifying the Globe for
the Antipodes in this Problem, is becauſe the
Moon muſt be directly oppofite to the Sun
whenfoever ſhe is eclipſed.
SE C T. XX.
Problems relating to Geography and Aſtro-
nomy, to be performed by the Ufe of the
Plain Scale and Compaffes.
IT
T is ſuppoſed that the Reader is already
acquainted with fome of the firft and eafieft
Principles of Geometry, before he can read
with underſtanding this or any other Treatiſe
of Aftronomy or Geography; and it is prefumed
alfo that he knows what is a Chord, a Tangent,
and a Sine, and how to make and to meaſure
f
an
t
1
Sect. 20. Geography and Aftronomy.
143
an Angle either by a Line or Scale of Chords,
or Sines, or Tangents, in order to practiſe the
Problems of this laft Section; though a very
flight Knowledge of thefe Things is fufficient
for this Purpoſe.
Becauſe ſeveral of the following Problems
will depend upon the Altitude, or Azimuth
of the Sun, and in order to obtain theſe, we
fometimes uſe a Pin or Needle fixed perpen-
dicularly, on an upright or horizontal Plane;
therefore the firſt Problem I propoſe ſhall be
this, namely,
Problem I. How to fix a Needle perpèn-
dicular on a Plane, or to raiſe a perpendicular
Style or Pointer in order to make Obfervations
of a Shadow.
Note, Any Thing fixed or fet up to caſt a
Shadow is called a Style.
One Way to perform this, is by having
at Hand a Joiner's Square, and while one
Edge of it is laid flat to the Plane, the other
Edge of it ſtanding up will fhew when a
Needle or Style is fixed on that Plane perpen-
dicularly, if it be applied to the Side of the
Needle.
Note, If you have a little Square made of
Box, or any hard Wood, one Leg being fix,
or the other eight or nine Inches long, one
Inch or 1 broad, and an Inch thick, with
a Thread and Plummet hanging from the End
1
3
of
1
144
The firft Principles of
}
Sect. 20.
of one Leg, down toward the Place where
the other Leg is joined, as in Fig. xiv. and
a large Hole for the Plummet to play in: It
will be of Ufe, not only to fhew you how to
erect a Needle truly perpendicular; but it will
alſo diſcover whether any Plane be truly
ſmooth, and be Horizontal or Level, as well
as whether any upright Plane be exactly per-
pendicular to the Horizon.
Such a Square will alſo be very uſeful in
the Practice of any Geometrical Problems, by
drawing one Line perpendicular to another
with the greateſt Eaſe.
Another Way to fix a Needle perpendi-
cular to any Plane, is this; deſcribe a Circle
as a, o, d, b, in Fig. xv. Fix a Needle s p
in the Centre p, then meaſure from feveral
oppofite Parts of it, as a, o, d, b, to the Tip
of the Needle, s, and faſten the Needle fo
as that the Tip s, fhall be at equal Diſtance
from all thoſe Points, then it is truly perpen-
dicular.
Note here, That in moſt of theſe Practices
where a perpendicular Needle is required, the
fame End may be attained by a Needle or
Wire ftraight or crooked, which may be called
a Style, ſet up floping at Random, as in Fig.
XVI. without the Trouble of fixing it perpen-
dicular, if you do but find the Point p on the
Plane, which lies perpendicularly under the
Tip
*
Y
145
Sect. 20. Geography and Aftronomy.
Tip of the Styles, and this may be found by
applying the Edge of the Square, deſcribed
Fig. XIV. to the Tip of the Style: Though
there are other Ways to find this perpendicu-
lar Point for nice Practices in Dialling by
Shadows, which require great Exactneſs.
But take notice here, that if you uſe this
Method of a Style ſet up floping at random,
as in Figure xvi. then with your Compaſſes
you muſt meaſure the Diſtance from the Tip
of the Styles to the Point p, and that Diſtance
muſt be counted and uſed as the Length of
the perpendicular Style s p in Fig. xv. where-
foever you have Occafion to know or uſe the
Length of it.
Obferve alfo, that if the Tip of your Style
(whether ſtraight or crooked) be more than
three or four Inches high from the Plane, you
will ſcarce be able to make the Point of Sha-
dow exactly, becauſe of the Penumbra, or
faint Shadow which leaves the Point or Edge
of a Shadow undetermined.
On a Horizontal or Level Plane
you muſt
ufe a much ſhorter Style when the Sun is low,
or in Winter, becauſe the Shadow is long;
but in the longeſt Days in Summer a four
Inch Style is fufficient, though the Shadow
at that Seafon be very fhort all the middle
Hours of the Day. From the Tip of the
Style to the Tip of the Shadow, fhould never
be above fix Inches Diſtance.
I
After
!
!
1
t
}
1
146
The first Principles of Sect. 26.
After all, if you have frequent Occafion
for a perpendicular Style to obferve a Shadow
by it, I know nothing eafier than to get a
Small Prifm of Wood, or Ivory, or rather of
Brafs, fuch as is deſcribed Fig. XVII. Let
the Bafe be a right-angled Triangle A B C:
The Line B C an Inch: A B two Inches:
And let the Height of the Prifm, namely,
A D, or C E, be three Inches, (or near four
Inches if you pleaſe.)
you pleaſe.) By this Means you
obtain three perpendicular Styles of different
Lengths, according as you want the Shadow
to be either longer or fhorter in Summer or
in Winter.
B
If you fet it upon the fquare Side A B D O,
your perpendicular Style will be в C, or o E:
If it be в o, then c is the Tip of the Style,
and в marks the Point on the Plane. If you
fet it on the Square Side B C O E, as it ſtands
in the Figure, then A B, or Do, is your
perpendicular Style. Or if you fet it on its
triangular Bafe A B C, then either A D, or
Bo, or c E, will be your perpendicular
Style.
This little plain Prifm has thefe great Ad-
vantages in it, namely, That you can fet it
up in a Moment on a perfectly ſmooth Plane,
and you are fure it is perpendicular to the
Plane; and then if you require it to ſtand
there any Time, and it ſhould happen to be
moved, if you have but fixed and marked
its
Sect. 20. Geography and Aftronomy.
147
its Place by the lower Edges on the Plane,
and remember which Edge you defigned for
the Style, you may fet it exactly in the fame
Pofition again.
Problem II. How to take the Altitude of
the Sun by a Needle fixed on an Horizontal
Plane, or by any perpendicular Style.
In all theſe Practices be fure that your Plane
be truly Level or Horizontal, which you can-
not well know without fome fuch Inftrument
as I have deſcribed before, Fig. xiv. which
ferves inſtead of a Level.
You muſt apply this Inftrument or Square
not only to one Part, but to every Part of
the Plane, wherefoever you can imagine the
Shadow will fall, to fee if it be precifely Ho-
rizontal or Level: For a very ſmall Varia-
tion from the Level will caufe a great Dif-
ference in the Length and in the Point of
Shadow; and upon this Account there are
few Window-Stools, or any Boards or Poſts
fixed by the common Work of Carpenters
fufficiently Level for a juft Obfervation in
Aftronomy or Dialling.
Fix your perpendicular Style P s, as in
Fig. XVIII. obferve the Point of Shadow caft
from the Tip of the Styles: Draw P c :
Then take the Height of the Style P s in your
Compaffes; fet it perpendicularly on PC;
L
draw
1
148 The first Principles of
Sect. 20.
draw the Line s c on the Plane, and the
Angle c is the Sun's Altitude, namely, 35
Degrees.
Here it is evident, that if you fuppofe c
the Centre, and c P to be the Radius, then
Ps is the Tangent of the Altitude 35 Degrees;
for it meaſures the Angle c, or the Arch PA.
But if you make s the Center, and fuppofe
SP to be the Radius of a Circle, c p is the
Tangent of the Coaltitude of the Sun, namely,
55 Degrees, for it is that Tangent which
meaſures the Angle s, or the Arch P E.
Hence it will follow, that if you fix a per-
pendicular Needle, Pointer or Style, or any
Horizontal Plane, and divide a Line, as P C,
according to the Scale of Tangents, whofe
Radius fhall be P s, beginning at P towards
C, and make this Line of Tangents moveable
round the Center P, the Shadow of the Style
will fhew you the Coaltitude of the Sun at
any Time on that moveable Scale of Tan-
gents.
Or if the Scale of Tangents P c be divided
on the immoveable Horizontal Plane itſelf,
and you deſcribe concentric Circles on the
Centre P through every Degree of that Scale,
the Shadow of the Tip of the Style will ſhew
the Coaltitude among thofe Circles; for they
will exactly reprefent the Parallels of Alti-
tude in the Heavens.
Notes
Sect. 20. Geography and Aftronomy.
149
}
Note, This is deſcribed thus particularly
rather for Demonftration than Ufe, becaufe
when the Sun is low, the Shadow P c will
be extended many Feet or Yards.
Problem III. To take the Altitude of the
Sun by a Style on a perpendicular or upright
Plane.
Fix your Style A в perpendicular to a flat
Board, as Fig. xIx. Raife your Board exactly
upright, and turn it to the Sun, ſo that the
Shadow of the Style A D may be caſt down-
ward directly perpendicular from the Center
A in the Line A Q. Then take the Length
of the Style A B in your Compaffes, and fet
it on the Board at right Angles to the Line
of Shadow, from A to B : Draw the Line
BD; and the Angle A D B fhall be the Sun's
Coaltitude, (or Zenith Diſtance as it is ſome-
times called) namely, 55 Degrees: The
Tangent of which is A B to the Radius D A,
and the Angle A B D (which is the Comple-
ment of it) or 35d fhall be the Sun's Alti-
tude; the Tangent of which is AD to the
Radius B A.
Or to make this more evident, draw the
obſcure Line Do parallel to A B, that is,
Horizontal, and the Angle B D o will plainly
appear to be the Angle of the Sun's Altitude
35 Degrees.
Hence it will follow, that if the Line A D
L 2
be
:
{
150
&
The first Principles of
Sect. 20.
be prolonged for Q, and divided according to
the Degrees of a Scale of Tangents, this Board
or Inftrument will be always ready to fhew
the Sun's Altitude on that Scale, by the Sha-
dow of the Style A B turned directly to the
Sun, when the Board is held up and made to
ſtand perpendicular to the Horizon.
N.B. This is the Foundation of thofe Dials
which are made on Moveable Columns, or on
Walking Canes, which fhew the Hour of the
Day by the different Altitudes of the Sun in
the various Seafons of the Year.
Note, There are feveral other Ways to
find the Altitude of the Sun by a moveable
or immoveable upright Plane, and a perpen-
dicular Style fixed on it. But none of thoſe
Ways of taking an Altitude by the Point or
End of the Shadow are the moft commo-
dious and exact for common Ufe; I have
chiefly mentioned them, to lead the Learner
into a more familiar and perfect Acquaintance
with the Nature and Reafon of theſe Ope-
rations.
If no regular Inftrument be at Hand to take
the Sun's Altitude, I prefer the following
Method above any others.
Problem IV. To find the Sun's or any
Star's Altitude by a plain Board, Thread and
Plummet.
Take
A
151
Sect. 20. Geography and Aftronomy.
Take a ſmooth flat Board, as n o p q, which
is at leaſt 8 or 9 Inches broad every Way.
See Fig. xx.
Mark two Points on it, as a c,
at leaſt at ſeven or eight Inches Diſtance, and
draw that Line. Fix a very ſhort Pin at c
perpendicular, which may be done fufficiently.
true by guefs. Hang a Thread and Plum-
met on it. Hold up the Edge of the Board
to the Sun till the Shadow of the Pin be caſt
all along the Line a c. Obferve where the
Thread falls; mark a Point in it as at d; draw
the Line dc, and the Angle a c d is the Com-
plement of the Sun's Altitude: Or you may
draw the whole Quadrant a ce, and then the
Angle dce is the Sun's Altitude. Now if
the Arch de be meaſured by a Line of Chords,
you find the Number of Degrees.
Note, That the Degrees of Altitude muſt
always be reckoned from that Side of the
Qurdrant which is held next to the Sun, (viz.)
The Coaltitude from the Side c a.
ce.
Note farther, That the Sun's Altitude
fhould ſcarce ever be taken within half an
Hour of Noon for any other Purpoſes befide
the finding the Meridian Altitude; becauſe
for an Hour together the Altitude then in-
creaſes or decreaſes ſo very little, the Sun
being then near the Middle of its diurnal
Arch.
Take Notice alfo, That when the Sun is
near the Horizon, it appears higher than
really
L 3
A
I
152
Sect. 20.
The first Principles of
4
really it is, by reaſon of the Refraction or
breaking of its Rays in paffing through a
larger Space of Atmoſphere, or thicker Air.
When the Sun is one Degree high, its Re-
fraction cauſes it to appear near half a De-
gree higher than it is. At two Degrees high
the Refraction is 20 Minutes, at three De-
grees the Refraction is 15 Minutes, at five
Degrees the Refraction is 10 Minutes, at 10
Degrees the Refraction is 5 Minutes. You
muft therefore allow proportionably by de-
ducting fo much from the apparent Altitude,
when you make an Obfervation near Sun-rife
or Sun-fet.
Now again, That the heavier your Plum-
met is, the more fteady it will hang, and
make the Obfervation more exact.
If you pleaſe you may draw the whole
Quadrant on the Board, and ſtick in the Pin
at the Center before you make your Obferva-
tion, which indeed is the moſt proper Way.
You may find the Altitude of the Moon the
fame Way. And the Altitude of any Star
may be found by the fame Board, if you
ſtick in another very fhort Pin perpendicular
at a, and fixing your Eye at s, bring both
the Pins a and c juft over the Star; then the
Thread will hang (ſuppoſe) on the Point din
the Arch, and fhew the Degree or Angle of
Altitude to be dce.
Problem
Sect. 20. Geography aud Aſtronomy.
153
1
Problem V. To obferve the Meridian Al-
titude of the Sun, or its Height at Noon :
And by the fame Method to find any Star's
Meridian Altitude:
If you know exactly when it is Noon, take
the Altitude of the Sun by any Inftrument
within a Minute or two of that Time, and
that is the Meridian Altitude; for two or
three Minutes at Noon, make no fenfible Dif-
ference in the Altitude.
But if you have no Clock or Dial, or any
Thing of that Kind whofe Truth you can rely
on, then a little before Noon obſerve and ſet
down the Altitude every four or five Mi-
nutes, till you find it begins to grow a little
lefs; then review your Obfervations, and
the greateſt Height was the true Meridian
Altitude.
You may, by the fame Method, find the
Meridian Altitude of any Star above the Ho-
rizon, if you make feveral Obſervations when
the Star is coming near to the North or South
Part of the Meridian.'
Problem VI. How to find out the Declina-
tion of the Sun, or of any large or known Star.
If you know the Latitude of the Place
where you are, with the Meridian. Altitude
of the Sun any Day in the Year, or if you
know the Sun's Place in the Ecliptick, you
L 4
may
154 The firft Principles of Sect. 20.
7
1
may find the Declination of the Sun thereby
Geometrically, as-fhall be fhewn afterward:
But if theſe are not known, then, in order
to other Aftronomical Operations, you muſt
feek the Declination of the Sun for that Day,
either by the Globe on the brazen Meridian,
or in a Scale of the Sun's Declination, which
is drawn on artificial Quadrants, or other
Mathematical Inftruments; or it may be
found in Tables of the Sun's Declination, cal-
culated exactly to every Minute of a Degrée
for every Day in the Year, which is the beſt
Way, where it may be had.
There are alſo Tables of Declination of ſe-
veral of the moſt noted Stars.
Theſe are
all the Year at the fame Diſtance from the
Equator, and their Declination does not vary
as the Sun's does.
Thefe Tables of the Sun's and Star's De-
clination are found at the End of this Book,
Sect. XXI.
But let it be noted here, that the Declina-
tion of the Sun not only changes every Day in
the Year, but it differs alfo fome few Mi-
nutes in the next Year from the Year forego-
ing, even on the fame Day of the Month:
Whence this Difference arifes, and how to
act with reſpect to it, fee Problem XX. fol-
lowing, and more in Sect. XXI.
Problem
{
Sect. 20. Geography and Aftronomy. 155
1
Problem VII. To find the Latitude of any
Place by the Meridian Altitude and Declina-
tion of the Sun any Day in the Year.
The Way to find the Latitude of any Place
(that is, the Diſtance of the Zenith of that
Place from the Equator) by the Meridian
Altitude of the Sun, is firft to feek its Cola-
titude, that is, the Complement of its Lati-
tude, or (which is all one) the Elevation of
the Equator above the Horizon of that Place.
Suppoſe the Day given be the 21st of June,
or the Summer Solstice.
This may be done by looking back to Fi-
gure 111. First, Draw the Line н o for the
Horizon, and from the Center c raife a Per-
pendicular cz to reprefent the Zenith. Make
the Semicircle н zo for the Meridian: Then
ſuppoſe the Meridian Altitude of the Sun at the
Summer Solstice be 62 Degrees, by the Uſe
of your Compaffes and a Scale of Chords ſet
up 62 from н to s: Alfo the Declination of
the Sun that Day being 23 Degrees North-
ward, fet 23 from s downward, and it will
find the Point E, and the Arch H E is the
Altitude of the Equator above the Horizon,
or the Colatitude of the Place, namely, 38 -/-/-
Degrees: Thence you find the Latitude is EZ
or 51' Degrees, which compleats a Quadrant.
Then if you draw the Line E z, it will repre-
fent the Equator in that Scheme,
2
Sup-
í
156
The first Principles of Sect. 20:
Suppoſe you take the Meridian Altitude
of the Sun on either of the Equinoctial Days,
namely, in March or September, and
you find
it to be 38 Degrees: Set up 31½ from н
to E, then the Sun having no Declination,
the Meridian Altitude itſelf fhews you the
Height of the Equator above the Horizon,
which is the Complement of the Latitude.
Suppoſe the Meridian Altitude of the Sun
at the ſhorteſt Day be 15 Degrees, fet
up
15
from н to v: Then the Sun's Declina-
tion is 23 Degrees Southward; therefore
fet 23 from v upward, and it finds the
Point E: And the Arch H E is the Comple-
ment of the Latitude as before, namely, 38
Degrees.
2
For all theſe Practices the chief Rule is
this. In the Summer Half-Year fet your
Declination downward from the Point of
the Meridian Altitude, and it will find the
Equator's Height above the Horizon. In
Winter fet your Declination upward from
the Point of the Meridian Altitude, and it
will fhew you the Height of the Equator. The
Reaſon of it is moſt evident in the third and
· fourth Figures.
It may be proper in this Place to recol-
lect what I have already demonſtrated in
Section V. Figure 1v. that the Latitude of
any Place (that is, the Diſtance of its Ze-
nith
Sect. 20. Geography and Aftronomy. 157
1
1
nith from the Equator) z E is equal to the
Elevation of the Pole P o above the Hori-
zon. Thereby it appears that the Elevation
of the Equator above the Horizon of that
Place on one Side, as E H, (which is the
Complement of the Latitude) is equal to the
Complement of the Pole's Elevation on the
other Side, as z P. If therefore the Latitude
(fuppofe of London) be E z, or PO 51
the Coaltitude P Z, or H E, will be 38 for
it muſt compleat a Quadrant, or 90 Degrees;
and therefore if you ſet the Point P 51 De-
grees above o on the other Side of the Ho-
rizon, and draw the Line P c, you have
the Axis of the World reprefented, or the
North Pole in its proper Elevation for Lon-
don, and ſtanding (as it ought) at right An-
gles with the Equator E C.
Z
I have repreſented the Solution of this
fixth Problem in a Geometrical Manner, to
fhew the Reafon of this Practice; but this
Problem of finding the Latitude by the Me-
ridian Altitude, is much eafier performed
arithmetically, thus.
In the Winter Half-Year add the Decli-
nation to the Meridian Altitude, and it gives
you the Coaltitude.
In the Summer Half-Year fubtract the
Sun's Declination from the Meridian Altitude,
and it gives the Coaltitude.
Example
158 The first Principles of
Sect. 20.
Example, June 11th
Merid. Alt.
Subtract
H S62
Sun's Declin. E s-
23/2/2
Coaltitude H E
-381-
-
December 11th
Merid. Alt. H V
15
=
Sun's Declin. E V23
Coaltitude H E-38% /
Add.
Then if you fubtract the Coaltitude from
the Zenith or 90, you find the Latitude, as,
Zenith
Coaltitude HE
H Z-
90
38-/-/
Latitude E Z—————511/
Subtract
After all, it muſt be obſerved here, that
all theſe Problems of finding the Latitude
of the Place by the Sun's or Star's Meridian
Altitude, &c. belong chiefly to thofe Places
which lie within the Temperate Zones. If
the Place lie in the Torrid or Frigid Zones,
thefe Methods of Solution are good, when
the Meridian Sun is on the fame Side of the
Zenith with the Equator, whether North
or
Sect. 20. Geography and Aftronomy. 159
1
or South.
But if not, then there muſt be
fome little Difference of Operation at ſome
Times of the Year. Yet if you project a Scheme
for the Solution of fuch an Enquiry like Fig.
III. the veryReaſon of Things will fhew you
when you muſt Add or Subtract.
Problem VIII. To find the Meridian Al-
titude of the Sun any Day of the Year, the
Latitude of the Place being given.
This is but the Converſe of the former
Problem, and therefore is to be performed
the contrary Way, namely, in Winter fubtract
the Declination V E from the Equinoctial Al-
titude or Coaltitude H E, and the Remainder
is н V the Meridian Altitude.
In Summer add the Declination E s to the
Equinoctial Altitude, or Coaltitude н E, and
it gives the Meridian Altitude н S.
The Meridian Altitude at the Equinoxes
is the fame with the Coaltitude, as before.
Problem IX. To find the Declination of
the Sun, its Meridian Altitude and the Lati-
tude of the Place being given,
It is hardly neceffary to deſcribe this Prac-
tice to thoſe who have perfectly learned the
two foregoing Problems.
Subtract the Coaltitude нE from the
Meridian Altitude in Summer нs, and the Re-
mainder is the Sun's Summer Declination Ẹ s.
HS,
Sub-
1
160
Sect. 20.
The first Principles of
{
$
}
Subtract the Meridian Altitude in Winter
HV from the Colatitude H E, and the Re-
mainder is the Sun's Winter Declination E v.
Or in ſhort, if the Meridian Altitude and
Colatitude be given, fubtract the lefs from the
greater, and the Remainder is the Sun's De-
clination.
Problem X. To find the Latitude of a
Place by the Meridian Altitude of a Star, when
it is on the South Meridian.
Find the Declination of that Star in fome
Table or Scale of the Star's Declination.
If it has Declination Northward, (as the
Sun has in Summer) fubtract the Declina-
tion from the Meridian Altitude, and it gives
you the Colatitude.
If the Star's Declination be Southward,
(as the Sun's is in Winter) add its Declina-
tion to its Meridian Altitude, and it gives
you the Colatitude.
Note, When I fpeak of North and South-
ward in relation to Winter and Summer,
in many of theſe Problems, I mean in Nor-
thern Latitude, fuch as ours is in Britain.
When the Star is on the North Meridian,
fee how to find the Latitude by it in Pro-
blem XXXII.
Problem XI. By what Methods is the Lon
gitude of Places to be found.
Though
Sect. 20. Geography and Aftronomy.
161
Though the Latitude (which lies North-
ward and Southward) may be determined
with the utmoft Certainty by the Methods
before propofed, yet the Longitude of a Piace
(which is the Distance of any two Places from
each other Eastward or Weftward) is very
hard to be determined by the Sun or Stars,
becauſe they always appear moving round
from East to Weft. The Longitude therefore
of Places is ufually found by meaſuring the
Diſtance on Earth or Sea from Weft or Eaſt.
The Map-makers, who defcribe Countries,
Provinces or Kingdoms, meafure the Diſtances
on the Earth by an Inftrument made on
purpoſe, with a Wheel fo contrived, that a
certain Number of its Revolutions is equal
to a Pole, or a Furlong, or a Mile; it hath
alſo a Mariner's Compass and Needle touched
with a Loadſtone faſtened to it, to fhew how
much their Courfe varies from the North or
South.
In this laſt Age they have alfo invented a
Way to find the Difference of Longitude be-
tween two Towns that are fome thoufands
of Miles afunder in diftant Nations; and
that is by a nice and exact Obfervation of the
Moment when the Eclipfes of the Moon begin
or end, made by Mathematicians at thofe
diſtant Places: And thus by the Difference
of Time in thoſe Eclipfes they compute the
Diſtance of Place.
This
t
162
The firſt Principles of Sect. 20.
This Invention is ſtill further improved by
Obfervations of the Eclipfes of the four Moons,
or little ſecondary Planets, which roll round
the Planet Jupiter as our Moon does round
our Earth: By theſe Means the ſuppoſed
Diſtances of fome Places in the East and West-
Indies have been altered, and the Miftakes of
feveral hundred Miles corrected.
The Sailors meaſure it at Sea by the Log,
which is a Piece of Board faſtened to a long
Line which they caſt out of the Ship while
a Minute or Half-Minute Glaſs begins to
run: Then drawing in the Log, they fee
how far the Ship has failed in a Minute; and
fuppofing the Circumftances of the Wind
and Water to be the fame, they compute
thereby how far they have failed in fome Hours.
But this being a very uncertain Way of rec-
koning becauſe of the continual Changes
either of the Strength or the Point of the
Wind, or Current of the Water, they are
often liable to Miftakes. Therefore it has
been the famous and folicitous Enquiry of
theſe laſt Ages, how to find out and afcer-
tain Longitude at Sea; and there is ſo vaft
a Reward as Twenty Thouſand Pounds of-
fered by the Parliament of Great-Britain
to any Man who fhall invent a Method for
it, which fhall be plain, eafy, and practi-
cable at Séa,
Problem
\
Sect. 20. Geography and Aftronomy.
163
1
Problem XII. To find the Value of the De-
gree of a greater Circle upon the Earth, or
how much it contains in Engliſh Meafure.
Here let it be noted, that one Degree of
à greater Circle on the Earth anfwers to one
Degree of a greater Circle in the Heavens.
It is true the heavenly Circles are incompar-
ably larger than the Circumference of the
Earth; and they are alſo larger than each
other according to the different Diſtances of
the Planets and Stars; yet every Circle (whe
ther greater or leffer) is divided into 360 De-
grees, and therefore though Circles differ né-
ver fo much in Magnitude, yet, when they
are ſuppoſed to be concentrical, (that is, to
have the fame Center) every fingle Degree of
each Circle is correſpondent to a fingle De-
gree of all other Circles.
Now that a Degree of the Heavens thus
anfwers to a Degree on the Earth, is very evi-
dent; for if we travel on the Earth, or fail one
Degree Northward or Southward on the fame
Meridian, we fhall find by the Sun or the fixt
Stars in Heaven, that our Zenith is juft a
Degree altered, our Latitude is changed one
Degree, and our Pole is one Degree more or
leſs elevated, namely, more elevated if we go
from London toward the North, and lefs ele-
vated if we go toward the South, till we come
to the Equator: Afterward, the contrary Pole
is elevated gradually. By fuch Experiments
M
as
1
1
}
164
Sect. 20.
The first Principles of
}
as theſe Philofophers infer alſo that the Earth
is a Globe, and not a plane Surface.
Wherefore to find the Value of a Degree on
a greater Circle of the Earth, you muſt travel
directly in the fame Meridian, meaſuring
your Miles all the Way, till your Latitude
be altered one Degree; and then (if you have
been exact in your Meaſure) you will find
that you have travelled about 70 English
Miles; though Geographers often reckon 60
Geographical Miles to a Degree for greater
Eafe in Computation, as I have ſaid before.
Problem XIII. To find the Circumference,
the Diameter, the Surface, and folid Contents
of the Earth.
Having found the Value of one Degree to
be 70 Miles, multiply that by 360, and it
produces 25200 Miles for the Circumference.
The Diameter is in proportion to the Cir-
cumference as 113 to 355, or as 50 to 157,
or in more brief and vulgar Account, as 7 is
to 22, which will make the Diameter of the
Earth to be about 8000 Miles.
Multiply the Circumference by the Dia-
meter, and that Product fhall be the Square
Feet, Furlongs, Miles, &c..of the Surface.
Multiply the Surface by the fixth Part of the
Diameter, and that will give the folid Content.
Note, That Geographers differ a little in
the Computation of thefe Meaſures, becaufe
they
Sect 20. Geography and Aftronomy.
155
they differ in the Meaſure of a fingle Degree:
And that is becauſe of the Crookednefs and
Inequality of any Road that you can travel.
for 70 Miles together: The jufteſt Meaſurers
: have made 69 Miles go to a Degree, or the
round Number of 70 Miles.
1
Dea
Problem XIV. To find the Value of a
gree of a leffer Circle on the Earth, that is, the
Value of a Degree of Longitude on the leffer
Parallels of Latitude.
I have mentioned it before under the IIId
Problem of the 19th Section, that all the Degrees
marked on the Equator, or on any of the
Meridians, are 70 Miles; becaufe all thofe
Lines are Great Circles; yet in the Parallels
of Latitude, the further you go from the
Equator, the Circle grows lefs and lefs, and
conſequently each Degree of it muſt be leſs
alfó; and for this Reafon the whole Circle
of 360 Degrees near the Pole, will not make
above 360 Miles; and as you approach ſtill
nearer to the Pole, it will not make fo
Furlongs or Feet.
2
many
To find therefore the true Value of a De-
gree, fuppofe in the Parallel of Latitude of
London 51 Degrees, ufe this Method, Fig.
xx11. Make a ſtraight Line A B to repreſent
one Degree in the Equator, divide it into
60 Geographical Miles, or into 70 Engliſh
Miles, all equal: Set the Foot of your
M 2
Com-
1
і
ل
i
166
The first Principles of
Sect. 20.
Compaffes in A, defcribe an Arch from в to
c of 51 Degrees, then from the Point c
let fall a Perpendicular to D, and A D is the
Meaſure of a Degree of Longitude in the Pa-
rallel of London, namely, about 43 Miles.
Σ
The Demonſtration of it may thus be ex-
plained. Prolong the Arch в c, and com-
plete the Quadrant E A B. Then E fhall
repreſent the North Pole: E A the Northern
Half of the Axis of the World, A в the Semi-
diameter at the Equator, and N c the Semi-
diameter of the Parallel of Latitude for Lon-
don. Then Arithmetically, if the Line A B
(fuppofe 1000 equal Parts) allow 70 Miles
for a Degree, what will N c (that is, about 621
equal Parts) allow? Anfw. 43.
Or Trigonometrically thus. A B is the
whole Sine of god, or Radius. NC is the
Sine of the Colatitude 38d. Then ſay, As
A B or the Sine god is to 70 Miles, fo is N C
or A D the Sine of 384 to 43 Miles.
2
I
Note, This Diagram or Figure will ſhew
the Value of a Degree of Longitude in any
Parallel of Latitude, if from every Degree
in the Arch ECB a Perpendicular were
drawn to the Line A B.
Therefore a whole Line of Sines, if num-
bered backward, and applied to a Scale of 70
equal Parts, will fhew the Miles contained in
one Degree of Longitude under any Parallel
of Latitude whatfoever.
Having
1
Sect. 20. Geography and Aftronomy.
167
1
Having fhewn in former Problems how to
take the Meridian, Altitude of the Sun, and
thereby to find the Latitude of any Place on
the Earth, I think it may be proper now to
ſhew how to project the Sphere for any Lati-
tude upon the Plane of the Meridian, and re-
preſent it in ftraight Lines, which is called
the Analemma: Becauſe the Erection of this
Scheme (and ſometimes of a little Part of it)
will folve a variety of Aftronomical Problems,
as will appear hereafter.
Problem XV.
}
To erect the Analemma, or
reprefent the Sphere in ftraight Lines for the
Latitude of London 51 Degrees.
2
First, It is fuppofed you have a Scale of
Chords at hand, or a Quadrant ready divided
into 90 Degrees. Take the Extent of 60
Degrees of the Line of Chords in your Com-
paffes, (or which is all one) the Radius of
your Quadrant, and defcribe the Circle N z
EHSQ for a Meridian both North and
South, as in Figure XXIII. namely, NE s,
which repreſents 12 o'Clock at Noon; and
N Qs, which reprefents the Hour of Mid-
night.
Through c the Center draw the Line
Ho for the Horizon. At 90 Degrees Dif-
tance from н and o mark the Point z and
D for the Zenith and Nadir; then draw the
Line z D, which will crofs Ho at Right
M 3
Angles,
1
168
Sect. 20.
The first Principles of
Angles, and will repreſent the Azimuth of
East and Weft; as the Semicircle z o D re-
prefents the North Azimuth, and z HD the
South.
I
Above the Horizon o mark N for the
North Pole elevated 51 Degrees: Through
the Center c drrw the Line N s for the Axis
of the World; which Line will alſo repreſent
the Hour Circle of Six o'Clock, being at 90
Degrees Diſtance from Noon and Midnight,
s will ſtand for the South Pole, depreſſed as
much below н the South Side of the Horizon,
as N the North Pole is raiſed above o on the
North Side of it.
H
At 90 Degrees from N mark E and Q on
each Side; then crofs the Axis of the World
N s with the Line E Q at right Angles, which
reprefents the Equator. Thus E will be 90
Degrees from N the North Pole, 51 De-
grees from z the Zenith, which is the La-
titude, and it will be 38 Degrees above H
the Horizon, which is the Complement of
the Latitude.
At 23 Degrees from E, on each Side mark
the Points M and w; then parallel to the E-
quator, or E Q, draw the Line M for the
Tropick of Cancer, and the ww for the Tro-
pick of Capricorn. After that, through the
Center c draw me which is the Ecliptick;
It cuts the Equator, E Q in c, and makes an
Angle with it of 23 Degrees.
From
1
Sect. 20. Geography and Aftronomy.
169
1
2
From the Points N s mark p and x on each.
Side at the Diftance of 23 Degrees, pp are
the Poles of the Ecliptick, and the Line px
and xp being drawn are the two Polar Cir-
cles, namely, the Arctic and Antarctic.
Thus the Analemma is compleated for all
general Purpoſes or Problems.
The further Obfervables in it are thefe,
namely,
Mis the Sun's Place in the Ecliptick, when
it enters Cancer at the Summer Solstice: And
the Arch E M is its North Declination 23
Degrees.
I
c is the Sun's Place in the Ecliptick enter-
ing Aries or Libra at the Equinoxes: And
then it has no Declination.
is the Sun's Place in the Ecliptick enter-
ing Capricorn at the Winter Solſtice: And
the Arch Qor (which is all one) E w, is
its South Declination 23 Degrees.
The Line M is the Sun's Path the Longeft
Day, or at the Summer Solstice; it is at at
Midnight; it rifes at R ; it is at fix o'Clock at
6; it is in the Eaſt Azimuth at v; it is on
the Meridian at м that Day, and the Arch
MH is its Meridian Altitude, namely, 62
Degrees.
The Line EQ is the Sun's Path on the
two Equinoctial Days at Aries and Libra:
It is at Midnight at Q; it rifes at c, and it
is in the fame Moment at the Eaft, and
fix o'clock; for on the Equinoctial Days
M 4
Z D
170
Sect. 20.
The firft Principles of
1
z D the Azimuth of Eaft and Weft, and N S
the fix o'Clock Hour Line, both meet at c in
the Horizon Ho, which never happens any
other Day in the Year: Then the Sun goes
up to E at Noon; and EH is the Arch of its
Meridian Altitude at the Equinoxes, namely,
38 Degrees.
ww is the Sun's Path the Shorteſt Day, or
at the Winter Solstice; it is Midnight at 3
it is in the Eaſt at K long before it riſes; it
is fix o'clock at G before it rifes alfo; then at
I it rifes or gets above the Horizon; it is
Noon at w, and its Meridian Altitude is
W н, or 15 Degrees.
The Sun's Afcenfional Difference (that is,
its Diſtance from fix o'Clock at its Rifing or
Setting) in the Summer Solftice is the Line
R 6, and at the Winter Solstice it is the Line
I G.
Its Amplitude (or Diſtance from Eaſt or
Weft at its Rifing or Setting) in Summer is
R C; in Winter it is I c.
Here you muſt ſuppoſe that the Sun goes
down again from the Meridian in the After-
noon on the other Side of the Scheme or
Globe, in the fame manner in which its Afcent
toward the Meridian is repreſented on this
Side: So that the Line M R repreſents the
Sun's Semidiurnal Arch at Midfummer, E C
at the Equinoxes, and w I at Mid-winter.
The Semidiurnal Arch is half the Arch it
makes above the Horizon.
Note
#
1
1
1
Sect. 20. Geography and Aftronomy.
171
Note, That as we have deſcribed the va-
rious Places of the Sun's Appearance above
the Horizon H o at the feveral Seafons of the
Year, fo the various Places of its Depreffion
below the Horizon н o may be eaſily found
out and defcribed by any Learner.
Pa-
Problem XVI. How to represent any
rallel of Declination on the Analemma, or to
defcribe the Path of the Sun any Day in the
Year.
Find out what is the Sun's Declination that
Day by fome Scale or Table: Obſerve whe-
ther it be the Winter or the Summer Half-
Year; and confequently whether the Decli-
nation be North or South: Then for the
North Side of the Equator, if it be Summer,
fet the Degrees of North Declination upward
from E toward z; if it be Winter, ſet the
South Declination downward from E toward
H: And from the Point of Declination (ſup-
poſe it be м or w) draw a Line parallel to
E Q the Equator, as м or w, and it re-
prefents the Parallel of Declination, or the
Path of the Sun for that Day.
Problem XVII. How to repreſent any Pa-
rallel of Altitude, either of the Sun or Star
on the Analemma.
As the Lines of Declination are parellel to
the Equator; fo the Lines of Altitude are
parallel
+
172 The first Principles of Sect. 20.
C
parallel to the Horizon: Suppofe therefore
the Altitude of the Sun be about 42 Degrees;
fet up 42 Degrees on the Meridian from н to
A, draw the Line A L parallel to н o, and it
deſcribes the Sun's Parallel of Altitude that
Moment.
Here note, That where the Sun's Parallel of
Declination for any Day, and his Parallel of
Altitude for any Moment crofs each other,
that is an exact Repreſentation of the Sun's
Place in the Heavens at that Time: Thus
the Point Solo is the precife Place where
the Sun is when he is 42 Degrees high on
the longeſt Day of the Year; for M repre-
fents his Path or Parallel of Declination that
Day, and A L repreſents his Parallel of Al-
titude that Moment.
I might add here alfo, that the pricked
Arch Nos repreſents the Hour Circle in
which the Sun is at that Moment; and
z O D repreſents its Azimuth or vertical Circle
at that Time. Note, Theſe Arches are trou-
bleſome to draw aright, and are not at all
neceffary to folve common Problems by the
Scale and Compaffes on the Analemma:
Problem XVIII. The Day of the Month
and the Sun's Altitude being given, how to
find the Hour or Azimuth of the Sun by the
Analemma,
The
Sect. 20.
173
Geography and Aftronomy.
}
The two foregoing Problems acquaint you
how to fix the precife Point of the Sun's Place
any Minute of any Day in the Year by the
Parallel of Declination and Parallel of Alti-
tude croffing each other.
Now fuppofe the Day of the Month be
the 6th of May, and the Sun's Altitude 34
Degrees in the Morning. Defcribe the Semi-
circle н zo in Figure xxiv. for the Meri-
dian. Make н сo the Horizon. Draw E C
making with H c an Angle of the Colatitude
38 Degrees to reprefent the Equator. Seek
the Declination of the Sun, and in the Tables
or Scales you will find it near 16 Degrees
Northward: Set 16 from E to D; draw
DR for the Path of the Sun that Day, pa-
rallel to E C the Equator.
titude 34ª from н to А.
H A,
I
Then fet the Al-
Draw A L- parallel
to Ho the Horizon. Thus the Point o
fhews the Place of the Sun as before.
Now if you would find the Hour, you muſt
draw the Line C N at right Angles with the
Equator E C, which reprefents the fix o'Clock
Hour Line; and the Diſtance 6 o is the
Sun's Hour from fix; that is, his Hour after
fix in the Morning, or before fix in the Af-
ternoon.
If you are to feek the Azimuth, then you
muft draw the Line c z perpendicular to н o,
which is the verticle Circle of Eaſt or
Weſt;
1
1
$
174 The first Principles of Sect. 20.
Weft; then the Extent F o is the Sun's Azi-
muth from East in the Morning, or from Weft
in the Afternoon.
Thus you fee that in order to folve thoſe
two difficult Problems of the Hour or Azi-
muth, you need but a very few Lines to per-
form the whole Operation; for if you want
only the Hour, c z may be omitted; if you
want only the Azimuth, CN may be omitted.
Yet in the Winter Half-Year, fuppofe the
13th of November, when the Declination is
near 18 Degrees South, it muſt be fet down-
ward, as E w from E toward H; then you
cannot fo well find the Hour without
pro-
ducing the fix o'Clock Line N c below the
Horizon down to s, that you may meaſure
the Hour from s or fix.
Obferve alſo, that this little Diagram in Fi-
gure xxiv. will folve a great Variety of Pro-
blems befides the Hour and Azimuth on the 6th
of May: It fhews the Length of the Day by
the Semidiurnal Arch D R. The Sun's Af-
cenfional Difference is 6 R. His Amplitude is
CR. His Azimuth from Eaft or Weſt at fix
is T 6. His Altitude at East and Weft is v c.
His Meridian Altitude is the Arch DH: And
his Azimuth from Eaſt or Weſt at rifing or
Jetting is the Line C R.
Problem XIX. How to measure the Number
of Degrees on any of the ſtraight Lines in the
Analemma.
I think
Sect. 20. Geography and Aftronomy. 175
I think there is no need to inform the Rea-
der that any Part of the outward Circleor Me-
ridian may be meaſured upon that Scale of
Chords or Quadrant, according to whofe Ra-
dius the whole Analemma is drawn.
As for the ſtraight Lines they are all to be
confidered as Sines; thofe Semidiameters
which are drawn from the Center c to the
Circumference, are fo many whole Lines of
Sines, or 90 Degrees, to the common Ra-
dius of the Semicircle. But if you confider
any whole Diameter which paffeth through
the Center c, it is a Line of verfed Sines, that
is, two Lines of right Sines joined at their Be-
ginning to the fame common Radius of the
Semicircle.
If therefore you have a Scale or Line of
Sines at hand to the fame Radius of the Circle,
you may meaſure any Part of thoſe ſtraight
Lines, fetting one Foot of the Compaffes in
the Center c, and extending the other to the
Point propoſed; then applying that Extent to
the Beginning of the Line of Sines, and ob-
ferving how far it reaches.
But if you have no Scale or Line of Sines
at hand, you may find a Quantity of any
Part of the Semidiameter by the outward
Limb or Semicircle, and by the Scale of
Chords, according to whofe Radius the
Semicircle is drawn. The Method of
per-
forming it fee in Figure xxv. where the
Quadrant
1
1
•
176 The first Principles of Sect. 20.
L
Quadrant yxb is drawn by the fame Ra-
dius as the Semicircle in Figure xxiv. But
I choſe to make it a distinct Figure, left the
Lines fhould interfere with one another, and
breed confufion; and therefore in Figure
XXIV. I have uſed capital Letters, in Figure
xxv. all the Letters are fmall.
Suppoſe I would find how many Degrees
are contained in v c which is the Sun's
Altitude at East or Weft: This is a Part
of the Semidiameter cz: Suppofe there-
fore cz to be a whole Line of Sines, be-
ginning to be numbered at c. Take the
Extent vc in your Compaffes, and carry
one Leg up in the Arch yx till the other
Leg will but juſt touch the Diameter
y b,
and the Leg of the Compaffes will reſt at n ;
wherefore it appears that c v in Fig. xxiv.
is the Sine of the Arch yn in Figure xxv. or
21 Degrees.
Another Way to perform it is this. Take
the Extent v c, fet one Leg of the Com-
paffes in y, and with that Extent make a
blind or obfcure Arch at e, and by the Edge
of that Arch lay a Rule from the Center b,
and it will find the 'Point n in the Limb,
namely, 21 Degrees.
By the fame Practice you may find the
Number of Degrees contained in any Part
of thoſe Lines which are drawn from the
Center
1
Sect. 20. Geography and Aftronomy.
177
1
Center c, namely, CH, CE, CM, CZ, CN,
C ó, all which are whole Lines of Sines to
the common Radius of the Quadrant.
But as for thofe Lines in the Analemma
which are not drawn from the Center c,
but are drawn acrofs fome other Diameter
and produced to the Limb, fuch as the Line
6 D, the Line s w, the Line F A, and the
Line F L, each of theſe are to be eſteemed
as a whole Line of Sines alfo, but to a leſs
Radius.
in
So 6 o Figure XXIV. is the Sine of
the Sun's Hour from 6; but the Radius is
6 D, and the Number of Degrees in 6 o
is to be found in this manner. Take the
Extent 6 D, or this whole leffer Radius in
your Compaffes, and fet it from b to
9
Figure xxv; then take the Extent 6 o,
and fetting one Foot of the Compaffes in q,
make an obfcure Arch at o, and a Ruler laid
from b the Center by the Edge of that Arch
o will find the Point D in the Limb, and
fhew that dy is 34 Degrees, which (turn-
ed into Hours) is two Hours 17 Minutes from
fix, namely, 17 Minutes past eight in the
Morning, to 43 Minutes paft three in the
Afternoon.
Again, Fo in Figure XXIV. is the Sine
of the Azimuth from East to West to the
Radius F A; take therefore FA in your
Compaffes,
178
The first Principles of
Sect. 20.
1
Compaffes, and fet it from b top in Figure
XXV; then take the Extent FO, and with
one Foot in p make the obſcure Arch a;
by the Edge of that Arch lay a Ruler from
b the Center, and you will find the Point s
in the Limb; therefore ys is the Azimuth
from East to West, that is, about 17 Dẹ-
grees.
Note, If you have the Inftrument called
a Sector at hand, and know how to uſe it,
you may with great Eaſe and Exactnefs find
the Value of any Sine in the Analemma, whe-
ther it be to a greater or a leffer Radius,
without theſe Geometrical Operations.
Problem XX. To find the Sun's Place in
the Ecliptick any Day in the Year.
It is well known that the 12 Signs of the
Zodiack, each of which has 30 Degrees, con-
tains in all 360 Degrees: And the Sun is
faid to go through them all once in twelve
Months, or a Year. Therefore in a vulgar
Account, and for the Ufe of Learners, we
generally fay, the Sun goes through one De-
gree in a little more than a Day, and thereby
finiſhes the 360 Degrees in 365 Days. But
this is not the juſteſt and moſt accurate Ac-
count of Things: Let us therefore now, to-
ward the End of this Book, with a little
more Exactneſs obſerve,
x. That
:
}
Sect. 20. Geography and Aftronomy.
179
1
1. That the annual Courſe which the Sun
appears to take through the Ecliptick round
the Earth, is much more properly and truly
afcribed to the Earth's moving or taking its
Courſe round the Sun; though the common
Appearances to our Eye are much the fame
as if the Sun moved.
2. This annual Courfe or Path of the
Earth is not properly a Circle, but an Ellipfis
or Oval : And as the Sun is fixed in one of
the Focus's of the Ellipfis, fo the fixed Stars,
(and among them the 12 Signs) furround and
encompaſs it. See Fig. xxxI. where the
black Point t is the Earth in its Orbit mov-
ing round, and o the Sun near the Middle,
and the outward Circle of Points is the ſtarry
Heaven.
3.
That Part of this Ellipfis or Oval,
which the Earth traces in our Winter Half-
Year, (that is, from Autumn to Spring) is
nearer to the Sun than the other Part of it
which the Earth traces in our Summer Half-
year, (that is, from Spring to Autumn.) And
as it is nearer to the Sun, fo confequently it
is the ſhorter or leffer Half, if I may fo ex-
preſs it.—The very Figure fhews it plainly.
Note, By our Winter and our Summer, I
mean thoſe Seaſons as they reſpect us in
Europe, and in thefe Northern Parts of the
Globe.
1
1
N
4. Thence
180
Sect. zo.
The first Principles of
*
4.
Thence it follows that the Sun appears
to finish its Winter Half-year from Septem-
ber 23d to March 20th, that is, from
by
to fooner by 7 or 8 Days than it does
the Summer Half-year, that is, from v by
to, or from March 20th to September
23d, which is proved thus: When the
Earth is at t, the Sun appears at, and it is
Midfummer. When the Earth is at e the
Sun appears at and it is Autumn. When
the Earth is at a the Sun appears at w, and
it is Midwinter. And when the Earth is at
a the Sun appears at and it is Spring. Thus
the Sun appears to paſs through thofe Signs
which are juſt oppofite to thofe which the
Earth paffes. Now as the Earth is longer in
going through the Arch at e, from to
, than it is in going through the Arch e o a
from v to, fo confequently the Sun ap-
pears to paſs through the oppofite Signs from
Aries to Libra, flower than he does from
Libra to Aries.
This is proved alſo plainly by the Com-
putation of Days.
After the Sun enters Aries on March
20th, that Month hath 11 Days; and af-
ter the Sun enters Libra on September 23d,
that Month hath eight Days.." Now let us
compute.
1
March
4X4
Se&t. 20. Geography and Aftronomy.
181
March
II
April
30
Y❘ September
October
8
31
May
June
July
31
November
30
30 Days. December
31 Days.
31
January
31
Auguft
31
September
22
February
March
28
20
Summer 186 Days.
Winter
179 Days.
5. Agreeably hereto it is found, that in the
Winter Months (chiefly from the latter End
of October to the Middle of March) the Sun
appears to move fomething more than one
Degree in a Day: But in the Summer Months
(chiefly from the Middle of March to the
latter End of October) the Sun appears to move
fomething less than one Degree in a Day.
This is one Reaſon why a good Pendulum
Clock meaſures Time more juftly than the
Sun And it is this Irregularity of the Sun's
meaſuring Time, that makes the Tables of
Equation of Time neceffary.
6. And thence arifes a fenfible Inequality
between the Times of the Sun's apparent
Continuance in different Signs of the Zodiack:
He ſeems to tarry longer in thoſe of the Sum-
mer, and ſhorter in thoſe of the Winter: So
that he does not leave one Sign, and enter
another juſt in the fame Proportions or Dif-
tances of Time every Month,
N 2
7.
This
រ
182
Sect. zo.
The first Principles of
}
7.
This occafions a little Variation of the
Declination of the Sun, and his Right Afcen-
hon from the Regularity that we might ex-
pect; for they are both derived from his ap-
parent Place in the Ecliptick: And therefore
none of them can be found by Learners with
the utmoſt Exactneſs, but in an Ephemeris or
Tables which fhew the Sun's Place, &c.
every Day in the Year.
8. Let it be noted alfo, that the Leap-year
with its additional Day the 29th of February,
returning every four Years, forbids the Sun's
Place in the Ecliptick to be exactly the fame
at the fame Day and Hour of the following
Year, as it was in the foregoing; ſo that
though you knew the Sun's Place, his Right
Afcenfion and Declination for one whole
Year, that would not ferve exactly for the
next Year, for the niceſt Purpoſes of Aſtro-
nomy.
9. Yet as in four Years Time the Sun ap-
pears very nearly at the fame Place in the
Heavens again at the fame Day, and Hour,
and Minute, as before, fo a Table that con-
tains the Round of four Years is a fufficient
Direction for 20 Years to find the Sun's Place
for any common Purpoſes : Provided always,
that we ſeek the Sun's Place, Declination or
Right Afcenfion, for any Year and Day in
that Year in the Table that is equally diftant
from Leap-year, whether it happens to be the
firft,
譬
​(
1
Sect. 20. Geography and Aftronomy.
183
firft, the fecond, or the third after Leap-
year, or whether it be the Leap-year itſelf.
See more of this Matter Sect. XXI. of the
Tables of Declination.
10. If we would make one fingle Table or
Scale of the Sun's Entrance into the Signs of
the Zodiack, or of his Declination or Right
Afcenfion to ſerve for every Year, we muſt
chuſe the ſecond after the Leap-year, becauſe
that comes nearest to the mean or middle
Courfe and Place of the Sun, and will occa-
fion the leaft Error in any Operations.
I have therefore here fet down a fhort Ta-
ble of the Sun's Entrance into the feveral
Signs, for the Year 1754, which is the ſecond
after Leap-year; and for Geometrical Opera-
tions with a plain Scale and Compafs, it is
fufficiently exact for 20 Years to come.
Anno 1754, the ſecond after Leap-year.
Day
March 20 - ရာ
April 20-
d.
m.
Day
o: 09
Sept.
23
0: 19
Oct.
23
m
II
o: 16 Nov.
22
15 Dec.
22
o: 25 Jan.
21
| May
21
Junë 22
July 23
August 23
O : II Feb. 20
Mw
w
d.
m.
O: 21
O 3
0 : 14
0: 44
0:33
X
Q
: 55
It is not poffible to form all this irregular
Variety of Times when the Sun enters the
feveral Signs into any Memòrial Lines or
Rhymes
N 3
184
Sect. 20.
The firft Principles of
Rhymes with any Exactnefs and Perfpi-
cuity; and therefore I have omitted the
Attempt. Such a ſhort Table as this may
be always carried about by any Perfon who
deals frequently in fuch Operations and In-
quiries.
1
But to give an Example of the Practice.
Suppoſe it be inquired, what is the Sun's
Place, April 25th, I find the Sun juſt entered
into Taurus & April the 20th, then I reckon
it is in the 5th Degree of 8 April 25th, which
added to the whole 30 Degrees of Aries, fhews
the Sun to be 35 Degrees from the Equinoc-
tial Point on the 25th of April.
If the 29th of November we inquire the
Sun's Place, we muſt confider the Sun is
juft entered ↑ the 22d of November : There-
fore on the 29th it is about ſeven Degrees in
4; which added to 30 Degrees of m, and
30 Degrees of, fhews the Sun on the 29th
of November, to be about 67 Degrees from
the Autumnal Equinox, or .
Thus by adding or ſubtracting as the Caſe
requires, you may find the Sun's Place any
Day in the Year: And thence you may com-
pute its Diſtance from the nearest Equinoc-
tial Point, which is of chief Uſe in Opera-
tions by the Analemma.
Problem XXI. The Day of the Month being
given, to draw the Parallel of Declination for
that
!
Sect. 20. Geography and Aftronomy.
185
that Day without any Tables or Scales of the
Sun's Declination.
2
This may be done two Ways. The first
Way is by confidering the Sun's Place in the
Ecliptick; as May the 6th, it is 46; Degrees
from the Equinox Northward. Therefore
in Figure xxiv. after you have drawn н z o
H
the Meridian, E c the Equator, fet up 23
Degrees the Sun's greateft Declination from
E to M ; draw me to reprefent the Eclip-
tick; then take 46 Degrees from a Line or
Scale of Sines, and fẹt it from c the Equi-
noctial Point to K in the Ecliptick; through
the Point K, draw DR parallel to EC the
Equator. Thus D R reprefents the Sun's Path
that Day, and fhews the Declination to be
E D, or 161.
Note, If you have not a Scale of Sines
at hand, then take the Chord or the Arch of
461 Degrees, ſet it up in the Limb from H
to G, fet one Foot of the Compaffes in G, and
take the neareſt Diſtance to the Line н o, or
Diameter, and that Extent is the Sine of 46½
Degrees.
The other Way of drawing a Parallel of
Declination, is by feeking what is the Mori-
dian Altitude for the 6th of May, and you will
find it to be 55 Degrees. Set up therefore the
Arch of H
55 Degrees from н to D; and from
the Point D draw DR a Parallel to E C, which
hews the Declination and Sun's Pathas before.
Thus
N 4
186
Sect. 20.
The first Principles of
$
'Thus tho' you have no Scales or Tables of
the Sun's Declination at hand, you fee it is
poffible to find the Hour and Azimuth, and
many other Aftronomical Problems by the
Analemma for any Day in the Year. But
this Method which I propofed of performing
them, by finding the Sun's Place in the Eclip-
tick by any fhort general Scale or Table, is
liable to the Miſtake of near half a Degree
fometimes.
Obferve here, if you have by any Means
obtained and drawn the Sun's Path, namely,
DR for any given Day, you may find both
the Sun's Place in the Ecliptick, and its Right
Afcenfion, by drawing c M the Ecliptick. For
then C K will be the Sine of the Sun's Place
or Longitude to the common Radius c м:
And 6 K will be the Sine of the Sun's Dif-
tance on the Equator from the neareſt Equi-
noctial Point, but the Radius is 6 D: From
hence you may eafily compute its Right Af-
cenfion.
Note, Though the little Schemes and
Diagrams which belong to this Book, are
fufficient for a Demonftration of the Truth
and Reaſon of thefe Operations, yet if you
have Occafion to perform them, in order
to find the Hour or Azimuth with great、
Exactneſs, you muſt have a large flat Board,
or very ſtiff Paſteboard with white Paper
paſted on it, that you may draw a Semi-
circle
Sect. 20. Geography and Aftronomy. 187
;
circle upon it of 9 or io, or rather i2 Inches
Radius and the Lines muſt not be drawn
with Ink, nor with a Pencil; for they cần-
not be drawn fine enough: But draw them
only with the Point of the Compaſs; and
you muft obferve every Part of the Opera-
tion with the greateſt Accuracy, and take
the Sun's Place or Declination out of good
Tables For a little Error in fome Places
will make a foul and large Miſtake in the
final Anſwer to the Problem.
Yet if the Sun be within feven or eight
Days of either Side of either Solſtice, you
may make the Tropic of Cancer or Capricorn
ſerve for the Path of the Sun, without any
fenfible Error; for in 16 Days together at
the Solſtices, its Declination does not alter
above 12 or 15 Minutes : But near the Equi-
nox you muſt be very exact; for the Decli-
nation alters greatly every Day at that Time
of the Year.
There might be alfo various Geographical
Practices or Problems, that relate to the
Earthly Globe performed by the Affiſtance
of the Analemma, and feveral other Aitro-
nomical Problems relating to the Sun and
to the fixed Stars; but fome of them are
more troubleſome to perform; and what I
have already written on this Subject is ab ɔn~
dantly fufficient to give the Learner an A
quaintance with the Nature and Rea
f
of
1
1
188
Sect. 20.
The first Principles of
}
1
of thefe Lines, and the Operations that are
performed by them. And for my own Part
I must confefs, there is nothing has contri-
buted to eſtabliſh all the Ideas of the Doctrine
of the Sphere in my Mind, more than a per-
fect Acquaintance with the Analemma.
Problem XXII. How to draw a Meridian
Line, or a Line directly pointing to North and
South on a Horizontal Plane, by the Altitude
or Azimuth of the Sun being given.
At the fame Time while one Perfon takes
the Altitude of the Sun in order to find the
Azimuth from Noon by it, let another hold
up a Thread and Plummet in the Sun-
Beams, and mark any two diftant Points in
the Shadow, as A B, Figure XXVI. and then
draw the Line A B: Suppoſe the Azimuth
at that Moment be found to be 35 Degrees,
draw the Line A E at the Angle of 35 De-
grees from A B, and that will be a true Me-
ridian Line.
You muſt obſerve to fet off the Angle on
the proper Side of the Line of Shadow Eaft-
ward or Westward, according as you make
your Obſervation in the Morning or in the
Afternoon.
Note, Where you use a Thread and
Plummet, remember that the larger and
heavier your Plummet is, the fteadier will
your
Sect. 20. Geography and Aftronomy. 189
1
your Shadow be, and you will draw it with
greater Eafe and Exactneſs.
In this and the following Operations to
draw a Meridian Line, you must be fure that
your Plane be truly Level and Horizontal, or
Performances will not be true.
elfe
your
Problem XXIII. To draw a Meridian
Line on a Horizontal Plane, by a perpendi-
cular Style.
Note, That when I ſpeak of a perpendicu-
lar Style, I mean either of thoſe three Sorts
of Styles before-mentioned in Problem I. name-
ly, A ftraight Needle ftuck into the Board
perpendicularly, as Figure xv. A ftraight or
crooked Wire fuck in floping at Random with
the perpendicular Point found under the Tip
of it, as Figure xvI; or the Brass Prifm,
as Figure XVII.
For what I call a perpen-
dicular Style may be applied and afcribed to
either of theſe.
Make feveral parallel Circles or Arches,
as Figure XXVII: In the Center of them
fix your perpendicular Style N c. Mark in
the Morning what Point in any Circle the
End of the Shadow touches, as A. In the
Afternoon mark where the End of the Sha-
dow touches the fame Circle, as o: Divide
the Arch A o juft in Halves by a Line drawn
from the Center, and that Line c M will be
a true Meridian Line.
The
1
190
The first Principles of Sect. 20.
The Reaſon of this Practice is derived
hence, namely, that the Sun's Altitude in the
Afternoon is equal to the Sun's Altitude
in the Morning, when it cafts à Shadow of
the fame Length: And at thoſe two Moments
it is equally diſtant from the Point of Noon,
or the South, which is its higheſt Altitude;
therefore a Line drawn exactly in the Middle
between theſe two Points of Shadow, muft
be a Meridian Line, or Point to the North
and South.
This Problem may be performed by fix-
ing your perpendicular Style firft, and ob-
ferving the Shadow a before you make the
Circles, (efpecially if you ufe the Brafs
Prifm, or the floping Style with the perpen-
dicular Point under it) then fet one Foot of
your Compaffes in the perpendicular Point
c, extend the other to A, and fo make the
Circle.
If you uſe the Prifm for a Style, you may
mark a Line or Angle at the Foot of it where
you firſt fix it, and place it right again, tho'
you move it never ſo often.
It is very convenient to mark three or four
Points of Shadow in the Morning, and
accordingly draw three or four Arches or
Circles, left the Sun fhould not happen to
ſhine, or you ſhould not happen to attend
juft at that Moment in the Afternoon when
the Shadow touches that Circle on which
you
Sect. 20. Geography and Aftronomy.
191
1
you marked your firft Point of Shadow in the
Morning.
If you would be very exact in this Opera-
tion, you ſhould tarry till the Sun be gone
one Minute further Weftward in the After-
noon, that is, till one Minute after the Shadow
touches the fame Circle, and then mark the
Shadow; becauſe the Sun in fix Hours Time
(which is one Quarter of a Day) is gone
Eastward on the Ecliptick in his Annual
Courfe one Minute of Time, which is fifteen
Minutes (or one Quarter) of a Degree.
Problem XXIV.
To draw a Meridian
Line on a Horizontal Plane by a Style or
Needle fet up at Random.
1
Another Method near akin to the former
is this: Set up a Needle or fharp-pointed
Style at Random, as N D in Figure xxvIII.
Fix it very faft in the Board, and obferve a
Point of Shadow in the Morning, as A. Then
with a Pin ſtuck on the Tip of the Style N,
(without moving the Style) draw the Arch
A SO: Mark the Point of Shadow o, in the
Afternoon when it touches that Arch (or ra-
ther when it is one Minute paft it.) Then
draw the Line A o and bifect it, or cut it in
Halves by a perpendicular Line ME, which
is a true Meridian.
Note, In this Method you have no
Trouble of fixing a Style perpendicular,
nor
1
1.
192 The firft Principles of Sect. 20.
nor finding the Point directly under it for a
Center; but in this Method as well as in the
former, it is good to mark three or four Points
of Shadow in the Morning, and draw Arches
or Circles at them all, for the fame Reaſon as
before.
Obferve here, That in theſe Methods of
drawing a Meridian Line by the Shadow of
the Tip of a Style, I think it is beſt generally
to make your Obfervations between eight and
ten o'clock in the Morning, and between two
and four in the Afternoon. Indeed in the
three Summer Months, May, June, and Ju-
ły, you may perhaps make pretty good Ob-
fervations an Hour earlier in the Morning, and
later in the Afternoon; but at no Time of
the Year ſhould you do it within an Hour of
Noon, nor when the Sun is near the Hori-
zon, for near Noon the Altitude of the Sun,
or the Length of Shadow varies exceeding lit-
tie; and when the Sun is near the Horizon,
the Point and Bounds of the Shadow are not
'full and ſtrong and diſtinct, nor can it be
marked exactly.
Therefore if in the three Winter Months,
November, December, or January, you make
your Obfervation, you ſhould then do it half
an Hour before or after ten o'Clock in the
Morning, and fo much before or after Two
in the Afternoon; for otherwife the Sun will
be either too near Noon, or too near the Ho-
rizon.
But
Sect. 20. Geography and Aftronomy. · 193
But in general, it may be adviſed that the
Summer Half-year is far the beſt for Obſer-
vation of Shadows in order to any Operations
of this Kind.
Problem XXV. To draw a Meridian Line
on an Equinoctial Day.
On an Equinoctial Day, or very near it, as
the eighth, ninth, or tenth of March; or the
11th, 12th, or 13th of September, you may
make a pretty true Meridian Line very eaſily
thus by Figure xxix.
Mark any two Points of Shadow as A B
from a Needle CD fet up at Random, (no
Matter whether it be either upright or
ftraight.) Let thoſe two Shadows be at leaſt
at the Diſtance of three or four Hours from
each other, and it is beſt they ſhould be ob-
ferved one in the Morning, and the other about
the fame Diſtance from 12 in the Afternoon;
and then draw the Line A-B which reprefents
the Equinoctial Line, and is the Path of the Sun
that Day: Croſs it any where at right Angles,
and м N, or o P, are Meridian Lines.
Note, It is beft to mark feveral Shadows
that Day, as S S S, and draw a right Line
ASS B by thoſe which lie neareſt in a right
Line, that you may be the more exact.
Problem XXVI. Todraw a Meridian Line
by a Point of a Shadow at Noon.
4
If
1
194
The firſt Principles of Sect. 20.
If you have an exact Dial to whoſe Truth
you can truſt, or a good Watch or Clock fet
exactly true by the Sun that Morning, then
watch the Moment of 12 o'Clock, or Noon,
and hold up a Thread and Plummet againſt
the Sun, and mark the Line of Shadow on a
Horizontal Plane, and that will be a true
Meridian Line.
Or you may mark the Point or Edge of
Shadow, by any thing that ftands truly per-
pendicular, at the Moment of 12 o'clock,
and draw a Meridian Line by it.
Problem XXVII. To draw a Meridian
Line by a Horizontal Dial.
If you have a horizontal Dial which is
not faftened, and if it be made very true,
then find the exact Hour and Minute by a
Quadrant, or any other Dial, &c. at any
Time of the Day, Morning or Afternoon ;
fet the horizontal Dial in the Place you de-
fign, to the true Hour and Minute; and the
Hour Line of 12 will direct you to draw a
Meridian.
Or if your Dial be ſquare, or have any
Side exactly parallel to the Hour Line of 12,
you may draw your Meridian Line by that
Side or Edge of the Dial.
Problem XXVIII. How to transfer a
Meridian Line from one Place to another.
There
Sect. 20. Geography and Aftronomy.
195.
1
There are ſeveral Ways of doing this.
Ift Way. If it be on the fame Plane, make
a parallel Line to it, and that is a true Meri-
dian.
IId Way. If it be required on a different
Plane, fet fome good Horizontal Dial at the
true Hour and Minute by your Meridian Line
on the firſt Plane, then remove it and ſet it
to the fame Minute on the fecond Planė,
and by the 12 o'Clock Line mark your new
Meridian.
Note, If the Sides or Edges of your Hori-
zontal Dial are cut truly parallel to the 12
o'Clock Line, you may draw a Meridian by
them as before.
IIId Way. Hold up a Thread and Plum-
met in the Sun, or fet up a perpendicular
Style near your Meridian Line any Time of
the Day, and mark what Angle the Line of
Shadow makes with that Meridian Line on
your firſt Plane; then at the fame Moment,
as near as poffible, project a Line of Sha-
dow by the Thread, or another perpendicu-
lar Style on the new Plane, and fet off the
fame Angle from it, which will be a true
Meridian.
Note, Two Perfons may perform this bet-
ter than one.
Problem XXIX. How to draw a Line of
East and Weft on a Horizontal Plane.
Where
}
196 The first Principles of Sect. 20.
Where a Meridian Line can be drawn,
make a Meridian Line firft, and then croſs it
at right Angles, which will be a true Line of
East and Weft.
But there are fome Windows in a Houſe
on which the Sun cannot fhine at Noon ;
in fuch a Cafe you may draw a Line of Eaft
and Weft ſeveral Ways.
Ift Way. You may ufe the fame Practice
which Problem XXII. directs, with this Dif-
ference, namely, inftead of feeking the Sun's
Azimuth from the South, feek its Azimuth
from Eaſt and Weft, and by a Line of Shadow
from a Thread and Plummet marked at the
fame Time, fet off the Angle of the Sun's Azi-
muth from the Eaft in the Morning, or the
Weft in the Afternoon. A common Obfer-
vation of the Courſe of the Sun will fuffici-
ently inform you on which Side of the Line
of Shadow to fet your Angle.
IId Way. You may ufe the fecond Method
of transferring a Meridian Line by a Hori-
zontal Dial, with this Difference, namely, in-
ftead of uſing the 12 o'Clock Hour Line, by
which a Meridian was to be drawn, ufe the
6 o'Clock Line, which will be East and Weft;
for in a Horizontal Dial it ſtands always at
right Angles with the Meridian.
IIId Way. The third Method of transfer-
ring a Meridian Line will ferve here alfo
but with this Difference, namely, fet off the
;
Gomple-
Sect. 20. Geography and Aftronomy. 197
}
Complement of the Angle, which the Line of
Shadow makes with your Meridian Line on
the firſt Plane, inſtead of ſetting off the fame
Angle, and obferve alſo to ſet it off on the
contrary Side, that fo it might make a right
Angle with a Meridian Line, if that could
have come on the Plane:
1
Problem XXX. How to use a Meridian
Line:
The various Ufes of a Meridian Line are
theſe.
Ift Ufe. A Meridian Line is neceffary in
order to draw an Horizontal Dial on the
fame Plane, or to fix an Horizontal Dial true
if it be made before.
İld Ufe.
A braſs Horizontal Dial may be
removed from one Place to another in feveral
Rooms of the fame Houſe; and fhew the
Hour wherefoever the Sun comes, if either
a Meridian Line, or Line of East and West
be drawn in every Window, by which to fet
a Horizontal Dial true.
IIId Ufe. By a Thread and Plummet, or
any perpendicular Pin, or Poft, caſting a
Shadow precifely along the Meridian Line,
we find the Hour of 12, or the Point of
Noon, and may fet a Watch or Clock ex-
actly true any Day in the Year, if we have
no Dial at Hand.
0 2
IV th
198 The first Principles of
Sect. 20.
IVth Ufe. It is neceffary alfo to have fome
Meridian Line in order to find how a Houſe
or Wall ſtands with regard to the four Quar-
ters of the Heavens, Eaft, Weft, North, or
South, which is called the Bearing of a House
or Wall, that we may determine what Sort
of upright Dials may be fixed there, or what
Sort of Fruit-trees may be planted, or which
Part of a Houfe or Garden is moſt expoſed to
the Sun, or to the ſharp Winds.
Vth Ufe. By obferving the Motion of the
Clouds, or the Smoke, or a Vane or Wea-
ther-Cock, you cannot determine which
Way the Wind blows, but by comparing it
with a Meridian Line, or with a Line of Eaft
and Weft.
When once you have got a true Meridian
Line, and know which is the South, then
the oppofite Point must be North; and when
your Face is to the North, the Eat is at
your Right Hand, and the Weft at your
Left.
VIth Ufe. A Meridian Line will ſhew the
Azimuth of the Sun at any Time, by holding
up a Thread and Plummet in the Sun, and
obferving where the Line of Shadow croffes
it. Or the fharp ſmooth Edge of an upright
Style or Poft will caft a Shadow acrofs
a Meridian Line, and fhew the Sun's Azi-
muth.
VIIth
Sect. 20. Geography and Aftronomy.
199
1
*
VIIth Ufe. If you have a Meridian Line
on a Horizontal Plane you may draw a Cir-
cle on that as a Diameter, and divide it into
360 Degrees: Then fet up a fixed or move-
able perpendicular Style, and it will fhew
the Azimuth of the Sun at all Hours.
VIIIth Ufe. A perpendicular Style on a
Meridian Line will fhew the Sun's Meridian
Altitude by the Tip of the Shadow, accord-
ing to Problem II. And thereby you may
find the Latitude of any Place by Problem
VII.
IXth Uſe. If you have a broad ſmooth
Board with a Foot behind at the Bottom, to
make it ftand, fuch as is defcribed in Prob.
XXIII. of the XIXth Section, and if it be
made to ftand perpendicular on a Horizon-
tal Plane, by a Line and Plummet in the Mid-
dle of it, you may fet the Bottom or lower
Edge of this Board in the Meridian Line,
and by your Eye fixed at the Edge of the
Board and projected along the flat Side, you
may determine at Night, what Stars are on
the Meridian; and then by the Globe (as in
Problem XXXIII. and XXXIV. Sect. XIX.
or by an Inftrument called a Nocturnal, you
may find the Hour of the Night, or by an
eafy Calculation as in the XXXIIId Problem
of this XXth Section,
Problem XXXI. How to know the Chief
Stars, and to find the North Pole.
0 3
If
1
!
200
Sect. 20,
The first Principles of
If you know any one Star,
any one Star, you may find
out all the reft, by confidering firft fome of
the neare Stars that lie round it, whether
they make a Triangle or a Quadrangle, ftraight
Lines or Curves, right Angles or oblique An-
gles with the known Star. This is eafily
done by comparing the Stars on the Globe
(being rectified to the Hour of the Night)
with the preſent Face of the Heavens, and
the Situations of the Stars there, as in Pro-
blem XXXII. Sect. XIX.
And indeed it is by this Method that we
not only learn to know the Stars, but even
fome Points in the Heavens, where no Star
is. I would inftance only in the North Pole,
which is eaſily found, if you firſt learn to
know thoſe feven Stars which are called
Charles's Wain, fee Figure xxx. four of which
in a Quadrangle may reprefent a Cart or
Waggon, b, r, c, d, and the three others
repreſenting the Horfes.
Note alfo, That the Star a is called Alioth,
d is called Dubbe, b and r are called the two
Guards or Pointers, for they point directly
in a ſtraight Line to the North Pole p, which
now is near 2 Degrees ditant from the Star
which is called the North Pole Star.
وى
You may find the North Pole alfo by the
Star Alioth, from which aftraight Line drawn
to the Pole Stars goes through the Pole
Point p, and leaves it at 24 Degrees Diſtance
from the Pole Star.
You
Sect. 20.
201
Geography and Aftronomy.
You may find it alfo by the little Star n,
which is the neareſt Star to the Pole Star s;
for a Line drawn from n to s is the Hypo-
thenuſe of a right-angled Triangle, whoſe
right Angle is in the Pole Point p.
Problem XXXII. To find the Latitude by
any Star that is on the North Meridian.
It has been already fhewn in the Xth Pro-
blem of this Section, how to find the Latitude
of a Place by the Meridian Altitude of a Star
on the South Meridian; but the Methods of
Performance on the North Meridian are dif-
ferent.
The first Way is this. Take the Altitude
of it when it is upon the North Meridian at
five, fax, or feven o'Clock in the Winter, then
12 Hours after vards take its Altitude again,
for it will be on the Meridian on the other Side
of the Fole; fubtract half the Difference of
thoſe two Altitudes from the greateſt Alti-
tude, and the Remainder is the true Elevation
of the Pole, or Latitude of the Place.
A fecond Way. Obferve when the Star
Alioth comes to the Meridian under the
Pole; then take the Height of the Pole Star,
and out of it fubtract 24 Degrees (which is
the Diſtance of the Pole Star from the Poie)
the Remainder will be the true Elevation of
the Pole, or the Latitude. The Reaſon of
this Operation is evident by the xxxth Fi-
04
gure,
1
}
202
Sect. 20.
The first Principles of
gure, for Alioth is on the Meridian under the
Pole juſt when the Pole Star is on the Meri-
dian above the Pole.
Note, The Pole Star is upon the Meri-
dian above the Pole juft at 12 o'Clock at
Night on the 4th of May, and under the
Meridian on the 5th Day of November: Fif-
teen Days after that it will be upon the Me-
ridian at II O'Clock: Thirty Days after at 10
o'Clock: So that every Month it differs about
two Hours.
Problem XXXIII. To find the Hour of
the Night by the Stars which are on the Me-
ridian.
If you have a Meridian Line drawn, and
fuch a Board as I have defcribed under the
9th Ufe of the Meridian Line, you may ex-
actly find when a Star is on the Meridian;
and if you are well acquainted with the Stars,
wherefoever you
fet up
that Board upright on
a Meridian Line, you will fee what Star is on
the Meridian. Suppofe Aldebaran, or the
Bull's Eye, on the 20th of January is on the
South Part of the Meridian; then in fome
Tables find the Sun's or that Star's Right
Afcenfion, and the Complement of the Right
Afcenfion of the Sun for that Day, namely,
3 Hours 6 Minutes to the Right Afcenfion
of the Star 4 Hours 17 Minutes, and it
makes 7 Hours 23
23 Minutes, the. true Hour
of the Afternoon.
Note,
Sect. 20, Geography and Aftronomy.
203
Note, If the Star be on the North Part of
the Meridian, or below the North Pole, it is
just the fame Practice as on the South: For
when any Star is on the Meridian, the Diffe-
rence between the Sun's R. A. and that Star's
R. A. is the Sun's true Hour; that is, its Dif-
tance from 12 o'Clock at Noon, or Midnight,
at which Time the Sun is on the Meridian
either South or North.
If you have no Meridian Line drawn, you
may find within two or three Degrees what
Stars are on the North Meridian thus: Hold
up a String and Plummet, and project it with
your Eye over-right the Pole Star, or rather
the Pole Point, and obferve what other Stars
are covered by it or cloſe to it, for theſe are
on or near the Meridian.
Or it may be done with very little Error
by ſtanding upright and looking ftrait for-
ward to the Pole Star, with a Stick, or Staff,
between your Hands, then raiſe up the Staff
as ſtraight as you can over-right the Pole, and
obferve what Stars it covers in that Motion.
But thefe Methods are rude, and only ſerve
for vulgar Purpoſes.
Problem XXXIV. To find at what Hour
of any Day a known Star will come upon the
Meridian.
Subtract the Right Afcenfion of the Sun
for that Day from the Right Afcenfion of
the
204
The first Principles of Sect. 20.
1
1
the Star, the Remainder fhews how many
Hours after Noon the Star will be on the
Meridian. Suppofe I would know at what
Hour the Great Bear's Guards or Pointers
will be on the Meridian on the 27th of April;
(for they come always to the Meridian nearly
both at once.) The Right Aſcenſion of the
Sun that Day is about two Hours 19 Minutes.
The Right Afcenfion of thofe Stars is always
ten Hours 24 Minutes. Subtract the Sun's
R. A. from the Stars R. A. the Remainder
is five Minutes past eight o'Clock at Night,
and at that Time will the Pointers be on the
Meridian.
Right Afcen. of Pointers is,
Right Afcen. of Sun April 27th is,
Time of Night,
H. M.
ΙΟ
10: 24
2:19
8: 5
Note, If the Sun's Right Afcenfion. be
greater than the Right Afcenfion of the Star,
you must add 24 Hours to the Star's Right
Afcenfion, and then fubtract as before.
You may eafily find alfo what Day any
Star (fuppofe either of the Pointers) will be
on the Meridian juft when the Sun is there,
namely, at 12 o'Clock. Find in the Tables
of the Right Afcenfion of the Sun what Day,
that is wherein the Sun's Right Afcenfion is
the fame (or very near the fame) with that
Star's, which is the 28th of Auguft. The Sun's
Right
Sect. 20. Geography and Aftronomy.
205
1
Right Afcenfion is 10 Hours 28 Minutes, then
the Sun and Star are both on the Noon Me-
ridian near the fame Time. But the Sun's
Right Afcenfion on the 23d of February is 22
Hours 24 Minutes. Therefore the Sun at
that Time is in the Noon Meridian when the
Star is in the Midnight Meridian, there being
just 12 Hours Difference.
Thence you may reckon when the Star will
be on the Meridian at any Time; for about
15 Days after it will be on the Meridian at
11 O'Clock, 30 Days after at 10 o'Clock. So
that every Month it differs about two Hours;
whence it comes to paſs that in 12 Months
its Difference arifing to 24 Hours, it comes
to be on the Meridian again at the fame Time
with the Sun.
Problem XXXV. Having the Altitude of
any Star given, to find the Hour.
To perform this Problem you fhould never
feek the Altitude of the Star when it is within
an Hour or two of the Meridian, becaufe at
that Time the Altitude varies fo very little.
When you have gotten the Altitude, then feek
what is the Star's Hour, that is, its Equatorial
Diſtance from the Meridian at that Altitude,
which may be done by the Globe, or any
Quadrant,
*The Sun or Star's Horizontal Diſtance from the
Meridian is the Azimuth: It is the Equatorial Diſtance
from the Meridian, which is called the Sun or Star's
Hour.
206 The first Principles of Sect. 21,
}
Quadrant, or by the Analemma, juft as you
would feek the Sun's Hour if its Altitude were
given. After this, feek the Difference between
the Sun's Right Afcenfion for that Day and the
Star's Right Afcenfion, and by comparing this
Difference with the Star's Hour, you will find
the true Hour of the Night.
Note, This Method of Operation, though
it be true in Theory, yet it is tedious and very
troubleſome in Practice. The moft ufual
Ways therefore of finding the Hour of the
Night by the Stars (whether they are on the
Meridian or not) is by making ufe of a large
Globe, or the Inftrument called a Nocturnal,
wherein the moſt remarkable Stars are fixed
in their proper Degrees of Declination and
Right Afcenfion: And their Relation to the
Sun's Place in the Ecliptick, and to his Right
Afcenfion every Day in the Year being ſo ob-
vious, makes the Operation of finding the
true Hour very eaſy and pleaſant,
SECT. XXI.
Tables of the Sun's Declination, and of the
Declination and Right Afcenfion of ſeveral
remarkable fixed Stars, together with fome
Account how they are to be uſed.
THE Refolution of fome of the Aftrono-
mical Problems by Geometrical Operations
on the Analemma, requires the Knowledge of
1
the
Sect. 21. Geography and Aftronomy.
207
1
the true Place of the Sun, his Right Afcenfion,
or his Declination at any given Day of the
Year. But fince the Knowledge of his De-
clination is of moſt eaſy and convenient Uſe
herein, and fince his true Place in the Eclip-
tick as well as his Right Aſcenſion may be
nearly found Geometrically when his Decli-
nation is given, (except when near the Sol-
ftices) I have not been at the Pains to draw
out particular Tables of the Sun's Place, but
contented myſelf with Tables of Declination
for every Day in the Year, and Tables of
Right Afcenfion for every tenth Day. Theſe
are fufficient for a young Learner's Practice
in his firſt Rudiments of Aftronomy. Thofe
who make a further Progrefs in this Science,
and would attain greater Exactneſs, muſt ſeek
more particular Tables relating to the Sun in
other larger Treatifes.
Here let thefe few Things be obferved,
I. Thefe Tables fhew the Declination of the
Sun each Day at Noon; for it is then that
the Aftronomer's Day begins. If you would
therefore know the Sun's Declination, ſuppoſe
at fix o'clock in the Morning of any given
Day, you muft compare the Declination for
that Day with the Sun's Declination the fore-
going Day, and make a proportionable Allow-
ance, namely, three-fourth Parts of the Dif-
ference of thoſe two Declinations. If at fix
in
¡
208
The first Principles of Sect. 21:
1
in the Afternoon, you muſt compare it with
the following Day, and allow in the fame
Manner one-fourth Part.
II. Thefe Tables are fitted for the Mëridian
of London. If you would know therefore the
Sun's Declination the fame Day at Noon at
Port Royal in Jamaica, you must confider the
Difference of Longitude. Now that Place
being about 75-Degrees Weftward from Lon-
don, that is, five Hours later in Time, it is
but ſeven o'clock in the Morning there when
it is Noon at London: and you muſt make a
proportionable Allowance for the Difference
of the Sun's Declination, by comparing it with
that of the foregoing Day. If that Place
had the fame Longitude Eastward from Lon-
don, it would be five o'Clock in the After-
noon there; and then you muſt compare the
Sun's prefent Declination with that of the
Day following, and make Allowance for the
five Hours, that is, almoft one-fourth of the
Difference of the two Declinations. But if
you would know the Sun's Declination at
any Place, and at any Hour of the Day at
that Place; find what Hour it is at London
at the given Hour at that Place, and find
the Declination of the Sun for that Hour at
London by Note the firft.
M
}
Note's
Scct. 21. Geography and Aftronomy. 209
Note, Thefe Allowances muſt be added or
Subtracted according as the Sun's Declina-
tion is increaſing or decreaſing.
Yet in any of theſe Geometrical Operations
the Difference of the Sun's Declination at other
Hours of the Day, or at other Places of the
World, is fo exceeding fmall, that it is not
fufficient to make any remarkable Alterations,
except when the Sun is near the Equinoxes
and then there may be fome Allowances made
for it in the Manner I have defcribed; nor
even then is there any need of fuch Allow-
ances, except in Places which differ from
London near 5 or 6 Hours in Longitude.
;
III. Let it be noted alſo, that as the Place
of the Sun, fo confequently his Declination
and Right Afcenfion for every Day, do vary
fomething every Year by reafon of the odd five
Hours and forty-nine Minutes over and above
365 Days, of which the Solar Year confifts.
Therefore it was proper to reprefent the Sun's
Declination every Day for four Years together,
namely, the three Years before Leap-Year,and
the Leap-Year itſelf. For in the Circuit of
thofe four Years, the Sun returns very nearly
to the fame Declination again on the fame
Day of the Year, becauſe thoſe odd five Hours
and 49
Minutes do in four Years Time make
up 24 Hours, or a whole Day (wanting but
four Times eleven, that is, 44Minutes;) which
Day
1
210
The firft Principles of Sect. 21.
Day is fuperadded to the Leap-Year, and
makes the 29th of February, as hath been
faid before.
It is true, that in a confiderable Length of
Time thefe Tables will want further Correc-
tion, becauſe of thoſe 44 Minutes which are
really wanting to make up the fuperadded Day
in the Leap-Year. But thefe Tables will ſerve
fufficiently for any common Operations for
forty or fifty Years to come, provided you al-
ways confult that Table which is applicable to
the current Year, whether it beaLeap-Year, or
the first, the ſecond, or the third Year after it.
IV. Obferve alfo, theſe Tables of the Sun's
Declination are fometimes reduced (as it were)
to one fingle Scale. And for this Purpoſe Men
generally chooſe the Table of Declination for
the Second after Leap-Year, and this is called
the Mean Declination, that is, the Middle be-
tween the two Leap-Years. This is that Ac-
count of the Sun's Place and Declination, &c.
which is made to be reprefented on all Ma-
thematical Inftruments, namely, Globes, Qua-
drants, Projections of theSphere, and graduated
Scales, &c. and this ferves for fuch common
Geometrical Practices in Aftronomy with-
out any very remarkable Error.
Concerning the Table of the fixed Stars,
let it be remembered, that they move flowly
round the Globe Eaſtward in Circles pa-
rallel
1
}
Sect. 21.
Geography and Aftronomy.
211
t
ર.
rallel to the Ecliptick, and therefore they
increaſe their Longitude 50 Seconds of a Mi-
nute every Year, that is, one Degree in fe-
But their Latitude never
venty two Years.
alters, becauſe they always keep at the ſame
Diſtance from the Ecliptick.
Let it be noted alfo, that this flow Motion
of the fixt Stars caufes their Declination and
their Right Afcenfion to vary (though very
little) every Year. Their Right Afcenfion
neceffarily changes becauſe their Longitude
changes, though not exactly in the fame
Quantity. And though their Latitude ne-
ver alters, becaufe Latitude is their Diſtance
from the Ecliptick, yet their Declination muſt
alter a little, becauſe it is their Diſtance from
the Equator. But the Tables of their Right
Afcenfion, which I have here exhibited, will
ferve for any commón Practices for at leaſt
twenty Years to come, and their Declination
for near fifty Years, without any fenfible Er-
ror in fuch Aftronomical Effays as theſe.
It
Learners, that the fame Stars may have North
Latitude, and South Declination; fuch are all
thoſe that lie between the Equator and the
Southern half of the Ecliptick; But all thoſe
Stars which lie between the Equator and the
Northern half of the Ecliptick, have South
Latitude, and North Declination.
may be proper here to give Notice to
P
A
212
Sect. 21.
The firft Principles of
A Table of the Sun's Declination for the Year 1753, being
the first after Leap Year, which will ferve for near 50
Years.
Day.
Janu. Febr. March April May June
S. S.
S*. N.
N. N.
d. m. d. m. d. m.
d. m.
d. m. d. m.
I
22 59 1657
07 24
04 43
15 12
15 12 22 08
5
6
8
~ ~ + i 700
2
22 53 16 40
07 01
05 06
15 30 22 16
3
22 48 16 22
06 38
05 29
15 48 22 23
4
22 41 16 04
06 15
05 52|16 05|22 30
22 35 15 46
05 51
06 14
16 23 22 36
22 27 15 28
05 28
06 37
16 40 22 43
22 19 15 09
05 05
07 00
16 56 22 49
22 11 14 50
04 42
07 22
17 13 22 54
9
22 03 14 31
04 18
07 44
17 28 22 59
10
21 54 14 11
03 55
08 07
17 44
23 04
I I
21 45 13 52
03 31 08 29|17 59
23 08
12 21 35 13 32
|
03 07 08 51 18 14
23 12
13 21 25 13 1202 4409 12
02 44 09 12
18 29
23 16
14
21 14 12 52
02 20 09 34
18 44
23 19
15
21 0312 3101 5709 55
18 58
23 22
16
17
20 52 12 1001 3310 17
20 39 11 49 01 09 10 37
19 12 23 24
19 26 23 25
18
20 27
11 28
00 45
10 58
19 39 23 26
19
20 14 11 06
00 22
11 19
19 5223 27
20
2Ο ΟΙ 10 45
N. 02
11 39
20 05 23 28
21
19 48 10 22
00 25
12 00
20 17 23 29
22
19 34 10 00
00 48
12 20
20 29 23 28
25
26
27
78 21 08 09
02 46 13 58 21 22 23 22
28
18 05
07 46
03 10 14 17
21 3223 19
29 17 49
30 17 31
03 33 14 36
21
42 23 15
03 56 14 54
21
51 23 11
31 17 14
04 19
21 59
23 19 2009 39 01 12
24 19 06 09 16 01 36
08 54 01 59 13 19
18 51
18 36 08 31 02 2313 39 21 12 23 24
12 40
20 4023 27
13 00
20 51 23 26
21 02 23 25
Sect. 21.
213
Geography and Aftronomy.
Table of the Sun's Declination for the Year 1753, being
the firft after Leap-Year, which will ferve for near 50
Years.
Day.
July
Sept. O&.
N.
Nov.
Aug.
N. N*. S.
Dec.
S.
S.
d. m.
d. m. d. m. d. m.
d. m. d. m.
1 2 3 tuo n∞
I
23 07
17 59
08 10
03 20
23 03
17 43
07 48
03 4314 55 22 04
14 36 21 55
5522
22 59
17 28
07 26
04 07 15 14 22 13
4
22
54
17 12
5
22 48 16 56
07 04 04 30 15 32 22 21
06 42 04 5315 51|22 28
22 42 16
об
39 1905 16
16 0922 36
7
22 36 16 23
05 57 05 39
16 27 22 42
8
22 29 16 05
05 34 06 02
16 44
22 48
9
22 22 15 47
05 11 06 25
17 01
22 54
10
22 15 15 30
04 49
06 48
17 18
23 00
II
22.06
15 12 04 26
07 11
17 35
23 05
12
13
15
16
17
18
23+ mo n∞
21 58
14 5404 03
07 34
17 51
23 09
21 49
14 36 03 40
07 56
18 07
23 13
14 21 40 14 18
03 17
08 19
18 22
23 17
21 31
13 59
02 5408 41 18 38
23 20
21 21 13 49
02 30 09 03
09 0318
53
23 23
II
21 11 13 21
02 07
09 25 19
08
23 25
21 ΟΙ 13 02
02 01 44
09 47 19 22
23 26
1920 50 12 4201 20
20 3912 22 00 58
20
10 09 19 36
23 27
10 31 19 50
3119 23 28
21
20 28 12 02 00 34
10 52 20 03
23 29
22 20 15|11 4200 10
11 14
20 16
23 28
23
20 03 11 22|S. 12
II 34
20 29
23 28
24 19 50 11 OI 00 36
11 55
20 41
23 27
25 19 37 10 4100 59
12 16
20 53
23 25
12 36
21 04
23 23
26 19 24 10 20 01 23
27 19 1109 59 01 46
28 18 57 09 37 02 10
29 18 43 09 16 02 33
18 28 08 55 02 57
18 1408 33
30
31
12 57 21 15 23 21
13 17 21 25 23 17
13 37 21 36|23 14
13 57 21 46 23 10
14 16
23.05
214
Sect. 21.
The first Principles of
A Table of the Sun's Declination for the Year 1754, being
the fecond afcer Leap-Year, which will ferve for near
50 Years.
Day
S.
Janu. Febr. March April
S. S*
April
May
May June
N.
N. N.
d. md. m.
d. m.
d. m. d. m.d. m.
I 23 01 17 01
07 29
04 37
15 08 22 06
2 22 55 16 44
07 06
05 00
15 26 22 14
4
322 50 16 27 06 43
22 44 16 09 06 20
05 23
15 44 22 21
05 46
16 01
22 28
5
22 37 15 51 05 57
06 09 16 19|22 35
6
22 2915 3205 34
06 32 16 37 22 41
7 22 21
15 14 05 11
06 54 16 51 22 47
5416
8
22 13
14 55
04 47
07 17 17 08
22 53
9
22 05
14 35
04 24
07 39
17 24
22 58
ΙΟ
21 56 14 16
04 00
08 01
17 40
23 03
II
21 47
13 56 03 37 08 23
17 55 23 07
12
13
21 37 13 37 93.1308 45 18 11 23 11
21 27 13 16 02 50 09 0718 26 23 15
14
15
21 17 12 56 02 26 09 29
21 0612 36|02 02|09 50
18 40
23 18
18 55
23 21
16
19 09 23 23
17
18
78
19
20
21
22
23
~ ~ ~
20 55 12 1501 3910 11
20 42 II 5401 1510 32
20 30 11 33 00 51 10 53
20 1711 12 00 28 11 14
20 0410 49 00 04 11 34
19 51 10 27 N. 1911 55
19 38 10 06 00 43 12 15
19 24 09 44 01 06 12 35
2419 09 09 2201 30 12 55
18 55 08 5901 53
19 22 23 25
19 36 23 26
19 49 23 27
20 02 23 28
20 14 23 29
20 26 23 29
20 38 23 28
20 49 73 27
25
13 15
20 59 23 26
2 2
26
I
18 40 08 37 02 17
13 34
21 10 23 24
27
78
18 24 08 14 02 40
13 53
21 20 23 21
18 08 07 52 03 04
14 12
21 30 23 18
28
29 17 5
17.52
30 17 36
31 17 88
03 27 14 31
03 5114 50
04 14
21 39 23 15
21 49 23 12
21 57
+
Sect. 21.
Geography and Aftronomy. 215
A Table of the Sun's Declination for the Year 1754, being
the fecond after Leap-Year, which will ferve for near 50
Years.
Day.
July Aug.
N. N.
Aug.
Sept. oa.
N*. S.
Nov. Dec.
S.
S.
15 34 9+ 54 06 43
d. m.
d. m.
d. m. d. m.
23 08 18 02 08 15 03 14
23 0417
17 47 07 54 03 38
323 0017 3207 3104 01
22 5517 0904
17 16 07 09 04 24
22 49 17 00
17 00
22 44
4
423 +56 N∞ a
06 47 04 47
16 43 об 25 05 11
22 37 16 26 06 0205 34
0905
16 99 05 4005 57
7
8
22 31
9
IO
22 24
22 17
d. m. d. m.
14 3121 53
14 50 22 02
15 09/22 11-
15 28 22 19
15 52 05 17 06 2016 57 22 53
15 46 22 27
16 0422 34
16 22 22 40
16 40 22 47
17 14 22 58
II
12
22 09 15 17
04 31 07 05
17 31
23 03
22 00 14 59
04 09 07 28
17 48
23 08
13
14
16
17
20
mtno no ao
21 51 14 40
03 45 07 51
18 04
23 12
21 4314 2208
14 22
03 22 08 13
18 19
23 16
15 21 33 14 03
02 5908 36
18 34
23 19
21 24 13 45
02 36 08 58
18 49
23 22
21 14 13 26
02 13 09 20
19 04
23 24
1821 0313 06 01 49 09 42
19 19
23 26
19 20 53 12 47 01 26
10 041 19 33 23 27
20 42 12 2701 03
10 25
19 47
23 28
2 2
21
20 30 12 07 00 39
10 46
20 00
23 29
22
20 18 11 47 00 16
11 08
20 13
23 29
2.320 06 11 27 S. 07
11 29
20 26
23 28
24 19 5311 06 00 30
11 51
20 38
23 27
25 19 40 10 46 00 54
12 11
20 50
23 26
26 19 27
19 2710 2501 17 12 31
2102
23 24
27 19 14 10 0401 4112 52
21 13
23 21
28 19 00 09.4302 04 13 12 21 23
23 18
29 18 46 09 21
02 27 13 3221 33 23 15.
23 06
30 18 32 08 59 02 51 13 52 21 43 23 11
31
18 17
08
37
14 12
е
116
Sect. 21.
The first Principles of
F
A Table of the Sun's Declination for the Year 1755, being
the third after Leap Year, which will ferve for near 58
Years.
Day.
Janu. Febr. March April May June
S.
S.
S*. N. N. N.
d. m. d. m.
d. m. d. m.
d. m. Id. m. d. m.
d. m.
w.nmtno não ao
I
23 02 17 06
07 3504 3015 04
22 04
2
22 57 16 48
07 12 04 54 15 22
22 12
3
22 51 16 3106 49 05 17 15 39
22 20
4
22 45 16 13
06 26
05 39 15 57
22 27
22 3815 55 06 03
06 0316 14
22 33
22 315 37 95 40
06 26
16 31
22 39
7
22 23 15 19 05 16
06 49
16 48
22 46
8
22 15 14 504 53
07 11
17 04 22 51
22 07.14 40 04 29
21 58 14 21 04 06
07 34
17 20 22 57
07
5617 36|23 02
II
21 4914 0103 43
0
18
17 52 23 06
I 2
21 40 13 41
03 19 08 40
18 07 23 10
13
21 30 13 21
02 55
09 02
18 22 23 14
14
21 19 I 13
02 32 09 24
18 37
23 17
15
21 09 12 41
02 03 09 45 18 51
23 20
16
20 57 12 2001 4410 0619 05
23 23
17 20 45 11 59 01 21
10 27 19 19
23 25
18
20 3311 38 00 57
io 48 19 33
23 26
19
20 20 11 17 00 33
11 09
19 46
23 27
20
20 08 10 55 00 10
11 29
19 59
23 28
21
19 54 10 33. 13
11 50
20 11
23 29
22
19 4110 100 37
12 10
20 23
23 29
23
19 27 09 49 01 00
12 30
20 35
23 28
24
19 13 09 2791 24
12 50
20 46
23 27
~ ~ ~ N
25 18
58 09 05 01 48
13 10
20 57
43 26
Zú
18 43 03 42 02 11
13 29 21 07 23 24
27
18 28 08 20
02 35
13 49 21 18 23 22
28
18 12 07 57
02 58
14 08
29
17 56
30 17 40
03 22 14 27
03 45 14 45
21 28 23 19
21 37 23 16
21
46 23 13
31
17 2
04 08
21
55
Sect: 21. Geography and Aftronomy. 217
}
A Table of the Sun's Declination for the Year 1755, being
the third after Leap-Year, which will serve for near
50 Years.
Day.
July Aug.
Aug.
Sept.
Sept.
Oct:
Nov.
Dec.
N.
N. N*.
S.
S.
S.
d. mn. d. m.
d. m.
d. m.
d. m.
d. m.
1 ~ Mtuno 7∞ a
I
23 09 18 06
08 21
03 09
14 26
21 50
2
23 051751
07 59
03 32
14 46
22 00
3 23 01
17 35
07 37
03 55
15 05
22 09
4
22 56 17 20
07 15
04 19
15 23
22 17
22 51 17 04
06 53
04 42
15 42
22 24
22 45 16 47
06 30
05 05
16 00
22 35
22 39 16 30
06 08
05 28
16 18
22 38
8
22 32 16 13
05 45
05 51
16 36
22 45
J
9
22 26 15 56
05 22
06 14
16 53
22 51
10
22 18 15 38
04 00 06 37
17 10
22 57.
1 I
22 10 15 21
04 37 07 00
17 26
23 02
12 22 0215 03
04 14:07 23
17 43
23 07
13
21 53 14 45
03 51 07 45
17 59
23 11
1
14 21 45 14 27 03 28
08 07
18 15
23 15
15
21 36 14 08 03 05
08 29
18 30
23 18
16
21 26 13 49 02 42
08 51
18 46
23 21.
17 21 16 13 30 02 18
09 14
19 01
23 23
1
18
21 06 13 11 01 55
09 36
19 15
23 25
19
20 5512 51
OF 32
09 57
19 30
23 27
20
20 44 12 32 01 08
10 19
19 43 23 28
21
28
22 20 21 11 52 00 21
23 200911 32 S. 02
24 19 561 II 00 25
25
19 44 10 5100 48
26 19 31 10 30 01 11
27 19 17 10 0901 35
19 04/09 48 01 58
20 33 12 12 00 45 10 41 19 5723 29
II 02 20 1023 29
11 2320 2323 48
11 45 20 35 23 27
29 47 23 26
12 05
12 26
20 58 23 24
12 47
21 09 23 21
13 07
21 20 23 18
29
18 50 09 25 02 21
13 27
21 31
31|23 15
30 18 35 09 04
02 45
13 47
21 41 23
31-18 2109 42
£407
23 08
Q 2
218
Sect. 21.
The firft Principles of
A Table of the Sun's Declination for the Year 1756,
being Leap-Year, which will ſerve for near 50 Years.
}
Day.
S.
Janu. Febr. March April
S. S*. N. N.
May
June
N.
d. m. d. m. d. m.
d. m. d. m. d. m.
1
- 2 3 4 5 6 7∞
23 03 17 10
07 17
22
58 16 53
06 54
22 52 16 35
06 28
04 4915 17|22 10
05 12 15 35 22 17
05 35 15 52
22 24
22
46 16 17
06 08
05 5816 09 22 31
22
39 15 59
05 45
06 21
16 26 22 381
22 32 15 41
05 22
06 43
16 43 22 44
22 25 15 23
04 59
07 06
17 00 22 50
8
9
ΙΟ
II
12
22 17 15 04 04 35
22 09 14 45 04 12
22 01 14 2603 48
21 5214 06 03 25
21 42 13 46 03 01
13 21 32 13 26 02 37
14 21 22 13 06 02 14
ZI II 12 46 01 50
21 00 12 25 01 26
20 49 12 04 01 03
15
16
17
07 28 17 16 22.56
07 50 17 32 23 01
08 13|17 48|23 05
08 35 18 03 23 10
08 57 18 18 23 14
09 1818 33 23 17
09 39 18 48 23 20
10 0019 02 23 22
10 22 19 16 23 24
10 43 19 29 23 26
18 20 37 11 4300 39|11 0419 42 23 27
19 20 24 11 22 00 16
20 20 II 10 00 N. 07
11 24 19 55 23 28
11 45
20 07
23 28
21
19 58
10 3800 31
12 05
20 19
23 29
22
19 44 10 16 00 55
12 25
20 31
23 28
23 19 30 09 54 01 18
12 45
20 43
23 28
24 19 16 09 32 01 42
13 05
20 54
23 27
25 19 02 09 10
02 06
13 25 21 05
23 25
26 18 47 08 48
27 18 32 08 25
28 18 16 08 03
29 18 00 07 40
3017 34
31 17 27
02 29
13 44 21 15
23 23
02 53
14 0321 25 23 20
03 16|14 22 21 35 23 17
03 39 14 41
04 03 14 59
04 26
21 44 23 14
21 53 23 10
22 02
Sect. 21.
Geography and Aftronomy. 219
A Table of the Sun's Declination for the Year 1756,
being Leap-Year, which will ferve for near 50 Years.
Day.
July
Oct.
Aug. Sept.
Nov.
Dec.
N.
N. N*.
S.
S.
S.
d. m. d. m. d. m. d. m.ld.
m. d. m.
#23456 7∞
2306
17 55 08 04:03 26
14 41
21 57
23 02
17 3907 42 03 50
15 00
22 06
22 57
17 24 07 20 04 13
15 19
22 15
22 52
17 08 06 58 04 36
15 37
22 23
22 46 16 5106 36 04 59
15 56
22 30
22 40 16 34 06 I 1305 2316 14
22 37
22 34 16 17 05 5105 46
16 31
22 43
8
22 27
16 00 05 28 06 09
16 49
22 50
9
22 20 15 43 05 05 06 32
17 06
22 56
10
22 12 15 25
04 42
06 54
17 23
23 01
II
22.0415 07 04 20
07 17 17 39
23 06
12
13
21 55 1 14 4903 57
21 47 14 31 03 33
07 40 17 55
23 10
08 0218 11
23 14
14
21 38
14 13 03 10
08 25 18 27
23 18
15
21 28
16
17
18
86 9.
19
20
20 36
13 54 02 47
21 19 13 35 02 24
21 08 13 16 02 01
20 58 12 56 01 37
20 47 12 37 01 14
12 17 00 51
08 47
18 42
23 21
09 09
18 57
23 23
09 31 19 12
23 25
09 5319 26
23 27
10 15 19 40
23 28
10 36 19 54
23 28
21
20 24 11 57 00 27
10 57
20 07 23 29
22
20 12 11 37 00 04
11 18
20 20 23 28
23 19 59 11 16 S. 19
24 19 47 10 56
11 39
20 32 23 28
00 42
12 00
20 45 23 27
25 19 34 10 35 01 06 12 21
20 56 23 25
26 19 21 10 14
27 19 0709 53
28 18 53
18 53 09 32
29 18 39 09 10
30 18 2408 48
31 18 10.08 26
01 29 12 42
01 53 I 13 02
02 16| 13
02 40
21 18
13 02
22
02 40 13 42
03 03 14 02
14 22
21 07 23 22
21 18 23 19
21 28 23 16
21 38 23 13
21 48 23 09
23 04.
220
Sect: 21:
The first Principles of
་
A Table of the Right Afcenfion and Declination of fome of
the most noted among the fixt Stars for the Year 1784,
which will ferve for near 20 Years without fenfible
Errors.
The Names of the Stars.
Magn.
Right Decli-
Afcen. Ination.
d. m.
N. or S
1
d. m.
Algenib in the flying Horfe's
Wing, called alfo Alla
Pegafi
Scheder in Caffiopea's Breaſt
Bright Star in Aries
Mandibula, or Mencar, the}
Algol in the Head of Meduſa
Aldebaran, the Bull's Eye
Capella, the Goat-Star
}
2
0 32 13 59N
32
3
7 5 55 21N
28 46 22 26N
2
42 45 3 14 N
34
3
I
43 33 40 7N
65 53 16
N
I
75 11 45 46 N
Regell, the bright Foot
Orion
of }
I 76 2 8 28S
Orion's preceding Shoulder
278 23
6 08 N
Middlemoft in Orion's Girdle
2
81 19 I 21S
Laft in Orion's Girdle
2
82 28 2 4/S
Orion's following Shoulder
Syrius, the Dog-Star
I
85 52
7 21N
Caftor's Head, i. e. the
Northermoft Twin -
Procyon, or the little Dog-}
Hydra's Heart
Regulus, the Lion's Heart
Deneb, the Lion's Tail
Firft in the Great Bear's Tail
Vindemiatrix, Virgins
North Wing
Virgin's Spike
Middlemoſt in the Great
Bear's Tail
}
Laſt in the Great Bear's Tail
Arcturus
I 98 54 16 26 S
2110 12 32 20|N
2112 이 ​5 46 N
2139 15 7 44/S
1149 13 13 IN
2 174 31 15 47N
3 191 9 57 8N
2192 52 12 7N
I 198 28 10 2 S
2 198 48 56 4N
2 204 45 50 26N
1211 28 20 19 N
Sect. 21. Geography and Aftronomy.
221
Names of the Stars.
Southern Balance
Northern Crown
Serpentarius's Head
Dragon's Head
Magn.
Right Decli-
Afcen. nation.
d. m. d. m.
.or S.
cs Z v Z Z Z Za c
2222 44 15 8S
2231 23 27 27 N
2261 14
12 44N
2267 55 51 31
1277 24 38 35
Antares, the Scorpion's Heart 1244 3 25 56
Lucida Lira, in the Harp
Eagle, or Vulture's Heart
1295 4 8 18N
3299 42 1 32 S
Antinous's Hand
Fomahant, the Southern
Fish's Mouth
1341 25 30 46 S
Scheat, in the flying Horfe's
Shoulder
2343 20 26 52|N
1
Marchab, in the flying
2343 30 14 0N
2/359 19 27 51N
Horfe's Neck
Andromeda's Head
Note, In this Edition, which is taken from
the Fourth publiſhed by the Doctor, there
are no Alterations made, except what were
neceffary to adapt the various Parts thereof,
particularly the Tables, to the New Style, and
the preſent Time.
Thefe Tables will answer pretty exact-
ly for every other 50 Years, counting from
the Date of the Years here mentioned, viz. the
Tables for 1803, will be the fame with thoſe
for 1703, Allowance being made for the Va-
riation of the Stile, and thofe for 1853, will
be nearly the fame with the Tables here ex-
hibited for the Year 1753. In like Manner
the Tables for 1754, 1755, 1756, will nearly
repreſent the Sun's Declination for the Years
1854, 1855, 1856.
222
Sect. 21.
The firft Principles, &c.
1
'
}
}
Tables of the Sun's Right Afcenfion for every tenth Day of the
Years 1753, 1754, 1755, 1756. The Sun's Right Afcenfion
for all the intermediate Days may be nearly computed by al-
dowing about four Minutes of an Hour, i. e. one Degree for
Every Day.
Y.D Jan. Feb. Mar. April
"
May
May June
1753
h. m.
h. m. h. m.Th. m.
118 49 20 5922 51
1119 33 21 40 23 28
21 20 1622 20 00 04
h. m. h. m.
O 44
2 35
4 38
I 20
3 13
5 19
1 57
3 53
6 01
1754
118 48 20 58 22 50
11 19 32 21 39|23 27
21 20 15 22 19.00 03
0 43
2 34
4 37
1.19
3 12
5 18
1 56
3 52
6.00
3755
118 4720 57 22 49
1119 31 21 38 23 26
21 20 14 22 18 00 02
032
2 33
4 36
I 18
3 11
5 17
1 55
3 5
5 59
118 50 21 00
22 52
• 45
2 36
4 39
1756
1119 34 21 41
23 29
I 21
3 14
5 20
21 20 1722 21
00 05
1 5,8
3 54
6 02
Y.D July Aug.
Sept.
Oct.
Nov.
Dec.
642 8 41
1753
I I
21
7 23
9 22
8 0410 03
10 43 12 31
11 1913 08
11 55 13 45
14 27 16 32
15 08 17 15
15 49 18 00
14 26 16 31
1
I I
21
I
}
1754 | 1755 | 1756
I
21
I I
21
6 41 8 40 10 42 12 30
7 22 9 21
8 0310 02
6 40
8 39
11 1813 97
11 54 г3 44
15 07 17 14.
15 4817 59
10 41 12 29 14 2516 30
11 17 13 0615 06 17 13
8 oz 10 OI 11 5313 43 15 47 17 58:
7 21
6 43
9 20
8 42 10 44 12 32 14 28 16 33
724 9 23 11 20 13 09
8
05 10 0411 56|13 46
15 09 17 16
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BOOK CARD
23
Jw3485
PNW
AUTHOR Watts,I.
The knowledge of the heavens
TITLE
& the earth made easy.
SIGNATURE
ISS'D
426285
RET'D
A 426941
DUPL
*