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S-PENINSULAM AMONA
UNIVERSITY OF MICHIGAN
LİBRARY VERITAS OF THE
061
SCIENTIA
ARTES
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THE
Young GENTLEMAN'S
ASTRONOMY,
A
CHRONOLOGY,
A N D
DIALLING,
3
Containing ſuch
ELEMENTS of the ſaid
Arts or Sciences, as are moſt
uſeful and eaſy to be known.
By EDWARD WELLS, D. D. late
Rector of Cotesbach in Leiceſterſhire.
The Fourth EDITION Reviſed and Correated,
with ADDITIONS.
.
L ON DON:
Printed for JAM E S, John, and PAVI
KNAPTON, at the Crown in Ludgate-Street.
MDCC XXXVI. 773 6.,
THE
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TH E
Young Gentleman's
ASTRONOMY,
Containing ſuch
ELEMENTS of the Aſtrono-
mical Science, as are moſt uſeful
and eaſy to be known.
B Y
EDWARD WELLS, D. D. late
Rector of Cotesbach in Leiceſterſhire.
The FOURTH EDITION.
I O N D ON:
Printed for JAMES, JOHN, and PAUL
KNAPTON, at the Crown in Ludgate-Street.
MDCCXXXVI.
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PRE FACE
T
HERE are two Ends of writing
Books, which relate to the ſeveral
Parts of Learning : one to advance
Learning it felf; the other to af-
Gift Learners.
In Purſuance of the former, the Capaci-
ouſneſs of the Subject is chiefly to be confide-
red; and nothing is to be omitted, which pro-
perly falls within the Compaſs of the Art or
Science treated of. In purſuance of the lat-
ter, the Capacities of the Learners are prin-
cipally to be regarded ; and notice is to be
taken, not of whatever may be known or done
by the Art or Science treated of, but only of
what is moſt uſeful, and withal eaſy to be
known.
Behdes, Regard is to be had, as to the Ca-
pacities principally, so ſecondarily to the Cir-
cumſtances of the Young Students. As for
thoſe who are to make their Fortunes by their
Learning, more Particulars are requiſite to be
known, and conſequently more Pains are re-
quiſte to be taken by ſuch, than by others;
who, being born to plentiful Eſtates, are by
their
A 3
The PREFACE.
1
their Learning not to make, but to adora
their Fortunes
already made.
And there is the more Need of this diftinet
Conſideration, becauſe one of the firſt Things
Young Gentlemen become ſenſible of, is this;
that they are not under a Neceſity of taking
Pains for their Livelihood. Which has ſuch
an Influence upon them, as that they are apt
not to reliſh uny Part of Learning, which re-
quires more than ordinary Pains or Applicati-
on of Mind. And indeed to expe&t they mould
act otherwiſe, is in effe&t no other, than to ex-
peet gray Hairs upon young Heads.
Wherefore, the moſt proper Method to make
Young Gentlemen Learned, is this; to teach
them at firſt only ſuch Elements of the liberal
Arts or Sciences, aś are moſt uſeful in the
common Affairs of Life, and withal moſt eaſy
to be known. They have a competent Appre-
henfion of the Uſefulneſs of ſuch Things as oc-
cur in the common Concerns of Life; and
conſequently hereby that Queſtion frequently
put by Young Students, of what Uſe is this?
will be anſwered afore-hand, and ſo they will
be rendered willing to underſtand what they
apprehend the Uſe of. And when they find
that the Underſtanding thereof carries in it no
Difficulty, then they will be alſo encouraged
to proceed. And when they have thus gone
through, and become Maſters of the moſt uſe-
ful and eaſy Elements of the liberal Arts and
Sciences,
The PREFACE.
I
Sciences, they will thereby be enabled with
much more Eaſe to conquer the more difficult
Parts of Learning, if their own Inclinations
Mall lead then thereto bereafter, when they
are come to Riper Years, and ſo can judge
more rightly of the Worth of Learning
On theſe Confiderations, and with this View
it was, that I drew up this Aſtronomical
Treatiſe, and gave it the Title of the Young
Gentleman's Aſtronomy; Such Aſtronomical
Treatiſes as were afore extant among us; ei-
ther treating only of the Doctrine of the
Sphere or Globe, or elſe taking in ſeveral Par-
ticulars of the other Part of Aſtronomy, too
difficult
for, and not neceſary to be known by
Young Gentlemen.
It only remains to be obſerved, that I ſup-
poſe Young Gentlemen to proceed regularly in
their Studies, and therefore to have learned
Arithmetick and Geometry, before they enter
upon Aſtronomy: as alſo, that ſuch Particu-
lars, as were not neceſſary to my preſent De-
hgn, and yet ſeemed too material to be quite
omitted; I have added by way of Annotations,
both in this Treatiſe, and the others of Chro-
nology. and Dialling.
*
Τ Η Ε
1
Τ Η Ε
CONTENTS
HE Introduction,
THE
Page 1
20
56
CHAP. I. Of the Copernican Syſtem in general, 7
CHA P. II. Of the diurnal Phænomena, common
to the Celeſtial Lights,
CHAP III. Of the Phænomena ( commonly af-
cribed to the ſeeming Annual Motion of the Sun,
but rather) depending on the real Annual Mo-
tion of the Earth,
26
CHAP. IV. Of the Phænomena relating to the
Moon,
47
CHAP. V. Of the Eclipſes of the Sun and
Moon,
:
CHAP. VI. Of the Phænomena of the primary
Planets, of Saturn, Jupiter, Mars, Venus, and
Mercury; as alſo of the ſecondary Planets, or
the Satellites of Saturn and Jupiter, 72
CHA P. VII. Of the Phänomena of the fixed.
Stars,
CHAP. VIII. Of the Phänomena of Comets, 91
CHAP. IX. A Deſcription of the Celeſtial (and
alſo Terreſtrial.) Globe,
96
CHAP. X. Of the more ufeful Problems ſolved
by the Celeſtial Globe,
127
Sixteen Plates, containing Thirty Cutts or Draughts,
belonging to this Treatiſe of Aſtronomy.
83
THE
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Place this facing Pag. 1.
-Aftronomy. Plate 1.
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T HE
Young Gentleman's
ASTRONOMY.
MICAECISXOXDUR
The INTRODUCTION.
I.
V
* E are informed by Mofes in
his Sacred Hiſtory of the The Cele.
Creation, that God made frial Lights
Lights in the (*) wide Space whatEnds.
of Heaven, to give Light
upon the Earth, and to divide the Day
from the Night, and to be for Signs and
for Seaſons, and for Days and Years,
Gen. i. 14—18.
(*) So the Hebrew Word Rakiang truly fignifies. It
is rendered in our Engliſh Bible the Firmament, in Con-
formity to the Septuagint Verſion. See more of this
in my Paraphrafe on Geneſis, juſt publiſhed, Chap. i. 6
and in Note (i) belonging thereto, in reference to the
Word Firmament.
B
The
The INTRODUCTION.
2.
ent to the
were crea
Motion.
We can on.
The principal Way, whereby the
The Cele- All-wiſe Creator of the World has
ftial Lights
are made rendered the Celeſtial Lights fubfervient
fubfervi, to the fore-mentioned Ends, is by cer-
tain eſtabliſhed Laws of Motion ; ac-
Ends, for
which they cording to which, they either really
ted, prin-
move themſelves, or at leaſt ſeem to us
cipally by to move.
What theſe Laws of Motion are,
3: the Divine Wiſdom has not thought
dy make fit to reveal unto us. Wherefore, all
probable that we can do, is to make probable
concerning Conjectures concerning them. Such
the Laws Conjectures are termed (*) Hypotheſes,
of their
Motion;
i. e. Suppoſitions ; becauſe it cannot be
mohich Con- poſitively affirmed of the moſt probable
called Hy- Conjecture, that the Celeſtial Lights do
potheſes, ſo move; but only, that it is reaſonable
to ſuppoſe, they move fo, rather than
any other Way; and that upon ſuch a
Suppoſition, their (+) Phænomena (or
Appearances) may be rationally ſolved
or explained.
4.
The Explanation of theſe Hypo-
Aftrono cheſes, and the Solution of the Ce-
my, what.
)
(*) It is a Greek Word, derived from the Verb
Utorius, to ſuppor e.
(+) lc is a Greek Word alſo, derived from the Verb
Qaww, to appear.
leſtial
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Aſtronomy
Plate 2
.
Place this facing Bag.3.
Fig. 2.
h.
**
X
The INTRODUCTION.
3
leftial Phænomena thereby, is what makes
up the Science called (*). Aſtronomy :
which is a Greek Word originally, and
denotes in that Language the Doctrine
or Knowledge of the Laws, or of the
Diſtribution and Situation of the Stars,
or Celeſtial Lights.
There are four more remarkable
5.
Hypotheſes, the (t) Ptolemaick, the The Co-
Copernican, the Tychonick, and the Hypotheſis
,
Semi-tychonick. Of theſe the Loperni- why the
moft Pro-
can bable.
(*) This Word may be derived, as to its latter Com.
ponent, either from róa a Law, or from youés a
Diſtribution, Seat, or siçuation.
(+) The Ptolemaick Hypotheſis is ſo called from Clasa
dius Prolemeus, a famous Mathematician of Pelufium in
Egypt, who lived in the former Part of the ſecond Cen-
tury after Chrift, under the Roman Emperours Adrian
and Antoninus Pius. He writ both of Aſtronomy and
Geography; and by his Aftronomical Writings, was
conveyed to ſucceeding Ages, the Hypotheſis which
goes under his Name, and which was generally, not to
ſay univerſally, received in theſe Parts of the World
till the Days of Copernicus. The Order of the Celeſtial
Lights as to their Situation, according to this Hypothe-
fis, is repreſented, Fig. 2. But ſince, by the Help of
Teleſcopes, the Phaſes of Venus and Mercury have been
diſcovered, this Hypotheſis is rejected, as not conſiſtent
therewith. I paſs by the Epicycles, and ſeveral other
Particulars juftly blameable in this Hypotheſis.
Copernicus, who was born in 1473 at Thorn, a Town
of Poliſh Prullia, perceiving the ſeveral Exceptions
that
B2
4
The INTRODUCTION.
can is now generally received by the
more learned in Aſtronomy, as the moſt
probable Hypotheſis: foraſmuch as it
not only agrees with the Celeſtial
Phænomena, but alſo explains the Mo-
tions
that the Prolemaick Hypotheſis was juſtly liable to, not
only revived the old Hypotheſis of Philolaus, ( which
Cardinal Cuſa had moved and defended ſometime before
hirn,) but alſo went ſo far as to illuſtrate how the Ce-
leſtial Phenomena might be very well ſolved thereby ;
inſomuch that this Hypotheſis began preſently after to
be embraced by many, if not by moſt, of the moſt
Learned Aſtronomers, and from the principal Reviver of
it, Copernicus, to be called the Copernican Hypothefis.
The Explication of this takes up great Part of this
Trsatiſe. To this belongs Eig. 1.
The Tychonick Hypotheſis is ſo called from Tyche
Brahe, a noble Dan, who lived in the latter Part of the
fixteenth Century, and is famous for his Aſtronomical
Obſervations at Uraniburg, (a Caſtle built by him in
the Iſland Weer or Huena in Denmark, and by him cal-
led by this Name, as importing the Tower or Cafle of
Heaven.) This great Perſon and Aſtronomer, though
he approved oi the Copernican Hypotheſis, in rejecting
the Epicycles, and other ſuperfluous and erroneous
Particulars of the Ptolemaick Hypotheſis, yet could not
reconcile himſelf to the Motion of the Earth, and the
Sun's ſtanding ſtill, both aſſerted by Copernicus. Here-
upon he ſe: himſelf to contrive a new Way for ſolving
the Celeſtial Phanomena, whereby he might avoid what
was culpable in the Ptolemaick Hypotheſis, and yet ſtill
retain the Motion of the Sun round the Earth, as round
the Center of the World. To this his Hypotheſis ap-
pertains, Fig. 3
The Semi-rychonick Hypotheſis is ſo filed, as agreeing
with the Tychonick, excepting only in this, that whereas
the
Place this facing Pag. 4.
Aſtronomy
Plate
3
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Fig. 3.
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The INTRODUCTION.
5.
tions whence the ſaid Phænomena a-
riſe, after the moſt (*) ſimple and
uniform Manner, and conſequently
after ſuch a Manner as is moſt agree-
able to the infinite Wiſdom of the
Creator. I proceed therefore to ſhew,
how the Celeſtial Phænomena, at leaſt
the more remarkable of them, may
be ſolved according to this Hypoche-
the Tychonick makes the Earth to have no Motion at all,
the Semi-tychonick makes it to move round its own
Axis, and ſo agrees therein with the Copernican. But
though the Tychonick and Semi-tychonice Hypotheſis were
both deſigned as Corrections of the Copernican, yet the
Generality of the more Learned in Aſtronomy do ſtill
prefer the Copernican as the moſt probable, and that for
the Reaſon above-mentioned in ſhort, and to be more
largely inſiſted on and explained in the Annotations next
following
(*) Theſe two Propoſitions, viz. Fruftrà fit per plura,
quod fieri poteft per pauciora : and Natura nihil agit frus
trà, being ſo evident to Reaſon, as by Logicians and
Philoſophers to be eſteemed Axioms, i. e. unqueſtionable
Truths; it hence follows, that That Hypotheſis is to
be eſteemed moſt agreeable to the Wiſdom of God, the
Author of Nature, which explains the Motions whence
the Celeſtial Phanomena ariſe, after the moſt ſimple (or
uncompounded) and uniform Manner ; that is, which
adjuſts the ſaid Motions to the feweſt Laws and Prin.
ciples. But herein the Copernican Hypotheſis excells
all the reſt, foraſmuch as according thereto, all the Bo-
dies, on whoſe Motion depend the Celeſtial Phenomena,
are retained in their proper Orbits by the fingle Principle
of Gravity, and move in their Orbits according to one
general Rule, or Law of Motion. Of which ſee more
in Chap. 1.
ſis.
B 3
6
The INTRODUCTION.
fis. And in order hereunto it will be
requiſite to begin with laying before
the Reader the Copernican (*) Syſtem,
i. e. in what Order the ſeveral Bodies,
whereon depend the Celeſtial Phænome-
na, are placed with Reſpect one to the
other, according to this Hypotheſis.
(*) The Word Syſtem is borrowed from the Greek
Tongue, whcieinit denotes that Frame or Model which
arife's from placing ſeveral Things together, it being a
Derivative of the Verb cujusmus, to put, or place #9-
Sether.
С НАР.
[7]
СНА Р. І.
Of the COPERNICAN SYSTEM in
general.
T!
I.
HE Copernican Syſtem is repre- CHAP.
ſented, Fig. 1. where the Sun
1.
is placed in the Center, and ſuppoſed
never to move out of it, but only to
move therein round its own (*) Axis
, The Place
from Weſt to Eaſt, in the Space of a- of the Sun,
bout 25 Days. This Motion of the Sun
round its Axis is inferred from the
Obſervations made of the Spots of the
Sun.
Round the Sun, as the Center of
their Orbits , move fix Spherical Bo- The place
dies in this Order and Time, viz. of Mercu-
ry, Venus,
Mercury next to the Sun, in about the Earth,
three Months ; Venus next to Mercury, pilters, and
in about ſeven Months and an Half; Saturn;
after that the Earth in a Year ; then and their
Mars in about two Years; then Jupi- Times,
Periodical
ter in twelve Years; and outermoſt
2.
(*) See Chap. 3. Sect. s. and the Note there.
3 글
​B 4
of
8
Of the COPERNICAN
by their
Of the
Moon,
and the
;
and Sa-
turn,
CHAP.of all Saturn in about thirty Years
I. Theſe are reſpectively denoted, Fig. I.
m
proper Characters.
3.
As the fore-mentioned fix Bodies
move round the Sun, ſo round three
of them move other Bodies viz.
Satellites round the Earth moves the Moon in
of Jupiter about 27 Days, 8 Hours ; round Yu-
piter move four, and 'round Saturn
move five Bodies, called reſpectively
the (*) Satellites of Jupiter and Saturn.
Of the Satellites of Jupiter, the inner-
moſt moves round Jupiter in 1 Day,
18 Hours; the ſecond in 3 Days, and
a little more than half a Day; the third
in 7 Days, 4 Hours; the fourth and
outmoſt in ſixteen Days, 18 Hours: Of
the Satellites of Saturn, the inmoſt
moves round Saturn in 1 Day, 21
Hours; the ſecond in 2 Days, 18 Hours;
the third in 4 Days, and a little more
than half a Day ; the fourth in almoſt
16 Days; and the fifth in 79 Days, 8
Hours.
(*) They are ſo called, as attending Jupiter and Sa-
tuin, as a Prince is attended by his Satellites or Life-
guard.
All
SYSTEM in general.
9
All the Bodies afore-mentioned, ex-CHAP.
cept the Sun, are called (*) Planets, I.
(which Word in the Greek Language
denotes Wanderers) foraſmuch as ne 4.
ver keeping for any Time the ſame Planets,
whylocal
Diſtance or Situation one to the other, led, and
they may be ſaid to be always Strag-wly diftin-
gling or Wandring from one another. Primary
And becauſe the Moon and the Satellites and Se-
condary
of Jupiter and Saturn are Planets of
Planets, hence they are diſtinguiſhed by
the Name of ſecondary Planets, and the
other ſix Planets agreeably thereto are
diſtinguilhed by the Name of primary
Planets.
The Diſtance of the primary Pla-
5.
nets from the Sun, is much the ſame The Di-
ſtance of
as is expreſſed, Fig. 1. For dividing the prima-
the Diſtance of the Earth from the ry Planets
Sun into ten Parts, the Diſtance of Sun.
Mercury from the Sun is almoſt four
ſuch Parts, of Venus, ſeven, of Mars
fifteen, of Jupiter fifty-two, and of Sa-
turn ninety-five.
(*) Whereas the Planets are commonly reckoned
ſeven, this is according to the Prolemaick Syſtem,
Fig. 2.
And
i
Of the COPERNICAN
IO
The Di-
mary.
СНАР. And as to the Diſtance of the ſecon-
I. dary Planets from their primary reſpec-
mitively, it is eſteemed to be ſuch as this;
6. viz. the Diſtance of the Moon from
the Earth to be about 6o Semi-diame-
ſtance of
the ſecon- ters of the Earth. The inmoft Sa-
dary plac telles of Jupiter is eſteemed to be di-
their Pri: ſtant 5 Semi-diameters of Jupiter
from the Center of Yupiter ; the fe-
cond Satelles is eſteemed to be diſtant
9
of the fame Semi-diameters; the third
14 ſuch Semi-diameters; and the
fourth 25 Semi-diameters. In like
manner the Diſtance of the inmoft Sa-
telles of Saturn from the Center of
Saturn is reckoned to be 4 Semi-dia-
meters of Saturn; the diſtance of the
ſecond to be 5 ſuch Semi-diameters of
the third, 8 Semi-diameters; of the
fourth, 18; of the fifth, 54 Semi-dia-
meters of Saturn.
7. The Reaſon of taking ſuch particu-
The Moti- lar Notice of the Diſtance of the pri-
on of all
the Pla- mary Planets from the Sun, and of
the ſecondary Planets from their re-
regulated
after an ſpective Primary, is this, viz. becauſe
uniform theſe ſeveral Diſtances (as well as the
Manner.
ſeveral Times, wherein the Planets,
whether Primary or Secondary, move
round their reſpective Orbits, and
which
$
nets is
SYSTEM in general.
II
1-
C-
;
n
which are therefore ſtiled their Perio- CHAP.
dical Times) are requiſite to be known, I.
for the apprehending the Excellency of in
the Copernican Syſtem ; according to
which the Motion of all the Planets,
both Primary and Secondary, are regu-
lated by one general Law, which is
this:
The Squares of the Periodical Times
Planets are one to
another, as the Cubes of their Diſtances
r
of the
from the Sun.
Center of the Primary.
Thus for Inſtance as to the primary 8.
Planets, the Period of Saturn is (ro- The ſame
tundè ) 30 Years, of Jupiter 12; the exemplifia
Squares of which Numbers are 900 primary
and 144. The Diſtance of Saturn Planets.
from the Sun is found by Obſervation
to be to the Diſtance of Jupiter from
the Sun as about (*) 9 to 5, the Cubes
of which are 729 and 125. But the
Squares goo and 144 are very nearly
in the ſame Ratio, as the Cubes 729
and 125. And the Ratio in this and
(*) Namely the Diſtance of Saturn (as is above, Sect.
5.obſerved) from the Sun is 95, and of Jupiter 52, both
Diſtances being meaſured by the fame Meaſure.
the
1
12
Of the COPERNICAN
CHAP. the following Inſtances would be
I. found more exact, were the Periods
mand Diſtances more exactly expreſſed
by Numbers. In like manner the Pe-
riod of the Earth is a little more than
four Times greater than the Period
of Mercury; and ſo the Squares of
the Numbers expreſſing thoſe Periods
will be almoſt as 17 and 1. And the
Diſtance of the Earth from the Sun
being divided into ten Parts, the Di-
ſtance of Mercury from the Sun is
found by Obſervations to be (little leſs
than 4 ſuch Parts, viz. ) 3 ſuch whole
Parts, and 9 Tenths of another, the
Cubes of which Numbers (viz. 10
and 34.) are 1000 and 59. But it is
obvious, that 17 is to I, much as 1000
to 59. And ſo of the other primary
Planets.
As for the ſecondary Planets, the
And allo Periodical Times of the Satellites of
as to the Jupiter are (as is above, Se&t. 3. obſerved)
reſpectively as 1, 3, 752 and 16
and their Diſtances are as 5j, 9, 143,
and 25. But the Square of the Peria-
dical Time of the innermoſt Satelles,
namely 3, is to 13 the Square of the
Periodical Time of the ſecond Satelles,
as 170 the Cube of the Diſtance of
the
9.
Planets.
SYSTEM in general.
13
the innermoſt from the Center of Yu-CHAP.
piter, to 736 the Cube of the Diſtance I.
of the ſecond from the ſame Center. m
Likewiſe 3 is to 51 the Square of the
Periodical Time of the third Satelles,
as 170 to 2890 the Cube of the Di-
ſtance of the third from the Center of
Jupiter. And again, 3 is to 280 the
Square of the Periodical Time of the
fourch and outermoſt Satelles, as 170
to 15800 the Cube of the Diſtance of
the ſaid outermoſt Satelles from the
Center of Jupiter. And the ſame holds
good as to the Satellites of Saturn.
But as to the Moon, it is not applicable
to her, foraſmuch as ſhe is the only
ſecondary Planet, that moves about the
Earth."
From what has been ſaid, evident-
ly appears, that the Periodical Mo- All the
tions of the Planets are performed u- retained in
niformly, or are regulated by one ge- their own
neral Law. And from hence it is de Orbits by
monſtrated (*) by the Learned, that Gravity.
the Planets are likewiſe retained in
their
IO.
Planets
3
See Dr. Gregory (late Savilian Profeſſor at Ox-
ford,) his Aſtron. Phys. and Geom. Elem. lib. 1. Prop.
27, 28, 29, and sec, 6. and 7. I fhail only obſerve
heie,
14
of the COPERNICAN
}
CHAP. their proper Orbits after an uniform
I. Manner, by one Sort of Force which
makes them tend to the Center of
their reſpective Orbits, and is thence
called the Centripetal Force, or in one
Word, Gravity. And this is another
Particular, wherein appears the Excel-
lency of the Copernican Syſtem above
any other ; foraſmuch as this Syſtem
may be preſerved by Gravity alone,
uniformly propagated through the Uni-
verſe; whereas (*) all the other Syſtems
require ſome (one or more) other Force,
beſides that of Gravity.
All the Planets, Primary and Se-
condary, are Opacous Bodies, i. e.
ſuch as have no Light of their own,
Light from but receive all their Light from the
she Sun. Sun; and ſo for this, as well as other
Reaſons, are accounted as ſo many
Dependants of the Sun. Whence the
II.
All the
Planets re-
ceive their
here, that any Body, when moved, will move uniform-
ly in a ſtraight Line, if not hindred. And agreeably
any Planet would fly out of its Orbit into a right Line,
which is a Tangent to its Orbit, was it not hindered or
pulled back and retained in its Orbit by fome Centripetal
Force, i.e. by Gravity.
(*) See Greg. Arron. Phyf. and Geom. Elem. pag. 111
112.
Sun
SYSTEM in general.
15
her om internehmen to one
}
I 2.
Sun with theſe its Dependants make up CHAP.
what is called the Solar Syſtem, deſcri I.
bed, Fig. 1.
As for the other Celeſtial Lights,
called the Fixed Stars, they are inde- of the Fix-
pendent of the Sun, as in other Re-ed Stars.
ſpects, ſo in reſpect of Light ; foraf-
much as they receive not their Light
from the Sun, but ſhine with their
own Native Light. Hence they are
eſteemed to be, not only without this
our Solar Syſtem, but as ſo many Suns
themſelves, each being placed in the
Center of fome ſuch Syſtem, as this our
Solar Syſtem, and there ſo fixed, as to
have no Motion, but round their own
Axis. They are ſuppoſed to be vaſtly
diſtant from this our Solar Syſtem;
which is the Reaſon that their Diſtance
is taken no Notice of in the Deſcripti-
on of the Copernican Syſtem, Fig. 1.
Beſides the Celeſtial Lights already
13.
mentioned, there appear ſometimes Co-of co.
mets; which is originally a Greek Word, mets.
denoting in that Language as much as
Hairy. Theſe Lights are called by the
Greeks, Hairy Stars, becauſe they fan-
cied the Streams of Light, which attend
ſuch Stars, to reſemble Hair. It is
found by Obfervations, that theſe Co-
mets
?
16 Of the COPERNICA N.
1
CHAP, mets do (*) paſs through the Planetary ,
I. Orbs of this our Solar Syſtem ; but i
m whether they depend only on the Sun, i
and fo belong only to this our Solar 1
Syſtem, or whether they move in Cir-
cular or ſuch like Lines, or whether i
they are ſo much as durable Bodies, is
not yet diſcovered. For which Reaſons,
there is no Notice taken of them,
Fig. 1.
14.
Before we conclude this Chapter con- 1
The Orbits cerning the Copernican Syſtem in gene-
of the pla.
ral, it ſeems proper to obſerve, that al-
Elliptical
. though the Orbits wherein the Planets
move, are deſcribed, Fig. 1. as ſo ma-
ny Circles, as may be well enough
conceived as ſuch in many Reſpects;
yet more ſtrictly ſpeaking, they are not
exactly Circular, but Elliptical. And
the like is to be underſtood as to the
Bodies of the Planets themſelves, viz.
though they are uſually call'd in ſhort
Spherical Bodies, yet exactly ſpeaking
they are Elliptical or Oval Bodies; ſuch
as the Moon is defcrib'd in the Draught
of the Eclipſe, 1715, publiſh'd by that
nets are
(*) Hence the Line the Comet deſcribes by its Motion,
is called its Trajectory.
3
moſt
SYSTEM in general.
17
'm
15.
y thoſt eminent Aſtronomer Dr. Halley :CHAP.
it From which it appears to what Acurate
I..
1, Skill in Aſtronomy our Great Profeſſors m
Ir thereof are now arrived.
Further, it ſeems not improper to ob-
r ſerve alſo here, that the fixed Stars being of the Zo-
s the moſt remote of all the Celeſtial díack and
Ecliptick.
» Lights, and appearing to us as placed in
, one Concave Sphere ; hence it is uſual
to denote the Place of any of the in-
- termediate Celeſtial Lights, bý aſſigning
· what Part of the Sphere of the fixed
- Scars they appear to us to be in, or
| more properly under. And accordingly
· it is uſual to diſtinguiſh that Tract of
the Sphere of the fixed Stars, under
which all the Planets do move, by the
Aſteriſms or Conſtellations that lie in
that Tract ; which being fancied to re-
preſent ſeveral Things, are therefore
called Signs; and becauſe the Things
repreſented by them are moſt of them
(*) Zodia, or Animals, hence all this
Tract is ſtiled the Zodiack. -Now the
Orbit, wherein the Earth performs its
Annual Period (and which the Sun ſeems
*
f*) It is a Greek Word ſignifying Animals or Living
Creatures.
C
to
18 Of the ĆOÚ ERNICAN
CHAP. to move routid every Year) runs
under
I. the
very
Middle of the Zodiack; whence
mthis middle Part of the Zodiack is of
ſpecial Note in Aftronomy, and is there-
fore diſtinguiſhed by a peculiar Name,
being called the (*) Ecliptick. It, as
well as the whole Zodiack, is divided
into twelve Parts, diſtinguiſhed by the
Name of the Conſtellation or Sign, to
which each Part was formerly aſſigned.
The (+) Names of the ſaid Signs, toge-
ther with the Characters whereby they
are denoted in ſhort, are as follows
viz.
.
IL
४
TY
Aries, Taurus, Gemini, Cancer, Leo, Virgo,
m
#
Libra, Scorpio, Sagittarius, Capricornus, Aquarius, Piſces,
16.
of the
of
nets.
Laſtly, It ſeems proper here to ob-
ſerve, that the Planets do not move in
the planet Orbits, which exactly run one over the
other, or are all contained in the ſame
(*) The Reaſon of this Name, See Chap. s. Seå.
21,
(+) The Names of the Signs are ſomewhat differently
expreſſed in theſetwo memorial Verſes, viz.
Signa, Aries, Tasrus, Gemini, Cancer, Leo, Virgo,
Librag; Scorpins, Arcisenens, Caper, Amphora Piſcesa
Plane
Ś YSTEM in general.
19
Plane; but their Orbits do all croſs one CHAP.
another according to ſeveral Degrees of 1.
Inclination, or which is the ſame, the m
Planes of their Orbits are variouſly in-
clined one to the other. Now the
Earth being that Planetary Body we live
on, hence the Plane of the Orbit of the
Earth is taken by Aſtronomers for the
Spandard ; and the Inclination of the
* Planes of the Orbits of the other Pla-
nets is reckoned greater or leſs, as the
faid Planes incline more or leſs in re-
ſpect to the Plane of the Earth's Orbit,
or (*) (which comes to the ſame) to the
Plane of the Ecliptick. The two Points,
wherein the Orbit of any Planet croſſes
the Ecliptick, are called the Nodes of
that Planet. And thus much for the
Syſtem of the World in general, and
ſuch Particulars as relate to it in general.
Per
(?) For the Ecliptick is that part of the Sphere of the
fixed Stars, which the Plane of the Earth's Orbis pro-
duced thereto touches. So that the Ecliprick is no other
shan the Extremity of the Plane of the Earth's Orbit.
Cg
CHAP
[ 20 ]
Ć HA P. II.
Of the DIURNAL PHÆNOMENA common
to the CELESTIAL LIGHTS:
HA
I.
na! Phe
are com-
to thein
2.
CHAP
Aving in the foregoing Chapter ex-
II.
plained, ſo far forth as is ſuffici-
ment to the Deſign of this Treatiſe, the
Copernican Syſtem in general, I now
The Diur- proceed to explain agreeably thereunto
the Phænomena of the Celeſtial Lights.
nomena
1 ſhall begin with explaining the Di-
mon to the urnal Phenomena common to
Celeſtial
Ligóts in in general, viz. their Riſing, Setting,
guneral
&c.
Now theſe Diurnal Pbænomena of
They are the Celeſtial Lights may be ſolved. by
ved by the the Diurnal Revolution of the Earth,
i. e. by one ſingle Revolution of the
Earth round its own Axis in 24
on of the
Hours. This is illuſtrated, Fig. 4.
where the Circle PR TH denotes
the Earth; C the Center of the Earth,
thro' which is to be conceiv'd to paſs
perpendicularly its Axis, round which it
makes its Diurnal Revolution. P denotes
any
Place on the Earth ; the Line EW',
that
Diurnal
Revoluti.
Earih.
Plate 4
Place this facing Pag. 20
4
b
E
P W
non
W
E
3
R
c
ft
exo
I 프
​&
2X-
ci-
he
w
to
its.
Di-
I
Ay
W
E
d
in
8
of
ру
do
h,
п
де
I
m
४
4
4.
es
b,
ſs
10
B
es
दा
А.
3
at
# F
GN
3,
et
2
非
​:
3
1
4
;
婆
​:
:
军
​流
​Of the DIURNAL PHÆNOMENA, &c.
21
that Circle which bounds the Sight in CHAP.
the ſaid Place, and is by Aſtronomers II.
called the (*) Horizon; E the Eaſt m
Point of the fad Horizon ; W the
Weſt: the Circle abcdef denotes
the Circumference of the Heavens ;
the Circle S the Sun in the Heavens ;
the Semicircle PR T, the enlightened
Hemiſphere of the Earth, or that half
of it which is oppoſite to the Sun;
the Semicircle PHT, the darkened
Hemiſphere of the Earth. Now the
Earth being ſuppoſed in this Sicuati-
on, and alſo to move round its Axis
towards the Sun ; it is evident, that
the Place P of the Earth will juſt be-
gin to be enlightened by the Sun, and
to the Sun will appear there to be juſt
Riſing, or aſcending the Horizon at E
the Eaſt Point of it. The Earth be-
ing moved round its own Axis, ſo as
that the Place P of the Earth, which
afore was under the Point a in the
Heavens, now is under the Point b ;
it is evident, that the Horizon of che
ſaid Place P, will be now ſo ſicuated,
as that the Sun will appear to a Spec-
(*) It is a Greek Word, denoting in that Tongue
ſomewhat that bounds.
tator
C 3
22
Of the DIURNAL PHENOMENA
CHAP. tator at P, as aſcended conſiderably
II. above E the Eaſt End of the Horizon.
And while, by the Revolution of the
Earth round its Axis, the Place P
paſſes from under the Point b in the
Heavens to the Point C, the Horizon
of the Place P will continually ſink
lower and lower in Reſpect of the
Sun, and ſo the Sun will appear to
aſcend higher and higher, till P is
come under c, where the sun will ap-
pear in its greateſt Height above the
Horizon for that Day; and ſo it will
be Noon or Mid-Day at the Place P.
For the Earth moving on,
the
Place P paſſes from under c to d, the
Weſt Point of its Horizon will aſcend
higher and higher, and ſo the Sun
will appear more and more to de-
ſcend, as is repreſented by the Hori-
zon at the Point of the Earth under
d. The Place P being carried by the
Diurnal Revolution of the Earth from
under d to under e, the sun will then
appear juſt on W the Weſt Point of
the Horizon, and ſo will appear to be
juſt Setting. The Place P being come
under f, it will be then Mid-night
there. Laſtly, the Place P being come
sound again under a, it will be there
Sun-
as
of the CelesTIAL LIGHTS.
23
Sun-riſing again. And thus it has CHAP.
been ſhewn, that the ſame Diurnal II.
Phanomena of the Sun will come to
paſs
, if the Sun. ſtands ſtill, and the
Earth move round its own Axis from
Weſt to Eaſt, or from under a, to
under b, c, d, &c. in the Heavens ;
as are commonly eſteemed to come to
paſs by the Earth's ſtanding ſtill, and
the Sun's moving round it from Eaſt
to Weſt, or from c to b, d, f, &c.
And that the ſame holds good as to
any other Celeſtial Light, and the
Earth, is obvious to ſhew from Fig. 4.
the Circle repreſenting the Sun being
taken to denote any other Celeſtial
Light.
But now it being juſtly received by 3.
Philoſophers as an unqueſtionable Truth, The pro-
that Nature works after the moſt fimple ability of
and compendious Manner; it thence fol- nican ayf
lows, that the Solution of the Diurnal temfursher
eſtabliſhed.
Phanomena by the Revolution of the
Earth alone round its own Axis, is much
more agreeable to Nature, than the So-
ļution of the ſaid Phænomena by the
Revolution of all the ſeveral Celeſtial
Lights round the Earth.
C 4
IC
24
Of the DIURNAL PHÆNOMENA
ww
mon and
proper
what.
СНАР. It remains only to obſerve, that
II. whereas by the Diurnal Revolution of
the Earth, all the ſeveral Celeſtial
4. Lights ſeem to move in the Heavens
The com- from Eaſt to Weſt, hence this ſeeming
Diurnal Motion of the Celeſtial Lights
Motion of is called their (*) common Motion, as
al Lighes," being common to all of them. 'Be-
ſides which all the Celeſtial Lights,
but the Sun, have a proper Motion ;
from which ariſe their proper Phæno-
mena, As for the proper Phænomeną
of the Sun, they likewiſe ſeem to ariſe
from the proper Motion of the Sun,
but are really produced by another Mo-
tion which the Earth has, and whereby
it moves round the Sun once every Year,
whence it's called the Annual Motion
:' Bavisar sistemi
(*) The Diurnal Motion is alſo called Motus Primus,
either becauſe it is uſually firſt treated of, or elſe becauſe
it is ſuppoſed according to the Vulgar or Ptolemasck Syf-
tein to be cauſed by the Primum Mobile, which accurdi
ing to the faid Syitem is a Sphere above the fixed Stars,
carrying all the Celeſtial Lights along with it from
Eaſt to Welt. Whence the laid Diurnal Motion is alſo
called ſometimes Mctus Raptus, lu like manner the
proper Motion is otherwiſe filed Morus Secundus, in
Contradiftinction to the Diurnal Motion, called Motus
Prin:4..
of
of the CELESTIAL LIGHTS.
25
of the Earth. Having therefore ex-CHAP.
plained in this Chapter the Diurnal II.
and common Phenomena of the Cele- m
fial Lights, I proceed to explain their
proper Phenomena
,
сHAP.
[ 26 ]
&
CH A P. III.
Of the PHÆNOMENA ( commonly
afcribed to the ſeeming Annual Mo-
tion of the Sun, but rather) depend-
ing on the real Annual Motion of the
EARTH
I.
2.
CHAP Eing to explain in the next Place
III.B the Phenomena proper to the le-
mveral Celeſtial Lights, I begin with the
proper Phenomena of the Sun; foraf-
The pro much as the Sun is the principal Light
nomena of of that Syſtem of the World, wherein
the Sun,
why first
we are placed.
explained. Now theſe Phenomena of the Sun,
which are vulgarly aſcribed to the
The feem, ſeeming Annual Motion of the Sun,
or Annual may be ſolved by the Annual Motion
Motion of of the Earth. In order whereunto it
cauſed by
is firſt to be ſhewn, that the Annual
the real Motion of the Earth will cauſe the
Morion of Sun to appear to us, as if it had ſuch
the Earth. an Annual Motion, though it really
has no ſuch Motion. And this is il-
luſtrated, Fig. 5, where the Sun is in
the
the Sun is
Annual
I
Of the ANNUAL PHÆNOMENA, &c.
27
3
the Center ; the Circle next round it CHAP.
denotes the Orbit of the Earth, or III.
that Circular Line which the Center
of the Earth deſcribes by its Annual
Motion ; the outermoſt Circle denotes
the Ecliptick, diſtinguiſhed into its
12 Parts or Signs. Now ſuppoſing the
Earth to be at A, the Sun will appear
to us to be at *; and ſuppoſing the
Earth to move from A to B, and ſo to
C, the Sun will thereby appear to us
to move from to m, and thence to 4.
And in like manner, by the Earth's
Motion along the Reſt of its own Or-
bit till it comes to A again, the Sun
will ſeem to us to move along the
Reſt of the Ecliptick till it comes to
again. 'Tis evident then, that, ſup-
poſing the Earth to move as has been
here deſcribed, the Sun, though it really
ftands ſtill, will ſeem to have the ſame
Annual Motion along the Ecliptick, as
it would have, if it really moved fo,
and the Earth ſtood ftill.
Only 'tis remarkable, that whereas
we commonly ſay, the Sun is in ., or Anobfer-
3.
Libra, when it is between us and Libra, vation as
and ſo of any other Sign,) if we would nohe.com
(peak properly, and agreeably to the of saying,
natural that the
28 Of the ANNUAL PHÆNOMENA
Sun is in
as
ſuch or
ſuch a
ty of the
Seaſons,
CHAP. natural Cauſe of this and ſuch like)
III. Phænomenon, we ſhould ſay, that the
m Earth is then in V or Aries; foraſmuch
the Earth in its real Motion is always
in the Point of the Ecliptick oppoſite
Sign. to that, wherein the Sun appears to
be. :
4. Having ſhewn that the Annual Mo-
The Varie-tion of the Earth along the Ecliptick
will make the Sun appear to us, as if it
OC. hon had ſuch an Annual Motion ; I pro-
to be fol, ceed now to ſhew, how the Variety of
Annual Days and Nights as to their Length,
Motion of and the various Seaſons of the Year,
(all commonly aſcribed to the ſeem-
ing Annual Motion of the Sun,) may
be ſolved by the Annual Motion of the
Earth. And this is illuſtràted Fig. 6 ;
for the clearer Underſtanding Whereof
there are to be premiſed the following
Particulars.
5. As the (*) Axis of the Earth (and
of the
ſo of the Sun, or any other Celeſtial
Equator,
its Axis Body) is the very, Mid-line of it,
and Poles; which conſequently paſſes through its
As alſo of
the Tro- Center, and is repreſented, Fig. 6,
picks,
the Earth.
(*) The sight Line, round which Podies or Circles
are conceived to move, are ſo called in Alluſion to the
Axis or Axle-tree of a Chariot or Cart-wheel.
(where
d
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the
the
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Sur
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1
3
of the Sun.
29
(where the Circle AQ BE repreſents CHAP.
the Earth,) by the right Line A B; ſo III.
che two Ends of any Axis are called
Polar Cir-
its Poles, and conſequently the two
cles, Equi-
Ends of the Axis of the Earth are noctial
called the Poles of the Earth ; which Points,
Solftitial
always pointing one Northwards, the Points,
other Southwards, hence the former c.
is called the North Pole, and is deno-
ted, Fig. 6, by B; the latter is called
the South Pole, and is denoted by A.
Between theſe Poles each Point of the
Earth by its Diurnal Revolution does
deſcribe a Circle ; of which that,
which is in the very Middle between
the Poles, and is the greateſt, is cal-
led the Equino&tial or Equator, (deno-
ted Fig. 6, by EQ,) becauſe when
che Sun is in the Plane of this Equi-
noctial Circle, it is equal Day and
Night all over the World. And did
this Circle exactly anſwer to, or run
along under the Ecliptick, there would
be equal Day and Night throughout
the Year all over the World. But
the Equator croſſing the Ecliptick,
hence it is equal Day and Night only
twice in the Year, namely, when the
Sun appears in one of thoſe
Points of the Ecliptick, where the
Equator
two
T
4
30 Of the ANNUAL PH #NOM E N A
P
th
th
ſt
ga
ca
GO
m
CHAP.Equator croſſes it, viz. in the firſt
III. Degree of Aries, and the firſt of Li-
bra; which are therefore called the
two Equinoctial Points; and the Times
of the Year anſwering thereto, the
two Equinox's, one the Vernal; the
other the Autumnal. Among the o-
ther Circles, which the ſeveral Points
of the Earth by its Diurnal Revolution
deſcribe between the two Poles of
the Earth, and which are all parallel
to the Equator, there are four more
remarkable, the two Tropický, and
the two Polar Circles. The two Tro-
picks are thoſe Circles on the Earth,
which the Sun ſeems to go directly
over, when it is at its greateſt Decli-
nation or Diſtance from the Equi-
tor, either Northward or Southward.
Whence one is called the Northern
Tropick, the other the Southern. And
becauſe when the Sun appears tơ
move vertically over the Northern
Tropick, he appears alſo to be in the
Beginning of Cancer, hence the faid
Tropick is frequently ſtiled the Tropick
of Cancer; and for the like Reaſon
the Southern is otherwiſe ſtiled the
Tropick of Capricorn. The Reaſon
why both theſe Circles are called Tro-
picks,
wa
E
Ec
Р
Yc
the
TI
Fis
Tr
tw
as
Eq
(+)
is de
Turn
(t
Revo
two,
HIDAI
of the Sun.
3i
picks, is becauſe the Sun appearing CHAP.
then at his greateſt reſpective (Nor. III.
thern or Southern ) Declination or Di-w
ſtance from the Equator, begins from
thence preſently to (*) turn back e-
gain towards the Equator. And be
cauſe the Sun in the firſt Degree of
Cancer and Capricorn does as it were
make a Stand, going neither North
ward nor Southward further from the
Equator, hence theſe two Points of the
Ecliptick are called the two Solftitial
Points; and theſe two Times of the
Year are called the two Solftices, one
the Summer the other the Winter,
The Tropick of Cancer is repreſented,
Fig. 6. by the circular Line TC, the
Tropick of Capricorn by MN. The
two Polar Circles are ſo called, either
as being near to the two Poles of the
Equator, or becauſe they on the Earth
(1) anſwer to thoſe Circles in the
Heavens,
(*) The Greek Verb spéw fignifies to turn; whence
is derived tporixòg denoting ſomewhat from whence a
Turn is made.
ft) As every Point of the Earth by its real Diurnal
Revolution, does really deſcribe a Circle between the
two Poles of the Earth; fo the Sun, by its ſeeming Di-
urnal Revolution, does ſeemingly deſcribe every Day, a
Circlej
32
Of the ANNUAL PHÆNOMENA
CHAP. Heavens, which the (*) Poles of the
III. Ecliptick ſeem to deſcribe by the ap-
w parent Diurnal Motion of the Hea-
vens. Hence theſe Polar Circles are
juſt as far diſtant from their reſpec-
tive Poles of the Equinoctial, as are
the Tropicks from the Equinoctial, viz.
231 Degrees, this being the Meaſure
of the Angle, which the Planes of the
Equator and Ecliptick make by their
mutual Inclination. Theſe Polar Cir-
cles do bound thoſe Tracts of the
Earth, where it is Day or Night du-
ring more or fewer whole Diurnal
Revolutions of the Earth, or for 24
H
tt
(*
as
P
fc
ta
fo
CU
or
ca
Circle, direetly anſwering in the Heavens to that Circle
on the Earth, to which the Sun is that Day Vertical.
Hence there are uſually conceived in the Heavens, E-
quinoctial and Tropical Circles, which direaly antwer
to the like Terreſtrial Circles.
(*) As the Earth, Sun, and all the other Celeſtial
Bodies are ſaid to have their reſpective Axes; ſo the
Aftronomical. Circles, ( viz. Ecliptick, Horizon, &c.)
are conceived by Aſtronomers to have their reſpective
Axes; each of which is conceived to be a right Line
paſſing through the Center of the ſaid Circles, ſo as
to be perpendicular to their reſpective Plancs : And the
Extremiries of any ſuch Axis is likewiſe called the
Pole of the Circle, to which the faid Axis belongs.
Aod conſequently (the Axis being always perpendicular
to the Plane) the roles of any Circle are always diftant,
each 90 Degrees from the fait Circle.
cal
ſig
th
Hours
of the Ġ U n.
33
Hours and upwards together. OfCHAP.
theſe Polar Circles, one is termed the HII.
(*) Arktick or northern Polar Circle, m
as being nigh the Arctick or North
Pole of the Equator, and the other
for the like Reaſon is termed the An-
tarEtick or ſouthern Polar Circle. The
former is denoted, Fig. 6, by the cir-
cular Line K L, the lacter by FG. It
only remains to obſerve, cha: the
Sun (or any other Celeſtial Light) will
appear to be vertical to chat Point of
the Earth, where a right Line drawn
from the Center of the Sun (or other
Celeſtial Light) to the Center of the
Earth, croſſes the Surface of the
Earth. Thus, Fig. 6, when the Earth
is in the Beginning of Capricorn or at
v, the Sun will appear to be verti:
cal to the northern Terreſtrial Tropick
or TC, becauſe a right Line drawn
from S to ve, will croſs the Surface of
the Earth at T. So when the Earth
is at V, the sun will appear vertical
(*) The north Pile of the Equator is called ohor.
wiſe the distick, becauſe ic is near the Conſtellations
called the great and little Bears; the Greek Word "Aput"
ſignifying a Bear; and bience the ſouthern Pole is Itjied
the Antar&tick, as being oppoſite to the Arcticke.
to
34 Of the ANNUAL PHÆNOMENA
CHAP.to che Terreſtrial Equator or E Q,
III. becauſe a right Line drawn from S to
VN r will croſs the Surface of the Earth
in a Point of EQ; for in this poſi-
tion of the Earth the Line S r is
to be conceived perpendicular to the
Axis A B. Theſe Particulars being
premiſed and apprehended, it will be
eaſy to apprehend how the various
Length of Day and Night, and the
various Seaſons of the Year are pro-
duced by the Annual Motion of the
Earth.
6. Suppoſe then the Earth to be at ,
The Ver- the Sun (as is afore obſerved, Seet.
nal Equi- 3.) will appear at V, and ſo in one
plained by of the Equinoctial Poincs, and in the
the Annual Middle between the Poles of the
Motion of
the Earth. Earth A and B; and conſequently
will enlighten from Pole to Pole,
that Hemiſphere of the Earth which
is oppoſite to it. Whence Half of
the Terreſtrial Equator EQ, and of
every Circle parallel thereunto, will
at that Time be enlightened by the
Sun, and Half will be in the Dark.
And conſequently every Place on the
Earth ( foraſmuch as it lies either in
the Terreſtrial Equator, or ſome Pa-
rallel to it) being carried round the
Axis,
I
of the Sun.
35
Äxis, of the Earth in an uniform Man-CHAP.
ner by the Diurnal Motion of the III.
Earth, will be as long in the Light, w
as in the Dark, i. e. the Day and
Night will be then equal all over the
Earth.
The Earth being moved by its An-
nual Motion from to we, the Sun The Reaa
7.
appears then to us to be in $, where ſon of the
is its greateſt Declination northward. ongelt at
And the Sun being in this Situation, the Sum-
'cis evident, that the Rays of the Sun mer sol,
fice.
which enlighten one Half of the
Globe of the Earth at a Time, reach
beyond the north Pole B to L, and
at the ſouth Pole reach no further
than F. Whence it follows, that the
Tract of the Earth within the north
Polar Circle K L, at this Time of the
Year enjoys Day-light throughout
the whole Diurnal Revolution of the
Earth; and on the contrary, that it is
continual Night throughout the whole
Diurnal Revolution of the Earth, in the
Tract of the Earth lying within the
ſouth Polar Circle FG. It follows alſo,
that the greater Portions of the Pa-
rallels to the Equator, which lie be-
tween the Equator and northern Polar
D 2
Circle,
36 of the ANNUAL PHÆNOMENA
CHAV. Circle, have the Light of the Sun ; but
III. the greater Portions of ſuch Parallels,
nas lie between the Equator and ſouthern
Polar Circle, have not the Light of
the Sun; and the Portion of the Pa-
rallel, which is or is not enlightened,
is ſo much the greater or leſſer, as the
Parallel is more or leſs diſtant from the
Equator, there being exactly one Half
of the Equator always enlightened, and,
the other not. And hence it is, that
in this poſition of the Earth in the
firſt of Capricorn, when the Sun ſeems
to be in the oppoſite, vizfirſt Degree
of Cancer, the Days are longeſt in the
northern Parts of the Earth, and the
Nights ſhorteſt, and ſo it is Summer
there. Whereas in the ſouthern Parts
of the Earth, the Days are then ſhort-
eft, and the Nights longeſt, and fo ic
is there Winter. And the longeſt Day
is ſo much the longer, as the Place
is more remote from the Equator. Buc
to ſuch as live on the Terreſtrial E-
quator it ſelf, Day and Night are now,
and throughout the whole Year, equal
one to the other, for the Reaſon above-
mentioned.
The
Place this facing: Pag. 36.
Aftronomy Plate 6 6
fo
A
+
월
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119.7.
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रा
S
P
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​9
뿌
​인
​R
au
9. 8.
w
Pg48.
T
T
인
​4
링
​W
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(8)
28
fat
I
C
OC
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全
​:
晴
​有
​of the Sun.
37
tumnal E.
The Earth moving from 1 to Y, CHAP:
che Sun will ſeem to move from to III.
, and ſo will appear in the Celeſtial
Equator, and make Day and Night 8.
equal, as when the Earth was at the The Au.
oppoſite Point for the like Rea-
quinox,
fons. In like manner the Earth mo- and the
Reaſon of
ving from r to %, the Sun will ſeem the Days
to move from – to V, where it is in being
ſhorteſt at
its greateſt ſouthern Declination. And the Winter
conſequently at this Time of the Solſtice
,
Year, the like Phænomena will happen explained.
to the Inhabitants of the ſouthern
Hemiſphere of the Earth, as happened
to thoſe of the northern Hemiſphere,
when the Earth was in v; and the
like Phenomena will be in the nor-
thern Hemiſphere, as were afore in the
Southern.
Having thus ſhewn, that the ſame
9.
Phænomena, as to the Length of Day The solu.
and Night, and ſo as to the various tion of the
Seaſons of the Year, will ariſe from tive Phæ-
the Annual Motion of the Earth round nomena at
the Ecliptick, as from that of the Sun, mediate
at the four Cardinal Points of the Ec- Points of
liptick, viz. the two Equinoctial, and tick, is
the two Solftitial Points; it is obvi- eaſily to be
ous, that the ſame Phænomena will inferred
from what
likewiſe happen at any the intermedi- has been
the inter-
D3
ate ſaid.
28 Of the ANNUAL PHÆNOMENA
Of the
different
Diſtance
Rate of
CHAP.ate Points of the Ecliptick, from the
III. Motion of the one as well as of the
mother, as to the Increaſe and Decreaſe of
Day and Night, and conſequently as to
the Difference of Seaſons.
IO. As the different Length of Day and
Night, and the different Seaſons at
different Times of the Year are Pha,
of the Sun nomena, which eſcape no one's Obſer-
from the
vation, and have been already ac-
Earth, its
;
ſeeming counted for ; ſo there are other Pha-
different
nomena of the Sun, which are not ſo
Magni-
tude, and eaſily to be obſerved, and therefore
different
are taken Notice of only by the more
Motion, curious in theſe Matters. Such is the
different Diſtance of the Sun from the
Earch ac different Parts of the Year ;
as alſo its appearing of a different
Magnitude, and its ſeeming to move
at a different Rate. For as the Sun's
Diameter appears leſſer about the
Middle of fune, and greater aboue
the Middle of December, ſo the Sun is
more diſtant from us in our Summer,
than in our Winter; and alſo ſeems
to move flower in the former, than
in the latter ; infomuch that it cakes
up about eight Days more in its ſeem-
ing to paſs from the Vernal to the
Autumnal Equinox, than in its ſeem-
ing
of the Sun.
39
ing to paſs from the Autumnal to the CHAP
Vernal; although in both Intervals III.
of Time it ſeems to paſs over but an vry
equal Portion of the Ecliptick, name-
ly, juſt Half. Theſe Phænomena of
the Sun, as they depend one on the
other, ſo may be all ſolved by the
Annual Motion of the Earth, in an
Elliptical Orbit, round the Sun placed
in one of the (*) Focus's of the El-
lipfis, as is illuſtrated, Fig 7. where
the Circle repreſents the Ecliptick,
the Ellipſis repreſents the Orbit of the
Earth, S the Sun placed in one of the
Focus's of the ſaid Ellipſis. Now
about the Middle of June the Sun ap-
pears to us in the Beginning of Can-
cer, and conſequently the Earth is in
the Beginning of Capricorn, and ſo at
the Point A of its Elliptical Orbit,
that is, at its (+) Aphelium or greateſt
Diſtance from the Sun; whence the
Sun
(*) In Fig. 6. the Sun is placed in the Center, not one
of the Focus's, only for more Conveniency luke in
drawing the Figure. It may be caſily conceived to be
in the Focus next to the Sign of so, where it ought to
be ſtrictly.
(+) What is here called the Aphelium and Periheli-
um, is by ſuch, as follow the Hypotheſis of the Sun's
D4
rial
F
40 Of the ANNUAL PHÆNOMENA
CHAP. Sun appears then leſs to us. About
III. the Middle of December, the Sun ap-
m pears to us in the Beginning of Capri-
corn, and conſequently the Earth is
then in the Beginning of Cancer, that
is, at the Point P of its Elliptical Or-
bit, and ſo at its Peribelium, or leaſt
Diſtance from the Sun; which there-
fore appears to us then greater. Fur-
ther, as the Line drawn from v tom
through the Center of the Sun S, di-
vides the Ecliptick into two halves, ſo
it unequally divides the Orbit of the
Earth; the greater Segment whereof
anſwers to the fix Signs of the Eclip-
tick, which the Earth paſſes under be-
tween the Vernal and Autumnal Equi-
nox ; and the leffer Segment anſwers to
the other fix Signs of the Ecliptick,
real Annual Motion, called the Apogee and Perigee; and
theſe ſuppoſe the Sun to move Annually round the Earth
in an Eccentrical Circle, which comes much to the
táme as an Elliptical Oroit. The Aphelium and Perihe.
lium are not always in the fame Points of the Eclip.
tick, but move a little and a little forwards according
to the Series of the Signs. The former is at preſent
reckoned about the 7th Degree of Capricorn, and the
latter about the 7th Degree of Cancer. They are both
Words derived from the Greek Language, and therein of
the Importance above ſpecificd.
which
of the Sun.
41
which the Earth paſſes under between CHAP.
the Autumnal and Vernal Equinox.
Equinox. III.
Whence it comes to paſs, that the m
Earth taking up more Time to go a.
long the greater Segment of its Orb,
than the leſſer, the Sun ſeems to take
up more Time, and conſequently to
move more ſlowly, in paſſing along the
ſıx Signs of the Ecliptick, which it
ſeems to paſs through between the Ver-
nal and Autumnal Equinox, than it
does in paſſing along the other fix Signs
of the Ecliptick, which it ſeem to paſs
through between the Autumnal and Ver-
nal Equinox.
As the Time of the Earth's Annual
Motion from any Point of the Ecliptick The Time
to the ſame again, is computed 365 Earth's
Days, 5 Hours, and 49 Minutes; fo Annual
the Time of the Earth's Motion from Motion, or
of the So-
the Vernal to the Aucumnal Equinox, is lar Year.
computed 186 Days, beſides fome odd
Hours and Minutes; and from the Au-
tumnal Equinox to the Vernal 178
Days, beſides fome odd Hours and Mi-
nutes. So that the Difference between
theſe two Intervals of Time is ( as a-
fore has been obſerved ) about eight
Days.
11,
1
Buc
42
Of the ANNUAL PHÆNOMENA
to us in
CHAP But there are two Difficulties, which
III. are to be removed. One is in reference
mu to what has been ſaid concerning the
12. Sun's being more diſtant from the
The Sun, Earth in Summer than in Winter. For
why botter
ſince the Sun is the Fountain of Heat
Summer, as well as Light to the Earth, ic may
though
farther
be aſked, how it comes to paſs, that
from us.
the Sun is hotter to us in Summer than
in Winter; if fo be it be further from
us in the former than in the latter:
Now this Difficulty will be removed,
by conſidering, that the Sun (or any
other Bady of Fire ) feels more or leſs
hot to us, not only as it is nearer or
further from us, but alſo as its Rays
come more or leſs directly to
Whence though the Sun be farther from
us in Summer than in Winter, yet be-
cauſe its Rays are much more nearly
perpendicular to us in the former than
in the latter, therefore it is hotter to us
in the former than in the latter Sea-
fon. That the Rays of the Sun fall
more nearly perpendicular, or more di-
rectly upon us in the Summer than in
Winter, is obvious to infer from Fig.
6. For when in Summer the Earth is
in the Beginning of ve, and conſequent-
ly
us.
of the Sun,
43
ly the Sun appears to be in the Begin-CHAP.
ning of s, the Sun is then in a per III.
pendicular Line to T, or the Rays of u
the Sun then fall perpendicularly on
the Terreſtrial Tropick TC; and there-
fore, although the Earth be about that
Time in its Aphelium or greateſt Dir-
tance from the Sun, yet the Sun is
then hotteſt to us in theſe parts of the
Earth north of the ſaid Trapick. But
as the Earth moves from the Beginning
of ve toward V and , ſo the Perpen-
dicular from the Sun to the Earth
moves from T towards MN the ſouth-
ern Tropick, ſo that the Sun is exactly
perpendicular to MN when the Earth
is in the firſt of $, or at the Winter
Solſtice. Wherefore, although the Earth
be about that Time in its Peribelium or
leaſt Diſtance from the Sun, yet the
Sun is not then ſo hot to us, becauſe
its Rays fall more obliquely, as is evi-
dent by ſuppoſing a right Line drawn
from the Sun to the Point T in that
Poſition of the Earth at ..
The other Difficulty is in reference
to the Annual Motion of the Earth
round its Orbit. For ſuch a Motion Change of
ſeems inconſiſtent with the Earth's
retaining its Annual
13:
The
the Earth's
Place in
44
Of the ANNUAL PHÆNOMEN A
it makes
Stars.
CHAP.retaining always the ſame Situation in
III. Reſpect to the fixed Stars. But it is
mto be known, that the Circle of the
Orbit
, why Earth's Orbit is ſo very liccle in Reſpect
no ſenſible of the Sphere of the fixed Scars, that
Change as the Earth's changing its Place in the
Earth's si faid Orbit by its Annual Motion, makes
tuation in no ſenſible Change of the Earth's Si-
the fixed tuation in reſpect of the fixed Stars.
In whatever Point of her Annual Orbit
the Earth is, its Axis and Equator (be-
ing each every where parallel to itſelf)
will, if produced, fall on the ſame fix-
ed Stars as to our Senſe, or ſo far forth
as we can diſcern by our Sight; and
conſequently all the Reſt of the fixed
Stars" (foraſmuch as they retain the
fame Situation among themſelves) will
(*) retain the fame Situation in re-
ſpect of the Celeſtial Equator and Poles;
the Celeſtial Equator being always di-
rectly over the Terreſtrial, and the Ce-
leftial Poles being always directly in a
right Line with the Poles of the
Earth.
(*) Excepting the Change mentioned, Chap. 7.
sea. s.
}
Theſe
of the SƯ N.
45
1
Theſe Difficulties being removed, the CH AP.
only Phænomenon which remains here III.
to be taken Notice of, is that com-m
monly called the Eclipſe of the Sun, but 14
which ought to be called the Eclipſe An Eclipſe
of the Earth. For the Word Eclipfe improperly
does in the Greek Tongue ſignify a De-so-called.
ficiency; and it is uſed in this Caſe to
fignify particularly that Deficiency of
Light, which ſeems indeed to us to be
in the Sun, but in reality is ſuch only
in Reſpect of the Earth. For the Sun
is the Fountain of Light to this our
Solar Syſtem; and conſequently not
receiving its Light by the Irradiation of
any other Body upon it, but having its
Light in it ſelf, cannot ſuffer any ſuch
Defect of Light truly and really. Its
Light may indeed be intercepted or hin-
dred from coming to us by the Interpo-
ſition of ſome opacous Body between
Us and the Sun. But then it is the
Earth, on which we are, not the Sun,
that is deficient of Light, or in an E-
clipſe; and the opacous Body, whoſe
Interpoſition between the Sun and
Earth, cauſes the Earth to be thus in
an Eclipſe, is the Moon. Wherefore che
Explanation of this phenomenon de-
pending
I
46 Of the ANNUAL PHÆNOMENA, &c.
CHAP. pending on the Motion of the Moon,
III. it will be requiſite to ſpeak firſt of that;
Nafter which I ſhall, in a diſtinct Chap-
ter, explain the Eclipſes both of the
Sun (as it is commonly called) and alſo
of the Moon.
CH AP.
[ 47
CH A P. IV.
Of the PhÆNOMENA relating to the
Μο ο Ν.
TI
I.
2.
HE Moon is a ſecondary Planet, CHAP,
foraſmuch as ſhe moves round
IV.
the Earth primarily and immediately; m
and round the Sun only in a ſecondary
Manner, viz. as ſhe moves round the The Moon
Earth, which moves round the Sun.
a ſeconda
ry Planet.
A Period or ſingle Revolution of the
Moon round the Earth from any Point A Periodi:
of the Zodiack to the ſame, is called cal Month,
the Moon's (*) Periodical Month ; and
conſiſts of 27 Days, 7 Hours, and 3
Quarters.
The Time from one Synod or Con 3.
junction of the Sun and Moon to ano-
A Synodi-
cal Month,
ther, is called the Moon's (*) Synodi-what
.
cal Month, and conſiſts of 29 Days,
12 Hours.
(**) The Words Period and Synod are both of Greek
Extraction, the former denoting a going Round a
Thing, the latter a Meeting together of two or more
Things.
The
48
Of the PHÆNOMENA
CH AP.
er than the
The Reaſon of the Synodical Month
IV. being ſo much longer than the Perio-
dical, is illuſtrated Fig. 8, where the
4. Circle S denotes the Sun, the Circle
The Sy. T Å the Orbit of the Earth, T the
nodical
Month,
Place of the Earth in the ſaid Orbit,
whiny long- the Circle M the Orbit of the
Periodical. Moon; M and m two ſeveral Places of
the Moon in her Orbit, the outer-
moſt and greateſt Circle of the Zodiack.
Now let the Earth T be ſuppoſed in
the firſt of Libra, and the Moon to be
in her Orbit at M ( in a right Line
between the Earth and the Sun, and
ſo) in Conjunction with the Sun in
the firſt of Aries, The Moon moving
thence Eaſtward, or according to the
Series of the Signs, after 27 Days and
7 Hours and 45 Minutes, appears to
us again in the firſt of Aries, i. e.
at the Point M of her own Orbit, in
the ſecond Poſition of the Earth. For
in the mean while the Earth has alſo
moved almoſt a whole Sign Eaſtward,
viz, almoſt to the End of Libra. And
hence the Moon M, though come a-
gain to the firſt of Aries, is almoſt a
whole Sign Weſtward of the Sun. This
is repreſented by the two prick'd Lines,
whereof that from M (in the ſecond
Poſition
of the Moon.
49
Pofition of the Earth to v repreſents CHAP
how the Moon appears then to us in IV.
the firſt of Aries, while the other Line
from m through S to the End almost
of r repreſents how the Sun appears
at the fame time to be almoſt out of
Aries, and ſo almoſt a whole Sign Eaſt-
Ward of the Moon. Wherefore the
Moon muſt ſtill move ſo much further,
viz. from M tom in her own Orbit,
before the will be in Conjunction again
with the Sun. In going of which to
overrake the Sun, is taken up the Time,
whereby the Synodical Month exceeds
the Periodical, viz. 2 Days, 5 Hours.
It is the Synodical Month, which is
5.
principally made uſe of in Computati- The Syno-
on of Time. Foraſmuch as the ſevedical
Month of
ral Parts of this Month are ſenſibly to chief Ree
be diſtinguiſhed by the ſeveral Phaſes or gard.
Appearances of the Moon, reſpectively
belonging thereunto,
The ſeveral Phaſes of the Moon 6.
are accounted for thus. The Moon The leve-
is conceived to be an opacous Body, of the Mooka
i. €, a Body which receives its Light accounted
from the Sun. It is alſo ſpherical, for.
and conſequently has always one Half
of it enlightened, namely, that Hemi-
E
fphere
ralPhaſes
50 Of the PHNOM EN A
ww
CH A P. ſphere which is towards the Sun. Now
IV. from this Hemiſphere being ſeen by us,
v ſometimes more, fomecimes leſs of it,
ariſe the ſeveral Phaſes of the Moon;
for the better Underſtanding whereof
it is to be further obſerved, that al-
though the Moon be a ſpherical Bo-
dy, yet the enlightened Porcion of it,
which is ſeen by us, appears by Reaſon
of its Diſtance, as if the Moon had a
plain Surface. All which is illuſtrated;
Fig. 9, where S denotes the Sun, T
the Earth, O TR part of the Earth's
Orbit, ACK G the Orbit of the Moon,
on the ſeveral more remarkable Points
whereof, viz. A, B, C, D, K, F, G,
H, is repreſented the Moon with its
enlightened and darkened Hemiſphere;
and at each Point ſo much of the ens
lightened Hemiſphere, as is within the
Circle ACKG, is ſeen by us; but ic
appears to us, not as it is there repre-
ſented, (i. e. not as a Portion of an
Hemiſphere, ) but as a Portion of
ſome plain circular Surface, as is re-
preſented by the ſeveral little circular
Draughts reſpectively adjoining. This
being premiſed, 'tis evident from the
ſaid Figure the gth, that the Moon
being
$
4 ſtronomy Plate
7
Place this facing Pag.50
Fig. 9
А
3
H
B В
So
T
R
૧૬
F
D
K
S
.
SNIE
容
​主
​}
3
of the Moon
51
appear like
being at A, all its enlightened Hemi-CHAP.
ſphere is towards the Earth, and feen IV:
by Us, whence the Moon appears to us.
with a full Orb, (i. e. with a plain cir-
cular Surface all enlightened, ) which
Phaſis or Appearance is therefore ſtiled
the Full Moon The Moon being mo-
ved to B, 'tis evident, that only ſome
Part of its enlightened Hemiſphere tvill
be towards the Earth, and ſo ſeen by
us ; whence the Moon will
à (*) plain circular Surface, not fully
enlightened, but ſomewhat defective of
Light on that Side which is from the
Sun, and conſequently will appear gib-
bous. The Moon being moved to C,
juſt half of its enlightened Hemiſphere
will be towards the Earth, and ſeen by
Us: whence the Moon will appear then
with an half Orb, or with a femi-
circular Surface. The Moon being mo-
ved to D, a very little Portion of its
enlightened Hemiſphere will be ſeen
by Us, and this will appear horned,
the Horns bending from the Sun, and
(*) Hence the Face of the Moon is called Diſcus, as
tefembling a flat round Dith.
E 2
ſo
52
Of the PHÆNOMEN A
CHAP.fo (*) weſtward. The Moon being come
IV. to K, none of its enlightened Hemiſ-
Uphere will be towards the Earth, and ſo
the Moon will not be ſeen by us, and
then it is ſaid to be New Moon ; be-
cauſe the Moon will a little appear a-
new in F, and that again horned, the
Horns now likewiſe bending from the
Sun, and ſo (*) eaſtward. After which
the Moon will appear at G with an half
Orb again, ( as at C ;) and at H gib.
bous again, ( as at B;) and ſo will pro-
ceed to A, where it will be again Full
Moon. And ſo the Moon will have un-
dergone her ſeverat Phaſes; which tho'
they ſomewhat vary every, Day, nay,
every Hour; yet are uſually taken No-
tice of, and diſtinguiſhed only in the
fore-mentioned Points.
(**) Hence the memorial Verſe,
Dextra cavum Veteris complebit, Leva Recentis, i. e.
when the Horns or Hollow of the Moon appear Eaſt.
Ward, or on the left hand as we look at it, then the
Moon is increaſing; and this Appearance of the Moon
is to be ſeen only in the Evening or former Part of the
Night, a little after its change. But when the Horns
or Hollow of the Moon appear Weſtward, or on the
right hand as we look at it, then the Moon is Decreaſing,
and this Appearance of the Moon is to be ſeen only in the
latter
part of the Night or towards Morning, a little be-
fore its Change.
Hence
of the Moon.
53
markable
five...
Hence the remarkable Phaſes of the CHAP.
Moon are five; whereof the two prin- IV.
cipal are the New and the Full Moon. m
The three other, viz. the Gibbous ; 7.
Half, and Horned Moon, occur both The red
between the New and Full Moon, and phaſes of
alſo between the Full and New Moon : the Moon,
only in a different Order. Between the
New (which is alſo called the Change)
and the Full, the Moon is firſt horned,
then halved, and laſtly gibbous; where-
as between the Full and Change, ſhe
is firſt Gibbous, then Halved, and laſtly
Horned.
When the Moon is thus Horned, or 8.
a little before and after the New Moon, The faint
(viz. when the Moon is at the Points which is
D and F,) beſides its bright Horns, the feen in the
whole Diſ-
Moon has à faint Light, whereby all
the Reſt of its Diſcus is rendered dif- Moon, a
litrie before
cernable. This faint Light has been
and after
thought by ſome to be the Moon's Na- itsChange ;
tive proper Light ; but is now general- Tupposed to
ly ſuppoſed by the learned in Aſtro-Arife
.
nomy to be no other than a Reflection
of the Sun's Rays upon the Moon,
the Earth's Polítion being ſuch as
this Time, as very well ſuits to ſuch
a Reflection, as may be ſeen, Fig. 9.
And this Suppoſition is rendered ſtill
Cus of the
E 3
more
54 Of the PHÆNOMEN A
CHAP. more probable, becauſe that as ſoon
as
IV. the Moon is moved beyond the Limits
w of ſuch a Reflection from the Earth, the
forementioned faint Light ceaſes.
9.
What has been afore obſerved of the
of the
Sun, is alſo obſerved by the Curious of
aloon's Ai the Moon ; namely, that in one Part
Perigee, of her Orbit ſhe appears lefſer, and (ca-
egc.
teris paribus) flower, in the oppoſite
Part bigger and ſwifter. Which Pha-,
nomena may be ſolved after the like
manner, ás are the like Phænomena of
the Sun; viz. by the Moon's Motion
in an elliptical Orbit, having one of its
Focus's in the Center of the Earth. Ac-
cordingly this may be illuſtrated by Fig. :
7, ſuppoſing the Ellipfis AP (which
there repreſents the Orbit of the Earth)
to repreſent the Orbit of che Moon and
the Circle S. ( which there repreſents
the Sụn) to repreſent the Earth. For
then A will repreſent the Moon's A-
pogee or greateſt Diſtance from the
Earth, when ſhe will appear leſſer; and
Pher Perigee or leaſt Diſtance, when
conſequently ſhe will appear greater,
And becauſe ſhe is longer in paſſing the
greater Segmenç of her Orbit between
her Apogee and that Focus of her Orbit,
which is in the Center of the Earth,
than
1
*
of the Moon
55
than the lefſer Segment between the ſaid CHAP,
Focus and her Perigee; therefore the IV.
will appear to move flower, while ſhe mu
paſſes along that Half of the Zodiack,
which anſwers to the greater Segment
of her Orbit; and ſwifter, while ſhe
paſſes the other Half of the Zodiack,
anſwering to the lefſer Segment of her
Orbit.
Among the Phænomena of the Moon
more obvious to our Senſe, there re-
mains only the Eclipſe of the Moon to
be ſpoken of, which ſhall be explained
in the following Chapter, ,
2
.
E 4
CHAB.
[ 56 ]
4
CHAP. V.
Of the ECLIPses of the Sun and
Moon.
&
ΤΗ
I.
CH AP.
HE Eclipſes of the Sun and
V.
Moon are here ſpoken of toge-
ther, becauſe as they ariſe from like
Cauſes, ſo are they to be explained
An Eclipſe much after the fame Manner. For it
of the sun is to be remembred, that it has been
and Moon,
what. afore (*) obſerved, that whac is' com-
monly called the Eclipſe of the Sun,
is in reality the Eclipſe of the Earth,
Wherefore, the Earth and Moon be-
ing both opacous Bodies, which re-
ceive Ligh¢ from the Sun, an Eclipſe
of the Earth (commonly called an
Eclipſe of the Sun) is no other than a
Deficiency of Light on the Earth, by
the Moon's coming between the Earth
and the Sun, ſo as to hinder the Rays
of the Sun from falling on the Earth ;
juſt as an Eclipſe of the Moon is a
{"! Chap. jui. Sect
. 14:
Deficiency
}
主
​1
}
老
​Place this facing Pag. 57 ·
.
.
IND
Aſtronomy Plate 8
w
:
Fig. 10
T
:
Of the ECLIPSE S, &c. 57
2.
Deficiency of Light in the Moon, by CHAP,
the Earth's coming between the Moon V.
and Sun, ſo as to hinder the Rays of u
the Sun from falling on the Moon.
Hence it is evident from Fig. 9, that
all Eclipſes of the Earth happen at the Eclipſes of
Change of the Moon, becauſe then only the Sun and
it is that the Moon comes between the when hap-
Earth and the Sun; and all the Eclipſes pen.
of the Moon happen at the Full of the
Moon, becauſe then only 'tis that the
Earth can come between the Moon and
the Sun.
It is to be ſhewn further, for what
3.
Reaſons there is not an Eclipſe of the Why not at
Earth at every Change, but only at Change or
Some certain Changes of the Moon , Full of the
nor an Eclipſe of the Moon at every only as
Full,. but only at some certain Full fome cer-
Moons. It is then to be known, that tain Ones.
the Orbit of the Moon croſſes the E-
cliptick, ſo as to make an Angle of
5 Degrees Inclinacion. The Points
where the Moon croſſes the Ecliptick,
are called the Nodes of the Moon, and
are denoted, Fig. 10. by theſe Charac-
ters 82 and 8; the former of which
is called the Dragon's Head, the latter
the Dragon's Tail. The Moon croſſes
the Ecliptick at the Dragon's Head,
when
Moon, but
i
2
Tax
58
Of the ECLIPSES
CH AP.when ſhe is entring on that part of her
V. Orbit, which incline's northward from
the Ecliptick ; and the croſſes the Dra-
gon's Tail, when ſhe is entring on that
Part of her Orbit, which inclines South-
ward from the Ecliptick. Now the
Nodes being the only two Points,
where the Moon croſſes the Ecliptick,
hence there can be no Eclipſe of the
Earth, but when the Moon happens to
Change in or near one of the Nodes;
becauſe in this Caſe only, the Moon
at her Change comes fo between the
Earth and the Sun, as to intercept the
Rays of the Sun, and keep them from
the Earth. And in like manner, there
can be no Eclipfe of the Moon, but
when the Moon happens to be at Full,
in or dear one of the Nodes; becauſe
in this Caſe only, the Earth comes ſo
between the Moon and the Sun, as to
intercept and hinder the Rays of the Sun
from falling on the Moon.
In an Eclipſe of the Earth, the
4.
Moon by intercepting the Rays of
dow, in E- the Sun, caſts a Shadow on the Earth.
clipſes of
And in an 'Eclipſe of the Moon, the
and Moon, Earth by intercepting the Rays of the
Figure.
Sun, cafts' a Shadow on the Moon.
Theſe
The Shan
the Sun
of what
of the Sun and Moon. 59
Theſe Shadows are of a () conical CHAP,
Figure, growing narrower and narrow V.
er, the further they go from the Earth m
and Moon, till at length they end in
a Point, and ſo ceaſe. Were theſe
Shadows, either of a (*) cylindrical
Figure, i. e. of an equal Thickneſs all
along; or of a (*) conical Figure, but
inverted the other way, i. e. did they
grow thicker and thicker, the further
they are extended, then they would be
extended in infinitum. But now. 'tis
certain, that the Shade of the Earth
does not extend to the Orbit of the pri-
mary Planet Mars; foraſmuch as when
the Earth is directly between the Sun
and Mars, the latter is not eclipſed, as
it muſt neceſſarily be, did the Shade
of the Earth reach to the Orbit of
Mars.
It being, thus demonſtrable, that
5.
the Shadow of the Earth ends in a The Sun,
Point, before it comes to the Orbit of how de-
monſtrated
Mars; hence it is alſo demonſtrable to be big-
that the Sun is bigger than the Earth; ger than
foraſmuch as an opacous Body can't and the
Earth than
the Moon
(t) As in Fig. 13,
**) This is evident from Fig. 11., and 12.
caſt
:
60
Of the ECLIPSE S
CHAP.caſt ſuch a conical Shade, but when
V. it is leſſer than the lucid Body, whoſe
m Rays it intercepts. For if the opa-
cous Body be equal to the lucid Bo-
dy, then the Shadow will be of an
equal Thickneſs all along. And if
the opacous Body be greater than the
lucid Body, then the Shadow will
indeed be of a conical Figure, but in
an inverted Manner, that is, fo aš
that the conical Shade, will grow
wider and wider, as it goes further
and further. And as the Sun may be,
thus demonſtrated to be bigger than
the Earth, ſo the Earth may be de-
monſtrated to be bigger than the
Moon foraſmuch as the Moon can :
be totally Eclipſed. '. For this could
not be, was not the Cohe of the
Earth's Shadow, even in that part of
it which the Moon' paſſes through'in
a total Eclipſe, bigger than the Moon,
though it be leffer than the Earth it
felf: what is here faid is illuſtrated,
Fig. 11, 12, 13
6.
The Shadows of the Earth and
The Grear. Moon being, thus of a conical Fi..
mits of an gure, it is obvious that an Eclipſe
pends in either of the Earth or of the Moon
one Reſpet will be (cæteris paribüs) greater of
longer,
on the
Place this facing Pag. 60.
Aftronomy Plate
9.
11
i
H
Fig. 12.
S.
T
• E1617
Р
P
A
S
T
А.
Р
P
29.607
NL
Fig.14
=
INT
Fig. 15.
E
. C
UP
9г hі,
O-
C
GE
3
:
*
of the Sun and MoÓN.
61
gee.. And in like manner, if the Earth
longer, when the Moon is in her CHAP.
Perigee, than when ſhe is in her Apo- V.
gee. For the Moon if ſhe be eclipſed
in her Perigee, meets with a thicker Moon's be-
Part of the Line of the Earth's Sha- Apogee or
ing in her
dow, than if ſhe be Eclipſed in her Perigee.
Apogee; as is obvious from Fig. 13,
where the Line PP denotes the Moon's
Paſſage through the Shadow in her
Perigee, and the Line AA in her Apo-
be eclipſed when the Moon is in her
Perigee, it meets with a thicker Parc
of the Cone of the Moon's Shade,
than it does if ic be eclipſed when
the Moon is in her Apogee ; as is ob-
vious alſo from Fig. 13, taking the
Circle T to denote the Body of the
Moon; and the Line PP to denote
the Paſſage of the Earth through the
Shade of the Moon in her Perigee,
and AA to denote the like in the Apo-
gee of the Moon.
But the Variety, that is obſerved 7.
in Reſpect to the Greatneſs and Du- But princi-
ration of Eclipſes, does principally Moon's Di.
ariſe from the Moon's being then ftance
more or leſs diſtant from a Node or Nodes.
che Ecliptick. Which ſhall be illuſ-
trated,
from her
I
62
Of the ECL TP s'é s
ww
tial.
9.
the Moon,
whar.
CHAP. trated, firſt in reference to the Mooni,
V. then in reference to the Earth.
An Eclipfe of the Moon, conſide-
8.
red as to its Greatneſs, is either Total,
An Eclipſe when the whole Moon is eclipſed ;
Moon, To-or Partial, when only a Part of it is
tal or Par. eclipſed.
As to Duration, every total E-
A Central clipſe holds longer than any partial
Eclipſe of One. And, as ſome partial Eclipſes
are of longer Duration than other
Parcial, ſo ſome total Eclipſes are of
longer Duration than other Total.
Such total Eclipſes, as are of the
longeſt Duration, happen when the
Moon is in a Node, and are called
central Eclipſes, becauſe, as the Moon
paſſes through that Section of the Cone
of the Earth's Shadow, which meets
with the Orbit of the Moon, the Cen-
ter of the Moon paſſes exactly through
the Center of the ſaid Section or
Shadow.
This is illuſtrated, Fig. 14, where
A Central the fhaded Circle repreſents the Sec-
Eclipſe ile tion afore-mentioned of the Earth's
Inftrated.
Shadow; OM the Orbit of the Moon,
EC the Ecliptick. 'Tis evident, chat
the Moon in this Cafe croſſing a Dia.
meter of the ſhaded Circle, makes the
longeſt
10.
1
of the Sun and Moo N.
63
longeſt Stay ſhe can make in the Sha- CHA.
dow of the Earth; and this Stay is V.
computed about four Hours long.
Whereof the Moon takes up one Hour
from her Beginning to enter into the
Shadow, till ſhe is quite immerged there-
in; two Hours more ſhe continues
quite immerged, paſſing on through the
Shadow.; and the fourth Hour is taken
up from her firſt Beginning to come
out of the Shadow, till ſhe is got quite
free of it. Whence by the Way, it ap-
pears, that the Wideneſs of the Shade
is equal to about three Diameters of
the Moon.
In Fig. 15, is repreſented a total, but
not-central Eclipſe; which happens 4 Total
when the Moon meets with the Shadow
of the Earth, though not at a Node, clipſe of
yet at a ſmall Diſtance from it. And the Moon,
as it is obvious from the fame Figure,
that every total, but not-central Eclipſe
muſt be of a ſhorter Duration than a
central, ſo it is alſo obvious that one to-
tal, but not central Eclipſe will be
longer than another, in Proportion to
the Moon's greater or leſs Diſtance from
a Node at that Time.
II.
but Nota
central E-
In
64
27
Of the E ciips Ś
CH AP. . In Fig. 36. is repreſented a partial
V. Eclipſe. And it is evident from the
mſame Figure, that as anỳ total Eclipſe
12. muſt be of longer Continuance than any
A partial partial; fo one partial Eclipſe is of long-
Eesti on er Continuance than another, according
as the Moon is then: more or leſs diſtant
from a Node. It is alſo obvious, that
the longer a parcial Eclipſe is, ſo much
greater is it, i. e. ſo much greater Part
of the Moon is darkned or paſſes
through the Shadow of the Earth.
Hence it is uſual to conceive the Moon's
Diameter, as divided into twelve Parts;
called Digits; by which the Greatneſs
of parcial Eclipſes are meaſured and
diſtinguiſhed ; they being ſaid to be of
ſo many Digits, as there are ſuch
twelve Parts covered by the Shadow
of the Earth, when the Eclipſe is ac
greateſt.
In all theſe Eclipſes of the Moon,
Of th: Pen- The enters the weſtern Side of the
Ecliples of
Shadow with her eaſtern Side ; and
the Moon. ſo it is her weſtern Side which laſt
quits the eaſtern Side of the Shadow,
when the Eclipſe ceaſes. But now as
the eaſtern Limb or Side of the Moon
draws towards the Shadow; before
it
13.
umbra in
1
뷁
​.
者
​*
Place this facing Pag. 65
NAD
Aftronomy Plate 10.
:
Fig. 17
:
P
T
E
M
L
R
:
N
of the Sun and MOON.
69
it enters the thick Shadow it ſelf, and CHAP.
is quite darkened, it grows more and V
more dim, as it comes nearer and m
nearer to the Shadow. Which Dim-
neſs ariſes from a Penumbra or Dus.
kiſhneſs, which always attends ſuch
Shadows, and encompaſſes them all
round. Thus Fig. 17, TUMR re
preſents the Shadow, (where comes
not any Part of the Sun's Light,)
which is encompaſſed all round with
the Penumbra U TPMRN, where
only ſome part of the Sun's Light is
intercepted by the Earth. And this
Penumbra is more dim towards TU
and MR the edges of the perfect
Shadow, becauſe the Rays of a leſſer
Portion of the Sun, and ſo fewer
Rays reach thither; and leſs dim to-
wards TP and RN, where more
Rays fall; and beyond which Limit,
all the Rays of the Sun have a free
Courſe.
In fome Eclipſes the Moon quite 14.
diſappears in the perfect Shadow. At The Moon
other Times ſhe appears even in the why at
Midſt of the perfect Shadow, of a reddiſh
reddiſh Colour like a burnt Brick. Colour in
Which reddiſh Colour is ſuppoſed to clipſes.
ariſe from the Rays of the Sun, ei-
F
thec
total E.
66
Of the ECLIPSE S
How ma
in a Year.
CHAP.ther refracted in the Atmoſphere about
V. the Earth, or reflected to the Moon
w by Particles flying without the Shadow
of the Earth ; or elſe to ariſe from the
Illumination of the Stars, or all theſe
Cauſes together.
15. There happen moſt Years two E-
clipſes of the Moon at leaſt. For
Dry Eclipses there being two Nodes, wherein the
of the Moon
#wally Moon croffes the Ecliptick, and which
happen
move contrary to the Series of the
Signs, and the Earth going round the
Ecliptick every Year the other Way,
or according to the Series of the
Signs; hence it is obvious that the
Earth muſt meet the Moon's Nodes
every Year. If therefore ic happens
then to be Full Moon, there muſt be
a central Eclipſe. If ic be not then
Full Moon, but more than ten Days
(and more than fifteen it cannot be )
either before or after a Full Moon;
yet ſo great is the Inclination of the
Moon's Orbit to the Ecliptick, and ſo
great is the Thickneſs of the Cone of
the Earth's Shadow, that the Moon
will ſcarce miſs going through ſome
Part of the Shadow; and conſequent-
ly there will be at leaſt a partial
clipſe. But if the Earth happens to
?
meet
of the Sun and MOON.
67
www
16.
meet a Node of the Moon on the very CHAP.
Day of a New Moon, or one or two V.
Days before or after, ( which happens
but ſeldom ) in this caſe the Moon
will be far enough to avoid the Sha-
dow of the Earth, both in the fore-
going, and alſo following Full Moon;
and ſo there will be no Eclipſe of the
Moon that half Year. And this may
ſuffice in Relation to the Eclipſes of the
Moon.
Proceed we now to the Eclipſes of
the Earth, which are commonly cal. An Eclipſe
led Eclipſes of the Sun, foraſmuch as Total or
the Moon, which more or leſs covers Partial.
the Sun, being not ſeen by us, the
Deficiency of Light appears to our
Sight as in the Sun it felf. Whence
an Eclipſe of the Sun is diſtinguiſhed
alſo into a total Eclipſe, wherein the
Moon covers the whole Body of the
Sun from us ; and a partial Eclipſe,
wherein the Moon covers only a Parc
of the Sun.
But it is to be well obſerved, that 17.
although an Eclipſe of the Sun be in of a Total
Eclipſe of
reality an Eclipſe of the Earth ; yet the sun.
what is called a total Eclipſe of the
Sun, is not to be conceived as in rea-
lity a total Eclipſe of the Earth; or
that
F 2
68
Of the ECLIPSE S
CHAP. that the whole upper and oppoſite
V. Hemiſphere of the Earth is then de-
prived of the Sun's Light, as in a To-
tal Eclipſe of the Moon is the whole
oppoſite Hemiſphere of the Moon. The
Reaſon of which Difference is this.
The Earth being bigger than the Moon,
the Cone of its Shadow is big enough
to involve the whole oppoſite Hemif-
phere of the Moon in its Darkneſs.
Whereas the Moon being leſs than
the Earth, the Cone of her Shadow
will involve at once only a ſmall
Tract (CD in Fig. 18,) of the oppo-
fite Hemiſphere of the Earth, ſo as to
hide the whole Sun from the Inhabi-
tants thereof; and conſequently there
will appear only to theſe a Total E-
clipſe of the Sun, whilſt to the Inhabi-
tants of the adjoining Tracts B C, and
DE, the Sun will appear to be but
partially Eclipſed; and beyond theſe on
each Side, there will be no Eclipſe at
all of the Sun, as is eviderit from the
ſame Fig. 18.
18.
The Moon moving from Weſt to
Eaſt, that is, from through m to
hence her eaſtern Limb appears
E.
cliple, but to us firſt to cover the weſtern Limb
of the Sun. And when there is a
Jvortable.
Total
The sun
continues
A very
I
Place this facing Pag. 68
8
Aſtronomy Plate 11.
Fig. 18.
Q
(L
D
T
Sol
E
F
S
**
Fig. 19
UN
1
1
1
소
​1
1
트
​F
of the Sun and Moon.
69
V.
Total Eclipſe of the Sun, for the Time CHAP.
that the Moon covers all the Sun from
us, it is ſo dark, as that ſometimes the
Stars have appeared, and there has been
need of Candle-light. But then this
Darkneſs laſts but a very little while;
for no ſooner is the (*) Diſcus or Face
of the Sun quite covered by the Moon,
but almoſt preſently ſome part of the
ſaid Diſcus begins to be uncovered a-
gain, and a very little Part of it being
ſo uncovered gives a conſiderable Light.
All which Particulars relating to a To-
tal Eclipſe of the Sun were actually
exemplify’d here in England no longer
than April 1715, and again, this pre-
ſent Year, May II. 1724.
It happens ſometimes, that a Cen-
19.
tral Eclipſe of the Sun is not a Total A central
Eclipſe; but about the Limb or Edge the Sun
of the Moon, which looks like a black
or dark Spot, may be ſeen the Limb a Total.
of the Sun, which appears like a Cir-
cle of Light, as in Fig. 19. This is
occaſioned by the Shadow of the
Moon being too ſhort to reach quite
may
be not
(*) The Sun's Face is called its Diſcus, for the like
Rcafon, as the Moon's Facę is ſo called, taken Notice
of Chap. 4. Seat. 6.
to
F 3
70
of the ECLIPSE S
20.
a Year,
CHAP.to the Earth ; and this Shortneſs of the
V. Moon's Shadow may be occaſioned,
Veither by the Moon being in her Apa-
gee, or elſe by the Rays of the Sun,
which paſs by the Edge of the Moon,
being bent by Inflection, and ſo fhort-
ening the Shade of the Moon.
The greateſt Eclipſe of the Sun
of the ( wherein the Shadow of the Moon
Eclipſes of paſſes along the middle of the Earth)
the sun in is, when the Moon happens to be in
a Node at the moment of her Change,
If ſhe be not far from a Node, the
Shadow of the Moon, or at leaſt ſome
Part of the Penumbra will fall on ſome
Tract of the Earth, ( as being large e-
nough,) and will there make a Total,
or at leaſt partial Eclipſe. And in this
Reſpect there are more Eclipſes of the
Sun, than of the Moon. But in Re-
fpect of any one given Place of the
Earth, there are much fewer viſible E-
clipſes of the Sun chan of the Moon,
for the Shade of the Moon is lefler than
the Shade of the Earth ; and conſe-
quently the former will not ſo often in-
volve any given Place of the Earth, as
the latter will fome Part of the Moon.
It
of the Sun and Moon.
71
ww
21.
It remains now only to obſerve, that CHAP.
the Ecliptick is ſo called, becauſe all the V.
fore-mentioned Eclipſes happen, only w
when the Moon is in or near a Node,
i. e. in or near the Plane of the Eclip-The Eclip-
tick. And as all Eclipſes of the Sun ſo called.
and Moon happen in the Ecliptick, ſo
likewiſe do the Eclipſes of the other
Planets, of which we come now to
ſpeak.
3
MOTORVINOMNIHAN
F 4
СНАР.
( 72 )
CH A P. VI.
of the PhÆNOMENA of the prima-
ry Planets, of SATURN, JUTITER,
Mars, Venus, and MERCURY; as
alſo of the ſecondary Planets, or the
SATELLITES of SATURN and
JUPITER.
A
1.
ed into
CH AP. S there are five primary Planets be-
VI.
Gides the Earth, ſo they are diſ-
Mtinguiſhed, by Reaſon of their Situation
with Reſpect to the Earth, into Infe-
The prima. riour and Superiour. The former are
aiftinguiſh ſuch as move between the Earth and
Sun, and are two, Venus and Mercury;
Superiour
and Infe the latter are ſuch, as have the Orbit
siour, with of the Earth between the Sun and their
the Earth. own Orbits, and theſe are three, San
turn, Jupiter, and Mars. This with
their reſpective Order
may
be ſeen,
Fig. 1.
Although both inferiour and ſupe,
ſiour Planets agree in this, that the
riſes fome Planes of their Orbits croſs the Plane
of the Ecliptick; yet their differenç
Situation
2.
Hence au
Differ-
ence,
等
​達
​基
​中
​!
:
主
​年
​:
69
Aſtronomy Plate 12
20
of 일
​me
A
B
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ta
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BEX
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:
fc
Fig. 21
.
.
Willy WWW*:*WWWww
Fig. 22
B
B В
H
q
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G
D
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D
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​to
Of the PHÆNOMENA, &c. 73
our Planet
Now Ve- sometimes
.
Situation with Reſpect to the Earth CHAP
occaſions ſome Difference in the Phe VI.
nomena reſpectively belonging to them. m
I ſhall begin with the inferiour Pla- as to their
nets, whoſe Orbits together with the mena.
Orbit of the Earch and Ecliptick are 3.
repreſented, Fig. 20, namely, M Pre-The inferi.
preſents the Orbit of Mercury, V 4 of Venus,
Venus, T the Earth in it Orbit T 8, why it ap-
the outermoſt Circle repreſents the E-par. Some-
cliptick ; the little Circle with S in the move Di-
Center repreſents the Sun. Now Ve.
nus moving in a leſſer Orbit than the Backward,
Earth, but the fame Way, viz. from and ſome
Weſt to Eaſt; it is evident, that when ſtand Aill
.
Venus is in DEF the more remote Part
of her Orbit from the Earth T, ſhe will
appear to us in T to move according
to the Series of the Signs, ( viz. from
to , &c.) and ſo to move di-
rectly forward. When Venus is come
to G, from thence to H, ſhe will ſtill
appear to move directly forward, but
flower than before ; foraſmuch as ſhe
now moves as it were in a ſtraight
Line towards T the Earth. As The
paſſes beyond H through A to B,
moving quicker than the Earth, the
will paſs between the Earth and the
Sun,
74
Of the PHÆNOMENA
CHAP. Sun, and will ſeem to us on the
VF. Earth to move contrary to the Series of
W the Signs, ( viz. from io to ,) and ſo
to have a retrogade Motion, or to move
backward. Between her direct and re-
trogade Motion, viz. about H, ſhe will
appear fationary, i. e. to ſtand ſtill;
forafmuch as the right Lines then
joining the Earth, and Venus will for
ſome Time continue parallel. And in
like manner between her retrograde
and direct Motion, viz. about B, ſhe
will appear a ſecond Time to ſtand
ſtill. From what has been ſaid 'tis
obvious, that Venus, when ſhe is re-
trograde, as at A, is nearer the Earth,
and cherefore ſeems bigger ; and on
the ocher hand when ſhe is direct, as
at E, ſhe is more remote from the
Earth, and ſo (cæteris paribus) ſeems
leſier.
The feveral Phaſes of Venus, ac-
4.
The leve- cording to her different Poſition with
ral Phales Reſpect to the Earth, are repreſented
of Venus.
as they are in themſelves, Fig. 21.
Whence it is evident, that when Ve-
nus is at A, that is, moſt retrograde
and neareſt to the Earth, ſhe does
not appear to us, her dark Face be-
ing
of Venus and MERCURY.
75
ing towards us, and if the then hap- CHAP.
pens to be in or near enough to a Node, VI.
ſhe will paſs directly between the Earth un
and Sun, and ſo ſeem as a ſpot in the
Sun. Otherwiſe, if ſhe be far enough
from a Node, ſhe will go on one ſide
of the Sun, either Northward or South-
ward. Ac B ſhe will appear horned,
at C with an half Orb, at D gibbous;
and at E (where ſhe moves moſt di-
rectly, and is moſt remote from the
Earth) with a full Orb; unleſs the be
then in or near enough to a Node, in
which Caſes ſhe will be hid from us by
the Sun. After her Full, Venus under-
goes the ſame Phaſes as afore, only in
an inverted Order, till ſhe comes to
her Change again. As Fig. 21, repre-
ſents the ſeveral Phaſes of Venus, as
they are in themſelves ; ſo Fig. 22, re-
preſents them, as they appear to us on
the Earth; the correſpondent Phaſes be-
ing denoted in both Figures by the ſame
Letters, A, B, C, &c.
Laſtly, Venus moving round the
6.
Sun at a leſſer Diſtance than the Earth Why Ve-
does, hence to us ſhe appears as al- nus appears
always ac-
ways accompanying the Sun ; her
company.
greateſt Elongation or Diſtance from ing the
the
Sun; and
7
I
76 Of the PHÆNOMENA
Phan0
mena of
CHAP. the Sun being about 45 Degrees, or a
VI. Sign and Half. When ſhe appears
m before the Sun in the Morning, and ſo
wohy called does as it were uſher in Day-light, ſhe
rus, and is then called Phoſphorus or Lucifer,
Heſperus, or the Morning Star ; when after the
dc.
Sun at Evening, then ſhe is called
Heſperus or Veſper, or the Evening
Star.
6.
What has been ſaid and illuſtrated
of the concerning Venus, is alſo to be under-
ſtood in reference to the like Phanome-
Mercury. na of Mercury; only it muſt be confi-
dered, that the Orbit of Mercury being
leſſer than that of Venus, hence Mer-
cury never appears at ſuch a Diſtance
from the Sun, being never a whole Sign
diſtant from it, and ſo very ſeldom to
be ſeen. In like manner, Mercury go-
ing round its Orbit in ſhorter Time
than Venus does her Orbit ; hence the
direct Motions, Stations, and Retrogra-
dations of Mercury will occur oftner,
than thoſe of Venus. And ſo much may
ſuffice for the two inferiour primary
Planets.
As the Agreement between the
7
Phænomena of Venus and Mercury a-
greement riſes from their being both inferiour
Planets
The A-
between
1
1
A
HO
Astronomy Plate
Place this facing Pag: 77
Fig. 23 &
133
II
M
mx
8
A А
BY
IH
XG
सा
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V
23
HOA
m
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24
Pag 30
B
Fig. 24
H
c
O
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U
NI
4,0
OF
A.
of Venus and MERCURY. 77
..
uation.
our Pla
net Mars
Planets to the Earth; ſo a like Agree-CHAP.
ment between the Phanomena of VI.
Mars, Jupiter, and Saturn, ariſes from
their being ſuperiour Planets to the the Phæ-
nomena of
Earth.
the ſupe
Let then in Fig. 23, T repreſent Tiour place
the Orbit of the Earth, M the Orbit from ſuch
of (any ſuperiour Planet, particularly their si-
Mars. ''Tis evident, that Mars will
8.
not appear to us always accompanying the ſuperia
the Sun, (as do the inferiour Planets,
Venus and Mercury,) but will appear appears
ſometimes as diametrically oppoſite to ſometimes
the Sun. For whereas the Earth goes cally op-
round its Orbit ſooner, than Mars does polite to
his ; 'tis obvious that the Earth will
ſometimes be in the middle between
Mars and the Sun; for Inſtance, while
Mars is at M, the Earth may be at
A.
Further, ſuppoſing Mars to be in 9.
The ſuperi
M, and the Earth to be in B, Mars
will
appear ſtationary, for the Rea- Mars, wby
fon afligned, Se&t. 3, concerning the appears
like Phænomena of Venus. As the to ſtand
Earth moves from B through C, D, nimesso
ftill, fome-
E, F, G to H, Mars will appear to move for-
move forward among the fixed Stars ; Ward,
Sometimes
but with this Difference, that he will backward,
appear
the Sun.
our Planet
78
Of the PHÆNOM EN A
CHAP. appear to move quicker, when he is
VI. moſt remote from the Earth, and in
Conjunction with the Sun, (i. e. when
he and the Earth are ſo ficuated, as is
repreſented, Fig. 23, by ſuppoſing the
Earth to be in DEF, and Mars in or
about M,) and flower, when he is ſo
ſituated with reſpect to the Earth, as
M is repreſented, Fig. 23, to be ſitua-
ted with reſpect to either of the two
Segments of the Earth's Orbit, BC or
GH. Whenever the Earth has ſuch
a Situation to Mars, as H hath to M
in Fig. 23, ( which will at length be,
foraſmuch, as although Mars moves the
mean Time round the Sun, the ſame
Way as the Earth, or according to the
Series of the Signs; yet the Earth
moves faſter, and ſo will overtake
Mars,) the Planet Mars will again ap-
pear to ſtand ſtill. And ſome ſhort
Time after will appear to go backward,
or contrary to the Series of the Signs.
For the Earth, as it moves from H
through A to B, having overtook and
gone beyond Mars, will make Mars
ap-
pear to us to move contrary to the Se-
ries of the Signs, or from towards
&c. And in this Situation Mars
ap-
pears
..
II,
4
of MARS, JUPITER, and SATURN.
79
IO.
and Saturn
Mars.
II.
pears oppoſite to the Sun, and alſo CHAP.
greateſt, becauſe it is then neareſt to the
VI.
Earth.
The like Phenomena happen to Yu-
piter and Saturn, ſave that the Retro- Jupiter
gradations of Saturn are more frequent have the
than thoſe of Jupiter, and of Yu-like fore-
piter than thoſe of Mars; foraſmuch Phæno-
as the Earth does oftner overtake Sa-mena with
turn than Jupiter, and Jupiter than
Mars.
'Tis obvious, that the Orbit of the
Earth being nearer the Sun than the None of
the ſuperi-
Orbits of the Superiour Planets, none our planets
of theſe can hide the Sun from the can hide
Earth. But on the contrary, any of the sun,
them may be hid by the Sun, while the them may
faid Planet is direct, if it be but near the sun
enough to a Node.
Laſtly. Saturn and Yupiter appear
not to us with ſeveral Phaſes, but Saturn and
always with a full Orb; foraſmuch Jupiter,
why appear
as that Hemiſphere of each, which is always
toward the Sun, and fo enlightened, with a full
is alſo always toward the Earth, che
Earth being (comparatively) never far
diſtant from the Sun, which is the
Center of the Orbits of Jupiter and
Saturn, For the Diſtance of Jupiter
from the Sun is above five Times,
and
I 2.
Orb.
80 Of the PHÆNOMENA
CHAP. and that of Saturn almoſt ten Times
VI. greater than that of the Earth from the
Sun.
13. But it is not ſo as to Mars. For
Mars, why the Diſtance of Mars from the Sun
not ap-
pear o
being but (*) half as much again as
Likewiſe, the Diſtance of the Earth from the
Sun, it follows that the Hemiſphere
of Mars, which is towards the Sun,
will not always (ſo much as ſenſibly
appear to ) be toward the Earth. In
Fig. 24. let T be the Place of the
Earth in its Orbit T t, and the Circle
ABCD denote the Orbit of Mars,
'Tis evident, that Mars being in A or
B, (that is, either in Conjunction
with, or in Oppoſition to the Sun,
turns the fame Face towards
towards the
Earth, as it does towards the Sun,
and fo ſhines with a Full Orb. Buc
in C or D the enlightened Face or
Hemiſphere of Mars is not at all ſeen ;
but Mars appears a little defective of
Light, in that Part of ic which is
from the Sun, and ſo appears gib-
bous. And thus we have folved at
leaſt the more remarkable Pbænomena,
(*) That is, as 15. to 10.
both
: ery,"
.
Fig. 25
Afronomy Plate 14
Fig. 26.
09
B
O
$:..-
A
A
P
Fig. 27
V
B
mohlace this facing p. 81
c
UM
of MARS, JUPITER, and SATURN.
81
mary Planets.
both of the inferiour and ſuperiour pri-CHAP.
VI.
It remains only to add ſomewhat un
concerning the ſecondary Planets, be 14.
fides what has been ſaid of them, The Satel-
Chap. I.
And the firſt Particular that piter and
deſerves Obſervation, is this, that the Saturn un-
like Phenomena to thoſe which happen cliples.be.
between the Earth and the Moon, hap-
pen between Yupiter and Saturn, and
their reſpective Satellites ; foraſmuch as
the ſaid Satellites are no other than ſo
many
Moons in reſpect to their reſpec-
tive primary Planet. Hence, whenever
either primary Planet ſo comes between
the Sun, and any one of its reſpective
Satellites, as to hinder the Rays of the
Sun from falling upon it, it ſuffers an
Eclipſe. And on the other hand, when-
ever any Satelles comes ſo bet widen the
Sun and its primary Planet, as to in-
tercepe the Sun's Rays from its Prima-
ry, the ſaid Primary undergoes an E-
clipſe.
The ſecond particular worthy of 15.
Obſervation is the Phænomenon of Sa- of the
turn, which appears like an Annulus Anſæ of
or Ring, encompaſſing Saturn, as is Saturn.
repreſented Fig. 25. From the vari-
G
Annulus or
OUS
82
Of the PHÆNOMEN A, &c.
n
CHAP. ous Poſition of this Annulus in reſpect
VI. of the Sun and the Obſerver, (it being
vopacous, like Saturn it ſelf, ) ariſes the
ſeveral Phaſes of (what they call) the
Anſæ of Saturn, becauſe they appear
like the two Handles of a Cup, or the
like. And this is ſufficient to our pre-
ſent Deſign, concerning the inferiour
and ſuperiour Planets, as alſo concern-
ing the Satellites of Jupiter and Sa-
turn.
С НА Р.
[ 83 ]
CH A P. VII.
Of the Ph ÆNOMEN A of the fixed
STARS.
I.
H
Aving ſhewn how the Phænomena CHAP.
of the Sun, and Moon, and pla- VII.
netary Stars may be ſolved, we are to
proceed next to the Solution of the Phe.
nomena of the fixed Stars. And theſe, The fixed
not borrowing their Light from the Stars not
Sun, but ſhining with their own native Eclipſes
.
Light, are therefore not ſubject to any
ſuch Deficiency of Light, as is called
an Ecliple.
It is indeed obſerved of (*) ſome of
the fixed Stars, that they do for a cer- Why, some
rain Period appear, and then diſappear. for a Time
Which Phenomena is ſuppoſed to ariſe appear,
from the ſaid Stars having ſome Macula
diſappear.
or Spots, which move round them in
certain Periodical Times : as the Spots
of our Sun are obſerved to move round
2.
and then
(*) Concerning ſuch fixed Stars, fee Dr. Gregory's
Aftron. Phys. and Geom. Elem. Libi 2. Prof. 30
it.
G 2
84 of the PHÆNOMENA
CHA P. it. Nay, it is thought, that the Spots
VII. do ſometimes grow ſo great, as to quite
mcover the Star to which they belong,
and ſo to make it diſappear altogether ;
and that this is the Reaſon, that ſeveral
fixed Stars obſerved by the Antients,
are now not to be ſeen. And this Opi-
nion is countenanced by the Obſerva-
tions that have been made, that ſome-
times a whole Year together our Sun has
Thone with a more faint Light than at
other Times; this being ſuppoſed to be
cauſed by the Spots of our Sun being
for that Time grown greater than Or-
dinary.
As to the fixed Stars appearing of
3.
of the dif. different Magnitudes or Bigneſs to us,
ferent this is aſcribed vulgarly to their being
Magnitude
of the fixed really ſome bigger than others. But the
more learned in Aſtronomy refer this
apparent Difference of Magnitude only
to their different Diſtances from us.
As this Difference of Diſtance is ſuffici-
ent to make ſome appear bigger, ſome
leffer; ſo the Diſtance of the neareſt to
us being vaſtly great, hence our Senſe of
-Viſion cannot diſcern the different Di-
ſtances, and conſequently they appear
us as all placed in one and the
ſame
Stars.
to
of the fixed STAR S.
85
ſame concave Sphere. By Reaſon of Chap.
their apparent different Magnitudes, they VII.
are uſually diſtinguished into fix Claſſes, m
being reſpectively called Stars of the
Firſt, Second, &c. Magnitude.
As to the Riſing, Setting, and Re-
4.
volution of the fixed Stars round the The ſeem-
ing proper
Earth once in 24 Hours, it has been motion of
above obſerved, that theſe Phænomena the fixed
may be ſolved by the diurnal Revolu-Scars very
tion of the Earth round its own Axis.
But beſides this apparent diurnal Mo-
tion, from Eaſt to Weſt, the fixed Stars
ſeem to have anocher Motion, where-
by they ſeem to move very ſlowly from
Weſt to Eaſt, or according to the Se-
ries of the Signs. This Motion is ſo
very flow, that it is computed to require
about 25 or 26 thouſand Years for the
fixed Stars to ſeem carried thereby
round the Heavens; whence it is
ſtiled (*) Annus Magnus, or the great
Year.
#
It is alſo ſtiled Annus Platonicus, becauſe the Pla.
tonifts teach, that every ſuch Period Things are reſtored
to the fame State and Condition, as they were ſo many
Years afore,
G 3
This
1
86
whence it
Of the PHÆNOMENA
CH AP. This Motion is commonly eſteemed as
VII. the real proper Motion of the fixed Stars.
ww But the more learned in Aſtronomy con-
5. ceive the fixed Stars to have no ſuch real
The proper Motion, as for other Reaſons, ſo parti-
the fixed cularly for this, viz. becauſe the ſaid
Stars
, not Motion of all the fixed Stars may be
Real, but
only Appa- more ſimply, and compendiouſly ſolved,
rent; and by the bare changing of the Places of
arifes.
the Equinoctial Points. For it comes to
the fame, whether we ſuppoſe the Equi-
no&tial Points to be unmoveable, and
the fixed Stars to move forward accord-
ing to the Series of the Signs ; or the
fixed Stars to be unmoveable, and the
Equinoctial Points to be moved back-
ward, or contrary to the Series of the
Signs. What has been ſaid, is illuſtra-
ted, Fig. 26, where r$ no repre-
ſent the Orbit of the Earth about the
Sun, AEBQ the Earth it felf, n and
the two Equinoctial Points for any one
Year. The Earth moving forward a-
gain from – through we towards r, the
Plane of the Terreſtrial Equator being
produced, will paſs throʻ the Sun (*) at
(*) Nøte, That theſe [V][] ftand for the
prick'd V and in the Figure, tha Types of which
could not be had in Time.
[v] be-
of the fixed STARS.
87
comes to V.
through w
[V] before that the Center of the Earth CHAP.
And in like manner, the VII.
Earth moving forward from v through
Oto , the Plane of her Equator be-
ing produced, will paſs through the
Sun at [-], before that the Center of
the Earth comes to But the Equi-
nox will be then, when the Sun is
found in the Plane of the Terreſtrial E-
quator; and choſe Points of the Eclip-
tick are rightly eſteemed the Equinoctial
Points, wherein the Sun is ſeen at the
two Equinoxes. Whereas, therefore,
v and were the Equinoctial Points
the laſt Year, the next Year [V] and
[+] will be the Equino&tial Points ; and
ſo the Equinoctial Points will
go
back-
wards, conſidered as to ſeveral Years.
And by this Change of the Equinoctial
Points, a fixed Star that keeps its Place
at that Point of the Ecliptick, which is
denoted by:r, and where afore was
the vernal Equinoctial Point, will now
ſeem to be moved forward from the
vernal Equino&tial Point to [V] as much
as the interval v [v.] Wherefore, this
being the moſt Simple, and conſequent-
moſt natural Way of ſolving the
Phænomenon we are ſpeaking of, it is ge-
nerally
G4
88 Of the PHÆNOMEN A
CHAP. nerally embraced now a days. And not
VII. only ſo, but it is alſo (*) mathemati-
cally demonſtrated, for what Reaſons
the Equinoctial Points do thus move
backward, or the Equator every Year
croſſes the Ecliptick" a little fooner or
forwarder than it did the laſt Year.
Whence that which is commonly called
the proper Motion of the fixed Stars, is
now a-days ſtiled by the learned in Aſtro-
nomy, the Præceſſion or Anticipation of
the Equinoctial Points.
6.
It remains only to ſet down the
The feve- Conſtellations, whereto the more re-
ral Con- markable of the fixed Stars are redu-
ſtellations,
to which ced. It has been ſhewn already, what
are the twelve Conſtellations or Signs,
ble fixed
whereby are comprehended the fixed
Stars are Stars that lie in the Zodiack. In reſpect
of which, the other Conſtellations are
diſtinguiſhed into northern or fouthern.
The northern Conſtellations firſt diftin-
guiſhed by the Antients, are the little
Bear, the great Bear (or Charles-wain,)
the Dragon, Lepheus, Bootes, the nor-
thern Crown, Hercules, the Harp, (or
as it is ſtiled by ſome, the Vultur cadens,)
the more
remarka.
reduced.
(*) Sce Dr, Gregory's Aftron, Lib. 1. Prop. 64.
the
of the fixed STAR S.
89
the Swan, Caſhopeia, Perſeus, Andro-CHAP.
meda, the northern Triangle, the Cha- VII.
rioteer, the great Horſe or Pegaſus, the
little Horſe, the Dolphin, the Arrow,
the Eagle, Serpentarius, the Serpent.
To theſe 21 northern Conſtellations
were afterwards added the Conſtellations
of Antinous, Berenice's Hair, and (by
us Engliſh) Charles's Heart. The ſouth-
ern Conſtellations known to the An-
tients are the Whale, Eridanus, the
Hare, Orion, the greater Dog, the leſſer
Dog, the Ship, the Hydra, the Crater
or two-handed-Por, the Raven or Crow,
the Centaur, the Wolf, the Altar, the
fouthern Crown, the ſouthern Fiſh. To
theſe 15 are not long ſince added 12
Conſtellations, made up of the fixed
Stars about the ſouth Pole, and not vi-
ſible to us, viz. the Phænix, the Crane,
the Indian, the Peacock, the Apus, the
ſouthern Triangle, the Fly, the Chama-
leon, the flying Fiſh, the Toucan or A-
merican Gooſe, the Hydrus, the Dorado,
and the Royal Oak.
Beſides theſe Conſtellations there
ap 7.
pears in the Heavens a certain Tract, of the
milky
which goes quite round the Heavens,
and from its appearing to be of a milky
White-
> Way.
I
90
Of the PHÆNOMEN A, &c.
CHAP. Whiteneſs, is called Via (*) Lastea, or
VII. the milky Way. It is now, by the Help
v mof Teleſcopes, diſcovered to be no o-
ther than an innumerable Multitude of
little fixed Stars.
8.
Such fixed Stars as belong not to this
of the fix- Milky Way, nor to any of the Con-
ed Stars, ſtellations, are called Informes, as not
formes. being yet reduced to any form or 1-
mage, as the Conſtellations are. And
ſo much for the fixed Stars.
(*) It is for the like Reaſon called Galaxia by the
Greeks.
С НАР.
[91]
CHA P. VIII.
Of the PHÆNOMENA of COMET S.
T
I.
our
HERE remains now only the CHAP.
Phenomena of Comets to be fol- VIII.
ved, which are ſpoken of laſt, becauſe w
there are not yet ſuch Diſcoveries made,
as afford the like Degree of Certainty Comets,
in the Solution of the Phænomena of ed of in the
Comets, as there is in ſolving the Phe_laſt Place.
nomena of the other Celeſtial Lights;
as alſo becauſe it is not known yet,
whether Comets belong only to this
Solar Syſtem, or whether they
may not alſo país into other of the
Mundane Syſtems, which have the
fixed Stars for their ſeveral reſpective
Suns.
It is ſuppoſed moſt probable by
the Learned in Aſtronomy, that they comets
move in ſome conick Section, which ſuppoſed to
has the Sun in one of its Focus's. For ſome co-
this Sort of Orbit is found beſt to nick Seca
agree to the Obſervations that have
been made concerning the Motion of
Comets. Some indeed have formerly
thought,
by 2.
tion:
92
Of the PHÆNOMEN A
CHAP. thought, that they move in right
VIII. Lines; and ſome Calculations that have
mu been made concerning their Motion,
have agreed well enough to this Hypo-
theſis. But then it is to be noted, that
this will hold the ſame, although Co-
mets move in a conick Section, if ſo
be the Obſervations be made in that
Part of their Orbits, which comes very
near to a right Line. Let APVBC in
Fig. 27, be a conick Section very ec-
centrical, and let one of its Focus's be
S the Center of the Sun. It may be,
that the Comet may be obſerved, whilſt
it is moving along the Part AP of its
Orbit ; and the reſt of the Time,
whilſt it moves from P through VB
to C, it may be hid from us by the
Rays of the Sun. Or the Comet may
be ſo hid from us, whilſt it moves
along AP VB, and may be then ob-
ferved, when 'tis come to B, as it is
about to deſcribe the Line BC. And
in both theſe caſes, the Line deſcri-
bed by the Comet will not be ſenſibly
different from a Right. Moreover,
the Comet being obſerved in AP
his Deſcent towards the Sun, and
then drawing daily nearer to the Sun,
and
of Comets.
93
and after that lying hid for ſome CHAP.
Time under the Sun's Rays, and at VIII.
Length getting again out of the Sun's m
Rays on the other Side of the Sun ;
hence it comes to paſs, that one and
the ſame Comet is looked upon to be
two different Ones, which both move
only in right Lines, viz. one in AP,
the other in BC. Whereas in reality
it may be all the while one and the
ſame Comet, whoſe Trajectory (or
Line, which it deſcribes by its Mo-
tion) if conſidered together, both as
to its Deſcent toward the Sun, and
alſo as to its Aſcent from the Sun,
will hence be found to be no other
than a conick Section, as was afore laid
down.
Of the three conick Sections, the El-
3.
lipfis is found moſt agreeable to the Mo- Comets
tions (as of the Planets, ſo alſo ) of ſuppoſed to
Comets. And it can be no other, if that conick
Comets be Bodies of a laſting Subſtance
as are the Planets, and like theſe have called an
a Periodical Motion round the Sun. If Ellipſis.
Comets have not ſuch a Periodical Mo-
tion, then their Trajectory is Paraboli.
cal, or Hyperbolical.
Section,
which is
Some
94 Of the PHÆNOMENA
СНАР.
ous Motia
Comets
two Parts,
Some Comets move like the Planets,
VIII. from Weſt to Eaſt; ſome from Eaſt to
m Weſt; others from North to South, and
4. others laſtly from South to North. And
The vari- their Orbits as to Greatneſs, Situation,
ens, &c. and Inclination, as well in Reſpect to
of Comets. one another, as to the Orbits of the
Planets, are various and different.
5
Laſtly, A Comet does viſibly conſiſt
of two Parts, one called the Head, the
confift of other called the Tail. The Head is the
an Head' Solid Body of the Comet, and is opa-
and Tail. cous, as appears from the Shadow it
caſts. The Tail is conceived by the
Learned to be no other than a thin Va-
pour ariſing from the Head by Heat.
Namely, whilſt the Comet is deſcend-
ing to its Perihelium, thoſe Vapours
which had afore ſettled on it, when it
was in the Regions remoteſt from the
Sun, being now rarefied by the Heat of
the Sun do aſcend, i. e. fly off that Way
which is from the Sun. Hence it comes
to paſs, that the Tail of a Comet grows
greater and greater, as the Comet ap-
proaches nearer and nearer to its Peri-
helium; and on the other hand, the Tail
grows leſs and leſs, as the Comet goes
further and further from the Sun and
conſe
3
;
of COMET S.
95
conſequently the Tail is greateſt and CHAP.
moſt ſhining, preſently after the Co- VIII.
met has been moſt heated in its Peri-
helium. And thus it has been ſhewn,
how the more remarkable Phenomena
of the Celeſtial Bodies may be ſolved
or explained according to the Coperni-
can Hypotheſis.
A6
CH A P.
I
[ 36 ]
CH A P. IX.
A Deſcription of the Celeſtial (and alſo
Terreſtrial GLOBE.)
IN
1.
ftial Phu. they
nomena
are repre-
artificial
CH AP.
N the foregoing Chapters, the Ce-
IX. leftial Pbænomena have been treat-
Wed of, as conſidered in themſelves. I
The Cele proceed now to treat of them, as
are repreſented by artificial
Inſtruments and Machines, among
fented by
which the chief is the Sphere or
Globe.
Machines,
the chief
The Word Sphere we borrow from
whereof is the Greek Language, as we do the
the Globe Word Globe from the Latin ; each
or Sphere.
Word, in its reſpective Language,
The import anſwering one to the other, and de-
noring a round Body, that is, accord-
Sphere and ing to the Mathematical Definition
thereof, a Body from whoſe inmoſt
Point, called its Center, all right
Lines drawn to its Surface are equal
to the other. But the Word
Sphere is now a days commonly uſed
to denote a Machine ſomewhat diffe-
rent from a Globe, and more pe-
culiarly
2.
of the
Words,
Globe.
one
در
Of the Celeſtial GLOBE, &c.
97
Culiarly ſtiled an Armillary Sphere ;CHAP.
foraſmuch as it does not conſiſt of a IX.
round continued Surface, but only of
ſome Circles duly placed together,
and fancied to reſemble Armilla, i. e.
Bracelets.
The Sphere and Globe are made to 3.
repreſent principally ſuch Pkænomena, Spherical
as ariſe from the Diurnal Motion.rical Aſtros
Whence that Part of Aſtronomy, which nomy:
treats of the Diurnal Motion, is fre-whar
, and
quently ſtiled (*) Spherical Aſtronomy, led.
or the Doctrine of the Sphere. In like
manner, the other part of Aſtronomy,
which treats of the annual and pro-
per. Motion, is ſtiled Theorical Aſtro-
nomy, from the Schemes or ( as it is
faid) little Paper Machines, formerly
made to illuſtrate the (7) Theory of
the ſaid proper Motion, and thence
called Theoriæ.
There are Spheres made agreeable 4.
to the Copernican Hypocheſis, and The com-
others made agreeable to che vulgar tilGlobe,
how far
uſeful in
Aſtrong iny
(*) This makes the firſt part in common Aftrono ni-
cal Treatiſes, and Theorical Aſtronomy the ſecon | Part.
(t) It is originally a Greek Word, denoting Speculia
tion or Contemplation:
H
or
98
Of the Celeſtial GLOBE, &c.
CHAP.or Ptolemaick Hypotheſis. But the
IX. former Sort being very coftly, and
w the latter Sort being not of ſo general
Uſe (even in their own Way, or ac-
cording to the Ptolemaick Hypotheſis)
as the Artificial Celeſtial Globe, hence
this is moſt commonly made uſe of to
illuſtrate to young Students the Cele-
ſtial Phænomena. And when they have
been once ſer right as to the true Syf-
tem of the World, and
the true
Cauſes of the ſaid Phænomena, by ha-
ving had the Copernican Hypotheſis
explained to them; then it is allow-
able for them to make Uſe of the com-
mon Celeſtial Globe, though it repre-
ſents the Celeſtial Phænomena, .not
according to their real Nature, but
only according to their Appearances :
Foraſmuch as it is convenient, not to
ſay neceſſary, in common Diſcourſe to
talk of the celeſtial Phenomena accord-
ing to the common Notions of them,
i. e. according to their Appearance to
our Senſes, from which the Vulgar de-
rive their Notions.
5.
On theſe Confiderations, having in
the eight foregoing Chapters of this
count of
fuuch its
Treatiſe explained the real Nature and
Uſefulneſs
, Cauſes of the Celcítial Phænomena, I
the Celes
ſhall
&
On Co
Of the Celeſtial GLOBE, &c.
99
is here
cribed.
ſhall in the remaining Part of this Trea-CHAP.
tiſe ſhew, how the ſaid Phenomena are IX.
repreſented by the Celeſtial Globe, as to v
their Appearance to
our Senſe. And tial Globe
therefore I Thall firſt (in this Chapter ) treated of,
deſcribe the artificial Celeſtial Globe, and def-
and then ( in the following Chapter )
ſhew the Uſe thereof.
Among the ſeveral Circles belonging 6.
to the celeftial Globe, I ſhall begin of the Ho-
wich the Horizon ; foraſmuch as the ar- the cele
tificial Horizon is the outermoſt Circle fial Globe.
of the artificial Globe, and that which
encloſes and upholds all the reſt of the
ſaid Globe.
It has been (*) afore obſerved in ſhort 7.
that the Horizon is ſo called, as being
that Circle which bounds the Sight.jold, Sen-
To which it is further to be added here, Rae anal.
that the Horizon is diſtinguiſhed by
Aſtronomers into the ſenſible and the ra-
tional Horizon.
For a right and clear Apprehenſion 8.
of the ſenſible Horizon, it muſt be cal- The fendi-
led to Mind, that the Sight, if not hin-ble Hori-
dered, extends it ſelf equally every Way. and why so
The Hori-
zon Imo
zon, whare
cailed
(*) Chap. 2. Sect. 2.
H 2
Hence
100
Of the Celeſtial GLOBE, &c.
CHAP. Hence (*) it comes to paſs, that, when
IX. we ſtand upon the Surface of the Earth,
m and the Eye has a free View all round,
ſo much of the Heavens as is ſeen, ap-
pears to us under the Figure of a con-
cave Spherical Surface, reaching to the
Surface of the Earth. The ſeeming In-
terſection or Meeting of the Surface of
the Earth with the fore-mentioned con-
cave ſpherical Surface of the Heavens,
being continued every Way round the
Eye, repreſents a Circle, which is cal-
led (by a Greek Word) the Horizon,
becauſe it bounds the Sight, and di-
vides the ſeen Part of the Heavens from
the unſeen; and it is particularly ſtiled
the fenfible Horizon, becauſe it does thus
actually fall under our Senſe of Viſion,
when the Eye has a (+) free View.
9. The rational Horizon is ſo called,
The ratio. becauſe it falls not under our Senſe
zon, what, of Viſion, but is only to be conceived
andwhyso by our Reaſon. For hereby is deno-
ted that Horizon, which would bound
nal Hori-
called.
See this illuſtrated, Fig. 1. of my Opticks.
(+) Hence it is obſervable, that every Horizon that
actually bounds the Sighis is not properly the ſenſible
Horizon.
the
Of the Celeſtial GLOBE, &c.
IOI
the Sight ſuppoſing the Earth biſected, CHAP.
and one Half of it removed, and the IX.
Spectator placed on the Center of the
Earth. What has been ſaid of each
Horizon, is illuſtrated Fig. 28, where
the greater Circle denotes the Heavens ;
the liccle Circle, the Earth; the Line
drawn through P, the ſenſible Horizon;
the other Line the Rational. Whence
is alſo evident, that the ſenſible Hori-
zon, and its reſpective rational Horizon,
are always parallel one to the other, and
that their mutual Diſtance is the Semi-
diameter of the Earth.
Now the whole Earth being but as
a Point in reſpect of that vaſtly dif- The Earth
tant Sphere, wherein the fixed Stars but as a
ſeem to be all placed ; hence the Dif- reſpect of
tance between the rational and ſen- the sphere
of the
fixed
fible Horizon, being no more than the Stars.
Semi-diameter of the Earth, makes
no ſenſible or conſiderable Difference
as to the Phenomena of the fixed
Stars.
But the Diſtance between the rati-
onal and ſenſible Horizon, bears a con- of the Pa-
ſiderable Proportion to the Diſtance the Cele.
of the other celeſtial Lights from fial Lights.
the Earth, and conſequently makes
a con-
IO.
Point in
JI.
H 3
102
Of the Celeſtial GLOBE, &c.
CHAP.a conſiderable Difference as to the (*)
IX. Places of theſe other celeſtial Lights,
m which are between the Earth and the
fixed Stars. This is alſo illuſtrated,
Fig. 28, where the outermoſt Semicir-
cle repreſents half the Sphere of the
fixed Stars; the other two Semi-circles
repreſent the Halves of the Orbits of
any two celeſtial Lights between the
Earth and the fixed Stars; and the lit-
tle Circle about the common Center
of the forementioned Semi-circles re-
preſents the Earth. The Lines drawn
from P (the Place of the Spectator )
on the Surface of the Earth, through
the Centers of the Celeſtial Lights M
and S, to the Sphere of the fixed Stars,
do there denote the apparent Places
of the faid celeſtial Lights ; and the
other Lines drawn from the Center of
the Earth,
through the Centers of
M and S, to the Sphere of the fixed
Stars, do there denote (what are cal-
(*) Here muſt he remembred what is ſaid, Chap. I.
SIE 15. viz. Tharibat Point or Part of the Sphere of
the fixed Stars, between wbich and the Spectacor any
other of the Celeft:al Lights appears to be, is counted
the Place of the ſaid Celeſtial Light.
led)
}
CH.
NID
Aſtronomy Plate 15
Fig. 28
bH
日
​S
T
M
S
M
T
A
Horizon
The Sen -
The Rational
vible
Horizon
Place this facing p. 103
Of the Celeſtial GLOBE, &c.
103
led) the true Places of M and S.CHAP.
Whence may be learned, the Reaſon IX.
of thus taking Notice of the Rational m
Horizon, foraſmuch as that is eſteemed
by Aſtronomers, the true Place of a
Phenomenon, (where it would be ſeen
to a Spectator placed on the Center
of the Earth, i. e. where ) it is with
reſpect to the rational Horizon. Thus
T is the true Place of M and S, A the
apparent Place of each. The Difference
between the true and apparent Place
( which are always in the ſame ver-
tical Circle) of any celeſtial Light
or Phænomenon, is called its (*) Pa-
rallax.
Having
(*) It is a Greek Word fignifying a Variation or Dif-
ference. It ſeeming too long a Digreſſion to inſertinto
the Body of this Chapter an Explication of the Parallax,
and on the other hand, the Parallax ſeeming a Particu-
lar too material to be only mentioned, I judged it beſt to
adjoin here by way of Note, what ſeems requiſite to be
ſaid of ir. The Parallax then may be conlidered, ei-
ther with reſpect to different Celeſtial Lights, or the
fame. In the former Reſpect, the Parallax is greater or
leſfer, as the Celeſtial Lights are leſs or/more diſtant from
the Earth. Thus Fig. 28, the Parallax TA of M, is
greater than the Parallax TA of S. And hence th
Moon has the greateſt Parallax, as being neareſt of a
H 4
th
104 Of the Celeſtial GLOBE, &c.
CHAP. Having ſhewn the Difference be-
IX. tween the ſenſible and rational Hori.
mzon, and withal taken Notice, that it
12. is the rational Horizon, which is prin-
The Hori cipally regarded by Aſtronomers, it is
Globe re- next to be obſerved, that accordingly
preſents it is the rational Horizon, which is
principally
principally
the ratio-
nal Hori.
zon.
the Celeſtial Lights to the Earth. In reſpect of the ſame
Celeſtial Light, its greateſt Parallax is at the Horizon ;
and as the Celeſtial Light afcends higher and higher above
the Horizon, fo its Parallax continually decreaſes, till it
quite ceaſes in the Zenith or Vertical Point. For there
the two Lines which mark out the apparent and true
Place, do fall in together, as is evident from Fig. 28.
What more ſeems requiſite to be here obſerved, is the
Angle made by the meeting of the two Lines juſt men-
tioned in the Center of the Celeſtial Light, is called the
Parallactical Angle, or the Angle of the Parallax, and 3 by
it th: Parallax is meaſured; as alſo that the apparent
Place is always lower or nearer to the Horizon, than the
true Place. Whence the Parallax has a quite contrary
Effect to Refraction; foraſmuch as this cauſes a Phano.
menon to appear higher, or more above the Horizon than
really it is. Thus in Fig. 29, let T devote the Earth,
ſurrounded with the Armoſphere A ED; S fome Star,
and O the Spectator on the Surface of the Earth. Were
there no Atmoſphere, or were it of an equal Thicknefs
with the Asher, the Rays of Light would come di-
rectly or in a right Line from sto O. But the Rays,
when they have paſſed through the #ther $Q, entring
at A into the Atmoſphere, which is thicker than the
Æther, hereby is refracted (i.e as it were broken) and
bent towards the right Line OP, which is perpendicu-
as to the Surface of the Atmoſphere at A. And becauſe
it
***
Aſtronomy Plate 16.
Q
ՄԻԱ
Fig. 29
E
T
:D
Fig. 30
HORI
zon
N
Place this facing p. 104
UN
My
* * :
":
Of the Celeſtial Globe, &c.
105
principally repreſented by the artifi-CHAP.
cial Horizon of the Globe; which IX.
therefore is (or at leaſt ought to be ) un
, to it
ſelf exactly into two Hemiſpheres or
equal Parts. But here it is to be re-
wie ...?! We wi" ...
it is likely, that the Atmoſphere it ſelf is not all along,
from the Æther to the Earth, of an equal Thickneſs,
but is thicker, as it is nearer to the Earth; hence a Ray
coming from the Star S will be refracted, not only at
A, but alſo at other Points within the Atmoſphere, (as
at B, C, doc.) and at each of theſe Points will be re-
fracted the ſame Way, viz. toward T. But of the Ray
ABCO, it is only the laſt Part CO, which affects the
Eye; and therefore the Eye ſees the Star at s. and con-
ſequently much higher, or much more above the Ho-
rizon O'H, than really it is. But Refraction (as well
as Parallax ) is greater, when the Phanomenon is near-
er to the Horizon; and as the Phenomenon aſcends high-
er, it continually decreaſes, and quite ceaſes in the
Zenith. To Refraction it is attributed, that the Sun
and Moon appear of an Oval Figure near the Horizon.
For the upper Rim of the Sun and Moon appearing a
little higher, and the lower Rim a great deal higher
than it really is, hence'this will ſeem to be nearer to that
than it really is; and ſo the erect or vertical Diameter
of either Luminary will ſeem contracted, while the
tranverſe or horizontal undergoes no ſuch Contraction,
foraſmuch as its Extremities are alike elevated by Re-
fraction. 'Tis alſo to the Refraction of the Sun's Rays
to the Atmoſphere, that the Crepuſculum or Twilight is
owing; for otherwiſe, as ſoon as the Sun is fet, it
would be preſently quite Dark. By Refraction alſo the
Sun and Moon appear above the Horizon, when their
Bodies are ſomewhat under the Horizon.
marked,
106 Of the Celeſtial GLOBE, &c.
CHA P. marked, that although the whole
*IX. broad wooden Circle, which encom-
paſſes the reſt of the Globe, may
ſometimes be called the Horizon of
the Globe, yet properly and ſtrictly
it is only the inner Rim or Edge of
the upper Surface of the ſaid broad
wooden Circle, that is che Horizon of
the Globe, and (*) repreſents the
true Horizon, whether Rational or Sen-
ſible.
13. For the Meaſuring of the Altitude
Of Almi- or Depreſſion of any Phænomenon, (i. e.
the Zenith its Diſtance above or below the Ho-
and Nadir. rizon, ) here are conceived Circles to
run parallel to the Horizon through
every Point of the Globe; which (as
is illuſtrated, Fig. 30, ) grow leſs and
leſs on each side of the Horizon, as
they are more remote from it, and at
length End in two Points. One of
theſe Points being always over the Ver-
(*) The Horizon (as is above obſerved) is that Circle,
i, e. that Circular Line, wherein the Surface of the
Heavens and the Surface of the Earth interſect, or are
conceived to interſect, one the other. But a circular
Line has only a circular Length, no Breadth, nor Thick-
neſs. And therefore it is properly the inner Edge of
the upper Surface of the broad wooden Circle, which
is the artificial Horizon of the Globe.
tex,
Of the Celeſtial GLOBE, &c. . 107
tex, or Head of the Spectator, is there-CHAP.
fore called the vertical Point, or by a IX.
ſingle Arabick Word, the Zenith. The mu
ocher Point, which is diametrically op-
poſite to the former, is called by an A-
rabick Word, the Nadir. The Zenith
is repreſented, Fig. 30, by the Point
Z, the Nadir by the Point N. The
fore-mentioned parallel Circles between
the Horizon and the Zenith or Nadir,
are called from their Uſe, Circles or
Parallels of Altitude, and by an Arabick
Word, Almicantars.
For denoting what Point of the 14.
Horizon any Phenomenon is in, or is of Azi-
muth's or
at leaſt to be referred to, there are Vertical
conceived alſo Circles croſſing every
Point of the Horizon at right Angles,
and all croſſing one another in the Ze-
nith and Nadir. And from their com-
mon Interſection being thus in the Ze-
nith or vertical Point, they are ſtiled
vertical Circles, or by an Arabick Word,
Azimuths. Theſe are alſo illuſtrated,
Fig. 30.
Among the Points of the Horizon
15.
there are four, which are called the of the four
Cardinal
Cardinal (i. e. Principal) Points, and points of
are diſtinguiſhed by the Names of the the Hori
Eaſt,
Circles,
}
zon.
I
108 Of the Celeſtial GLOBE, &c.
16.
CHAP. Eaſt, Weſt, North, and South Points.
IX. The eaſt and weſt Points of every Ho-
Wrizon are thoſe, wherein the Sun riſes
and ſers, when he is in the Equinocti-
al. The other two are each go De-
grees
diſtant from the former, one to-
wards the north Pole, and thence called
the north Point; the other toward the
ſouth Pole, and thence called the fouch
Point.
Among the vertical Circles, thoſe
of the two are of ſpecial Note, which paſs
prime
Vertical through the Cardinal Points of the
and Meri- Horizon. That which paſſes through
dian.
the eaſt and weſt Points is called the
prime Vertical ; the other which paſſes
through the north and ſouth Points
is ſtiled the Meridian, becauſe
Day, when the Sun comes to that
Circle, it is then Meridies or Mid-day
within that Horizon. When any Ce-
leſtial Light is riſen, it aſcends ſtill
higher and higher, till it comes to the
Meridian; and as ſoon
ſoon as it has
croſſed that, it begins to deſcend low-
er and lower. Hence, when it is at
the . Meridian, it is ſaid to culminate,
(i. e. to be at its Culmen or Top-
height for that Day, ) and ſuch its
greateſt
becauſe every
of the Celeſtial GLOBE, &c.
109
..
...S..************
greateſt Height is therefore called its me-CHAP.
ridian Altitude.
IX.
As the Horizon divides the World i
into an upper and lower (or viſible
17.
and inviſible ) Hemiſphere ; fo the Me- The upper
ridian divides the World into an eaſt-afternaná
ern and weſtern Hemiſphere ; the for-weſtern
Hemir
mer being ſo called, becauſe it is that
pheres,
wherein the celeſtial Lights do riſe ; what.
the other, becauſe it is that wherein
they ſet.
Though the whole braſs Circle, 18.
which is immediately upheld by the The Meri-
Horizon at its north and ſouch Points, the Globe,
be frequently called in groſs the Me whar.
ridian of the Globe ; yet properly and
ftriály ſpeaking, the artificial Meridian
is only the graduated Edge of the ſaid
braſs Circle.
The Meridian is the only vertical 19.
Circle which is diſtinctly repreſented of the
on the Globe. As for all the reſt, Quadrant
they are repreſented in Part by the rude.
Quadrant of Altitude reſpectively ap-
plied to the Body of the Globe, from
the Zenith to the Horizon. It is a
long narrow Strip of Braſs, made
thin, that it might be pliant to the
Body of the Globe ; and made to
reach from the Zenith to the Horizon,
ſo
.I
+
IIO
Of the Celeſtial GLOBE, &c.
CHAP. ſo much of it as is contained between
IX. the Zenith and Horizon, being divided
minto 90 Degrees, as being juſt equal to
the fourth Part of the Circumference
of the Globe; whence it takes the Name
of the Quadrant, being peculiarly ſtiled
the Quadrant of Altitude, from its Uſe
in taking the Altitude of any Point of
the Globe. And as the Strip of Braſs
ſo called does by its Length from the
Zenith to the Horizon, repreſent the
fourth Part of a vertical Circle ; fo be-
ing rightly faſtned on Top at the Ze-
nith, and then moved round the Body
of the Globe, by ſuch its Motion, the
ſeveral Points thereof will repreſent the
ſeveral Almicantars between the Zenith
and Horizon.
Within the braſs Circle called the Me-
20.
of the
ridian of the Globe, hangs che Body of
Axis
, and the Globe, being upheld by two Iron
Poles of
the World, (as it were) Pins faſtened to the Meridi-
in the arti- an, the Body of the Globe being made
ficial Globe.
to turn round upon theſe two Pins,
which therefore repreſent the two Poles
of the Equator, or (as they are otherwiſe
called) of the (*) World ; that by the
(*) They are, ſo callej, becauſe all the. Word, but
the Earth, ſeems to turn round upon them.
3
little
Of the Celeſtial GLOBE, &c.
III
21.
litcle Bear on the Surface of the Globe, CHAP.
repreſenting the Arctick or north Pole; IX.
and the other, the Antarctick or fouch
Pole. The Piece of Iron paſſing thro'
the Center of the Globe, and of which
the two Irons Pins afore-mentioned are
the Extremities, repreſents the Axis of
the World.
From what has been above • ſaid,
( Chap. III. Seet. 5.) it is obvious, of the E-
that the Equator of the Celeſtial gritos;
Globe is the great Circle, drawn on two Tro-
the Surface of the Globe in the
picks, and
very
polar Cire
Middle between the two Poles already cles of the
mentioned ; as alſo, that the
as alſo, that the great Globe.
Artificial
Circle, which croſſes obliquely the
faid Equator, is the Ecliptick of the
Globe; and that the two leſſer Cir-
cles, which the faid Ecliptick touches
at its greateſt Declination (northward
or ſouthward) from the Equator, are
the two Tropicks of the Globe ; that
on the north Side of the Equator, the
Tropick of Cancer ; that on the ſouth
Side, the Tropick of Capricorn; laſtly,
that the two leſler Circles drawn on
the Surface of the Globe at the ſame
Diſtance (viz. 23 Degrees) from
each Pole of the Equator, as the Tro-
picks
I 12
Of the Celeſtial GLOB É, &c.
9
22.
zon.
CHAP.picks are from the Equator it felf, are
XI. the polar Circles of the Globe that
Vabout the Arctick or north Pole, the
ArEtick Circle ; that about the Antar-
Etick or fouth Pole, the Antarctick
Circle.
In reference to the Equätor, it is here
The Equa- to be added, that whereas it has been
tor always afore in this Chapter, Sect. 15, obſer-
the Horios ved, that the eaſt and weſt Points of
any Horizon are thoſe, where the Sun
riſes and ſets when he is in the Equa-
tor; and whereas alſo it is then equal
Day and Night all over the World; it
hence follows, that the artificial Equa-
tor in any due Poſition of the Globe,
muſt cut the Horizon exactly in its eaſt
and weſt Points; and there cut it fo, as
to be equally divided by the Horizon
into two Parts, one half being above
the Horizon, the other below. And by
theſe Particulars it may be further
pro-
ved, whether a Globe is truly made.
The Poſition of the Equator to the
The Poſition Horizon, is in general three-fold. For
of the Eo the Equator cuts the Horizon, either at
the Hori- right Angles, or at oblique Angles, or
zon three- elfe it is Parallel to the Horizon.
fold.
23
Such
Of the Celeſtial GLOBE, &c. 113
Such as live under the celeſtial (or CHAP.
which is the fame, upon the terreſtrial) IX.
Equator, their Horizon is croſſed by
the Equator, and conſequently by all 24.
its Parallels at right Angles; and of a right
hence theſe are ſaid to live in a
right Sphere. The Property of which
Sphere is this, that it is therein e-
qual Day and Night through the whole
Year. For the Equator and all its
Parallels being biſected by the Hori-
zon in a right Sphere, ( as may be
ihewn by putting the mechanical Globe
into ſuch a Poſition, viz. fo as that
the Equator of the Globe may move
round under the Zenith,) and the
Sun's diurnal Motion being always ei-
ther in the Equator, or one of its Pa-
rallels ; hence it follows, that the Sun
(moving all the 24 Hours alike) muſt
always make as long a Stay above, as
below the Horizon, in a right Sphere;
and conſequently, that it muſt be there
equal Day and Night through the whole
Year.
Such as live on either Side the
25.
Equator, between it and its Poles, of sno-
their Horizons do croſs the Equator, lique
Sphere.,
and conſequently its Parallels, at An-
I
gles
114
of the Celeſtial GLOBE, &c.
CHAP.gles leſs or more oblique, according as
IX. they live leſs or more diſtant from the
WEquator. Hence theſe are ſaid to live
in an oblique Sphere, and their Horizons,
though they all biſect or equally divide
the Equator it ſelf, yet do all leſs or
more unequally divide its Parallels, ac-
cording as the Parallels themſelves, and
the Places to which the Horizons ref-
pectively belong, are leſs or more diſtant
from the Equator. Wherefore, the di-
urnal Motion of the Sun, when it is
not in the Equator, being in ſome one
of its Parallels thus leſs or more une-
qually divided by the reſpective Hori-
zons, it thence comes to paſs, that the
Day and Night are leſs or more unequal
at the ſame time of the Year (excepting
the two Equinoxes ) in different Places,
according as the ſaid Places are leſs or
more diſtant from the Equator ; and alſo
that the Day and Night are leſs or more
unequal at different Times of the Year
in the ſame Place, according as the Sun
is leſs or more diſtant from the Equator.
All which is evidently to be ſhewn up-
on the Globe.
Laſtly,
Of the Celeſtial GLOBE, &c.
115
of a pa-
Laſtly, Under the very Poles of the CHAP.
Equator, or of the World, the Hori IX.
zon and Equator run parallel one to them
other, which Poſition is therefore cal 26.
led a parallel Sphere. The property
rall
of this Sphere is, that therein it is Day sphere.
for half the Year together, and Night
for the other half. For the Equator
and Horizon being here Parallel , as
long as the Sun ſtays on the ſame Side
of the Equator, ſo long muft it ſtay
above the Horizon of that Pole, and
conſequently, ſo long together is id
Day at the reſpective Pole, and Night
at the oppoſite Pole. This is alſo
evidently ſhewn upon the Globe, being
placed ſo, as that its Equator and Ho-
rizon become parallel one to the other.
It remains to obſerve in reference 27.
to the Equator, that a Revolution The Revo-
thereof is the Meaſure of
the Meaſure of a (*) the Equa-
Nuchthemeron, or the Space of 24
Meaſure of
Hours. Accordingly, whilſt any Point a Nuch-
of the artificial Equator moves from themeron,
lution of
tor, the
or of 24
Hours.
(*) It is a Greek Word, ſignifying the Space of one
Day and Night taken together.
I 2
the
116
Of the Celeſtial GLOBE, &c.
CHAP. the artificial Meridian round to the
IX. fame Side of the faid Meridian again;
n the Index, which is faſtened to the
north Pole of the Globe, will move
quite round the Hour-circle faſtened
upon the Meridian about the ſaid Pole.
And by comparing the Motion of the
Equator with that of the Hour-Index,
it will ſenſibly appear, (if the Globe
be made true that as the whole Cir-
cumference of the Heavens, divided
into 360 Parts, called Degrees, paſs
under the Meridian of any place in
a Nuctbemeron or 24 Hours; ſo 15
Degrees of the Circumference of the
Heavens paſs under the fame Meri-
dian every Hour. For according to
the Rule of Proportion, as 24 Hours,
are to 360 Degrees, ſo one Hour, is to
15 Degrees.
28. Proceed we next to obſerve in re-
The Zodi- ference to the Zodiack or Ecliptick,
ack why that, the Reaſon, which induced the
to twelve Old Aſtronomers to divide it into
twelve Signs, is thought to be (*) prin-
each sign
into thirty
Degrees,
*) Some conceive the Reaſon to have been, becauſe
the Number Twelve has many aliquot Parts.
cipally
Signs, and
Of the Celeſtial GLOBE, &c. 117
cipally this; viz. becauſe the Moon CHAP.
goes twelve Times round the Zodiack, IX.
whilſt the Sun goes once.
And form
the like Reaſon it ſeems to be, that,
whereas one Revolution of the Sun
round the Zodiack, is called the Solar
Year, there are reckoned cwelve Re-
volutions of the Moon round the
Zodiack to make up the Lunar Year.
Laſtly, The Reaſon why each Sign of
the Zodiack was diſtinguiſhed into thirty
Degrees, ſeems to be this, becauſe the
Moon always overtakes the Sun in (*)
about thirty Days after ſhe has left
him.
And becauſe the Sun graditur, i. e.
29.
goes, in a Day and Night or 24 Degrees,
Hour's Space, near upon one of theſe whence so
thirty Parts of a Sign ; hence the ſaid
Parts are thought to be ſtiled by the
Latins, Gradus, and ſo by us, Degrees.
And from the Circle of the Zodiack,
or more particularly of the Ecliptick,
came this Name to be transferred to
the like Diviſions of all, not only af-
tronomical, but alſo other mathematia
cal Circles.
(*) Sec Chap. 4. Sect. 3.
I 3
Agreeably
118 Of the Celeſtial GLOBE, &c.
How to
Globe,
lendar
CHAP. Agrecably to the 12 Signs of the
IX. Ecliptick, the Solar Year is alſo divi-
Muded into twelve Months, called Solar
30. Months; each being the Space where-
in the Sun goes through a Sign, and
find on the
ſo containing almoſt 30 Days. How
what Sign theſe Solar Months ſtrictly ſo cal-
anſwers to
each Ca.. led, anſwer to the common Calendar
Month, or (which amounts to the
Month.
ſame ) what Degree of the Ecliptick
the Sun is in each Day of the 12 Ca-
lendar Months, is to be ſeen on the
npper Surface of the broad wooden
Circle of the Globe commonly called
its Horizon; for thereon the 12 Signs
of the Ecliptick, and the 12 Calendar
Months are ſo placed, both according
to the Julian and Gregorian Account,
as that the Days of theſe may duly
anſwer to the reſpective Degrees of
thofe.
13.
In reference to the 12 Diviſions of
The Divi, the Ecliptick on the Surface of the
Zodiack Body of the Globe, it is to be obſer-
or Eclip- ved, that neither the Conſtellations
themſelves, nor their Names, but their
be known,
por by the Characters ſhew, which Diviſion of the
Constella. Ecliptick is eſteemed reſpectively to be-
long to each Sign, or goes under the
Name
tick are to
tions or
Signs
them.
1
Of the Celeſtial GLOBE, &c. 119
Name of each Sign. Thus the Cha-CHAP.
racter w is placed at the Beginning of IX.
that Diviſion, which is eſteemed to bem
long to Aries; and the ſaid Diviſion (elves, tuo
of 30 Degrees between V and 8, is Charac-
that which is denoted by the Sign of ters.
Aries; whereas the Conſtellation ſo
called, is now, great or moſt part of
it, out of that Diviſion, and the Word
Aries is affix'd to the ſaid Conſtella-
tion almoſt at the End of the ſaid
Diviſion. So the Diviſion between I
and is that which is denoted by the
Sign of Gemini, though the Conſtel-
lation fo called, is almoſt entirely out
of that Diviſion, and conſequently, the
Word Gemini affixed to the Conſtel-
lation.
The Reaſon hereof is this. The 32.
Conſtellations themſelves (*) conti-
nually (though very flowly) changing thereof.
their Situation in the Zodiack or E-
cliptick, in Conformity thereto, con-
tinually to change the Names of the
ſeveral Diviſions, would create great
... "W".**
And the
Reason
(*) To what this Change of Situation is owing really,
is obſerved, Chap. 7. Sect. 5.
Con-
14
eme.
120
Of the Celeſtial GLOBE, &c.
;
CHAP. Confuſion in Aſtronomy ; foraſmuch
IX. as it would make it an intricate Mat-
ter rightly to diſtinguiſh what Parts
of the Zodiack belonged to the ſeve-
ral Signs in different Ages of the
World. Wherefore to avoid ſuch
Confuſion, it has been with great
Prudence judged Expedient, not to
make any change as to the Names of
the Diviſions, though the Conſtella-
tions themſelves do in Proceſs of
Time change their Places but al-
ways to look on that which is eſteem-
ed the firſt Diviſion of the Zodiack as
belonging to Aries, at leaſt to let it
go always under the Name of Aries,
(and ſo of the reſt) though that Con-
ſtellation it ſelf ( and ſo of the reſt)
have now fo changed its Situation, as
to be moſtly, or in great Part out of
its reſpective Diviſion, and will in Pro-
ceſs of Time be removed farther and
farther from it.
33.
Befides the Circles hitherto menti-
of one oned, there are uſually drawn on the
ther Cira Surface of the celeſtial Globe, twelve
cles of the other Circles; ſix whereof croſs per-
Globe, viz.
pendicularly the Ecliptick between its
Signs, the other fix croſs perpendicu-
larly
F
twelve o-
**.de
Of the Celeſtial GLOBE, &c.
I 21
The fix
************************* de wereld.....
larly the Equator at every like ( viz. 30 CHAP.
Degrees) Diſtance, beginning to reckon IX.
from the firſt of Aries.
The fix former are called Circles of 34.
Latitude, becauſe that Arch of ſuch a
Circles of
Circle, which is intercepted between Latitude.
any Phanomenon or Point of the Hea-
vens and the Ecliptick, is the Meaſure
of the ſaid Pbænomenon's or Point's
Latitude, i. e. Diſtance from the Eclip-
tick northward or fouthward. For the
Ecliptick being the Circle in the Hea-
vens of principal Regard, therefore, by
it the Heavens are diſtinguiſhed into two
Hemiſpheres, one northern, the other
ſouthern.
By the ſame Circles is alſo meaſu-
35.
red the Longitude of any Phænomenon which are
allo Cir.
or Point in the Heavens. For by the
cles of Lon-
Help of theſe Circles, any Phænome-gitude.
non in the Heavens is referred to the
Ecliptick, the ſaid Phenomenon being
underſtood to be in that point of the
Ecliptick, which is interſected by ſuch
a Circle paſſing through the ſaid Phe-
nomenon ; and the Arch of the Eclip-
tick between the firſt of Aries and
the ſaid Point of Interſection, is the
Meaſure of the ſaid Phænomenon's
Longitude,
I 22
Of the Celeſtial GLOBE, &c.
tion; de
CHAP. Longitude, or Diſtance from the firſt of
IX. Aries reckoned according to the Series
m of the Signs.
By the fix other Circles, any Pha-
36.
nomenon or Point in the Heavens is re-
And fix
Circles of ferred in like manner to the Equator ;
Declina.
and they are called Circles of Decli-
mong which nation, becauſe that Arch of ſuch a Cir-
are the two cle, which is intercepted between the
ſaid Phenomenon and Equator, is the
Meaſure of its Declination, i. e. of
its Diſtance from the Equator, north-
ward or fouthward.
Among theſe
Circles, the two of chief Note are
the two (*) Colures ; one whereof crof-
ſes the two Equinoctial Points, and is
therefore called the Equino&tial Colure;
the other croſſes the two Solſtitial Points,
and is therefore called the Solftitial Co-
lure.
37.
And thus we have deſcribed the
The princi- ſeveral Circles, and more remarkable
pal Circles Points of the Celeſtial Globe. It re-
Globe, ſu- mains to obſerve, that of all the fore-
ally recko- mentioned Circles, theſe are uſually
and diffin-
guiſhed in-
10 fix grea-
(*) The Import and Reaſon of this Name is not
well accounted for by any Writer of Afronomy, as I
of the
nel Ten,
ter, and
four leffer
know ot.
Circles.
reckoned
Of the Celeſtial GLOBE, &c.
123
:
reckoned the ten principal Circles of CHAP.
the Globe, viz. the Horizon, the IX.
Meridian, the Equator, the Zodiack my
or Ecliptick, the two Colures, the two
Tropicks, and the two Polar Circles.
And theſe are diſtinguiſhed into grea-
ter and leſer Circles; the fix former
being greater Circles, as being con-
centrical with the Globe it ſelf, and
fo dividing, each of them, the Globe
into two Hemiſpheres or equal Parts ;
the four latter being leffer Circles
as being not concentrical with the
Globe, and ſo dividing, each of
them, the Globe into two unequal
Parts.
All the ten Circles laſt mentioned, 38.
are uſually drawn on the terreſtrial of the
Globe ;
ás alſó Circles croſſing per-Globe.
pendicularly the Equator at every ten
Degrees, and other Circles running
parallel to the Equator at every ten
Degrees. The former are called Cir-
cles of Longitude, the latter Circles
or Parallels of Latitude ; foraſmuch
as thoſe ſerve to ſhew the Longitude
of Places, (i. e. their Diſtance from
fome one of the ſaid Circles taken at
Liberty, and commonly called the
firſt
terreſtrial
124
Of the Celeſtial GLOBE, &c.
CHAP. firſt Meridian, all theſe Circles of
IX. Longitudes being alſo Meridians ; )
m theſe ſerving to Thew the Lacicude of
Places, or their Diſtance from the
Equator. Beſides theſe Circles fore-
mentioned, there are alſo uſually
drawn on the Surface of the terre-
ſtrial Globe, Rumbs, i. e. Circles
croſſing one another in ſome certain
Points of the Globe, where there is a
Vacancy, and repreſenting the ſeve-
ral Winds, or 32 Points of the Com-
paſs, fet down alſo on the outward
Rim of the Horizon, both of the ce-
leftial and terreſtrial Globe. But the
main Difference between theſe two
Globes, is this, that on the Surface of
the celeſtial Globe are defcribed the
Conſtellations, and other fixed Scars in
their due Situation; on the Surface of
the Terreſtrial Globe are deſcribed the
ſeveral Parts of the Earth and Sea in
their due Situation.
Proceed we now to the Uſe of the ce-
39.
An Obſer- leſtial Globe, or to thew how the diur-
varion con-
nal Phænomena of the celeſtial Lights
Difference are repreſented thereby. For the clearer
the natural Apprehenſion whereof it ſeems requiſite
Appear to obſerve, that there is this Difference
in
cerning the
..I
Of the Celeſtial GLOBE, &c. 125
tificial Re-
in general between the natural Appea- CHAP.
rances of the celeſtial Lights, and the IX.
artificial Repreſentation of them by the
Globe, viz. that the ſaid celeſtial Lights tances of
do naturally appear to us as in the Con- al Lights,
cave, or inner Surface of the Heavens, and the ar-
whereas they are repreſented upon the preſentati-
Convex or outer Surface of the celeſtial on of them
Globe. Wherefore to make the artifici- upon the
al Repreſentation to anſwer more exactly Globe.
to the natural Appearance, either the
Spectator muſt be conceived to be placed
within the celeſtial Globe at its Center,
and the Body of the Globe to be tranſ-
parent like the Heavens, and in ſuch a
Poſition of the Eye, the celeſtial Pha-
nomena on the Surface of the Globe will
appear to the Eye in a concave Surface,
as they do naturally; or elſe the Spec-
tator is to be conceived as placed with-
out the concave or inner Surface of the
Heavens.; and conſequently as viewing,
from ſomewhere above, the correſpon-
dent convex Surface of the Heavens ;
and upon ſuch a Suppoſition, the ce-
leftial Phænomena would naturally ap-
pear to us in a convex Surface, as they
are repreſented by the Globe. Now we
being placed upon the Convex, or
outer Surface of the Earth, and the ſe-
veral
1
I
126
Of the Celeſtial GLOBE, &c.
CHAP. veral Parts of the Earth and Sea being
IX. repreſented likewiſe on the convex Sur-
wface of the terreſtrial Globe; therefore
there is an exact Agreement in this Par-
ticular between the natural Poſition of
the ſeveral Parts of the Earth and Sea,
and their artificial Repreſentation by the
terreſtrial Globe, without the Help of
any ſuch Fiction, as has been afore ob-
ſerved requiſite, to adjuſt the natural
Appearance of the celeſtial Phanomena,
to their artificial Repreſentation by the
celeſtial Globe.
Irynar HONDA AWO Wland
--
С НАР.
[ 127 ]
1
CH A P. X.
Of the more uſeful Problems ſolved by
the Celeſtial GLOBE.
PRO B L E M I.
IN
To find the Sun's PLACE in the
ECLIPTICK for any Day given,
v. g. Oet. 13. Old Style.
N the Julian Calendar (placed next CHAP.
to the Ecliptick) on the Horizontal X.
wooden Circle of the Globe find the w
Day given, to which adjoins the Degree
of the Ecliptick, where the Sun is that
Day. Thus to OET. 13, adjoins the firſt
Degree of Scorpio, the Sun's Place for
that Day.
The Sun's Place being thus found by the Ecliptick on
the Horizon, the fame Degree of the Ecliptick on the
Surface of the Globe is to be taken, in order to ſolve
any of the following Problems.
PRO-
128
Of the Uſe of the
m
CH AP.
X.
PROBLEM II.
To find the Sun's DECLINATION at
any Time given, v. gr. Oet. 13.
Old Style.
H
Aving (by Problem 1.) found the
Degree of the Ecliptick, wherein
the Sun is at the Time given, bring the
ſaid Degree to the graduated Edge of
the Meridian of the Globe; the De-
grees of the ſaid Meridian, intercepted
between the Equator and the Sun's
Place, ſhews the Sun's Declination. Thus,
OE. 13. the Sun is in the eleventh De-
gree
of the ſouthern Declination.
As in this, ſo in the following Problems, by bring-
ing any point of the Globe to the Meridian, is under.
ftood the bringing it to the graduated Edge of the Me
ridian of the Globe, as being that which repreſents the
true Meridian.
In like manner, the Latitude of a Place is found upon
the terreſtrial Globe, by bringing the Place to the gradu-
ated Edge of the Meridian, and reckoning the Degrees
of the Meridian between the Place and the Equator.
For as the Diſtance of any Point in the Heavens from
the Equatør is Aſtronomical Declination, ſo the Diſtance
of any Point on the Earth from the Equator is Geogra-
phical Latitude. Which is requifite to be here known,
foraſmuch as although the two foregoing Problems re-
ſpect indifferently all Latitudes and Places, the following
Problems reſpect only particular Places, the Phenomena
relating thereto varying according to the different La-
titude of Places.
PRO-
Celeſtial GLOBE.
129
СНАР.
X.
PROBLEM III.
a
To rectify the GLOBE to any Lati-
tude given.
Mobi
OVE the reſpective Pole (viz.
che noth Pole, if the Latitude
given be northern ; the ſouth Pole, if
ſouthern) above the Horizon, till there
are ſo many Degrees of the Meridian
between the ſaid Pole and the Horizon,
as anſwer to the Latitude given. Thus
the north Pole being elevated 51 De-
grees and an half, the Globe is rectified
for the Latitude of London,
K
PRO
130
Of the Uſe of the
CH AP.
X.
n
PROBLEM IV.
To find what STARS never riſe, or
never ſet in any Place or Latitude
given.
T
ven.
He Globe being (by Problem 3.)
rectified to the Latitude given,
ſuch Stars as go not under the Horizon
of the Globe, during its whole Revolu-
tion, they never ſee in the Latitude gi-
And ſuch Stars as riſe not above
the Horizon of the Globe, during its
whole Revolution, they never riſe in the
Latitude given. Thus the little Bear,
the Dragon, Cepheus, and Caſſiopeia,
never ſet in the Lacitude of London; as
alſo the great Bear, except the lower
Part of its right Foot. On the other
hand, the Peacock, the Indian, the
Toucan, che Hydrus, the Dorado, the
Chameleon, the ſouthern Triangle, the
Apus, never riſe in the Latitude of Lon-
don.
1
PRO-
?
Celeſtial GLOBE.
131
A
CH A P.
X.
m
PROBLEM V.
To rectify the GLOBE, so, as that
it
may be ready duly to repreſent the
diurnal PHÆNOMENA, at any
Place, and Time given, v. gr. at
London, O&t. 13. Old Style.
T
HE Globe being rectified by
Problem 3.) to the Latitude of
the Place given, bring the Sun's Place
in the Ecliptick for the Day given
( found by Problem 1.) to the Meri-
dian, and make the Hour-Index to
point juſt to 12 on the Hour-Circle.
The Globe in ſuch its Poſition will
actually repreſent the Poſition of the
Heavens, in Reſpect of the Place gi-
ven, at the Noon or 12 a Clock of
the Day given. And conſequently by
the due Motion of the Globe, may be
repreſented the Poſition of the Hea-
vens, in Reſpect of the Place gi-
ven,
K 2
A
132
Of the Uſe of the
CHAP. ven, at any other Part of the Day
X. given.
Thus the north Pole being elevated
51 Degrees, which is the Latitude of
London, and the firſt Degree of Scor-
pio (which is the Sun's Place, Oétober
13. Old Style,) being brought to the
Meridian, the Globe will repreſent
the Poſition of the Heavens in Re-
ſpect of London, at Noon, October 13. -
Old Style ; that is, ſuch Stars as are
at or near the Meridian or Horizon
(&c.) of the Globe, will then be re-
ſpectively at
at or near the Horizon
(&c.) of London. And conſequently
by the due Motion of the Globe,
may be repreſented the Poſition of
the Heavens in Reſpect of London, at
any other Hour of the ſame Day;
and thereby may be found the Time
of the Sun's Riſing or Setting, &c.
that Day, as is ſhewn in the follow-
ing Problems. Only it muſt be re-
membred, that in Order to ſolve
fuch Problems, as relate to the Time
of any ſuch Phænomenon, the Hour-
Index' muſt always be put exactly to
12 on the Hour-Circle, before the
Sun's Place be moved from the Meri-
dian ;
Celeſtial GLOBE.
133
dian ; and alſo ſpecial Care muſt be CHAP.
taken, that the Hour-Index moves X.
duly round with the Body of them
Globe.
PROBLEM VI.
To find the Time of the Sun's Riſing
and Setting, and its Amplitude, at
any Place or Time given.
T
4
HE Globe being (by Problem 5.)
duly ordered and prepared, turn
the Globe, till the Degree of the
Ecliptick, wherein the Sun is for the
Day given, comes to the Eaſt-Side of
the Horizon ; the Hour-Index will then
Thew upon the Hour-Circle the Time
of the Sun's Riſing: and the Degrees
of the Horizon, intercepted between
the true eaſt Point, and that Point of
the Horizon the Sun's Place comes to,
ſhew its Morning Amplitude, this being
the
K 3
134
Of the Uſe of the
CHAP. the Diſtance of the Point of the Ho-
X. rizon where the Sun riſes, from the
true eaſt Point of the Horizon. In
like manner, the Degree of the Eclip-
tick, wherein the Sun is, being brought
to the weſt Side of the Horizon, the
Hour-Circle will ſhew the Time of the
Sun's Secting ; and the Degrees of the
Horizon, intercepted between the true
weſt Point, and that Point of the Ho-
rizon which the Sun's Place is brought
to, rhew its Evening Amplitude, or
how far the Sun fets diſtant from the
true weſt Point. Where it is to be
noted, that the Sun fets ſo long be-
fore or after fix in the Evening, as it
riles after or before ſix in the Morn-
ing; and in like manner, che Sun
fets ſo far diſtant (northward or
ſouthward, according to the reſpec-
tive Time of the Year) from the true
weſt Point, as it riſes from the true
eaſt Point.
Thus it will be found by the Globe,
that at London, October 13, the Sun
riſes much about 7, and fets much
about 5 a Clock; as alſo, that its
Amplitude is 18 Degrees, the Sun
riſing ſo many Degrees to the South
of
Celeſtial GLOE E.
135
of the true eaſt Point, and ſetting fo CHAP.
many Degrees ſouth of the weſt X.
Point.
The Time of the Sun's Setting, be-
ing doubled, will give the Length of
the Day; and the Time of the Sun's
Riſing, being doubled, will give the
Length of the Night. Thus, Oktob. 13.
the Day in the Latitude of London,
is much about 10 Hours long; and
the Night much about 14 Hours
long.
1
PROBLEM VII.
To find the Time of the Sun's Riſing
and Setting by its Aſcenſional Dif-
ference.
HAT Degree of the Equator,
which, reckoned from the Be-
ginning of Aries, riſes or ſets with
the
T
K4
137
Of the Uſe of the
CHAP. the Sun in a right Sphere, is called
X. the Sun's right Aſcenſion. And that
Degree of the Equator, which, rec-
koned in like manner, riſes or ſets
with the Sun in an oblique Sphere, is
called the Sun's oblique Aſcenſon. And
the Difference between its right and ob-
lique Aſcenſion, is called its afcenfional
Difference.
The oblique Aſcenſion of the Sun
is found (the Globe being firſt rectifi-
ed by Problem 5.) by bringing the
Sun's Place to the Eaſt or Weſt Side of
the Horizon, and there noting what
Degree of the Equator comes to the
ſame Side of the Horizon, together
with the Sun. The right Aſcenſion
of the Sun, is likewife found by (puta
ting the Globe into a right Sphere,
and then noting what Degree of the
Equator comes together with the Sun
to the fame Side of the Horizon ; or
more readily and without changing
the Globe from an oblique into a
right Sphere, by) noting what Degree
of the Equator comes up to the Mer
ridian, together with the Sun : ( for
the Equator always cuts the Meridian
at right Angles, as it does the Hori-
ܪ
1
2012
Celeſtial GLOBE.
137
zon in a right Sphere; and conſequent-CHAP.
ly, the fame Degree of the Equator, X.
that would come, together with the mu
Sun, or any Degree of the Ecliptick,
to the Horizon in a right Sphere, will
come, together with the Sun, to the
Meridian in any oblique Sphere.) The
quantities of the right and oblique
Aſcenſion being thus found, the aſcen-
fional Difference is found by ſubſtract-
ing the lefſer out of the greater.
Now the right Aſcenſion of the Sun
being that Degree of the Equator,
which riſes and fets with the Sun in
a right Sphere, i. e. to ſuch as live juſt
under the Celeſtial (or upon the Ter-
reſtrial) Equator, to whom the Sun al-
ways riſes at ſix, and ſets at fix; hence
the aſcenſional Difference (turned into
Time by reckoning one Hour for every
15 Degrees, and ſo proportionably) ſhews
how long the Sun riſes and ſets afore or
after ſix, according to the Time of the
Year.
Thus
138
Of the Uſe of the
CH AP. Thus the Sun's right Aſcenſion,
X. O&tober 13. is much about 208; and
nhis oblique Aſcenſion on that Day in
Reſpect of London, is much about
223; and conſequently, the afcenfio-
nal Difference is 15, which anſwers
to one Hour in Time. Wherefore, the
Time of the Year conſidered, the Sun
riſes much about an Hour after fix, i. e.
much about ſeven ; and ſets much about
an Hour before fix, i. e. much about
five ; agreeably to what was found by
Problem 6.
j
PROBLEM VIII.
To find the Sun's Altitude at
any
Place
and Time given.
T"
THE Globe being rectified by Pro-
blem 5th, the Degrees of the Meri-
dian reckoned from (the South Side of)
the Horizon to the Sun's Place, give
the Sun's Meridian Altitude. Thus,
O&tober
Celeſtial GLOBE.
139
Oetober 13. the Meridian Altitude of CHAP
the Sun at London, will be much about X.
27 Degrees.
The Alcitude of the Sun is found at
any other Time of the Day given, by
turning the Globe (rectified alſo by Pro-
blem 5.) till the Hour-Index points to
the Time aſſigned ; and then faſtening
the Quadrant of Altitude on to the Me
ridian at the Zenith; (i. e, at ſo many
Degrees from the Equator, as is the
Latitude of the Place given ;) and bring-
ing the ſaid Quadrant ſo faſtened to the
Sun's Place in the Ecliptick : che De-
grees intercepted on the Quadrant be-
tween the Sun's Place and the Horizon,
ſhew the Sun's Altitude at the Time af-
ſigned. Thus, Ostob. 13. the Sun's Al-
titude at nine in the Morning, will be
about 17 Degrees in Reſpect of the
Horizon of London. And the ſame will
be its Altitude at three in the Afternoon.
For it is to be noted, that at Times e-
qually diſtant ( before and after ) from
12, the Sun's Altitude is alſo equal.
PRO
140
of the Uſe of the
СНАР, ,
X.
n
PROBLEM IX.
To repreſent the Face or Appearance of
the Heavens, or to Mew the Situation
of the fixed Stars, at any Time of
the Night, in Reſpect of any place
and Night given.
T
HE Globe being rectified by Pro-
blem 5th, and (by the Needle )
fer ſo, as that its cardinal Points anſwer
the cardinal Points of the Compaſs,
turn the Globe till the Hour-Index points
to the time of the Night aſſigned. Such
Stars as appear at or near the Meri-
dian or Horizon (and ſo of any inter-
mediate Point) of the Globe, will ap-
pear likewiſe at or near the Meridian or
Horizon of the Place given ; (and ſo
of any intermediate Point in the
Heavens.)
-
Thus;
Celeſtial GLOBE
141
Thus, Ostob, 13. at Ten at Night, CHAP
the glorious Conſtellation Orion will X.
appear on the Eaſt Side of the Hori- m
zon of London ; the Star Rigel in the
left Knee of Orion being juſt at the
Horizon; the three Stars in the ſame
Conſtellation, called by our common
People the Yard, a little above the
Horizon. About twenty Degrees (on
a vertical Circle) above the uppermoſt
of theſe appears the bright Star in Tau-
rus, called Aldebaran, and the Bull's
Eye; and ſomewhat above this in the
fame Conſtellation, the Celebrated
Stars called the Hyades, and the Plei-
ades, theſe being in the Back, thoſe
in the Forehead of Taurus. Juſt un-
der the Meridian Southward appears the
Star called Andromeda's Head, and at
or near the Meridian the Conſtellati-
ons of Caſiopea, Cepheus, Pegaſus ,
&c. Between the Meridian and the
Weſt Side of the Horizon appears the
Conſtellations of the Swan, Harp, &c.
And at or near the Weſt Side of the
Horizon, the Conſtellations of Anti-
nous, Serpentarius, the northern Crown,
&c.
Hence
142
Of the Uſe of the
CHAP. Hence it is obvious, that this Pro-
X. blem is of good Uſe to find out and
mu know the ſeveral Conſtellations, and
the more remarkable Stars in each Con-
ſtellation.
PROBLEM X.
To find the Hour of the Night, the Al-
titude of any Štar being given, or
firſt found by fome Inſtrument for that
Purpoſe.
T
HE Globe being rectified ac-
cording to Problem 5. and the
Quadrant of Altitude duly fixed to
the Meridian, move the Globe till
the ſaid Quadrant croſs the Star in
the given Altitude ; then the Hour-
Index will ſhew the Hour of the
Night.
Thus,
1
1
Celeſtial GLOBE.
143
w
Thus, Ottob. 13. the Altitude of Al- CHAP.
debaran, or the Bull's Eye, is found to X.
be 27 Degrees, 30 Minutes. Where-wy
fore moving the Globe till the Quadrant
of Altitude croſſes the ſaid Star in 271
Degrees of Altitude, the Hour-Index
will then point to Ten at Night.
Here it is obvious, that if the Star be
in the Meridian, then there is Occaſion
only to turn the Globe ( rectified by
Problem 5.) till the ſaid Star comes to
the Meridian of the Globe : for then
the Hour-Index will ſhew the Hour.
PRO-
144
Of the Uſe of the
СНАР.
X.
::
PRO B L EM XI.
To find the Beginning of the (Crepuſ-
culum, i.e.) Twilight, or the Time of
the Day-break, at any proper Time of
the Year.
T
HE Globe being (by Problem 5.)
rectified, elevate that Degree of
the Ecliptick, which is diametrically
oppoſite to the Sun's Place at the Time
given, 18 Degrees above the Weſt Side
of the Horizon ; and the Hour-Index
will ſhew the Time fought. Thus,
O'êtober 13. Day breaks, or the Twilight
begins about a Quarter before five at
London.
The Reaſon of elevating the De-
gree of the Ecliptick, diametrically
oppoſite to the Sun's Place, 18 De-
grees above the Weſt Side of the Ho-
rizon, is this ; becauſe, thereby the
Degree of the Ecliptick wherein the
Sun is at the Time given, is depreſſed
18 Degrees below the Eaſt Side of
the
Y
3
Celeſtial GLOBE.
145
che Horizon. At which Depreſſion it is CHAP.
obſerved by Aſtronomers, that the morn X.
ing Twilight begins ; as alſo, that the mu
evening Twilight ends at the like De-
preſſion of the Sun, under the weſt Side
of the Horizon. Whence it is obvious,
that che Beginning of the morning Twi-
light being found, it is obvious to
know, when the evening Twilight ends;
this ending ſo much after or before fix
in the Evening, as that begins before or
after ſix in the Morning. Thus, Osto-
ber 13. the evening Twilight ends a-
bout a Quarter after ſeven, at Lon-
don, or any Place in the ſame Lati-
tude.
It is to be further noted, that the
morning Twilight beginning, when the
Sun is 18 Degrees below the eaſt Side
of the Horizon; and the evening Twi-
light ending, when the Sun is 18 De-
grees below the weſt Side of the Ho-
rizon, it thence follows, that, during
that Part of the Year, wherein the
Sun's Depreſſion is never ſo much as
18 Degrees, there is no Beginning of the
morning Twilight, or Ending of the
evening Twilight, but one concinued
Twilighc from Sun-fecting to Sun-ri-
L
Ging
146
Of the Uſe of the
:
CHAP. ſing. Now that part of the Year, where
X. in there is ſuch a continued Twilight in
m the Latitude of London, is while the
Sun is paſſing from about the fifth De-
gree of Gemini, to the twentieth of
Cancer, i. e. from about the 15th of
May, to about the 7th of July. For
during this Space, the Sun is never dem
preſſed 18 Degrees below the Horizon.
PROBLEM XII.
To find the Longitude and Latitude of
any Star given.
L
AY one End of the Quadrant of
Altitude upon
upon the
proper Pole of
the Ecliptick, (viz. if the Star be in
the northern Hemiſphere of the Heavens,
upon the north Pole; otherwiſe, on
the ſouth Pole,) and the graduated
Edge thereof upon the Center of the
Star, ſo will the Quadrant cut the E-
cliptick
*
147
Celeſtial GLOBE.
cliptick in the Star's Longitude, (i. e. CHAP.
its Diſtance from the firſt of Aries,) and X.
the Degrees of the Quadrant intercepted
at the fame Time, between the Star, and
the Ecliptick, will give its Latitude,
this being no other than the Star's Di-
ſtance from the Ecliptick. Thus the
Longitude of the Star called Lucida
Lyrę, will be found to be 283 De-
grees, and its Latitude about 60 Degrees
Northwards.
It is obvious, that the Sun, being al-
ways in the Ecliptick, never hath any
Latitude ; and its Longitude is found
without any more ado, than by com-
puting the Number of the Degree it
is in from the firſt of Aries. Thus,
.
the Sun is in the 19och De-
gree of Longitude, that being the Di-
ſtance or Number of the firſt Degree of
Scorpio, where the Sun then is, from
the firſt of Aries.
October 13
There are ſome other Problems,
which may be ſolved by the Globe
but they being of little Uſe are here.
omitted. And ſo we are come to the
End of this Aſtronomical Treatiſe,
wherein
3
L 2
148
Of the Uſe of the &c.
CHAP. wherein are contained ſuch Particu-
X. lars, as ſeem more uſeful to be known
mu by Young Students, eſpecially Young
Gentlemen, at their firſt Inſtirution in
Aſtronomy.
F IN I S.
te
THE
THE
Young Gentleman's
CHRONOLOGY,
Containing ſuch
Chronological ELEMENTS,
as are moſt uſeful and eaſy to
be known.
BY
EDWARD WELLS, D. D. late
Rector of Cotesbach in Leiceſterſhire.
The FOURTH EDITION.
L O N D ON:
ܛܼ
Printed for J A MES, JOHN, and P A UL
KNAPTON, at the Crown in Ludgate-Street.
MDCCXXXVI.
Τ Η Ε
PREFACE.
T
HE Art of Chrono-
logy has so cloſe a
Dependance upon Af
tronomy, that it is
not uſual for Writers of Aſtro-
nomical Treatiſes to compriſe
therein
L 4
The PREFACE
therein a great deal of what
more properly belongs to Chro-
nology; and which therefore I
þave bere laid together, with
the other moſt uſeful and eaſy
Elements of Chronology, in a
diſtinɛt Treatiſe from my Aſtro-
nomy. But the Deſign both of
the One and the Other being the
Jame, as therefore I have given
riy Aftronomical Treatiſe the
Title of The Young (Gentle-
man's Aſtronomy, ſo I have
my Chronological
Treatiſe the Title of The Young
Gentleman's Chronology :
thing being here inſiſted on,
but what relates to the common
(Civil or Eccleſiaſtical) Compu-
tation of Time, and to the two
Cele-
given this
no-
:'3
The P R EF A C E.
Celebrated Era's of the Olym-
piads, and the Building of
Rome, the former chiefly uſed by
Greek Hiſtorians, the latter by
Roman
Τ Η Ε
.
T H E
CON TENTS.
СНА Р. І.
O
F a Day; and the Parts of Time
ariſing from a Day by Diviſion,
viz. Hours and Minutes, Page 1
CH A P. II.
Of the ſeveral Parts of Time, which
ariſe from a Day by Collection, viz.
Weeks, Months, and Years. 9
СНАР,
The CONTENTS.
CH A P. III.
Of the ſeveral Characters of Time in
general: and particularly of the Cy-
cle of the Moon, and the Epacts,
31
CH A P. IV.
Of the Cycle of the Sunday-Letter,
commonly called the Cycle of the
Sun,
43
CHAP. V.
WC
Of the Indiction, and Julian Period,
54
c H A P. VI.
Of Epoch's and Æra's; and eſpecially
of the Æra or Year of Chriſt, the
Æra of the Olympiads, and the Æra
of the Building of Rome,
60
С НАР.
The CONTENT S.
CH A P. VII.
of the Method to find Eaſter-Day ac-
cording to the Nicene Rule, (as fill
followed by our Church) by Help of
the Golden Numbers affixed to the
Calendar. To which is adjoined the
Roman Method of Dating, or denoting
the Days of the Month,
774
:
.مه
-
1
THE
*
T H E
Young Gentleman's
3
CHRONOLOGY,
&c.
CHAP. I.
Of a Day; and the Parts of Time a-
riſing from a Day by Diviſion, viz.
Hours and Minutes.
B
Y (*) CHRONOLOGY is un- CHAP.
derſtood the Art or Skill of I.
adjuſting Things paſt to their
proper Times.
I.
2.
Hence Chronological Inſtitutionscon- Chronolo-
ſiſt of the Explication of the ſeveral gy, what
.
Diftin.
guiſhed into
two Parts.
(*) The Word Chronology denotes literally in th:
Greek Language a Diſcourſe, or Account of Time, being
compounded of xpóv@ Tine, and aó a Diſcourſe or
3
Account.
Parts,
-
2
Of Ď A .
by Diviſi.
on, or
CHAP. Parts, into which Time in general is
I. divided ; and of the feveral Cháraõters,
mby which particular Times are diſtin-
guiſhed one from another.
The ſeveral Parts of Time are, Mi-
3.
All other nutes, Hours, Days, Weeks, Months,
Parts office and Years. Amongſt which we ſhall
Time ariſe
from a ſpeak firſt of a Day, becauſe from it
Day, either ariſe the other Parts of Time, confi-
dered as they are applied to common
Collection. Uſe. For as Hours and Minutes ariſe
from a Day by Diviſion and Subdivi-
fion; fo Weeks, Months, and Years a-
riſe from a Day by Collection, or recko-
ning ſuch or ſuch a Number of Days
together.
4.
By a Day then, according to the
A Day, primary (*) Intention of the Name, is
what, pris denoted the Time of Light; and in
marily and
properly. chis Senſe it is oppoſed to Night, or
the Time of Darkneſs. And the Sun
being made to (+) rule the Day, hence
a Day, according to the primary In-
tention of the Name ſeems moſt pro-
perly and naturally to be determined
܂
(*) God called the Light Day; and the Darkneſs he
called Night, Gen. i. s.
(t) God made two great Lights; the greater Light to
Tule the Days, Gen. i. 10.
by
Of D A Y S.
3
by the Sun's Riſing and Setting; and CHAP.
ſo to be moſt properly and naturally I.
defined, the Stay of the Sun above me
the Horizon, or the Time between
the Sun's Rifing and Setting. Agree-
ably whereunto, Night is the Stay of
the Sun below the Horizon, or the
Time between the Sun's Setting and
Riſing.
But the Word Day is frequently ta 5.
ken in a larger Senſe, ſo as to compre- Another
hend alſo the Night, and to denote a
Acceptati
whole Revolucion of the Sun round Day for a
the Earth. This Sort of Day is moft Nuchthe-
apely denoted by the Greek Word (*) 24 Hours.
Nucbthemeron.
The Nuchthemeron may be reckon 6.
ed, either from Sun-ſetting to Sun- Different
ſecting, as did the Jews and Athenians, ways of
and as the Italians ſtill do ; or from the Nuch-
Sun-riſing to Sun-riſing, as did the themeroa.
Babylonians; or from Mid-day to
Mid-day, as do the Generality of
on of a
meron, or
1
5
E
(*) It is a compound of vote a Night, and so bpc a
Day. The two-fold Acceptation of the Word Day, is
diſtinguiſhed uſually by the Names of a Natural and an
Artificial Day. But ſome calling that a natural Day,
which other's call an Artificial, hence ariſes great Con-
fuſion; to avoid which I judge it beſt, wholly to omit
this Diſtinction.
Aſtro-
4
Of HOURS.
CHAP. Aſtronomers, and likewiſe the Arabs;
1.
or laſtly, from Mid-night to Mid-
Wnight, as did the old Egyptians, and
We of this Iſland, together with the
French, Germans, and other Europeans,
ſtill do.
7.
Proceed we now
now to the part of
of an Time, called an Hour. And hereby
is principally denoted the 24th Part
of a Nuchtbemeron. Now a Nuchtbe-
meron being the Space of an entire Re-
volution of the Sun about the Earth,
during which the Equator makes alſo
an (*) entire Revolution, hence it
..
Hour.
3
--
:!', sepse tim 20 m
ๆ
(*) In ſtrictneſs the Equator makes fomewhat more
than one Revolution, during a Nuchthemeron; viz. ſo
much more as anſwers to the Sun's apparent proper
Motion in the Ecliptick during the ſaid Space of Time.
Now this Overplus being various ; viz. 57 Minutes in
the Sun's Apogee, and 61 Minutes in its Perigee, hence
Aftronomers take the Mean between the two fore-men-
tioned Numbers for a ſtanding Meaſure through the
whole Year, and ſo compute that to every, Nuchtheme-
ron there anſwers 50'.8", and almoſt 20
over and
above a Revolution (or the 360 Degrees) of the Equa.
But now the Difference between the Sun's Revo.
lurion (or a Nuchthemeron) and the Equator's, when at
greateſt, being but 61 Minutes, or a little more than a
Degree, which anſwers but to a little more than 4
Minutes in Time, hence it may be paſſed over unre-
garded in common Uſe; and the Hour here ſpoken of
may be well enough eſteemed to anſwer juft to 15 De,
grees of the Equator.
3
comes
tor.
Of H Ö U R S.
5
comes to paſs, that as the whole Cir-CHAP.
cle or all the 360 Degrees of the Equa- I.
tor anſwer to a whole Nuchthemeron, ſom
a 24th Part or 15 Degrees of the E-
quator anſwer to a 24th Part of a
Nuchthemeron, or ſuch an Hour. And
becauſe theſe Hours are all thus uſually
meaſured by 15 Degrees of the Equa-
tor, hence they are all looked on as E-
qual one to another at all Times.
But the Jews, Greeks, and Romans 8.
did antiently divide (not the Nuchthe-of Tema
meron into 24 equal Hours, but ) the porate
Day, whether longer or ſhorter, into Hours.
12 Hours ; and ſo likewiſe the Night.
Whence it is obvious, that their Hours
were Unequal one to another, except
only at the two (*) Equinoxes ; when
the Day and Night being Equal, their
Hours would likewiſe be Equal, and
to the ſame as to Extent with our
Hours, though not as to Denomina-
tion
(*) Hence the equal Hours uſed by us are ſometimes
filed Equinodtial Hours; and the uncqual Hours uſed by
the Jews, &c. are ftiled Temporary Hours, from their
varying in Length according to the other various Parts
of the Year.
M
For
6
Of Hours.
common
Hours.
Which ob.
under-
CH AP. For they always reckoning their firſt
I. Hour of the Day from the Sun's Riſing,
w which at the Equinoxes anſwers exactly
9. to our fix a Clock in the Morning, it
How the follows that their firſt Hour of the Day
Hours an- muſt anſwer at the Equinoxes to our
fwer to our ſeven a Clock in the Morning ; and con-
equal
ſequently their third Hour to our nine
a Clock in the Morning; their fixth to
fervation is our twelve a Clock at Noon; their ninch
of uſe for to our three a Clock in the Afternoon,
& c.
fanding
And although there is not ſo exact
the Bible- a Correſpondence between the Hours
Hiſtory. uſed by them and us, at other Times of
the Year, yet the fore-mentioned Obſer-
vation is of good Uſe for the better
Underſtanding the ſeveral Hours of the
Day mentioned in the Sacred Hiſtory.
Upon the like Account it is not to
As is alſo
be here omitted, that the Jews divided
zire Jewiſh the Night (not only into twelve Hours,
Diviſion of as is afore obſerved; but alſo) into four
the Night
Quarters, called Watches, each Watch
Watches
, containing three of their Night-hours.
ego.
Theſe Watches were diſtinguiſhed, ei-
ther by their numeral Order, whence
we expreſsly read in the Sacred Hiſtory
of the (*) Second, Third, and (+) Fourth
IO.
into
(*) Luh. xii. 38.
(t) Matt, xiv. 25.
Watch
;
Of MINUTE S.
7
II.
Watch ; or by ſome other Denomina- CHAP.
cion. Thus the firſt Watch is other I.
wiſe filed the (*) Head or Beginning
of the Watches; the Second, the (t)
Middle Watch, becauſe it laſted till
Mid-night ; and the Fourth, the (II)
Morning Watch. Again, the Firſt was
cermed (1) the Evening ; the Second,
Mid-night; the Third, the Cock-crow-
ing; the Fourth, the Dawning.
The common Diviſion of an Hour is
into Quarters. But Aſtronomers, and Of Mi.
nutes, and
ſuch as are more accurate in accounting Seconds;
Time, divide an Hour into ſixty Parts, and the
Difference
called Minutes ; and a Minute again in- between
to fixty Parts, called Seconds, as being Horary
Minutes of Minutes, and ſo ſecondary duary Mi-
Minutes. And here it is to be obſerved, nutes.
that the Word Minute is taken in a dou-
ble Senſe, either to denore the fixtiech
Part of an Hour, which therefore is
peculiarly filed an Horary Minute; or
elſe to denote the ſixtieth Part of a
Degree, which therefore may be diſ-
tinguiſhed by the Name of a Graduary
Minute. And this Graduary Minute is
(4) Lam. ii. 19.
(Exod. xiv. 24.
(1) Fudg. vii. 19.
(5) Mark xiii. 35.
ſubdi-
M 2
8
Of MINUTES.
CHAP. ſubdivided by Aſtronomers into fixty
I. Seconds, and alſo each Second into fixty
WTbirds, and each Third into fixty
Fourths, &c. whereas it is uſual to ſub-
divide an Horary Minute only into Se-
conds. Now as 15 Degrees of the E-
quator anſwer to one Hour or fixcy Ho-
rary Minutes, ſo one Degree of the E-
quator, or fixty Graduary Minutes an-
ſwer to four Horary Minutes; and ſo one
Horary Minute to fifteen Graduary Mi-
nutes. And thus much for the ſeveral
Parts of Time, which ariſe from a Day
by Diviſion, and Subdiviſion.
С НАР.
भ
[9]
M., story
CHA P. II.
Of the ſeveral Parts of Time, which
ariſe from a Day by Collection ;
viz. WE EKS, MONTHS,
, and
YEARS.
I.
"N,
mos med
#m. Et vous
MONG the ſeveral Parts of CHAP.
Time, which ariſe from a Day
I.
by Collection, it is proper to ſpeak first
of the Week, not only as denoting the
ſmalleſt Collection of Days, namely, properly lo
Of Week
no more than ſeven ; but alſo as be-callid.
ing the moſt Antient Collection, as
we learn from the Sacred Hiſtory,
whereby we are taught that it was in-
ſtituted preſently after the Creation,
and in Memory of God's creating the
World in ſix Days, and reſting on the
Seventh from all bis Works, which be
bad made.
The ſeven Days of the Week are
commonly diſtinguiſhed by the Name The ſeven
of the Planets, accounted alſo juſt the Week,
ſeven according to the Vulgar Syſtem, whence
and placed in this Order from the take their
common
Higheſt to the Loweſt, viz. Saturn, Denomi-
Jupiter,
-
2.
******** ***** stigningen. Det er
M 3
nations.
IO
Of WE E K S.
CHAP. Jupiter, Mars, the Sun, Venus, Mer-
II.
cury, and the Moon. Now the Aſtro-
m logers ſuppoſing the fore-mentioned
Planers to preſide or 'rule over the ſe-
veral Hours of the Nuchthemeron ac-
cording to their Order above-mentio-
ned, hence denominate each Day of the
Week from chat Planet, which is ſup-
poſed to preſide over the firſt Hour of
the Nuchtbemeron, Whence it comes
to paſs, that the Days are denominated
from the Planets according to the com-
mon Method. For aſſigning the firſt
Hour of Saturday to Saturn, the fe-
cond will fall to Jupiter, the third to
Mars, the fourth to the Sun, the fifth
to Venus, the fixth to Mercury, and the
ſeventh to the Moon. And ſo the eighth
Hour will fall to Saturn again, and
alſo the fifteenth and twenty-ſecond
of the ſaid Nuchthemeron; and confe-
quently, the twenty-third Hour will fall
to Jupiter, the twenty-fourth to Mars.
By which means the firſt Hour of the
next Nuchthemeron will fall to the Sun,
and the firſt Hour of the next to the
Moon, of the next to Mars, of the next
to Mercury, of the next to y upiter, of
the next to Venus; and of the next to
Saturn
Of WE E K S.
II
mana, " <******
Saturn again, and ſo through the next CHAP.
Week as afore. Hence the Days of II.
the Week came to be diſtinguiſhed in m
their Order by the Latin Names of
Dies, Saturni, Solis, Luna, Martis,
Mercurii, Yovis
, and Veneris ; and ſo
among us by the Names of Saturday,
Sunday, Munday, Tueſday, Wedneſday,
Thurſday, and Friday. For as Satur-
day, Sunday, and Munday, plainly de-
note the Day of Saturn, the Sun, and
the Moon ; 'fo Tueſday, Wedneſday,
Thurſday, and Friday, denote the Day
of Tuiſco, Woden, Thor, and Friga;
which are the Saxon Names reſpectively
anſwering to Mars, Mercury, Yupiter,
and Venus.
It is alſo not to be omitted, that,
3.
becauſe the Eaſter Week was formerly The Days
eſteemed the Firſt or Principal Week Low deno-
of the Year ; and each Day thereof minated by
was a Feria or Holy-Day ; hence the
ſeveral Days of the Week were diſtin- tians.
guiſhed in their reſpective Order, a-
mong the Primitive Chriſtians, by the
Names of feria Prima, Secunda, &c.
i. e. the Firſt
, Second, ( &c.). Holy-
Day: Sunday, or the feria Prima be-
ing otherwiſe ſtiled by them the Lord's
Day,
- come to respondente la prova di sini
the Anti-
ent Chrif
M 4
I 2
Of WE E K 8.
A Week
taken to
CHAP. Day, as being the Day of our Lord's
II. Reſurrection.
Hitherto we have ſpoken of a Week
4. in its common Acceptation, as ic denotes
Sometimes
a Week of Days, or ſeven Days., But
it is not wholly to be paſt by, that as the
denote the Original or Hebrew Word which we
Space of
feven render a Week, does literally denote
Years, only in general a Colle&tion of Seven,
and therefore may be applied to Years
as well as Days, (and the fame holds
as to the correſpondent (*) Greek and
Latin Words,) ſo it is actually uſed in
(+) fome Places of the Sacred Hiſtory
to denote, not ſeven Days, but ſeven
Years. And in Conformity to the Uſe
of the ſaid Original Word, our Engliſh
Word Week is uſed in the ſaid Places of
Sacred Scripture to denote, not a Week
of Days, but a Week of Years, or a
Collection of ſeven Years.
Proceed we next to ſpeak of Months,
A synodi- which, as they are of various Sorts,
fal Momb, ſo are called by this one common
primarily Name, not by mere Chance, or with-
Month. quç any Reaſon, but by Reaſon of
Hebdomas and Septimana,
(+) so Dan. ix. 24-27,
6
their
the meaning the remote pre deti a mano
Of MONTH s.
13
their all agreeing in ſome Relation to CHAP.
a Month primarily ſo called. Now II.
the (*) Hebrew Word, to which our
Word Month anſwers, does literally
import the Time from one New Moon
to another; and ſo does properly de-
note a Synodical Montb.. And foraſ,
much as this ſort of Month is moſt dif-
tinguiſhable by our Senſe, and ſo moſt
obvious and proper to be uſed as a
Meaſure of Time in the common Af-
fairs of Life ; hence it is more than
probable, that, as our Word Month
is evidently derived from the Word
Moon, ſo it was primarily intended to
denote likewiſe the Time from one
New Moon to another, or a Synodical
Month. For it is more than probable,
that this Word in our Language (and
ſo of the correſpondent Words in all
other Languages) was firſt uſed to de-
note thaç Sort of Month, which was
firſt obſerved as a Meaſure of Time.
But now it is not reaſonably to be
3
*****
* Fabricante Hote,,
(*) The Hebrem Word Chodeſh (is derived from a
Radix, which fignifies to Renew, and accordingly) does
primarily denote the New Moon, or the Day of the New
Mpon; and thence it is ſecondarily taken to denote a
Month, being the Space from one New Moon to ano-
ther,
doubted,
14
Of MONTHS.
rsodical
***** wa
Month.
CHAP.doubted, but the Synodical Month was
II. firſt uſed as a Meaſure of Time, for-
aſmuch as it is obvious to the bare Senſe,
even of the Vulgar and moſt illiterate
Perſons.
5. As for the Periodical Month, or the
The pe-
Time wherein the Moon goes round
Monsk, why her Orbit, this could not be determi-
called a
ned without ſome Obſervation and
Study; and therefore no doubt was not
taken Notice of, till ſometime after
the Synodical Month was uſed. And
conſequently it is not to be doubted,
but the Name Month was applied to
the Time of the Moon's Periodical
Courſe, not primarily, but ſecondarily,
or after it had for ſome Time been ap-
plied to the Moon's Synodical Courſe.
And the Reaſon of impoſing the fame
Name upon the Time of that, as had
been impoſed afore upon the Time of
this, was, becauſe both Times agree
in the general, viz. as they relate to
the Courſe of the Moon, and ſo may
both from the Moon be called Months.
6. It has been afore (in the Aſtronomi-
of the dif- cal Treatiſe, Chap. 4. Se&t. 2, 3.) ob-
Lengths of ſerved, that the Periodical Month con-
the Syno- fiſts of 27 Days and 7 Hours; and
the
Of MONTH S.
15
ཀྱིས་ སྤྱི མེ ཀagr88%E ཙྩ *
3
I
dical and
i je postao namna ya kuwa mwenye mit denen la information
the Synodical Month of 29 Days and CH AP.
124 Hours. And the Reaſon of this II.
Difference has been there accounted m
for.
Periodical
It is here to be further noted, chat, Month.
becauſe during (either a Synodical or 7.
Periodical) Month of the Moon, the A Solar
Sun paſſes well-nigh through a whole that, and
Sign of the Ecliptick; hence the Time why called
A Month,
of the Sun's paffing quite through a
Sign is called a Solar Month, as nearly
anſwering to the Space of a Lunar
Month, eſpecially the Synodical Month.
For as this Sort of Lunar Month is a
little above 29 Days, ſo the fore-men-
tioned Solar Month is almoſt 30 Days:
and conſequently the Difference between
them is but about one Day.
But now becauſe the fore-mentioned 8.
Solar and Lunar Months do not conſiſt Civil
Months,
juſt of whole Days, but of ſome odd what, and
Hours and Minutes over, which cannoc w by called
Months
be confidered in the common Account
of Time; therefore ſome certain Num-
ber of juſt whole Days are made uſe of
inſtead of the fore-mentioned Aftrono-
mical Months; but however are called
likewiſe Months, foraſmuch as they
come as near as can be to the faid Aſtro-
nomical Months, from which they are
3
diftin.
16
Of MONTHS.
9.
A Month
of Weeks,
what.
CHAP. diſtinguiſhed by the Name of Civil
II. Months, as being adapted to Civil or
ü
vCommon Uſe.
Thus in the firſt place, what is moſt
commonly called a Month among us,
is made to conſiſt juſt of twenty-eight
whole Days, and ſo juſt of four whole
Weeks; whence it is peculiarly ſtiled
a Month of Weeks. It is obvious,
that in Order to render the Computa-
tion of Time from Weeks to Months
more eaſy, and ſo more fit for common
Uſe, it was neceſſary that the Month
fhould conſiſt juſt of ſome certain
Number of whole Weeks: which being
thus neceſſary, four whole Weeks were
made Choice of for the Number, which
ſhould conſtitute the Month; becauſe
this Number comes nearer than any other
Number of Weeks, to the ſeveral Al-
tronomical Months afore-mentioned.
The Aſtronomical Synodical Month
The Civil is adapted to Civil or Common Uſe,
Synodical
by making the Civil Synodical Monch
Month,
to conſiſt alternately of (*) twenty-
IO.
what.
(*) A Civil Synodical Month conſiſting of thirty
Days, is called Plenus, i. e. a Full Month; and a Civil
Syncdical Month confifting but of twenty-nine Days, is
called Cavus, i. c, an Hollow or Defective Month.
nine
Of MON T H s.
17
nine and thirty whole Days ; for 29 CHAP.
+30 = 59 = 291 x 2, that is, two II.
Civil Synodical Months are equal com
two Aſtronomical Synodical Months,
omitting in both the odd Minutes.
And conſequently, according to this
Method, the New Moon will keep to
the firſt Day of every ſuch Civil
Month for a long time together, when
once adjuſted thereto. This was the
Month in Civil or Common Uſe among
the Jews, Greeks, and Romans, till the
Time of Julius Cæfar, and is ſtill ſo
among the Turks.
In like manner, the Aſtronomical So-
lar Month may be adapted to common
Uſe, by making the Civil Solar Months might be
to conſiſt alternately of thirty and thir- uniformly
ty-one Days, excepting one Month of Civil or
the twelve, which ſhould conſiſt of thir-Common
ty Days every four Years; the other Ufe.
three Years it muſt conſiſt only of
twenty-nine Days. This is illuſtrated
by the adjoining Scheme or Table of
the Solar Months.
II.
The Solar
Months
Months.
18
Of MONTHS.
CH AP.
II. Months. Days. Months. Days. Months. Days.
March
Quintilis
31 November
31
April 30
Sextilis
30 December
30
May 31 September
31
31
June 30
October
30
February 29
And every fourth Year, 30
31
January
.
I 2.
Months
hom came
in Urea-
For according to this regular and uni-
form Method, there will be 365 Days
in the twelve Solar Months for three
Years together, and every fourth Year
366 Days, juſt as it is now.
It is evident then, that the Civil
The Solar Solar Months might be thus uniform-
ly conſtituted. And indeed they were
to be inflic ſo conſtituted in the main at firſt by
inted as Julius Cæfar, who brought the Solar
Monchs into common Uſe among the
mong us.
Romans, whereas they uſed afore the
Civil Lunar Month, as was (*) ob-
ſerved when we were ſpeaking of the
ſaid Lunar Month. The Alteracion
was made afterwards, when ( as the
fifth Month, which had afore been
called from its Rank, Quintilis, was
new named Julius in Honour of the
Emperor of that Name; ſo ) the ſixth
Month, which had afore been called
.
(*) Sect. tosh of this Chafter,
from
2
Of MONTH s.
19
from ics Rank, Sextilis, was new CHAP.
named Auguſtus in Memory likewiſe of II.
che Einperor of the ſame Name; and m
not only ſo, but (whereas this Month
conſiſted afore but of thirty Days,
and ſo was a Day ſhorter than the
foregoing Month of July,) there was
a Day more added to it, that fo che
Honour paid to Auguftus might not
ſeem to fall ſhort of the Honour paid
to Julius, even in this Punctilio. Now
this Alteration being made as to the
Month of Auguſt, it (according to the
alternate Method at firſt inſtituted, and
ſtill preſerved in the following Months)
made an Alteration in all the follow-
ing Months, except January, which
upon this Alteration ſhould have had
but thirty Days according to the alter-
nate Method primarily inſticuted. But
this Month being ſo named in Honour
of Janus, eſteemed by the Romans, the
God of Time, on the like Conſiderati-
on that it ſeem'd proper to lengthen the
Month of Auguſi by a Day, it might
ſeem not proper to leſſen the Month of
January by a Day, but rather to con-
tinue it ſtill thirty-one Days long, and
to make February, which afore was
twenty-
20
Of MONTH s.
CHAP.twenty-nine, and every fourth Year
II. thirty Days long, to be commonly but
twenty-eight, and every fourth' Year
but twenty-nine Days long. And ſo
the Solar Months came to ſtand, as
they do now now in our Calendar,
(whence they are called the Calendar
Months ) in reference to the Names and
Number of Days aſſigned to each, fet
down in ſhort in the following Ta-
ble.
Months. Days. Months. Days. Months. Days.
March
31 July 31
November
30
April 30 Auguſt
31
December
31
May
31 September
anuary
31
June
October
February 28
But every fourth Year, 2g
30
30
31
so
By comparing this and the forego-
ing Table, will be illuſtrated what-
ever has been here faid, either con-
cerning the firſt Inſtitution of the So-
lar Monchs among the Romans by Ju-
lius Cæfar; or concerning the Changes
that have been ſince introduced. And
alſo it will appear, that the whole
Number of Days, contained in the
twelve Solar Months taken together,
hath been all along the ſame, viz.
365 Days, and every fourth Year 366
Days. The former of which Sums is
3
the
is
Of MONTH s.
21
the Time, wherein the Sun ſeems to CHÂÞ.
paſs through the twelve Signs, (*) omit- II.
ting the odd Hours and Minutes, and
the latter Sum is the Time, wherein che
Sun ſeems to paſs through the twelve
Signs, adding thereto the odd Hours and
Minutes which were omitted the three
foregoing Years, and ſo many Minutes
more as make the ſaid odd Hours and
Minutes equal to a whole Day in four
Years.
Now as theſe twelve Solar or Ca.
130
lendar Months make up the Civil So- Atwelve
Month,
lar Year in uſe among us (in which
Senſe it is, that a Twelve-Month is uſed valent to a
by us as an Equivalent Term to a Tear.
Year) ſo what has been ſaid concern-
ing the Sums of 365 and 366 Days
being contained in the twelve Calen-
dar Months taken together, will be
more particularly explained, when we
come preſently to ſpeak of the Civil
Year in uſe among Us ;
after that
we have made ſome ſhort Obſerva-
tions concerning the Year in gene-
ral.
how Equi-
(*)See St.7. 16. of this chapter.
N
Ву
1
22
w
sh
Artur
perly taken
Of YEARS.
CHAP. By a (*) Year then (the only Part
II. of Time remaining to be treated of)
mis denoted in general a Revolution of
14. a Celeſtial Light round the Heavens by
4 Year; (what is eſteemed) its proper Motion.
general. Thus an entire (apparent) Revolution
It is pro- of the fixed Stars is ſtiled the Great
so denote a Year; and the Time wherein Saturn,
Solar Year. Jupiter, and Mars, go round their
Orbits, is reſpectively ſtiled the Year
of Saturn, Jupiter, and Mars; and ac-
cordingly the Time of the Moon's go-
ing round her Orbit, commonly called
her Periodical Month, is ſometime
ſtiled her Year. But by a Year is prin-
cipally and properly denoted the Time,
wherein the Sun appears to move round
the Ecliptick, which is 365 Days, 5
Hours, and very near 49 Minutes.
15.
Now becauſe during the Time of
A Lunar one Solar Year, there are twelve Sya
Year, what. nodical Months; hence twelve Syno-
- **
** 3 *** Parliamentaris ******
(*) As the Latin Word Annus primarily denotes a
Circle (whence Annulus fignifies a Ring) and is thence
taken to denote a Year, as being a Circle of Time, which
being once gone round is begun again; ſo the Greek
Word ivbores, and the Hebrem Word Shanah is of the like
Importance.
dical
Of Y EARS.
23
how adap-
fourth Year confittin?
dical Months conſtitute (what is called CHAP.
a Lunar Year ;) which therefore conſiſts
II.
of 354 Days, 8 Hours, and a little morem
than 48 Minutes. So that the exact
Difference between the Aſtronomical
Solar and Lunar Year is 10 Days, 2 1
Hours, and 1 Minute.
But whereas the Hours and Minutes 16.
The Attroa
above the whole Days of a Solar Year, nomical
can't be taken Notice of in Civil or Solar Year,
Common Uſe; therefore the Civil So-
ted to Civil
lar Year in uſe among us, is made to or Common
conſiſt only of 365 Days for three Years Uſe.
together, and every fourth Year of 366
Days. Namely, whereas in an Aſtro-
nomical Solar Year there are, above the
whole Days, 5 Hours, and very near
49 Minutes ; there are added every
Year about 11 Minutes, to make up
this juſt fix Hours; and theſe ſix Hours
amount juſt to a whole Day in four
Years.
Each of the three Years conſiſting
only of 365 Days, is called a Common 4 Biffex-
Leap
of 366 Days, is called a Biſextile or Year, wly
Leap-Year. The Reaſon of its being ſo called.
called Biſſextile is, becauſe the Day a-
riſing in four Years out of the fix Hours
afore-
17.
tile or
N 2
24
Of YEARS.
CHAP. afore-mentioned, is this Year interca-
II. lated, i.e. inſerted into the Calendar, by
Wreckoning (according to the Roman
Way, bis ſextum Kal. Martii, i. e. by
reckoning ) twice the ſixth Day before
the Calends of March, which anſwers
to our twenty-fourth of February. But
although we took our Civil Solar Year
from the Romans, yet we do not imi-
tate them in this particular, but inſtead
of reckoning February the twenty-fourch
twice, we reckon this Year twenty-nine
Days in February, whereas in common
Years we reckon but twenty-eight. But
although we reckon not February twen-
ty-fourth twice, yet we reckon twice
the Calendar Letter always belonging
to February the twenty-fourth; namely
f. And by this means, that which was
the Sunday Letter from January the
firſt to February twenty-fourth, will be
ſo no longer, but the Letter next before
it in the Order of the Alphabet, will
be the Sunday Letter for the remaining
Part of the Year. From which Leap
or Change from one Sunday Letter to
another, this Year came to have the
Name of Leap-Year amongſt us.
,
IC
Of YEARS.
25
Solar Year
nutes; and
It has been afore obſerved, that the CHAP.
Aſtronomical or true Solar Year does
II.
conſiſt of 365 Days, 5 Hours, 49 Mi-m
nutes. . Whereas to adapt it to Civil 18.
Uſe, the Solar Year is conceived co con- The Civil
fiſt of 365 Days, and juſt ſix Hours ; too long by
( which ſix Hours in four Years make eleven Mi.
up juſt another whole Day;) ſo that of the Gre-
the Civil Solar Year is about eleven gorian Re-
formation
Minutes longer than the true Solar Year.
of the ca-
Hence it comes to paſs, that the Sea-lendar
ſons, or ( which comes to the ſame ) caufed
thereby
the Equinoxes and Solſtices, depending
on the true Solar Year, do not keep al-
ways to the ſame Time or part of our
Civil or Common Year, but vary every
Year about eleven Minutes, (viz. 10,
and 48",) and confequently about a
whole Day in 133 Years. Wherefore
from A. D. 325, when the famous Ni-
cene Council was held, to A. D. 1582,
wherein Pope Gregory the XIIIth re-
formed the Calendar, there was found
to have aroſe a Variation of ten Days ;
the Vernal Equinox, which ac the Time
of the Nicene Council fell about the
21ſt of March, in A. D. 1582, being
found to fall on March the nith.
Hereupon the fore-mentioned Pope,
intending
N 3
26
Of YEARS.
................ 1)
,,.. 'W.Y!********************
CHAP. intending to bring back the Equinox to
II. the Time of the Year it fell upon at
M the Nicene Council, ordered October 5th,
(in the Year 1582.) to be reckoned
Oktober 15th, thereby ſuppreſſing ten
Days, and making the following March
IIth to be reckoned March 2iſt; and
ſo the Vernal Equinox, which other-
wife would have been reckoned to fall
on March 11th, to fall on March
21ſt, as at the Time of the Nicene
Council. And that the like Variation
might not happen again, the ſaid Pope
ordered, that once in 133 Years a Day
ſhould be taken out of the Calendar;
or ( which comes to the ſame that three
Days ſhould be taken out every four
Hundred Years, after this Method, viz.
whereas, according to the Account a-
fore (and ſtill by us) uſed, every Hun-
dredth Year from the Nativity of our
Saviour is a Leap-Year ; from thence-
forth only every four Hundredth Year
ſhould be a Leap-Year ; and the other
Hundred Years ſhould be common
Years.
As the Account afore in uſe, is
19.
C!d-style thence called the Old Style; as alſo the
and New Julian Account or Julian Year, from
Style,
Julius Cæfar, by whoſe Authority ic
5.
wat.
was
Of Y EAR S.
27
was firſt introduced among the Romans, CHAP.
forty-ſix Years before Chriſt, according II.
to the Common Account by the Years
of our Lord : So this Form of the Ci-
vil Solar Year introduced by the fore-
mentioned Pope Gregory, is from him
called the Gregorian Account ; as alſo
from its being (comparatively with the
former) newly introduced, the New-Style.
And this is uſed in Italy, France, Spain,
and where-ever the Pope's Authority is
acknowledged; and as it had been re-
ceived from the firſt by the Popiſh Coun-
tries of Germany, ſo towards the End of
the laſt Century it was received alſo by
many of the Reformed People of Germa-
ny, as to their Civil or Common Account
of Time. For as to their Eccleſiaſtical
Account, or finding the (Eaſtern Moon,
or) Time of Eaſter, theſe do or did till
(*) very lately follow the Rudolphine
Tables of Kepler. The Old-Style is ſtill
uſed by Us of this Iſland, as alſo in
Ireland, and by ſome others.
Although the Calends or Firſt of
January is now-adays, almoſt through-of the va-
ginnings
of the Ci.
(*) The Publick News-Papers have in general given wil Solar
Account of ſome Reformation or Alteration made lately
in this Reſpect by the Proteſtants in Germany.
out
20.
rious Be-
Year in VA-
rions Counu
tries.
N 4
E
28
Of YEARS.
CHAP.out all Europe, commonly looked on as
II. the Beginning of the Year, whether
m Julian or Gregorian; yet there are
ſome, who reckon the Beginning of
it from ſome other part of the Year,
Thus the Venetians, Florentines, and
Piſans in Italy, and the Inhabitants of
Triers or Treves in Germany, reckon
the Beginning of the Year from the
Vernal Equinox. The Church of Eng-
land, in Conformity to the Antient U-
ſage of the Chriſtian Church, reckons
her Ecclefiaſtical Year from the Feast
of the Annunciation, commonly called
by us Lady-Day. And our Civil Year,
according to our Law, takes alſo its
Beginning from the ſame Day; though
the common People, and others among
us in Matters not requiring the Nicety
of a Legal Date, reckon the Begin-
ning of our Year from the firſt of Ya-
nuary
Ic has been afore obſerved, that the
The Altro.Lunar Year, ſtrictly or according to Al-
nomical tronomical exactneſs, conſiſts of 354
Tear, bow Days, 8 Hours, and a little more than
adapted to 48 Minutes. But to adapt this alſo to
and firſt of Civil Uſe, the Civil Lunar Year is ef-
zhe Wan- teemed to conſiſt only of 354 whole
dring Ls.
Bar Year.
Days.
21.
Lunar
1
Of YEARS.
29
Days. So that the Difference between Chap
the Civil Lunar Year of 354 Days, and II.
the Civil Solar Year of 365 Days, is m
eleven Days; the former being ſo
much ſhorter than the latter. Hence it
comes to paſs, that ſuch as uſe the Civil
Lunar Year, without any regard to
the aforeſaid Difference, their Year,
ſuppoſing it to begin now in Spring, will
after eight years Time begin in Win-
ter; and after eight Years more in Au-
tumn, and ſo after that in Summer; and
laſtly, after about thirty three Years in
all, will begin in Spring again. Hence
it is called Annus Lunaris Vagus, or
the Wandring Lunar Year ; becauſe its
Beginning thus wanders through the
ſeveral Seaſons, and that in the Me-
mory of Man. And this is the Sort of
Year uſed by the Turks.
Others, though they uſed or uſe
the Civil Lunar Year, yet remedy the of the
fore-mentioned Inconveniency of its fixed Lis-
thus changing the Time of its Begin- Luna So-
ning, by having Regard to the fore- lar Year.
mentioned Difference of eleven Days,
between the Civil Solar and Lunar
Year ; namely, by intercalating ſo
many Months, as the ſaid Difference
3
of
22.
30
Of YEARS
CHAP.of eleven Days ariſe to in ſuch a num.
II. ber of Years. By which means the
Lunar and Solar Year are kept ſo ad-
juſted one to the other, as that the Be-
ginning of the Lunar Year will keep
in a manner fixed to the ſame part of
the Solar Year. Hence this sort of
Year is called the fixed Lunar Year
as alſo the Luni-Solar Year ; and it is
uſed by the Jews, and the Church of
Rome in her Ecclefiaftical Account .
And thus much for the ſeveral Parts,
into which Time in general is diſtin-
guiſhed.
;
СНАР,
[ 31 ]
n.
he
d.
le
CHA P. III.
ep
of
of
i;
is
of
Of the ſeveral CHARACTERS of Time
in general : and particularly of
the CYCLE of the Moon, and the
EPACTS.
t.
S,
P
n
I.
The Cha-
2.
The Natu-
Roceed we now to ſpeak of the ſe-CHAP,
veral Characters, whereby particu- III.
lar Times are diſtinguiſhed one from the
other. And theſe are either Natural
or Inſtituted by Men.
sacters of
The Natural Characters of Time are timerman
ſuch as depend on Natural Cauſes, and fold.
are theſe ; viz. New Moons, Full
Moons, Eclipſes, either of the Sun (as Fale Chan
they are commonly callid) or Moon, rutters of
the two Equinoxes, the two Solſtices, Time,whar.
the Cycle of the Moon, and the Epacts
of the Moon. All which have been
ſufficiently ſpoken of in the foregoing
Treatiſe of Aſtronomy, except the Cycle
and Epacts of the Moon ; which are
therefore to be here explained.
The
32 Of the CYCLE of the Moon.
cleof the
Moon.
e
CH AP. The Cycle of the Moon then is to be
III. eſteem'da (*) Natural Character of
m Time, becauſe it depends on a Natural
3. Cauſe, viz. the Motion of the Moon :
of the Cy" which is ſuch, that, afrer nineteen Years
very nearly, the New Moons and Full
Moons are obſerved to fall on the
fame Nuchthemeron of the Julian Year,
as they did nineteen Years afore. Hence
this Cycle is otherwiſe termed the Cy-
cle of nineteen Years.
4.
The New Moons being obſerved to
of the fall out thus, they were wont former-
Nuoler, ly to calculate or find out the Time of
er Prime. the New Moons (without the Help of
Aſtronomical Tables) after this man-
ner. They obſerved, on what Day
of each Calendar Month the New
Moon fell, in each Year of this Cycle;
and to the ſaid Days they ſet reſpec-
tively the Number of the ſaid Year.
Thus obſerving, that the New Moons,
in the firſt Year of this Cycle, fell on
January 23d, February, 21/1,March 23d,
Golden
(*) Some eſteem this, not a Natural, but an Infitu-
ted Character of Time. But not fo properly, ſince it
depends on a Natural Cauſe.
&c.
Of the Cycle of the Moon.
33
le
if
1
:
'S
1
e
,
&c. they ſet the Number 1 to the ſaid CHAP.
Days. And in the like manner, obſer- III.
ving that, in the ſecond Year of this
Cycle, the New Moons fell on Janu-
ary 12th, February 10th, March 12th,
&c. to the ſaid Days they ſet the
Number 2.
And after this Method
they went through all the nineteen
Years of this Cycle; as may be ſeen
(*) in the Calendar adjoining to the
End of this Chronological Treatiſe.
The Numbers thus ſet to the Days
whereon the New Moons fell in each
Year, are called the Golden Numbers,
either becauſe they were formerly
wont to be writ in Gold, or elſe be-
cauſe of their Golden or great Uſe.
Any one of theſe Golden Numbers is
otherwiſe called the (+) Prime, be-
cauſe the ſaid Numbers were placed
in the Prime or Firſt Column of the
Calendar, as they ſtill are in our
Church Calendar, and in the Calen-
dar adjoining to this Treatiſe : Or elſe
)
(*) As alſo in the Calendar of the Common Prayera
Book.
(+) It is called by this Name in the Directions be-
longing to the Table for finding Eafter for ever in the
Common-Prayer-Book.
becauſe
34 of the Cycle of the Moon.
CHAP. becauſe each Golden Number denotes
III. Luna Prima, or the firſt Day of the
mNew Moon, according to which way
of ſpeaking the Full Moon is frequent-
ly ſtyld Luna Quartadecima, as fall-
ing on the Fourteenth Day after the
New Moon incluſively. The Golden
Numbers being thus placed, it was eaſy
to find, what Day of any Monch in
any Year given the New Moon will
fall upon, it being known to what Year
of the Moon's Cycle the Year given
anſwered. Thus ſuppoſe, A. D. 354,
to be the Year, given, which anſwers
to the 13th Year of the Moon's Cycle;
and ſuppoſe it be enquired, what day
of March the New Moon fell upon that
Year, I look for the Number 13 in the
Month of March, and find it ſet to
the rith Day ; whereby is ſhewn, that
the New Moon fell that Year on that
Day of March.
And by this Method the New
How to find Moon could be found with Accura-
cy enough at the Time of the Nicene
preſent by Council, foraſmuch as the Golden Num-
the Golden ber did then ſhew the Day (i. e. the
Nuchthemeron) within which the New
Moon fell out. And hereupon is found-
3
ed
5.
the New
Moons at
Number.
9.
Of the CYCLE of the Moon. 35
tes
the
ау
nt-
Il-
he
en
fy
in
11
ur
n
ទេ
;
ed the Rule of the Nicene Council for CHAP..
finding Eaſter, of which more in Chap- III.
ter 7th. It is here to be obſerved, that
the Golden Numbers do not now ſhew
the Days, whereon the New Moons
fall. For the Cycle of the Moon is
leſs than nineteen Julian Years, by i
Hour, 27 Minutes, and almoſt 32 Se-
conds. Whence it comes to paſs, that,
although the New Moons fall again
upon the ſame Days, as they did
nineteen Years afore, yet they fall not
on the ſame Hour of the Day or Nuch-
themeron ; but 1 Hour, 27 Minutes,
and almoſt 32" Sooner. And this Dif-
ference ariſing in about 3 12 years to
a whole Day, hence the New Moons
after every 3 12 years fall a whole Day
i.e. Nuchthemeron) ſooner. Upon this
Score the New Moons fall now four
Days ſooner, than they did at the Time
of the Nicene Council. Which being
obſerved, the Day (i. e. the Nuchthe-
meron, though not the Hour of it) on
which the New Moons fall, may be
now found by the Golden Number.
For Inſtance, I would know on what
Day of January the New Moon will
fall next Year, viz. 1712. This, by
the
36
Of the CYCLE of the Moon.
n
So I'.
CH A P. the Rule delivered in the following
III. Paragraph, will be found to be the
mthird year of the Moon's Cycle. I look
therefore for the Golden Number 3, and
find it (in che Calendar ) placed to
January the 1ſt, and again to January
the 31/t, ſo that about the Time of the
Nicene Council, there were two New
Moons in the Month of January, every
third
year of the Moon's Cycle. Where-
as, according to the fore-mentioned
Obſervations, each of the ſaid two New
Moons falling now four Days ſooner,
the firſt of them falls upon December
28th of this preſent Year, 1711; and
only the other falls in the January
following, viz. on January 27th,
1712.
6. It remains now to ſhew, how it is
To find
to be found, what Year of the Moon's
Cycle any given Year of Chriſt an-
ſwers to. And this is done by (*)
Cycle any
given Year adding i to the given Year of Chrift,
of Chriſt and then dividing the Sum by 19. If
Anſwers to.
19 juſt divides the Number of the
Year given, then it is the 19th or
laſt Year of the Moon's Cycle ; If 19
trhat Year
of the
Moon's
(+) The Reaſon of adding i is, becauſe the Æra of
Chrift began in the ſecond Year of this Cycles
does
Of the Èpacts of the M o0 N.
37
ig
ne
ik
d.
O
'y
does not juſt divide the ſaid Number, CHAP.
but ſomewhat of the ſaid Number re III.
mains over, then the ſaid Remainder m
Thews the Year of the Moon's Cycle.
For inſtance, I would know to what
Year of the Moon's Cycle A. D. 1712
anſwers. And by this Rule I find it to
anſwer to the third Year of the Cycle ;
for 1712 + 1 being divided by 19, there
will remain 3. And thus much for the
Cycle of the Moon.
Come we next to the Epacts of the 7.
Moon. It has been afore obſerved, that of the E-
the Civil Lunar Year is eleven Days the Moon;
ſhorter than the Civil Solar Year. Con-
ſequently, two ſuch Lunar Years will
be cwenty two Days ſhorter than two
ſuch Solar Years; and three Lunar Years
will be ſhorter than three Solar Years by.
thirty-three Days. Now ſuch as uſe
the fixed Lunar (otherwiſe called the
Luni-Solar Year, in order to adjuſt the
ſaid Lunar Year to the Solar, as often as
the Lurar Year does thus come to be
thirty three Days ſhorter than the Solar,
do intercalate á Month of thirty Days
into the Lunar Year ; except only
every sgth Year, viz. the laſt Year of
the Moon's Cycle) when the interca-
O
lated
38
Of the Cycle of the Moon.
CHAP.lated Month conſiſts but of cwenty-nine
III. Days.
ya , pero wala
I.
2
3
4
5
6
7
8
9.
10
II.
12.
ME TE
13
14
15
0
Golden Number, Epacts. By this means
the Civil Lunar
XI.
..XXII. and Solar Years
III.
are kept ſo ad-
.XIV.
.XXIV. juſted together,as
VI. that the firſt Year
. XVII.
of the MOON's
XVIII.
JX. Cycle comes not
XX.
ſhorter of the So-
... 1.
XII. lar Year than e-
XXIII. leven Days; the
IV.
... XV.
ſecond Year of
16
XXVI. the ſaid Cyclenot
17
.. VII.
ſhorter than : 22
18.
XVIII.
19
XXIX. ! Days; the third
Year ſhorter only
by three Days, &c. as may be ſeen in
the adjoining Table. Namely, as the
New Moons are the ſame (i. e. fall on
the ſame Day ) every nineteen Years, ſo
the difference between the Lunar and
Solar Year is the ſame every nineteen
Years. And becauſe the ſaid Difference
is always to be added to the Lunar Year,
in order to adjuſt or make it equal to
the Solar Year; hence the ſaid Diffe-
rence reſpectively belonging to each
Year
Of the Epacts of the Moon. 39
ine
ing
lar
ars
d-
jas
ar
T's
ot
Year of the Moon's Cycle, is called the CHAP.
Epact of the ſaid Year, i. e. the Num III.
ber co be added to the ſaid Year to make
it equal to the Solar Year:
Upon this mutual Reſpect between the 8.
Cycle of the Moon, and the Cycle of Hom to
the Epacts, there is founded this Rule find the
Epacts of
for (*) finding the Epact belonging to the Moon
any Year of the Moon's Cycle. Multi-according
to the Jus
ply the Year given of the Moon's Cycle lian Ac
into it; if the Product be leſs than 30,
it is the Epact fought; if the Product
be greater than 30, divide it by 30; and
the Remainder of the Dividend is the
Epact, Ex. gr. I would know the E-
pact for A. D. 1712, which has been al-
ready found to be the third Year of the
Moon's Cycle. Wherefore three is the E-
pact for A. D. 1712: for 11 x3 = 33
and 33 being divided by 30, there is
left three of the Dividend for the Epact:
count:
-
e
he
of
C
2
d
у
2
]
(*) Namely in reſpect of the Julian Account. For in
reſpect of the Gregorian Account there is a different Me-
thod, the Epact being different. However, the Julian
Epact being known, it is eaſy thence to know the Gre-
gorian Epact. Namely, if the Julian Epact begreater than
11, Subitract u froin it: it leis, add 30 to it, and out
of the Sum Subſtract us, and the Reſidue will be the Gre-
gorian Epact. For inſtance; it has been found, that Three
is the Julian Epact for A. D. 1712. Wherefore 3 to
30 = 33, and 33
11=22. which lait Number (vizi
22.) is the Gregorian Epift for the ſaid Year, 1712.
02
Ву
40
Of the Epacts of the Moon.
of any
30; if
Month in
CHAP. By the Help of the Epact may be
III. found, what Day of any Month in any
Year the New Moon falls on, thus: To
9.
the Number of the Month from March
To fined by incluſively, add the Epact of the Year
what Day given ; if the Sum be leſs than 30, Sub-
ſtract it out of
greater, Subſtract
any Year it out of 60; and the Remainder will
the New be the Day, whereon the New Moon
Moon falls will fall. N. B. If the New Moon be
fought for the Month of January or
March, then nothing is to be added to
che Epact ; if for February or April,then
only 1 is to be added. Ex.
Ex.gr. I would
know what Day of December the New
Moon will fall on this A. D. 1711,
the Epact whereof is 22. By the a-
foreſaid Rule, I find it will be Decem-
ber 28th, for 22 +10=32, and 60-
on.
3
1
32 = 28.
10.
Moon. .
To
The Day, whereon the New Moon
"
To find the falls, being thus found, it is eaſy from
Age of the
thence to infer, what the Age of the
Moon is on any Day given. However,
there is a peculiar Rule commonly made
uſe of to this purpoſe, which is this:
Add the Epact of the Year, the Num-
ber of the Month from March inclu-
ſively, and the given Day of the Month
all into one Sum : which, if it be leſs
than
3
эс
41
Of the EPACT S.
ly
'o
cb
ir
)-
st
11
n
e
r
0
n
1
than 30, ſhews the Age of the Moon ; CHAP.
if it be greater than 30, divide it by 30, III.
and the Remainder of the Dividend m
ihews the Age of the Moon, or how
many Days it is from the laſt New
Moon. And this Method will never
err a whole Day. For inſtance, I would
know, what will be the Age of the
Moon on December 31ſt of this Year
1711. By this Rule I find, that the
Moon will then be three Days Old, i. e.
that it will then be three Days from the
laſt New Moon. For 22 + 10 +-
31 = 63, and 63 being divided by 30,
there will remain of the Dividend
3.
And this exactly agrees to the other fore-
going Rule, whereby it was found, that
the New Moon will fall on December
28th of this Year 1711.
It remains only to obſerve, that the
Epacts of the Moon are juſtly to be ef- The Epafts
teemed as (*) Natural Characters of
Time; foraſmuch as they depend on a eftcemed
Natural Cauſe, viz. the Motion of the
Moon. For the Reaſon, why the Civil
II,
of fiheitsoon
are to be
Natural
Characters,
(*) This is inſiſted upon, becauſe the Epacts are by
ſome eſteemed, not Natural, but infiitu:ed Characters,
O 3
Lunar
42
Of the EPACT S.
CHAP. Lunar Year is leſs than the Civil Solar
III. (i. e. Julian) Year by eleven Days, is,
m becaule as the Moon goes round her
Orbit, there are twelve Conjunctions of
her and the Sun, (or twelve Synodical
Months, which make up a Lunar Year)
in leſs Time by eleven Days very nearly,
than the Sun ſeems to go once round
the Ecliptick. And in like manner, the
Reaſon why the Cycle of the Epacts, as
well as that of the Moon, confifts of
nineteen Years, is, becauſe in that Inter-
val of Time, the Moon's Motion has
(much) the ſame Reſpect to the Sun, as
it had nineteen Years afore. And thus
much for the Natural Characters of
Time,
С НАР,
[ 43 ]
11
S,
r
CH A P. IV.
f
.
:)
's
1
Of the Cycle of the SUNDAY-LETTER,
commonly called the Cycle of the
SUN.
in tend
TH
i
1.
'HE Cycle of the Sun is very im-CHAP.
properly ſo called, foraſmuch as IV.
it relates not to the Courſe of the Sun, on
but to the Courſe of the Dominical
or Sunday-Letter ; whence it ought to of the sun
be called the Cycle of the Sunday-Letter, improper,
It conſiſts of twenty-eight Years, for- ly ſo called.
aſmuch as after every twenty-eight
Years the Courſe or Order of the
Sunday-Letter is the ſame, as it was
afore.
The Uſe of this Cycle ariſes from
(*) the Cuſtom of Aſligning in the of the Uſe
Calendar to each Day of the Week, le.
of this cho
one of the firſt ſeven Letters of the
Alphabet ; A being always affixed to
2.
(*) This Cuſtom being Arbitrary, hence this Cycle
not a Natural Character, but of Humine Inſtitution.
04
Yanu-
44 Of the Cycle of the Su N.
CHAP. January if, whatever Day of the
VI. Week it be; B co January 2d, C to
fanuary 3d ; and ſo in order G to
January 7th. After which the fame
Letters are repeated again, 'A being
affixed to January 8th, &c. According
to this Method, there being 52 Weeks,
in a Year, the ſaid feven Letters are re-
peated 52 Times in the Calendar. And
were there but juſt 52 Weeks, the Let-
ter G would belong to the laſt Day of
the Year, as the Letter A does to the
firſt; and conſequently, that Letter,
which was at firſt conſtituted the Sun-
day-Letter, (and the ſame is to be un-
derſtood of the other Days of the Week)
would always have been ſo ; and there
would have been no Change of the
Sunday-Letter. But our Year conſiſting
of 52 Weeks, and an odd Day over,
hence it comes to paſs, that the Letter
A belongs to the laſt, as well as to the
firſt Day of every Year. For, although
every Leap-Year conſiſts of 366 Days,
and fo of two Days over 52 Weeks,
yet it is not uſual to add a Letter more,
viz, B, to the End of the Year ; but in-
tead thereof to repeat the Letter F,
which
R
Of the Cycle of the Su N.
45
he
to
to
је
d
f
which (*) anſwers to the 24th of Fe-CHAP,
bruary, and to affix it again to the in IV.
tercalated Day (as has been (+) aforem
obſerved) which we call February 25th.
By which means the ſaid ſeven Letters
of the Alphabet remain affixed to the
ſame Days of a Leap-Year, as of a
Common Year, through all the reſt of
the Calendar, both before and after.
The Letter Athen thus always belong-
ing to the firſt and laſt Day of the ſame
Year, and conſequently to the laſt Day
of the Old Year, and firſt Day of the
New; it thence comes to paſs, that
there is a Change made as to the Sun-
day-Letter in a backward Order, that
is, fuppofing G to be the Sunday-Let-
ter one Year, F will be the next, and
ſo on : which is illuſtrated by the fol-
lowing Table ;. where it muſt be obfer--
ved, that the great Letter is the Sunday-
Letter for each Year.
2
(*) As may be ſeen in the Calendar adjoined to the
End of this Treatiſe.
(t) Chap 1. 5. J7+
* * * * * * * * *
easy in
December
46
Of the Cycle of the Sun.
CH A P.
· IV.
December 1711.
24
Monday
b.
25 Tueſday
с
26 Wedneſday
d.
27 | Thurſday
28 Friday
f 29 Saturday
G
30 Sunday
31 Monday
January 1712.
Il Tueſday
b... 2 Wedneſday
3 Thurſday
d
5 Saturday
F. 6 Sunday
7 Monday
8 Tueſday
.
به مه ما به م ر م م
4 | Friday
e
.
2
☺
Day in
every Com-
makes a
ter
As from the foregoing Table it is
3.
The Odd evident, how the odd Day above 52
Weeks in a Year does make the Sunday-
men Year" Letter change from one Letter to the
next to it in a backward Order ; ſo it
Change in is obvious, that were there but this ſingle
the Sun- Change, Sunday would be denoted by
day-Let- each of the ſeven Letters every ſeven
Years, and ſo the Cycle of the Sunday-
Letter would conſiſt of no more than
ſeven Years. But now there being in
every fourth or Leap-Year two Days a-
bove 52 Weeks, hence it comes to paſs,
that there is every ſuch Year a double
Change made as to the Sunday-Letter.
Namely, as the odd ſingle Day above 52
Weeks in a common Year, makes (as
has been ſhewn by the foregoing Ta-
ble) the firſt Sunday in January to ſhift
from that which was the Sunday-Let-
ter of the foregoing Year, to the next
Letter
Of the Cycle of the Sun. 47
I
ri
lay
V
Letter to it in a backward Order ; fo CHAP.
the other Day, intercalated every Leap- IV.
Year after the 23d of February, (tho'
it makes no change as to the Days of
the Month, to which the Alphabetical
Letters reſpectively belong ; which is
brought about by the Artifice of
repeat-
ing che Letter F twice, as was before
obſerved: yet it) does make a Change
as to the Days of the Week, to which
each Alphabetical Letter is to belong
for the remaining Part of the Year ; as
is evident by the following Table con-
taining the latter Part of February 1712,
being Leap-Year, and the former Parc
of March.
.
is
52
ty-
he
it
le
ру
en
-
n
n
1
24 F
2
February.
23 Saturday
Sunday
25
f
Monday
Tueſday
27 a Wedneſday
28b
Thurſday
29 Friday
26 g
3
4
5
6
7
March.
d Saturday
E Sunday
f Monday
g Tueſday
Wedneſday
b Thurſday
c Friday
a
C
As the former Table Thewed, how 4.
it comes to paſs, that G is the Sunday. The inter-
Letter for 1711, and F for 1712, at Day makes
the Beginning of the ſaid Year, even a double
to February 23d; fo this later Table Change
thews
in the Sun-
48
Of the Cycle of the Sun.
every
CHAP. Thews, how it comes to paſs, that af-
IV. ter February 23d, not F as afore, but
E is the Sunday-Letter for the Reſt of
day-Letter the Year. And conſequently as the
Leap-Year, former Table will ſerve to ſhew, how
by the odd Day in a common Year,
there is made every common Year a
ſingle Change as to the Sunday-Letter;
ſo the latter Table, compared with the
former, will ſhew how by the inter-
calated Day of a Leap-Year there is
made after February 23d, in every Leap-
Year another Change of the Sunday-
Letter, beſides the former made at the
Beginning of the ſaid Leap-Year ; and
conſequently how there comes a double
Change of the Sunday-Letter every
Leap-Year.
Now as the Cycle of the Sunday-
5
This Cycle Letter would have conſiſted but of
why con- feven Years, had there been only a
fifts of
twenty- ſingle Change of the faid Letter; fo,
eight
by Reaſon of there being a double
Change of the ſaid Letter every Leap
or fourch Year, it comes to paſs, that
the ſaid Cycle conſiſts of four Times
feven Years, i. e. the Sunday-Letter
does not proceed in the ſame Courſe
as it did afore, under twenty-eight
Years; and after that Number of
Years
Years.
Of the Cycle of the Sun. 49
n
Years its Courſe or Order is the ſame CHAP.
as it was afore. Which is illuſtrated IV.
by the following Table ; where it is u
to be obſerved, that the firſt Year,
and every fourth Year after, of the
Cycle is a Leap-Year, and therefore
has two Sunday-Letters appertaining to
it.
af.
but
t of
the
10W
ear,
ra
er;
the
er-
is
P-
zy-
he
nd
Sle
гу
A TABLE of the Cycle of
the Sun.
I GFI BA
9 DC|13 FE 17 AG|21 CB125 ED
2 E 6 GIO B
14 D 118 F
22 A 126 C
3 D 7 F
15 C
19
E
27
B
14 C 18 E
12 G 16 B
20 D 24 F 128 A
IL A
23 G
y-
of
a
o,
le
To find what Year of this Cycle any 6.
given Year of our Lord anſwers to, 10 find the
and conſequently, what is the Sunday- sun for any
Letter for the Year given, work thus: given Year
To the Year of our Lord given (*) of Christ
.
add
9,
and divide the Sum by 28. If
р
10
S
r r
e
C
f
(*) The Reaſon of adding 9, is becauſe the Æra of
Chriſt began in the Tenth Year of this Cycle.
any
GO Of the Cycle of the Sun.
CHAP. any of the Dividend remains, the ſaid
IV. Remainder ſhews the Year of the Cy-
Mcle foughc; if nothing remains of the
Dividend, then it is the laſt or 28th
Year of the Cycle. For inſtance, I
would know, what Year of the Cycle
of the Sun, A. D. 1712. anſwers to.
By the foregoing Rule I find it to an-
ſwer to the 13th Year of the ſaid Cy-
cle; (for 1712 + 9 = 1721, and 172 1
being divided by 28, there will be left
13;) and by the Table of this Cycle I.
find the Sunday-Letters for the ſaid Year,
being a Leap-Year, to be FE, viz. F
from the Beginning of January to
February 23d, and after that E for the
Reſt of the Year, according to the (*)
Julian Account.
It may not be altogether unuſeful
To find
to obſerve further, that each of the
what Day firſt ſeven Alphabetical Letters always
Week the (as is afore noted) belonging to the
forf Day of lame Day of each Month in the Year,
7
7
any Month
falls upon.
(*) Having found the Sunday Letter according to the
Fulian Account, the Gregorian Sunday. Letter will be the
third in a backward Order from the Julian. Thus FE
being the fulian Sunday. Letters for 1712, being Lep-
Year, C3 will be the Gregorian Sun.lay- Letters for lhe
fame.
3
hence
Of the Cycle of the Sun.
35
37
hence the two following Engliſh Verſes CHAP.
ſhew by the firſt Letter of each Word, IV.
what Letter belongs to the firſt Day of
each Month ; the Order of the Words
anſwering to the Order of the Months
thus :
Jan. Feb. March, April, May, June,
At Dover Dwells George Brown Eſquire,
July, Aug.
Sept.
067. Νου. Dec.
Good Chriſtian Faith, And
Doctor Fryar.
Wherefore the Sunday-Letter being
known, it is eaſy by the Help of the
foregoing Verſes to tell, what Day of
the Week the firſt Day of any
Month
falls upon; namely, by conſidering
the Order or Diſtance of the Letter
belonging to the firſt Day of the given
Month from the given Sunday-Letter.
Ex. gr. I would know, what Day of
the Week the firſt of February 1712:
will be, when the Sunday-Letter will
be (at that Part of the ſaid Year) F.
By the foregoing Verſes I know D is
the Letter belonging to February ift,
and therefore F being the Sunday-Let-
ter D, (as being two in the Alphabe-
tical Order before F) muſt denote
Friday, which is agreeably two Days
before Sunday
In
52 Of the Cycle of the Su N.
of the
CH A P. In like manner, if it be enquired,
IV. what. Day of the Week March in
mwill fall upon in 1712, when the Sun-
day-Letter will be changed from F to
E It being known by the foregoing
Verſes, that D, is the Letter that be
longs alſo to the firſt of March, it
follows that, as D is the Letter next
before E, ſo March iſt muſt fall on
(that Day of the Week which is next
before Sunday, viz.) Saturday.
8.
It being thus to be known, what
To find Day of the Week the firſt Day of any
that Day Month falls upon;
falls upon; thereby may
be
eaſily known alſo, what Day of the
other Day Week any other Day of the ſame
Month (bea
Month falls upon ; namely, by confi-
ſides th: dering, that the iſt, 8th, 15th, 22d,
firm) falls and 29th Day of any Month always
fall upon the fame Day of the Week ;
and then reckoning, how far diſtant
the Day propoſed is from any of the
aforeſaid Days. For inſtance, I would
know, what Day of the Week March
18th falls upon next Year, viz. 1712.
It being afore known, that the firſt
Day of March will then fall on Satur-
day, it follows, that March 15th will
be likewiſe on Saturday; and there-
fore March 18th (as being three Days
after
Week any
of the
upon.
Of the Cycle of the Sun. 53
ed,
IA
IN-
to
after March 15th) will fall on Tueſday,CHAP.
as being three Days after Saturday. And IV.
therefore, by the Sunday-Letter and the m
foregoing Verſes, may be found, what
Day of the Week any Day of the Year
in general will fall upon. And thus we
have largely ſhewn the Uſe of the Cycle
of the Sun, or of the Sunday-Letter.
ng
le.
it
*
in
xt
It
у
e
e
e
S
LONU HWN What will
P
CH AP;
( 54 )
CH A P. V.
Of the INDICTIon, and JULIAN
PERIOD.
TH
I.
of the
CHAP . HE Indiction is a Cycle of fif.
V.
teen Years, which has no Rela-
tion to any Celeſtial Motion, but was
inſtituted wholly on a Political or Ci-
Indiction,
vil Account, viz. in reſpect to certain
Taxes (as is the moſt received Opini-
on) which were to be paid every fifteen
Years. When this Cycle was firſt inſti-
tuted, is not left upon Record; buc ic is
evident from Hiſtory, that it has been
in Uſe ever ſince the Time of Conſtan-
tine the Great, or from A. D. 312.
was uſed both by the Greeks and Ro-
mans, buc after (*) a manner ſomewhat
different. The Roman Indiction is ſtill
uſed by the Pope in his Bulls, &c. And
the Year of the Roman Indiction an-
IC
(*) The Greek Indiction begins from the firſt of Sep
tember, the Roman Indiction from the firſt of January,
And the foriner is uſed in the Acts of Councils, and the
Niveis of the Emperois.
ſwering
Of the JULIAN PERIOD.
55
N
AN
6f.
la.
ſwering to any given Year of Chriſt is CHAP
found, by (*) adding 3 to the given V.
Year of Chriſt, and dividing the Summ
by 15. The Remainder of the Divi-
dend, if any there be, ſhews the Indic-
tion ; if nothing remains, then it is the
15th or laſt Year of the Indiction. The
principal Reaſon of taking Notice of this
Cycle in this Treatiſe, is becauſe it con-
duces to the Underſtanding of the Yu-
lian Period, of which we ſhall ſpeak
next.
The Julian Period is no other than
a greater Cycle, made up of the three of the ſu:
fore-mentioned Cycles of che Moon
Sun, and Indiction, multiplied one into
the other, and ſo conſiſting of 7980
Years. For the Cycles of the Moon
and Sun, viz. 19. and 28, being multi-
plied together make (4) 532 ; which
being multiplied again by 15, the Cycle
of the Indiction, makes 7980, the Space
vas
Cic
2.
lian Pe.
uin
hi-
en
ti-
is
riod.
en
no
TC
Je
RE
11
d
(*) The Reaſon of adding 3, is, becauſe A. D. , bem
gan in the fourth Year of the laid Roman Indiction.
(+) This Number of Years, ariſiag from the Cycles
of the Moon and Sun being multiplied together, is pe-
culiarly ftiled the Dionyſian Period, and alſo the Vi&orian
Period, from Perſons of the like Names, who intro-
duced the Uſe thereof.
P 2
of
.
56
Of the JULIAN PERIOD.
CHAP. of the Julian Period. It is called the
V. Julian Period, becauſe it was adapted
mby the Author or Inventor of it, Joſeph
Scaliger, to the Julian Year, and its
fore-mentioned Cycles. It is of excellent
Uſe in Chronology, or Diſtinguiſhing
of Times ; becauſe the ſame Years of
the Cycles of the Moon, Sun, and In-
diction, which belong to any one Year
of this Julian Period, will never fall
together again till after 7980 Years, and
conſequently not as long as the World
ſtands, according to the Opinion pro-
bably received concerning (*) the Dura-
tion of the World. And as this Pe-
riod will probably not expire before
the End of the World, and thereby
conſequently may be diſtinguiſhed the
Times of all Future Events ; ſo it ex-
tends backwards (+) before the Begin-
(*) Namcly, That it shall endure but 6000 Years. Of
which about 4000 Years being expired before our Sa.
viour's Nativity, and ſomewhat above 1700 Years being
expired fince; there remains but about 300 Years more
for the World to laſt, according to the faid Opinion.
(+) Namely, Julian Period 4714, anſwering to A.D.
1. and our Saviour being born but about the 4000th Year
of the World, it thence follows, that the Julian Period
muſt be conceived to commence or begin about 700
Years before the Creacion,
ming
1
Of the JULIAN PERIOD. 57
the
ted
eph
its
ene
ng
of
n-
ar
all
od
ld
lian Period
2-
4-
-
ning of the World, and thereby conſe-CHAP.
quently may be diſtinguiſhed the Times
V.
of all Paſt Events from the very Cream
tion. Hence Chronologers do endea-
vour to adjuſt all other Accounts of
Time, and conſequently all Tranſactions
and Events recorded in Hiſtory, to the
Julian Period.
To find what Year of the Julian 3;
Period any given Year of Chriſt anſwers what rear
to, work thus. To the given Year of of the Ju-
Chriſt add 4713, (becauſe ſo many
anſwers to
Years of the Julian Period were expi- any given
red before A. Ď. 1.) and the Sum gives Year of
the Year of the Julian Period ſought.
For inſtance, I would know, what Year
of the Julian Period A. D. 1712. an-
Now 1712 +4713=6425,
the Year fought of the Julian Period.
On the contrary, having the Year of 4.
the Julian Period given to find what To find
A. D. anſwers thereto, work thus. From of Chriſt
the Year of the Julian Period given, anſwers to
ſubſtract 47134 (for the Reaſon above- rear of the
mentioned,') and the Reſidue will be che Julian Pea
A. D. ſought. For inſtance, I would riod.
know, what A. D. anſwers to the Yu-
lian Period 6425. Wherefore 6425
4713 = 1712, the A. D. fought.
'e
V
e
(wers to.
whut Year
1
P3
If
58 Of the JULIAN PERIOD.
what rear
before
CHAP. If the Year of the Julian Period gi-
V. ven be 4713, or leſs than it, then ſub-
w ſtract the ſame from 4714, ( which is
5. the Year of the Julian Period, that an-
To find
ſwers to A. D. 1.) and the Reſidue will
ſhew, how long afore (the Beginning of
Christ an- the common Computation from the Na-
any given tivity of) Chriſt the given Year of the
Year of the Julian Period was. For inſtance, the
Period, leſs City of Rome is ſaid to have been built,
than 4714. 7. P. 3960. I would know therefore,
how long it was built before Chriſt.
Now 4714—3960 = 754. Wherefore
Rome was built 754 Years before (the
Beginning of the common Æra of)
Chriſt.
6. To know what Year of the Cycle of
To find the the Sun, Moon, or Indiction, anſwers to
Cycle of
the Sun, any Year given of the Julian Period;
Moon, or divide the given Year reſpectively by
Indictior,
28, or 19, or 15. The Remainder of
Anweriog
10 any rear the firſt Diviſion will ſhew the Year of
of the Ju- the Sun's Cycle ; the Remainder of the
ſecond Diviſion will ſhew the Year of
the Moon's Cycle; and of the third Di-
viſion, the Year of the Indiction. If
nothing remains in each Diviſion, then
it is the laſt Year of each Cycle reſpec-
çively.
lian Pe-
riod.
On
Of the JULIAN PERIOD. 59
in
).
is
1-
11
of
contrary.
e
e
:
On the contrary, to know what Year CHAP.
of the Yulian Period anſwers to any gi V.
ven Year of the Cycle of the Sun, orm
Moon, or Indiction ; multiply the Cy- 7.
cle of the Sun into 4845, the Cycle of And the
the Moon into 4200, the Cycle of the
Indiction into 6916. The Sum of the
Products being divided by 7980, the
Remainder will ſhew the Year of the
Julian Period ſought.
And thus we have gone through the 8.
feveral Characters of Time, whoſe Com-Cycles and
putation after a certain Number of Years why so
begins anew; whence each of them is cailed.
ſtiled, either a Cycle, as the Cycle of the
Sun, Moon, and Indiction; or a period,
as the Julian Period.
ce
P4
С НАР.
[ 60 ]
CH A P. VI.
Of Epoch's or Æra's; and eſpecially
of the Æra or Year of Christ, the
Æra of the OLYMPIADS, and the
ÆRA of the BUILDING of Rome.
w
CH AP. E are now to ſpeak of thoſe Cha-
VI.
racters of Time, whoſe Com-
putation does not begin a-new after a
I.
certain Number of Years, but is ſtill
of Epoch's continued on further and further from
or Æra's.
their reſpective Heads or fingle Begin-
nings. And theſe
are diſtinguiſhed
from the circular Characters of Time
already deſcribed, by the Name of (*)
Epoch's or Æra's.
2.
There are ſeveral Epoch's or Æra's
0; the
made uſe of, both formerly and at
Æra of
Chrilt,
preſent, in the ſeveral Parts of the
uſed by US
ard other
Chriftians.
(*) Theſe Words are frequently uſed promiſcuouſly.
Some takean Ærn to denoie properly any continued Com.
futation, and an Epoch to fignity properly the Beginning
of the said Compuiation; the Greek Word nogen denoting
( as it were ) a Pauſe (r Stop in Time, from whence
Time is computed. As to the Etymology of Æra,
there is no good Account of it.
+
World,
1
of the Year of CHRIST. 61
ially
the
the
ha-
m.
.
ra
till
World. That of principal Concern to CHAP.
us Chriſtians is the Æra of Chriſt, or VI.
the common Way of computing Time me
from the Nativity of Chriſt ; according
to which this preſent Year is reckoned
the 1711th from the Nativity of Chriſt,
or rather from the firſt of January next
following the Nativity of Chriſt, ac-
cording to the common Computation
generally receiv'd in Chriſtendom, or
Europe. The Æra or Way of recko-
ning from Chriſt, was firſt introduced
by one Dionyfius, firnamed (*) Exiguus,
ſomewhat more than 500 Years after
Chriſt : Since which Time Chriſtians
have reckoned their Years, either from
the Birth or Incarnation of our Bleſſed
Saviour ; whereas before they were wont
to reckon ſome other Ways. According
to Dionyſus, the Author of the Æra
computed from Chriſt, our Lord was
conceived on the 8th of the Calends of
April (now called Lady-Day) in the
firſt Year of this Æra; and was Born
about the then Winter-Solſtice next
following ; that is, December 25.--
And this Account was at firſt univer-
im
n-
ed
је
*)
's
C
(*) He was ſo ſirnamed from his little Stature.
ſally
62 Of the Year of CHRIST.
CHAP, fally received among Chriſtians : but
VI. is now a-days uſed only in England
mand Ireland, where not only the Ec-
cleſiaſtical, but alſo the Civil Year, is
ſtill reckoned according to Law, from
the Feaſt of the Annunciation, or Lady-
Day, as it was at firſt by Dionyſus him-
felf. Whereas in other parts of Chrif-
tendom, as is afore obſerv'd, and even
in England as to common Affairs which
require not a Legal ( Eccleſiaſtical or
Civil) Date, the Year of Chriſt is
reckoned now a days, not from the
Annunciation or Lady-Day, but from
the Firſt of January next before the
Lady-Day from which the Legal Date
of our Ecclefiaftical or Civil Year be-
gins. It is alſo to be obſerv'd, that the
Common Account by A. D. introduced
by the foreſaid Dionyhus Exiguus does
not agree exactly to the True Years of
Chriſt's Age. Foraſmuch as according
chereto, Herod the Great muſt be dead
before our Saviour was born, which
is contrary to the Goſpel Hiſtory. How
much the Difference between the True
and Common Account is, the Learned
are not agreed. But I prefer that Opi.
nion, which makes the common Ac-
count
Of the Year of the WORLD. 63
It
d
Æra of the
World, or
count too little by two Years. So that CHAP.
whereas this preſent Year is commonly VI.
eſteemid A. D. 1711, it is Truly A. D.
1713, or the 1713th Year from the
Birth of Chriſt or January 1. next en-
ſuing.
There is alſo another Æra fre-
3.
quently made Uſe of by Chriſtian of the
Writers, namely, the Æra of the Cre
ation, which is generally agreed to have Creation.
been about 4000 Years before Chrift.
And becauſe to ſay ſuch or ſuch a
Thing fell out in ſuch a Year of the
World, does not give us ſo clear an
Idea of the Diſtance of the ſaid Oc-
currence from us, as it does to ſay,
that it happened in ſuch or ſuch a
Year before Chrift; therefore, the Com-
putation from the Creation of the
World begins to be laid aſide, even in
Matters relating to the Sacred Hiſtory
of the Old Teſtament, and inſtead
thereof the Occurrences of the Old
Teſtament are now a-days computed
by their Diſtance before Chriſt. Thus
inſtead of ſaying, that the Univerſal
Deluge happened A. M. or in the Year
of the World 1656, it is thought more
Inſtructive to ſay, that it happened
2294 Years before Chriſt, this laſt
Manner
I
64
Of the Year of the WORLD.
CHAP. Manner of Computation giving us a
VI. clearer Notion of the Time when the
mFlood happened in reſpect of its Di-
ſtance from us. For we being wont
to reckon our Time from Chriſt, and ſo
reckoning this preſent Year to be the
Ith from Chriſt; when we are told,
that the Flood was 2294 before Chriſt,
we can from thence eaſily gather, that
the Flood was about 4000 Years ago in
reſpect of this preſent Time. And on
the ſame Conſiderations, it appears to
be much the beſt or eaſieſt and cleareſt
Way for us, to compute likewiſe all
Occurrences mentioned in any other as
well as the Sacred Hiſtory, by their
Diſtance either before or after Chriſt ;
and fo to make the Nativity of Chriſt
the Univerſal Head or Epoch of all
Chronology, counting therefrom all
Occurrences either Backward or For-
ward.
The moſt Antient and Renowned
4.
Epoch uſed by the Heathens is that of
Æra of the the Olympiads or Olympick Games,
Olympic
which were inſtituted by one Iphitus,
in the fields of Olympia, à City or
Town of the Region Elis in the Pelo-
ponneſe ; and which laſted five Days,
the laſt whereof fell on the Full Moon,
which
of the
ads.
1
Of the OLYMPIA DS.
65
a
mo
le
i-
it
o
е
1,
C
which was next after the Summer Sol-CHAP.
ſtice. Theſe Games were celebrated em VI.
very four Years, that is, there were three m
Years between the Years wherein the
next preceding and the next following
Olympiad was celebrated. Hence by a
compleat Olympiad, is denoted the Space
of four Years; the Year wherein the
Olympiad was celebrated, being ſtiled the
firſt Year of the ſaid Olympiad, and ſo
on. The Celebration of the firſt Olym-
piad is referred to the 3938th Year of
the Julian Period; and conſequently to
the 777th Year before Chriſt, viz. to the
Calends of July, in the Summer of the
ſaid Years. Wherefore,
Any Year of the Olympiads being
5.
given, to find the correſpondent Year of To find eke
the Julian Period, work thus; Mul-Year of the
tiply the compleat Olympiads by 4, and riod an-
to the Product add the Year (if it be ſwering to
given) of the Olympiad running, and
given of
alſo 3937, the Sum is the Year of the Olym-
the Julian Period ſought. For Inſtance, piads.
Rome is ſaid to be built, according to
Varro's Account, in the fourth Year of
the ſixth Olympiad. Wherefore I mul-
tiply 5 (the Number of the compleac
Olympiads) by 4, which makes 20,
,
and thereto. I add 4 more, (the Year
given
any rear
66
Of the OLYMPIA D 9.
pondent
C# A P. given of the Olympiad running, or 6th
VI. Olympiad,) and alſo 3937. All which
m together amounts to 3961, the Year
ſought of the Julian Period.
6. Having found the Year of the Yu-
And there- lian Period anſwering to any given Year
by so find of the Olympiads, thereby may alſo be
the correl-
found the correſpondent Year ( reſpec-
Year of tively) before or after Chriſt, Name-
Chrift.
ly, if the Year found of the Julian
Period be leſs than 4713, then ſub-
ſtract the ſame from 4713, and the
Remainder will ſhew the correſpondent
Year before Chrift: But if the Year
found of the Julian Period be greater
than 4713, then ſubſtract 4713 from it,
and the Remainder will ſhew the corre-
ſpondent Year after Chriſt. Thus, it
being found, that Rome was built in
Julian Period 3961, I ſubſtract 3961
from 4713, and there remains 752, the
correſpondent Year before Chriſt where-
in Rome was built.
But if there be no Occaſion to find
7.
the correſpondent Year of the Julian
Way to find Period, the Year before or after Chriſt,
of Chriſt reſpectively anſwering to any given Year
anſwering of the Olympiads may be found thus.
Olympick Multiply (as afore) the compleat Olym-
piads by 4, and to the Product add
the
Another
Year.
Of the OLYMPIA DS. 67
5th
ich
ar
'u-
ar
be
2-
in
) -
e
IC
r
1
r
the Year given (if any be ſpecified ) of CHAP.
the Olympiad running. This Sum, if it VI.
be leſs than 776, ſubſtract it from 776, UN
and the Remainder will ſhew the correſ-
pondent Year before Chriſt: but if the
Sum be greater than 776, then ſubſtract
776 from it, and the Remainder will
ſhew the correſpondent Year after Chriſt.
Thus I would know what Year of Chriſt
anſwers to the fourth Year of the ſixth
Olympiad, wherein Rome was built ac-
cording to Varro. Wherefore ( as afore)
5 *4= 20, and 20+4= 24. Which
Šum being leſs then 776, I ſubſtract it
from 776, and there will remain 752,
the correſpondent Year before Chriſt, as
was found before by the other Method.
Any Year of the Julian Period be- 8.
ing given, to find what Olympick Year to find
anſwers thereto, work thus: From the what O-
lympick
Year given ſubſtract 3937, and divide Year an-
the Remainder by 4, the Quotient (wers se
will ſhew the compleat Olympiads, and more sig
Year of the
the Fraction or Remainder of the Di- Julian Pe,
vidend will ſhew the Year of the Olym-
piad running. If there be no ſuch Re-
mainder, then it is the laſt or fourth
Year of the Olympiad running Ex. gr.
I would know, what Olympick Year an-
ſwers to 7. P. 3961. From 3961, I
ſubſtract
riod.
68
Of the Computation
U.C. or
Rome.
CH A P. ſubſtract 3937, and there remains 24
VI. which divided by 4, gives 6 in the
mi Quotient, and leaves no Fraction of
the Dividend. Wherefore the Olympick
Year fought, is the fourth Year of the
fixth Olympiad.
As the Account by the Olympiads
9.
of the
was, the principal Æra among the
Æra of
Greeks; ſo the principal Æra among
the Build. the Romans was, that of the (*) U. Č.
ing of or Building of Rome; which, according
to Varro began Julian Period, 3961,
but according to the Faſti Capitolini in
the following Year, viz. Julian Period
3962. Wherefore,
Any Year of U. C. being given, add
To find the
thereto 3960, and you'll have the cor-
Year of the reſpondent Year of the Julian Period,
Julian pe according to Varro's Account; or add
fwering to 3961, and you'll have the correſpondent
any given Year of the Julian Period, according to
rear of
the Capitoline Account.
On the contrary, from the given
Year of Julian Period, ſubſtract 3960,
and the Reſidue will give the Year
of U. C. according to Varro; or ſub-
IO.
U, C.
(*) U. C. are the Initial Letters of Urbs Condita, and
fo are put to denote in ſhort the Building of the City, viz.
Rome,
Itract
from the Building of ROME. 69
24
the
of
bick
the
II.
ads
:he
ng
C.
og
I,
in
ad
ſtract 3961, and the Reſidue will be the CH AP.
Year of U. C. according to the Capito- VI. .
line Account.
Foraſmuch as Rome is computed to
have been built 752 Years before Chriſt; to find the
therefore from 752 ſubſtract any given fore or af-
Year of U. C. leſs than the ſame, and ter Chriſt,
the Reſidue will ſhew the correſpondent to any gi-
Year before Chriſt : Or if the Year given ven Tear
of U. C. be greater than 752, then ſub-Of U. C.
ſtract 752 from it, and the Reſidue will
ſhew the correſpondent Year after
Chriſt. Thus the Regal State of Rome
is computed to have ended in U. C.
245, to which anſwers the Year
fore Chriſt: for 752_-245=507. And
the Removal of the Imperial Seat from
Rome to Conſtantinople by Conſtantine
the Great, is computed to have hap-
pened U. C. 1084, and ſo 332 Years
after Chriſt: for 1084—7525332,
As for other Epoch's or Æra's, they
being of leſs Note and Uſe to us, it of other
Epoch's or
will be ſufficient to thew in ſhort, how Æra's.
long before or after Chriſt each of them
began.
507 be-
d
12.
ए
The
70 Of Epoch's or ÆR A's
CH AP.
VI.
Before Chrift.
The Deſtruction of Troy,
is computed to fall in with
(*) Julian Period, 3531, 1183
and ſo the Æra taken
from thence to begin.
The Æra of Nabonaſſar
King of Babylon, from the
Beginning of whoſe Reign
the Chaldeans and Egypti 747
ans reckoned their Years,
began February 26. 7. P.
3967, and conſequently
The Æra (+) of the
Death of Alexander the
324
Great, began Novemb. 12.
7. P. 4390, and ſo
they
(*) Herein is followed the Opinion of Dionyſius Ha-
licarnaſſeus, and Diodorus Siculus.
(+) Some diſtinguiſh between the Alexandrean Æra,
and the Philippean, making the Philippean (ſo called from
Philip Arideus, Brother to alexander the Great) to be-
gin from the Death of Alexander, or mcre exactly from
the 12th of November following the Death of Alexander,
and fo Julian Period, 4390; and the Alexandrean to be
gin not till twelve years after Alexander's Death, viz.
October 11, Julian Period, 4102. This Jarter Æra is el-
teemed by fume learned Men to be the ſame with the
Ara Seleucidarum, otherwiſe called Ara Contractuum,
and the Years of the Greek in the Books of the Maccabees.
The
Of Epoch's or ÆR A's.
7I
CHAP :
Before Chriſt. VI.
The Æra of the City
Antioch, uſed by Euſebi-
us, Evagrius, Cedrenus,
49
&c. began from the Au-
tumn 4. P.4665, and ſo
The Æra of the Ju-
lian Reformation of the
Calendar,began January
45
I, J. P.4669, and ſo
The Æra Astiaca, ſo
denominated from the
Victory obtain'd by Au-
guſtus over Anthony at
Aetium,began Auguſt 29,
7. P. 4684, and ſo
30
Before Chrift.
*
The Dioclehan Æra,
or Æra of the (*) Mar-
tyrs, otherwiſe called the
Æra of the Abiſinians,
began Auguſt 29. A. D.
284
(*) So called from the N ltitude of Chriſtians that
fuffered Martyrdom in the Dioclefian Perſecution.
Q 2
The
72
of Epoch's or ÆR A's.
СНАР.
VI.
After Chriſti
Come?
622
The Æra of the Hegira,
or Flight of Mahomet from
Mecca to Medina, uſed by
the Turks and Arabs, be-
gan July 16, A. D.
The Æra of Yezdegird,
or the Perhan Æra, began
July 16, A. D.
632
From this Table of the Beginnings
of the fore-mentioned Æra's, it is eaſy
to find out the Year before or after
Chriſt, which anſwers to any Year gi-
ven of any of the ſaid Æra's, which
are computed by Julian Years; as are
the Æra's of the Deſtruction of Troy,
of the Julian Reformation, of Dio-
clehan, &c. But it is more difficult
to do ſo in reſpect of the Æra of
Nabonaſar, of Alexander's Death, and
of the Hegira, becauſe they are
computed by Years different from
the Julian Years. It will be ſuffi-
cient to our preſent Deſign to ob-
ſerve here, that 1461 Nabonaſar
3
Years,
1
Of EPOCH's Or Æra's
73
Years, make only 1460 Yulian Years ;CHAP.
and the ſame is to be underſtood VI.
of the Alexandrean Years, as being m
of the fame Kind with the Nabo-
naſſars.
n
MOTERODUTHATUALITATEA
Q3
CHAP .
[ 74 ]
CH A P. VII.
Of the Method to find EASTER-DAY,
according to the NICENE Rule, (as
fill followed by our Church,) by the
Help of the Golden Numbers affixed
to the Calendar. To which is ad-
joined the ROMAN Method of D A-
TING, or denoting the Days of the
Month.
A
T
CH AP.
"HE Rule preſcribed by the Fa-
VII.
thers of the Nicene Council for
the finding of Eaſter, and which is
ſtill followed by the Church of Eng-
The Ni- land, is thus expreſſed in our Common-
cene Rule Prayer-Book: (*) Eaſter-Day is always
for finding
I.
Eaſter-
Day.
(*) It is obſervable that the Nicene Fathers in pre:
fcribing this Rule did not act arbitrari'y, but conformed
themſelves as near as the Difference of Circumstances
would permit, to the Rule preſcrib'd by God for obſer-
ving the Paſſover. Namely, the Rule for the Femish Paſ-
fover was, that it ſhould be kept on the Fourteenth Day,
which is much the ſame as on the Fuil Moon of the firſt
Ecclefiaftical Month called Niſan. And the Nicene Rule
for Eaſter is, that it fall be kept on the Sunday next
after the Fourteenth Day or Firn Moon of our Firſt Eccle-
fiaftical Mouth, or that part of our March, which an-
Iwers to the Jewiſh Month Niſan.
I
the
Of finding E ASTER-D A Y.
75
2.
Easter-
the firſt Sunday after the firſt Full Moon, CHAP.
which happens next after the One and VII.
Twentieth Day of March. And if the
Full Moon happens upon a Sunday,
Eaſter-Day is the Sunday after.
According to this Rule, Eaſter-Day
may eaſily be found by the Help of the To find
Golden Numbers (*) duly affixed to the
Day accor-
Calendar, and by retaining in Memory, ding to the
and applying to Practice, what has been ſaid Rule ,
ſaid of the Golden Numbers, and Do- of the Gol-
minical Letter, Chap. 3d and 4th.
For Inſtance, I would know, what
Day Eaſter-Day, will fall upon the
next Year, viz. 1712. In order hereto,
firſt I enquire what is the Golden Num-
ber for the given Year, and I find it to
be three, according to the Rule given
Chap. III. Sect. 6. Then I enquire what
is the Dominicalor Sunday Letter for the
given Year, and (according to the Rules
given, Chap. IV. Sect. 5, 6.) I find
den Num.
bers.
(*) In our old large Common Prayer-Books, great
Care was taken duly to affix the Golden Numbers to
their proper Days; and to that End black Lines were
drawn between every Day of the Calendar. But of
late Years no ſuch Care is taken, inſomuch that it is
not to be known with any certainty what Days the
Golden Numbers do anſwer to in the Church-Calendars,
of late priated without ſucb black Lines.
that
Q4
76 Of finding EASTER-DAY.
WA
CHAP. that there will be two Sunday Letters
VII. next Year, it being Leap-Year. Of
m which two Letters, viz. FE, the latter E
will be the Sunday Letter after Feb. 23d,
and ſo that whereby I am to be guided
in finding out Eaſter-Day.
Now becauſe the Full Moon, on
which Eaſter depends, is (according
to the Nicene Rule) that which happens
next after the 21ſt of March ; and be-
cauſe the ſaid Full Moon is (agreeably
to Exod. xii. 6.) to be eſteemed the
14th Day after its New Moon incluſive-
ly, (i. e. the Day of the ſaid New
Moon, being reckoned the firſt of the
14th, and the Day of the Full Moon
the laſt,) hence the ſaid Eaſter New
Moon can never fall before the gth of
March, nor after the 5th of April
, .
Wherefore I look for the Golden Num-
ber
3
between March gth, and April
5th, and find it placed to March 31/1,
which therefore was the Day on which
the Eaſter New Moon fell at the Time
of the Nicene Council, in the 3d Year
of the Moon's Cycle: and conſequently
is eſteemed ſo ſtill by us. Wherefore
the Eaſter Full Moon (being fourteen
Days after incluſively) will be April
13th; which being thewn by the Let-
mga
I
ter
Of the ROMAN Date.
77
rs
of
E
1
ter E affix'd to it to be a Sunday, there-CHAP.
fore, by the Nicene Rule, Eafter-Day VII.
muſt be the Sunday after, viz. April
20th. And in like manner may Eaſter-
Day be found for any other given Year,
by the Help of the Calendar adjoined
to the End of this Chapter ; and con-
ſequently Tables may be made, ſhewing
the Day, whereon Eaſter will fall, for
any Term of Years.
It remains now only to obſerve, that
3.
in Order to render the following Ca- of the Ro-
lendar more uſeful, therein is ſet down man way
of Dating,
the Roman Manner of Dating, or de-or denoting
noting the ſeveral Days of the Year. The Days of
Where it is to be noted, that the Roman
Numbers between the Words Kalends,
Nones, Ides and Calends of the ſucceed
ing Month, do reſpectively refer always
to the following Word. Thus the Num-
ber IV over againſt January 2d, refers
to the following Nones, and denotes as
much as the 4th Day of, or before the
Nones of January. So XI ſec co Janu-
ary 22d, denotes the 11th of, or before
the Calends of February.
Wherefore any Roman Date given,
may be turned into our Date, by
finding in the Calendar the Date given,
( ſuppoſe 3 Id. Februar.) and ſeeing
what
the Year,
1
78 Of the ROMAN Date.
CHAp. what Date of ours anſwers thereto, (viz.
VII. February the 11th.) And on the other
hand, any Date of ours being given,
v.g. January 31ſt; it may be turned
into the Roman Date, by finding the
Roman Date affixed thereto, viz. Prid.
Kal. Febr.
January
The CALENDAR.
79
JANUARY
FEBRUARY
Golden
Number
Month.
Day of
Letters.
Weekly
Roman Golden
Roman Golden
Date. Number.
Month.
Day of
Letters.
Weekly
Roman
Date.
3.
IA
ID
II
2 E
II
19
8
19
8
5A
16.
5.
3 F
4.G
A
6 B
7.C
8 D
9E
10F
16.
5. .
3
13.
2.
13
2
10C
IID
IZE
IO.
·
IIG
• I2A
13B
• 14/C
• 15 D
16E
10,
I4 G
18.
Calendæ
IV
III
Prid.
Nonæ
VIII
VII
VI
V
IV
III
Prid.
Idus.
XVI
XV
XIV
XIII
XII
XI
X
IX
VIII
VII
VI
V
IV
III
Prid. Kal.
15A
Calenda
2B IV
3C
III
4D
Prid..
5 E
Nonæ
6F VIII
G
VII
81A VI
91B
V
IV
III
Prid,
13
F Idus.
XIX
XVIII
XVII
17
XVI
18 D XV
XIV
XIII
21G
XII
XI
X
IX
. 25 D VIII
26E VII
2 27
F VI
2816
V
29A IV
. 301B III
Prid. Kal.
7
18.
7.
16B
·
17
0
15
4
15.
4.
19/E
201F
I 2
•
F
18 G
19/A
20/B
211C
22 D
23 E
I.
12
I
22 A
. 231B
24/C
9.
24 F
9.
17
6.
· 25 G
26A
17
6.
27B
14
28C
14
3
31/0
Golden
80
The CALENDAR.
MARCH
APRIL
Golden
Numder.
Month.
& Day of
Letters
Weekly
Roman Golden
Month.
Day
of
Letters.
Weekly
Roman
Date.
Date, Number.
3.
ID
Tar
IG
2/A
2E
3
F
II
31B
4,6
410
19
8.
5A
6B
16.
7C
5 D
6 E
ZF
81G
91A
16.
5.
8D
9
E
Calendæ
IV
III
Prid.
Nona
VIII
VII
VI
V
IV
III
Prid.
Idus.
XVIII
XVII
XVI
ху
XIV
13.
2
IOF
• IIG
12A
JOB
Il/C
12D
13B
13E
14
F
10.
15 G
Calenda
VI
II.
V
19
IV
8
III
Prid.
Nonæ 5.
VIII
VII
13
VI
2
V
IV
IO.
III
Prid.
18.
Idus. 7.
XVII
XVI 15
XV
XIV
XIII I
XII I
XI
X
9
IX
VIII
17
VII 6.
VI
V
14 .
IV
3
III
Prid. Kal.
141C
15D
. 16E
. 17/F
18
7
16A
17B
18/G
4
15.
4.
· 19A
18/C
19D XIII
20 E
21F
22/6
23/A
I 2
. 20B
211C
22 D
• 23
24F
25 G
26A
I.
2311
MMMMMMMM
24/B
9.
XII
XI
x
IX
VIII
VII
VI
V
IV
III
Prid. Kal.
.
251C
. 261D
17.
6.
· 27B
27/E
28C
28/F
29G
29/D
30 E
311F
14.
3.
30 A
Golden)
The CALENDAR.
81.
MAY
UNE
Golden
Number.
Month.
Day of
Letters.
Weekly
Roman Golden
Daté. ||Number.
Month.
Day of
Letters.
Weekly
Roman
Date.
1
II
.
IB
IE
2F
19..
8.
19
8
16...
5.
4A
5B
16
5.
ZA
13.
2.
6C
7 D
8 E
9F
IOG
www
13
2.
10..
IIA
10.
IIE
121F
18..
7.
121B
131C
18
14/A
14D
15E
Calendæ
IV
III
Prid.
Nonæ
VIII
VII
VI
V
IV
III
Prid.
Idus.
XVIII
XVII
XVI
XV
XIV
XIII
XII
XI
x
IX
VIII
VII
VI
IV
IV
Calendæ
IC
VI
3D
V
4E IV
5F III
6G Prid.
Nonæ
81B VIII
9 C VII
10D VI
V
IV
13 G
3G III
Prid.
15B
Idus,
. 16C
XVII
D XVI
XV
XIV
2016
XIII
XII
XI
23C X
IX
VIII
VII
27 G
VI
28 A IV
IV
III
311D Prid. Kal
.
15.
4.
7
6F
17/G
18E
12.
15
4
. 19F
1.
I8A
19B
2010
123
9.
. 21A
22B
I.
17
6.
9
24D
25E
21D
22 E
23 F
24 G
25 A
26 B
270
26F
17
6.
14
3
28 D
29E
14 ,
II
3.
• 29B
3010
30F
Prid. Kal.
11.
Golden
82
The CALENDAR.
JULY
AUGUST
Roman Golden
Golden
Number
Roman
Date.
GC
NU
Il
Date. | Number.
IG
16
19
8.
2A
2D
.
3)B
16.
410
Prid.
1
2
5.
13
5D
6E
13
IC
2.
.
8G
9
A
IS
IO
IOB
11C
12D
MVM
IOE
I'IF
12/G
13A
18
7,7
I !
13 E
15.
14
F!
I?
15
15;G
4;..
16A
Calendæ 8.
VI
16.
V
5.
IV
III
Prid. 2
Nonæ
VIII IO
VII
VI
18.
V
7
IV
III
Prid. 4.
Idus.
XVII I 2
XVI I
XV
XIV 9
XIII
XII 17
XI 6,
X
IX 14.
VIII
3.
VII
VI. II.
V
IV
III
Prid. Kal.
IC · Calenda
IV
{
3
III
4
G
Nona
61A VIII
7
B.
VII
8C VI
D. V.
IV
ILI
Prid.
Idus.
14
B XIX
15C XVIII
16 DIXVII
XVI
XV
G. XIV
XIII
XII
XI
23D x
IX
VIII
26 G
VII
VI
28/B
V
291C IV
III
Prid. Kal.
Golden
IZB
IZE
I 2
18 C
I
19 D
20 E
18/F
19G
20/A
211B
22/C
I
9
211F
17
6.
2216
23 A
24.1
24 E
251C
25 F
26 D
14
3
271E
2714
23 F
II
29/G
3014
19
8
30/D
19
19
31B
ŽIE
The CALENDAR.
83
SEPTEMBER
OCTOBER
Golden
Number.
Month.
Day of
Letters.
Weekly
Roman Golden
Date. Number:
Month.
Day of
Letters.
Weekly
Roman
Date.
IF
16 ..
5.
A
13
3C
41D
4/B
5/C
2.
.
10.
6D
ZE
8F
18.
VMw
7.
10A
IIB
12/C
9B
IOC
IID
15
4
13
14
D
E
14G
15A
I 2
15F
I
16G
171A
18B
Calendæll16.
IV.
5
III 13.
Prid, 2.
Nonæ
VIII IO
VII
VI
18.
V
7.
IV
III 15
Prid. 4.
Idus.
XVIII | 12
XVII I
XVI
XV
9.
XIV
XIII 17
XII 6
XI
X
IX 3,
VIII
VII II.
VI
V
19
IV. 8
III
Prid. Kal.! 16.
5
TA Calendæ
2B VI
V
IV
5E III
6F Prid.
ZIG
Nonæ
8A VIII
VII
VI
V
I 2E
IV
13F: . III
· Prid.
Idus.
16B' · XVII
1710 XVI
18 D · XV
XIV
20F
XIII
XII
. 22A XI
X
IX
VIII
26 E
VII
. 27
F VI:
. 2816
IV
IV
III
Prid. Kal.
Golden
·
9.
19/C
. 19E
17
6.
20 D
.21E
22 F
+
21G
14
14
23G
24/A
3
23/B
241C
25D
25B
II
. 26.0
. 27 D
19
2711
8.
281E
29F
301G
29/A
. 30 B
3110
84
The CALENDAR.
NOVEMBER
DECEMBER
Golden
Number.
Month.
Day of
Letters.
Weekly
Roman Golden
Date. Number.
* Month.
Day of
Letters.
Weekly
Roman
Date
ID
2G
13
2
2 E
3 F
4/G
5 A
6B
10.
18.
70
7.
INVY
9/G
8 D
9 E
10F
. IIG
I2A
15.
4
IIB
I2C
I2 .
I.
13B
14C
15D
• 15F
9.
16E
Calendæ 13.
IV
2.
III
Prid. Ιο
.
Nonæ
VIII
18.
VII
7.
VI
V
15.
IV
4
III
Prid. 123
Idus. I
XVIII
XVII
9..
XVI
XV 17
XIV
6.
XIII
XII 14
XI
3.
X
IX II
VIII
VII 19
VI 8
V
IV
III
5
Prid. Kal
113
IF Calenda
IV
3A III
B Prid.
Nonæ
6D
VIII
z E VII
8F VI
V
IOA
IV
III
Prid.
.
D
Idus.
14
XIX
XVIII
16 G XVII
XVI
. 18B
XV
XIV
. 20D XIII
XII
XI
X
IX
VIII
26.C
VII
VI
V
• 29 F
IV
III
31/A Prid. Kal
.
Having
• 17A
17
6.
17F
18 G
19A
20 B
211C
190
14
3 .
22 D
23 E
21E
22 F
· 23G
24/A
• 25B
II
· 24 F
- 25 G
19
26 A
8.
27B
27 D
28/C
16.
. 28/E
16..
5 .
29 D
30 E
30 G
Of finding EASTER-DAY.
85
Having ſhewn how to find Eaſter. Day, according to CHAP.
the Julian or Old Account, uſed by Us in Great Britain
and Treland, it may not be improper to adjoin here, by VII.
way of Annotation, the Method of finding Eaſter. Day in
according to the Gregorian or New Account, uſed in all
Countries where the Popiſh Religion is eſtabliſhed. Now
this is done by Help of the Table here ſubjoined, where
in in the firſt Column are contained the Gregorian Epacts,
that are now and will be in Uſe till 1800 excluſively;
and in the ſecond Columnareſetdown the Days whereon
falls the Eaſter Full Moon; and in the third Column is ſet
down the Weekly Letter anſwering to the ſaid Days of
the Eaſter Full Moon.
Epacts. Full Moons.
Lerters.
Weekly
Epacts. Full Moons.
24 March F
1
Weekly
Letters.IUS AVOCOS
x
13 April E
XI 2 April A
XXII 122 March D
III
10 April B
XV
XXV 18 April C
VI
7 April F
XVII
27
March
XXVIII15 April
도
​IX
4 April C
XX
I 12 April D
XII 1 April G
XXIII 21 March C
IV
9 April A
XV
29 March D
XXVI 17 April B
VII 6 April E
IXXVIII 26 March 'A
30 March E
Q to ID
TIJOS
The Uſe of the foregoing Table is this. Having found
(as is above ſhewn in the Note on Chap 3. Sect. 8. and
Chap. 4. Sect. 6.) the Gregorian Epact and Sund.ry. Letter,
over-gainſt the ſaid Epact in the foregoing Table is placed
the Day whereon falls the Eaſter Full Moon, and thereto
is affixed its reſpective Letter. From which therefore
you are to reckon in an Alphabetical Order, till you
come to the Sunday-Letter for that Year, and the Day of
the Month anſwering to the ſaid Sunday-Letter, is the
Gregorian Eaſler-Day. Only if it happens, that the Full
Moon falls on a Sunday, then (according to the Nicene
Rule) the Sunday next following is the Gregorian Esfler.
Day. For Inſtance: It has been alrcady (viz. in Nores
on Chap. 3. Sect. 8. and Chap. 4. Sed. 6.) found, thar
R
tho
86 Of finding EASTER-DAY.
ww
CHAP, the Gregorian Epact for A. D. 1712 is 22, and that the
VII.
Gregorian Sunday. Letters are CB, viz. C to the interca.
lated Day in February, and after that B; which laſt Let-
ter B is therefore the Sunday-Letter, whereby you arc to
be guided in finding Eaſer-Day. Now by the foregoing
Table you learn, that when the Gregorian Epact is 22,
the Eaſter Full Moon, according to the Gregorian Account,
will fall on March 22d, N. S. li.e, March uth O.S.)
to which anſwers the Letter D, as may be ſeen in the
foregoing Calendar. Wherefore reckoning in an Alpha-
betical Order from D to B, which laſt is the Gregorian
Sunday. Letter, you'll find, that according to the Grego-
rian Computation, Eaſter-Sunday will be March 27th N.s.
which anlwers to our March 16th; and conſequently the
Gregorian Eaſter-Day will fall A. D. 1712, five Weeks
before our Eafter-Day, this falling on April 20th, as has
been afore ſhewn.
.
1
It only remains to obſerve in ſhort, that it having been
ſhewn, how to find both the Julian and Gregorian Eaſ-
ter-Day, thereby may be known the Time of all the
Moveable Feſtivals in any given Year ; foraſmuch as they
all depend on Eaſter-Day. And conſequently hereby,
and by what has been ſaid of finding the Days whereon
fall the New and Full Moons, may be drawn up an Al-
manack fufficient for common Uſe. And thus I have
laid together ſo much of Chronology, as ſeems requiſite
to be known by Young Gentlemen, at leaſt at their firft
Inftitution in the ſaid Ärt or Science.
F I N I S.
THE
Young Gentleman's
D I ALL I N G,
Containing ſuch
1
ELEMENTS of the ſaid Art,
as are moſt uſeful and eaſy to
be known.
BY
EDWARD WELLS, D. D. laté
Rector of Cotesbach in Leiceſterſhire.
The FOURTH EDITION.
L ON D ON:
Printed for J AMB S, John, and PAUL
KNAPTON, at the Crown in Ludgate-Street
.
MDCCXXXVI.
**
You
T H E
PREFACE.
А A
S the Dependance of
the Art of Dialling
கு upon Aſtronomy, was
the Reaſon of my Draw-
ing up and Publiſhing this Trea-
tiſe, at the Same Time with my
Aſtronomical Treatiſe ; ſo my De-
fign
R 3
The PRE FAC E.
content
hgn in drawing up this Treatiſe,
and the Reaſon of my giving it
the Title of The Young (en-
tleman's Dialling, may be learnt
from the Preface to my Treatiſe
of Aſtronomy, entitled in like
manner The Young Gentle-
man's Aſtronomy. I need only
obſerve further, that I have not
contented my ſelf with laying
down in this Treatiſe the bare
Practical Part of Dialling, but
bave added thereunto the Rea-
fons or Grounds of ſuch Prac-
tice, as moſt proper to be known
by Young Gentlemen; and with
al have obſerved, in the Annota-
tions to this Treatiſe, how the
Grounds of Dialling may be moſt
naturally repreſented even to the
Eye,
The P R EF A C E.
Eye, by the Help of a Machine
or Inſtrument, which from its
Ule may be called a Dialling
Sphere.
it
?
Ons
G
R4
THE
CONTENTS
CH À P. I.
O
F Dialling in general, Page 1
CH A P. II.
Of an Horizontal Dial,
9
CHA P. III.
ht
Of an Erect Direct South and North
Dial,
21
С НА Р.
The CONTENT S.
CH A P. IV.
of an Erect Direct Eaſt and Weſt
Dial,
26
.
CHAP. V.
Of duly Placing a Direct ( Eaſt or
Weft, North or South ) Dial; and of
the Manner of finding whether a Wall
has a Direct or Declining Poſition or
Situation,
30
CH A P. VI.
of Drawing a Declining Dial,
43
A CA-
The CONTENT S.
A CATALOGUE of the ſeveral
Draughts of Dials, and of other
Cutis, belonging to this Treatiſe,
54
THE
ID KUVA KUINUTO
ral
ber
ife,
54
Τ Η Ε
Young Gentleman's
DIALLING, &c.
CH A P. I.
Of DIALLING in general.
B
Y (*) Dialling is underſtood CHAP.
the Art of Shewing the Time
I.
of the Day, by the Sun's Shade
falling on ſome Surface, whe-
ther Plain or not Plain.
Dialling,
I.
what.
(*) The Word Dial is derived from Dies, becauſe
thercupon the Time of the Day is ſhewn. And from
the peculiar Manner of fhewing the Time of the Day
upon a Dial, viz. by the Shadow of the Sun, this Art
is frequently termed Ars Scioterica, i. e. the shadow- Art,
from the Greek Word oxide, denoting a Shadow or Shade.
3
Plain
2
Of DIALLING.
*
2.
CHAP. Plain Surfaces are moſt uſeful, and
I. therefore moſt uſed : for which Reaſons
mwe will here ſpeak only of Plain-Dial-
ling, i. e. of drawing Dials on Plain
Plain Dial- Surfaces, ſimply called Planes.
Every Dial-plane (i. e. plain Sur-
The vari- face on which a Dial is drawn) re-
ons Names preſents the Plane of ſome (*) Circle
in the Heavens. If the Dial-plane
Reaſon of
repreſents
the faid
ling, what.
3.
and the
Names.
(*) This, and the whole Foundation of Dialling, is
moſt naturally, and ſo moft clearly illuſtrated by the Help
of an Inſtrument or Machine, which may be properly
enough called from its Uſe a Dialling sphere. It need
confiſt but of an Horizon, and two (Wooden or Braſs)
Circles faſtened together, croſſing each other at Right
Angles, and ſo as to biſect one the other. Either of
thele Circles may be taken to repreſent the Meridian,
and the other the Equator. The former is to be divi-
ded into four go Degrees, and the latter into 360, as in
other Spheres or Globes. And.in like manner, as in o-
ther Spheres, the Meridian of this Dialling Sphere muſt
be let into the Horizon at the North and South Points of
it. There muſt be a plain Piece of Board to move up
and down within the fore-mentioned Circles, ſo as to
repreſent the Poſition of any Dial-planc. And through
the Center or middle Point of the plain piece of Board,
there muſt be made an Hole, through which, when there
is occaſion, a String is to be put; which String being
alſo put through the two Points of the Meridian, which
are 90 Degrees each from the Equator, will repreſent
the Axis of the World. The Dialling Sphere being
thus prepared, the Manner how the Sun by the Shade
of the Style of the Dial, comes to thew the Time of
the Day on any Dial.plane, may be ocularly demon-
strated,
Of DIALLING.
3
ind
ons
21
lin
I.
e-
le
le
ts
repreſents the Plane of the Horizon, CHAP.
the Dial is called an Horizontal Dial. I.
If the Dial-plane repreſents the Plane w
of the Prime Vertical, then the Dial
is called an Erect Direct North or
South Dial, reſpectively as the Dial is
drawn on the north or fouth Side of the
ſaid Dial-plane. If the Dial-plane re-
pr
eſents the Plane of the Meridian, the
Dial is called an Erect Direct Eaſt or
Weft Dial, reſpectively as the Dial is
drawn on the eaſt or weſt Side of ſuch
a Dial-plane. If the Dial-plane repre-
ſents the Plane of any other Vertical
Circle, beſides the Prime Vertical and
Meridian, then the Dial is called a Deo
clining Dial ; foraſmuch as it does not
directly face any one of the four Car-
dinal Points of the Heavens, but declines
+
ſtrated, by moving the Meridian of the Dialling Sphere,
that the String repreſenting the Axis may have ſuch a
Poſition as duly anſwers to the Latitude of the Dial; and
by placing the plain Piece of Board in ſuch a Poſition as
to anſwer the Plane of that Circle in the Heavens,
which is repreſented by the Dial-plane; or in Mort, to
anſwer) the Poſition of the Dial-plane. Then a Cans
dle duly moved round the String in Imitation of the Sun's
Motion, will Mew by the Shade of the String, how the
Shade of the Dial-Style by the Motion of the Suo, ſhows
the Time of the Day on the Dial-plane.
I
more
2 *
4
OF DIALLING
CHAP. more or leſs from them. Laſtly, if
I. the Dial-plane repreſents the Plane of
any greater Circle in the Heavens,
beſides fome Vertical Circle or the
Horizon, then the Dial is called (nor
an Erect, but) an (*) Inclining or Re-
clining Dial, reſpectively as
as it is
drawn, either on that Side of the
Dial-plane, which inclines (or leans
forward) towards the Horizon; or on
the other Side, which reclines (or
leans backward) from the Zenith.
And amongſt theſe are the (+) Equi.
(*) Theſe are ſubdiſtinguiſhed into Direct Incliners or
Recliners, and Declining Incliners or Recliners.
(+) The Equino&tial Dial is Erect in reſpect of thoſe
who live exactly under the Celeſtial Equator; and like.
wiſe the Polar Dial is Erect to ſuch as live (if any there
be) exactly under either of the two Polesof the World.
For in reſpect of the former Inhabitants, the Plane of the
Equinostial, and of the Prime Verticle are one and the
fame; and in reſpect of the latter Johabitants, the Plane
of the Prime Vertical, and the Plane of the Circle se.
preſented by the Plane of a Polar Dial is one and tha
ſame. Again, the Equinoctial Plane is the ſame with the
Horizontal Plane, in reſpect to thoſe that are under the
Poles; and the Polar Plane is the fame with the Horia
zontal Plane, in reſpect of thoſe that live under the E-
quaror. And the like Change is to be conceived in re-
ipect of other Dial-planes, as they regard ſeveral places ;
Every Dial-plane being an Horizontal Flane at ſome Place,
and on the other Side every Horizontal Plane being a
prime Vertical, and Meridian (&c.) Plane at ſome o.
ther Places.
noctial
Of DIALLING.
5
f
f
ܕܪ
t
9
noftial and Polar Dials. The Equi- CH AP.
noctial Dial is ſo called, as being I.
drawn on a Plane, that repreſents them
Plane of the Equinoctial. The Polar
Dial is lo called, as being drawn on
a Plane, that repreſents the Plane of
that Circle, which paſſes through the
Poles of the World, and alſo (the In-
terſection of the Equator, and the
Horizon at the eaſt and weſt Points,
i. e. in ſhort) the Poles of the Meri-
dian.
Among the ſeveral Sorts of Dials
4.
afore-mentioned, the Equinoctial Dial of the E-
is the moſt eaſy to be drawn; this
quinoctial
being done only by drawing a Circle,
and dividing it into twenty-four equal
Parts, (to which right Lines drawn
from the Center of the Circle, will
repreſent the ſeveral Hour-Lines,) and
erecting perpendicularly a Pin in the
Center of the Circle for · the Style.
But becauſe (*) the Equinoctial Dial,
when chus drawn on one Surface of
the Plane, will ſerve only for one
Dial.
(*) The like is to be underſtood alſo as to the Polar
Dial: on which Account it is of lefſer Uſe; and there-
fore the Manner of deſcribing it is omitted in this
Treatiſe.
Half
6
Of DIALLING.
CHAP. Half of the Year, namely, whilſt the
I. Sun is on one side of the Equinoctial ;
m and therefore to make it ſerve for the
whole Year, it muſt be doubly drawn,
viz, on the lower as well as upper
Side of the Plane; on Account of
this and other Inconveniences, the
Equinoctial Dial is ſeldom uſed. And
therefore it had not been taken No-
tice of here, but that the Knowledge
thereof is requiſite for the Under-
ſtanding the Reaſon of that Method,
which (as being the moſt Natural, and
withal eaſy Method) is principally
made Uſe of in this Treatiſe, for
drawing the other Dials here ſpoken
of. For, as the Reaſon why the
Circle in an Equinoctial Dial is divi-
ded into twenty-four equal Parts, an-
ſwering to the twenty-four Hours in
a Nuchthemeron, is becauſe 15 De-
grees, which is a 24th Part of the
Equinoctial Circle in the Heavens,
anſwer to one Hour's Motion of the
Sun; ſo, becauſe (at the fame Time
that the Sun is conceived, by the
Shade of the Axis of the World, to
fhew any Hour on the Equinoctial
Plane, it does alſo by the ſamne Shade
thew, at the Interſection of any other
Plane
OF DIALLING
!
w
Plane with the Equinoctial Plane, the CHAP:
Point of the ſaid other Plane belong I.
ing to the fame Hour ; or thus; becauſe) mu
the Hour-points of any other Plane are
thoſe Points of the ſaid Plane, which
fall in with or touch the Hour-Points
of the Equinoctial Plane, at the com-
mon Interſection of the ſaid two Planes;
therefore by the Help of the Equinocti-
al Dial may be drawn other Dials, name-
ly, the Equinoctial Dial being duly ap-
plied to the Plane given, the Hour-
Points of the Equiuočtıcl Dial will fall
on the correſpondent Hour-points of (the
Dial to be drawn on the) Plane given.
And this will be diſtinctly exemplified
5.
as to the ſeveral Sorts of Dials above- The Bursa
mentioned, (excepting Inclining and more of
Reclining Dials, as being of lefler Uſe) reducibie
after that it has been here obſerved to three
further in general, that the whole Bu-
Operations.
fineſs of Dialling may be reduced to
three general Heads or Operations.
Whereof the firſt conſiſts in finding the
Place of the Subſtyle, or where the Style
is to be placed : the ſecond in drawing
the Hour-Lines : the third and laft, ei-
ther, if the Dial-plane be Moveable, in
duly Placing and Fixing the ſame, after
S
thac
Heads or
8
Of DIALLING.
CHAP, that the Dial is drawn thereon; or elſe,
I. if the Plane whereon the Dial is to be
w drawn, be unmoveable and already fix-
ed, in Finding the Poſition or Situation
of the ſaid Plane, viz, whether it be a
Direct or Declining Plane ; and if the
latter, how far it declines.
С НА Р.
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be
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on
a
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.
1
tes
1
3
An HORIZONTAL Dial drawn by help af ý E QUINOCTIAL Dial :
VIII
IV
Dial. Plate i
Sl:
VIL
V
Place this
facing p.g.
Fig
cs
W
VI E
VI
VII
P
T
Q
G
IV
VIII
Æ
N
IX
II
I XI XI
X Х
[9]
CH A P. II.
*
Of an HORIZONTAL Dial.
in HORIZONT
I
y
I.
zontal
of.
Begin with the Horizontal Dial, as CH AP.
being the moſt Uſeful ; foraſmuch II.
as it fingly anſwers the whole (*) End of m
Dialling, by ſhewing the Time of the
Day from Sun-riſing to Sun-ſetting The Hori-
throughout the whole Year, within that
Dial; why
Horizon for which it is made: whereas firſt ſpoken
no other Dial does this. And having
made this Obſervation as to the Uſeful-
neſs of the Horizontal Dial, we proceed
now to the Delineation thereof.
Whereas the four Cardinal Points of
the Heavens are diſtant one from the O- To draw
ther 90 Degrees; and whereas the Me- the Meri-
ridian runs from North to South, and
the prime Vertical runs a-croſs the Me- Vertical
ridian from Eaſt to Weſt; hence it fol- Lines of an
Horizontal
2.
dian and
Prime
Dial.
(*) The whole proper End of Dialling is, to few
the Time of the Day by the Sun's Shade. As for ſhewing
the Place of the Sun in the Ecliptick (and the like) by
the Shade on a Dial-plane, this does not properly belong
to Dialling.
S 2
lows,
10
Of an HORIZONTAL Dial.
CHAP.lows, that, two right Lines being drawn
II. croſſing one the other at right Angles
(whoſe Meaſure is each 90 Degrees )
and either of theſe two right Lines be-
ing taken to repreſent the Meridian, the
other will repreſent the Prime Verti.
cal. That taken to repreſent the Me-
ridian, may be fitly denoted by NS,
as running in this Dial from North
to South ; the other by EW, as
running from Eaſt to Welt.
See
Fig. 1.
3
The Point, where the Lines NS
The Cen- and EW croſs one another, denotes
ter of an
Horizontal (*) that Point in the Plane of the
Dial, which Horizon, (as alſo of the Meridian and
Prime Vertical) through which the
Axis of the World paſſes. And be-
cauſe the ſaid Point is the (+) Center
(of all the ſaid Planes, particularly) of
(*) This may be evidently ſhewn by the Help of a
Dialling Sphere.
(+) The Axis of the World paſſing through the Cen-
ter of the World, which is alſo the Center of all great
Circles in the Heavens, and conſequently of the Horizon,
Meridian, and Prime Vertical; hence it follows, that
That Point in the Planes of the ſaid Circles, through
which the Axis of the World paſſes, muſt be che Center
of the ſaid Planes.
ز
the
Of an HORIZONTAL Dial.
II
1
5
the Horizontal Plane, whereon the Di- CHAP.
al is to be drawn, and conſequently the II.
Center of the Dial it felf, hence itu
may be fitly marked or denoted by C,
as Fig. 1.
The Axis of the World being the (*) 4.
common Interſection of the Planes of all of the
Subtyle
Meridians, and therefore running from and Style.
Pole to Pole along the Plane of every
Meridian ; hence the Line N S repre-
ſenting the Plane of the Meridian of
that Place, for which the Dial is made,
muſt be the Subſtyle, or the Line
whereon the (f) Style, which repre-
ſents the Axis of the World is to be
(ll) erected.
(*) This may alſo be evidently ſhewn by the Help of
the Dialling Sphere.
(t) It is ſo called, becauſe it needs be, and often actu.
ally is, no more than a long Araight Iron Pin, like an
Engraving or old sort of writing Pin, called a Style. It
is called alſo by a Latin Word, the Index, becauſe it tells
or ſhews what is the Time of the Day. And it is called
likewiſe by a Greek Word the Gnomon, (from yrów to know)
becauſe thereby is known the Time of the Day.
(1) By being erected is underſtood here, and all along
this Tract of Dialling, being placed perpendicularly upon
the Subſtyle, ſo as not to lean anything more towards the
Hour-lines on one side of the Subſtyle, than towards
the Hour-lincs on the other Side of the Subſtyle.
S 3
And
12-
Of an HORIZONTAL Dial.
II.
CH AP.
And becauſe the Style does repreſent
the Axis of the World, therefore it
w muſt be ſo erected upon the Subſtyle,
(which is the common Interfection of
the Horizontal and Meridian Planes)
as therewith to make an Angle equal
to the Elevation of the reſpective
(North or South ) Pole above the Ho-
rizon of the Place, or (which comes
to the fame) to the (*) Latitude of
the Place. Wherefore taking C for
the Center, draw (+) an Arch of a
Circle from NS (on either Side ) to
EW. On the ſaid Arch (1) ſet off from
NS towards E W, (viz, at P. Fig. 1.)
fo
(*) How the Elevation of the Pole and Latitude of
the Place come to be always Equal, may be evidently
Thewn on the Globe.
(t) This Arch may be drawn, at what Extent of the
Compaſſes or Diſtance from the Center you pleaſe ; but
it is convenient to have regard to the Largeneſs of the
deſigned Dial. And alſo it is convenient to make Ufe
of a Line of Chords, in this, and all ſuch Operations, in
Order to the ſetting off on the Arch drawn any Number
of Degrees, with much more Eafe and Readineſs than
can be done otherwiſe. The Reader is here ſuppoſed to
be already inſtructed in the Uſe of the Line of Chords,
(1) That is, the Style, if it be only a long ſtraight
Piece of Iron, muſt be ſo placed on the Subſtyle of the
Dial, as to have the ſame inclination thereto, as CP
bas
Of an HORIZONTAL Dial. 13
}
ſo many Degrees as anſwer to the Ele-CHAP.
vation of the Pole; for Inſtance (Fig. II.
1.) 51 } the Latitude of London or
Elevation of the north Pole there. The
Line CP being drawn will ſhew the
Style.
Having found the Subſtyle NS, 5.
and the Style CP, draw a long Line of the
croſſing the Subſtyle in any Point, gent Line,
( which ſhall ſeem moſt convenient, ) and apply.
ſuppoſe Q, at right Angles. This Line quinoctial
repreſenting the common Interſection of
Plane of
the Equinoctial Plane and Dial Plane, your Ho-
is therefore called the (*) Contingent rizontal
,
Line, and is denoted (Fig. 1.) by the
Line TG. That Point in the Subſtyle,
which is ſo far diſtant from Q, as the
Point Q is found by the Compaſſes to
be diſtant from the neareſt Point of the
Style, repreſents the Center of che E-
quator, or that Point from which an
Equinoctial Dial is to be delineated on
Dial to the
has to NS. If you would have the Style a broad Plate
of Iron or the likç, then it muſt be made exactly equal
to the Triangle NCP. In both Caſes, the lower Point
of the Style, namely, wherein the Lines CN and Pn
meet, muſt be placed exactly on C, as being the Point
of the Horizontal Plane, through which paſſes the Axis,
repreſented by the Style.
(*) It is ſo called, becauſe herein the two Planes are
conceived to touch one another.
the
S4
14
Of an HORIZONTAL Dial.
may fit.
CHAP.the Dial-plane, and therefore it
II. ly be marked Æ. Taking then Æ for
W the Center, at (*) any Diſtance, draw
toward the Contingent a (+) Semicircle
repreſenting half the Equinoctial, ſo as
that one Half of the Semicircle (i. e.
fourth Part of the Equinoctial) may be
on each side of the Subſtyle. Then di-
vide the ſaid Semicircle into twelve equal
Parts, (viz. fix on each side of the Sub-
ſtyle,) each containing an Arch of 15
Degrees, (II) Lines drawn from Æ the
Center of the Equinoctial to each Divi-
fion of the Semicircle will be the Hour-
Lines of the Equinoɛtial Plane or Dial;
among
(*) However it is convenient to be guided herein by
the Length of the Line of Chords made uſe of, and by
the Size of the intended Dial.
(+) This may be otherwiſe done by only drawing one
Halt of this Semicircle on one side of the Subſtyle, and
dividing it into ſix equal Parts; and thence transferring
the ſaid fix Diviſions to that Part of the Contingent,
which is on the other side of the Subſtyle. And this is the
beſt Way for practice, being ſhorter, and not cumbring
the Work with Multitude of Lines. And 'tis adviſeable
to draw the faid Quadrant, or fourth Part of the Equi-
noctial Circle or Dial on that Side of the Subſtyle, where
the Style is not drawn: becauſe then the Equinoctial Di.
aland the Style will ſtand both clear one from the other ;
as in the Figures hereunto belonging:
(II) Thele, and all other Lines or Circles or Arches
of Circles are to be obſcure ones, i, e. ſuch as may be
tubbed out again, excepting only the proper Hour-
lines
Of an HORIZONTAL Dial. 15
the Hours
tal Dial,
among which Hour Lines, the Subſtyle CHAP.
and Meridian NS of the Horizontal II.
Dial will alſo be the Meridian of the m
Equinoctial Dial.
Having thus fitted the Equinoctial 6.
Dial to the Horizontal Plane, on which To dramo
the Horizontal Dial is to be drawn, it lines of an
will be very eaſy to find the Hour-points Horizon-
of the ſaid Horizontal Dial : namely,
by continuing the Equinoctial Hour-
lines to the Contingent, and thereby fee-
ing on what Points of the Horizontal
Plane the Hour-lines of the Equinoctial
Plane will fall. For the ſaid Points of
the Horizontal Plane are reſpectively the
Points, on which the correſpondent
Hour-lines of the Horizontal Dial will
fall, being drawn from (*) C the Cen-
ter of the Horizontal Dial. Among
theſe Hour-lines, the Line NS being
both the Meridian and Subſtyle of the
Horizontal Dial, (and ſo falling in
with ţhe Meridian of the Equinoctial
Dial ) will therefore be the twelve a
Clock
lines in each Dial. Theſe obſcure Linęs are diſtinguiſied
in the Dsaughts hereunto belonging by being made
prick'd
Lines,
(*) The Hour-lines repreſent the shade conceived
to be made by the Axis of the World; which Axiş
being
16 Of an HORIZONTAL Dial.
CHAP. Clock Line of the Horizontal (as well
II. as Equinoctial ) Dial. Which being
w known, the Numbers II, 10, 9, 8, and
7, are to be affixed to the Hour-lines on
the weſt Side of the Dial, according to
their reſpective Order from the twelve
a Clock Line. And in like manner the
Numbers 1, 2, 3, 4, and 5, are to be
ſet to the reſpective Hour-line on the
eaſt Side of the Dial. The Line EW,
as repreſenting the Prime Vertical, is
always the 6 a Clock Line, both Morn-
ing and Evening. And as for the Hours
before fix in the Morning, and after fix
in the Evening, their Lines are drawn
by continuing the Lines of thoſe Hours,
which are of the fame Denomination in
the contrary Part of the Day, through
the Center C of the Dial. Thus the
being conceived to paſs through C the Center of the
Dial, hence all the Hour lines muſt be drawn from the
faid Center. Only it is obſervable, that it is more Or-
namental, not to draw actually the Hour-lines from C
(becauſe if they were ſo drawn, they would be apt to
fun together, and blot at the point C,) but making a
Circle at fome ſmall diſtance from C, actually to draw
the Hour-line's only from the ſaid Circle, by the Ruler
duly applied to C, as Fig. 1. 'Tis alſo obſervable, that
the Dial-plane may be of any Shape, viz. Round or
Triangular, c. as well as Square or Oblong, though
this Shape is moſt uſed among us.
Hour-
Of an HORIZONTAL Dial.
17
1
I
!
Hour-lines of 5 and 4 in the Morning are CHAP.
drawn, by continuing the Hour-lines of II.
5
and
4 in the Afternoon through c.mn
And the Hour-lines of 7 and 8. in the
Evening are drawn, by continuing the
Hour-lines of 7 and 8 in the Morning
through C. And thus the Delineation
of an Horizontal Dial is finiſhed, (as is
repreſented, Fig. 1.) according to the
Mechod of Delineating the ſame by the
Help of an Equinoctial Dial. For as to
the intermediate. Spaces between each
Hour, (viz. Quarter, Half, and three
Quarters,) they are had by dividing the
Space between each two Hours, firſt into
Half, and each Half again into Quarters.
It may not be unuſeful (not only for
7.
Variety, (*) but alſo Proof fake) to add To drama
here the Method of drawing an Hori-zontal Dial
zontal Dial, by Dialling Scales and Ta- by a Dial
bles. The former is thus: The Linesling Scale.
NS and EW being drawn and the
If you have drawn your Dials right, the ſame
Hour-lines, at equal Diſtance from the Center of your
Dial, will be equally diſtant alſo one from the other, by
which Method foever you draw them, vig. The Di-
ſtance between 12 and 1, (or 12 and 2, or 1 and 2,
enc.) will be the ſame, at equal Diſtance from the Cen-
ter of your Dial, whether it be drawn by the Equinoctial
Dial, or by Scales, or by Tables,
Style
18 Of an HORIZONTAL Dial.
CH A P.Style CP erected, as afore ; the Length
II. of the Line EW is to be determined, lo
was to bear a due Proportion to the Scale
of Hours you are to Uſe. This is done
by placing one Foot of the Compaffes at
the Beginning of the Scale of Latitudes,
(contained in the Dialling Scale,) and
opening the other Foot, till it reaches
to the Number of Degrees in the faid
Scale of Latitude, which anſwers to the
Latitude of the place. This Extent is
to be ſet off on the Line EW, from C
towards E, and alſo toward W; and
where it ends, it may be reſpectively
marked e, w, as Fig. 2. Then out of
the Dialling Scale take the whole Length
of the Scale of Hours, with the Com-
paſſes; and ſetting one Foot of the
Compaſſes in e, with the other make an
Arch croſſing the Line NS cowards N;
and then do the like on w. From the
Point x of the Line NS, where the two
Arches (*) croſs one another, draw the
(*) If the Lines drawn by the Compaffes, ſet upon e
and w, do not croſs one the other exactly in ſome
Point of the Meridian NS, then ſome Fault has been
made in ſetting off the ſaid Lines, and the Work muſt
be repeated, till they do thus croſs.
Lines
-.
Place this
facing p. 18.
8
4
S
NIL
7
Fig. 2.
5
E
6
N16
W
R
W
5
7
4
8
N
3
9
2
1
N2 11
10
X
An HORIZONTAL Dial drawn by ý help of Dialling Scales.
܀
:
ܕ
ܢܣ܂
ܢܫ
ܗܝ ܀
܀
ܙ ܚܕ
܀ ܀
-
ܡܗ܀
ܕܐܐ ܪܐܬܙܚ܂
ܠܐܫܟ ܐܝ܀
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.
;
Of an HORIZONTAL Diol.
19
Lines xe and xW; which will be of CHAP,
an equal Length with the Scale of Hours II.
in the Dialling Scale : from which Hour-mu
ſcale the ſeveral Hours (and the inter-
mediate Spaces) are to be reſpectively
transferred unto the Lines x e and xw.
Lines drawn from C to the ſeveral Hour-
points on the Lines x e and cw, will be
the reſpective Hour-lines. And ſo the
Dial is finiſhed by the Scale: for the
Hour-lines before 6 in the Morning,
and after 6 in the Evening, are to be had,
as afore.
Horizon-
If you would work by Dialling Ta- 8.
bles, having drawn the Lines NS and To draw ar
EW to what Length you pleaſe, upon tal Dial by
C the Interſection of the ſaid Lines Dialling
Tables.
draw a Semicircle es w, as in Fig. 3.
Then on the ſaid Semicircle ſet off the
Degrees and Minutes anſwering to each
Hour (and each Quarter, Half, or three
Quarters of an Hour) in the Table for
Horizontal Dials. · After which draw
the Hour-lines from C to the ſeveral
Hour-points in the ſaid Semicircle.
The Subſtyle and Style are found, as
afore.
Having
20
Of an HORIZONTAL Dial.
CHAP. Having ſhewn, how to draw an Ho.
II. rizontal Dial three ſeveral Ways, it re-
m mains now to ſhew how to place aright
the ſaid Dial, when drawn, and this
will be beſt ſpoken of together with the
placing of other Dials, Chap. 5.
С НАР.
Dial. Plate 2
Place this facing
8 Horizontal Dial drawn by Dialling Tables.
pag. zo.
4
S
7
5
Fig. 13
6 E
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7
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.:
A Direct South Dial drawn by ý z help of ý Equinoctial Dial
6
6
W
Pag. 21.
Fig. 14
.....
7
5
P
Q
*$$s
8
4
Æ
N
9
3
10
12
1
2
..
[-30 ]
CH A P. III,
Of an (*) Erect Direet South and
North DIA L.
3
TI
I.
the most
ADirect South Dial drawn by y z help of ý Eouino
HE Erect Direct South Dial ſhall CHAP.
be ſpoken of next, as being next
III.
to the Horizontal Dial the moſt uſeful : m
foraſmuch as it ſhews the Time of the
A Direct
Day from 6 to 6 throughout the whole South Dial
Year.
This Sort of Dial is drawn after uſeful nexe
the ſame manner, by the Help of the rizontal
Equinoctial, as the Horizontal Dial,
excepting the Particulars following i to draw a
viz. Firſt, That the Meridian or 12 a Direct
Clock Line, (which in this, as well as
Dial, by the
the Horizontal Dial, is always the Sub- Help of the
ſtyle, ) foraſmuch as it muſt be fo Equinoc.
placed as that one of its Ends muſt
Point to the (+) Zenith, the other to
the
Dial, Dial.
2.
South
tial Dial.
Inclining and Reclining Dials being ſeldom uſed,
hence theſe Dials are frequently Iftiled only Direct South
and North Dials.
(t) The Meridian of any Place or Dial, as it paſſes
through the North and South Poles, ſo it pafles like-
wife
22 Of a Direct South DIAL,
CHAP. the Nadir, may therefore be moſt
III. properly here denoted by ZN Sem
mcondly, the Style CP muſt be erected
upon the Subſtyle Z N, ſo as to make
therewith an Angle equal (not to the
Elevation of the Pole, as in an Hori-
zontal Dial; but ) to the Complement
of the Pole's Elevation. For ſuch is
the Meaſure of the Angle, which the
(*) South Pole, repreſented by the
Style of this Dial, makes with the
Plane of the Prime Vertical. Now
the Elevation of the Pole above the
Horizon of London being 51. De-
grees, its Complemenc is 38. De-
grees. Thirdly, "On this Dial there
need be inſcribed no Hour, either be-
fore 6 in the Morning, or after 6 in
the Evening: for the Plane of this
?
4
wiſe through the Zenith and Nadir of the ſaid Place.
in an Horizontal Dial the Meridian Line is to be placed
with its Ends towards the North and Souch Points, and
therefore is therein fitly denoted by NS. Bur in a Direct
South Dial, the Meridian Line is to be placed fo, as that
its Ends may Point to the Zenith and Nadir, and there-
fore is here more firly denoted by ZN.
(*) This may be evidently repreſented to the very
Eye by the Dialling Sphere; and conſequently the Rea-
ſon why the End of this Style muſt be placed down
wards.
the video
Dial
Place this facing p22.
Dial. Plate 3
Direct South Dial dr awn by Dialling Scales
6
Fig. 15
W
6
C
e,
7
5
wo
8
4
9
3
N
1
(
(
1
1
PARTE
***
parente
ireet South Dial drzaun by Dialling Tables
6
Fig. 6.
7
P
8
4
N
9
3
10
11
12
1
2
Of a Direct North DIAL. 23
See Fig. 4.
Dial repreſenting the ſouth Side of the CHAP.
Plane of the Prime Vertical, the Sun III.
never ſhines upon it before 6'in the air
Morning, or after 6 in the Evening,
If you work (not by the Equinoctial 3.
Circle or Dial, buc) by a Dialling Scale, To draw
then (beſides the fore-mentioned Parti- South
culars, wherein the drawing of this Dial by **
Dial differs from drawing an Horizon-Dialling
tal Dial) it is alſo to be known, chat
upon the Line E W, from C towards
E and W, muſt be ſet off the Ex-
tent (taken from the Scale of Latitude:
not of the Latitude it ſelf, but ) of the
Complement of the Place's Latitude.
Scale.
See Fig. 5.
If you work by Tables, then the De- 4:
grees of the Angle, which every Hour-70 drar
line makes with ZN the Meridian or by dialing
Subſtyle, muſt be taken from the Table Tables.
for a Prime Vertical or Direct South
Dial. See Fig. 6.
A Direct North Dial differing from
5.
a Direct South Dial primarily in this To drama
alone, that the former repreſents the Direct
north Side of the Plane of the Prime Dial.
Vertical, and the latter the ſouth
Side ; hence the drawing of a Direct
T
Norch
-
24 Of a Direct North DIAL.
ta
Chap. North Dial is the ſame, as of a Di-
III. rect South Dial ; excepting if, that
w the Hours requiſite to be inſcribed on
this Dial in our Country are no more
than theſe, viz. 4, 5, 6, in the Morn-
ing, and 6, 7, 8, in the Evening. For
the Sun with us never riſes till after
3
in the Morning, and always fets be-
fore 9 in the Evening ; and from 6
in the Morning till 6 in the Evening
it turns off from the North to the
South Side of the Plane of the Prime
Vertical. 2dly, Foraſmuch as the
Style of this Dial repreſents the
north Segment of the Axis, and ſo
its End P repreſents the North Pole,
therefore the End P muſt be placed
looking upwards toward the North
Pole. And conſequently that End of
the Subſtyle, which anſwers to the
End P of the Style, muſt Point to-
wards the Zenith, and therefore is
here properly to be denoted by Z,
and the other End of the Subſtyle
by N, as anſwering to the Nadir,
contrary to the Poſition and Notation
of them in a Direct South Dial. See
Fig. 7
.
As
Place this facing Bag. 24
Dial. Plate 4
A Direct North Dial
8
4
Fig. 7.
7
A
5
6 E
W6
P
e
Æ
up
This prickt Draught of a Direct South Dial evidently
shews, how it and a Direct North Dial are related one
to y other viz that ý Direct North Dial takes ů
Upper Part.and ý Direct South Dial , takes up the .
Lower Part of ý Plane of the Prime vertical.
N
IN2
of a Direct North DIAL. 25
As to the Placing of a Direct Chap:
South or North Dial, it will be III.
more conveniently ſpoken of Chap. w
5
5.
T 2
сHAP.
Ý
T
:
( 26 )
.
.:
CH A P. IV.
Of an (*) Erect Direct Eaſt or Weſt
DI AL.
I
I.
СНАР.
Begin with a Direct Eaſt Dial,
IV. whoſe Plane repreſents the eaſt Side
m of the Plane of the Meridian. Now
to draw this Dial, there muſt be firſt
To draw a drawn an Horizontal Line, i. e. a Line
Eaft Dial. repreſenting the Horizon, or running
Parallel to it, and ſo level. One End
of this Line will repreſent the north
Point of the Horizon, and may there-
fore be fitly denoted by N; and the
other End by S, as repreſenting the
ſouth Point of the Horizon. See
Fig. 8.
2. Taking any Point C towards S, the
To find the ſouth End of the Line NS for a Cen-
Subſtyle.
ter, deſcribe an Arch toward N; and
upon
that Arch ſet off the Height P of
the Pole, and draw the Line CP for the
Subſtyle.
C) There alſo are frequently ftiled only Direet Eaſtor
Weſt Dials.
Having
Dial Plate
Place this facing pag. 26.
A DirectE aft Dial
4 5
6 7
8
6
10,
?"
>
Q
4
Fig. 8.
5
AL
6
7
$_1
---
IN
8.
9
20
27
A Direct weft Dial
8
7
6
4
3
2
62.60
Æ
8
Fig. 9
7.
P
6
S
1
t
INT
4
3
2
2
Of a Dire&t Eaft DIAL. 27
Having found the Subſtyle, draw Chap.
thereon the Contingent Line TG; and IV.
then proceed to draw an (*) Equinoctial i
Dial, taking any point X'in the Sub 3.
ſtyle for the Center of the ſaid Equi-To draw
noctial Dial. That Diameter of the Se- lines.
micircle (repreſenting half the Equinoc-
tial Circle) which runs Parallel to the
Contingent, is here the Meridian of the
Equator; from which you are to begin
to divide the Semicircle into Hours, or
into 6 equal Parts, each containing 15
Degrees. Through each of theſe Di-
viſions of the Equino&tial Semicircle
draw Lines from Æ to the Contingent ;
and again through each Point of the
Contingent, whereon the ſaid Lines
fall, draw other Lines (+) parallel to the
Subſtyle. Theſe laſt will be the Hour-
lines; that which falls in with the
Subſtyle C P being always the 6 a Clock
Line, thoſe above is the Hour-lines of
4
(*) There is no Mention made of drawing a Direct
Eat or Weſt Dial by Scales and Tables, becaule it is in
Effect done both Ways, by the Help of the Equinoctial
Dial.
(+) Becauſe the Axis of the World runs parallel to
the plane of the Meridian (as may be nown by the Di-
alling Sphere,) and fo muſt be conceived to cart its Shade
parallel alſo to its felf .
the
T 3
28 Of a Direct Eaſt DI AL.
CHAP.the Hours before 6, and thoſe below it
IV. the Hour-lines of the Hours after 6.
mWhere it is to be noted, that as 4 and 5
are the only Hours before 6, which need
be inſcribed on this Dial becauſe the
Sun never riſes to us till after 3 ; ſo the
Hours to be inſcribed on this Dial after
6, are no more than 7, 8, 9, 10, and
11; foraſmuch as this Dial-plane repre-
fencing the Plane of the Meridian, the
Sun ſhines not upon its Surface, but
upon its ſouth Side or Edge, at 12 a
Clock.
4.
The Hour-lines being drawn, the
To place Style is to be placed (*) parallel to the
she' style. Subſtyle CP, and ſo far diſtant from
ir, as the Center Æ of the Equinoctial
was taken diſtant from the Contingent.
And ſo the Dial is finished ; as Fig. 8.
5.
A Direet Weſt Dial differing from a
To draw Direct Eaſt Dial primarily in this alone,
Weft Dial,
that the former repreſents the weſt Side
:
Dircet
*) Becauſe the Style repreſents the Axis of the World,
which runs parallel to the Plane of the Meridian, Hence
Direct Eaſt and Weſt Dials have no Centers, through
which the Axis paffes, and from which confequently
are to be drawn all the Hour-lines, as in Horizontal and
Direct South and North Dials, which are therefore
called Central Dials.
of
..
Of a Dire&t Wef DIAL.
29
of the Plane of the Meridian, and the Chap °
latter the eaſt Side ; hence the drawing IV.
of a Direct Weſt Dial, is the ſame wich
that of a direct Eaſt Dial, excepting
only the different Denominations of the
Hours to be inſcribed on this Dial, viz.
I to 8 in the Afternoon; which muſt
be placed reſpectively from 6, (the
Hour-line whereof always falls in with
the Subſtyle,) as the Morning Hours are
in a Direct Eaſt Dial. See Fig. 9.
How theſe Dials, when drawn, are to
be placed, ſo as to have a due Situation
in reſpect of the Heavens, is ſhewn in
the following Chapter.
$
.
.is
T 4
С НАР.
Sale
3.
( 30 )
CHAP. V.
w
Of duly PLACING a Direct (Eaſt, or
Wet, North, or South,) Dial; and
of the Manner of finding, whether a
Wall bas a DIRECT or DECLINING
Position or SITUATION,
E
1
I.
CH AP.
VERY Dial-plane repreſenting the
V.
Plane of fome Circle in the Hea-
mvens, therefore, when any Dial is drawn,
that it may go true, it is requiſite that
A Dialis its Plane be ſo placed, as to anſwer ex-
ben duly
placed, actly to the Plane of the Celeſtial Cir-
when its cle, which it repreſents. Wherefore,
(wers to the if it be an Horizontal Dial, its Plane
Plane of muſt be placed Horizontally, or parallel
al Circle," to the Horizon, i. e. exactly level. If
which it it be any Vertical Dial, (as a direct
repreſents. North or South, Eaſt or Weſt Dial,)
sokereto the it muſt be placed Vertically, i.e. per-
mut blame pendicular to the Horizon, or exactly
placed pa. Upright. Now the Inſtrument repre-
rallel to its fented, Fig. 1o. will ſhew, when any
Celeſtial of the fore-mentioned Dials are thus
duly
Planas
un this facing Pag. 30
Dial. Plate 6
z.
A4
.
wym
Plummet to
:
.
An Hole
for the
play in.
Fig. 10.
hig
H
P
N
Pag. 33
M
M
AL
Fig. 11
C
B
A Plane, whose Meridian Zline M.L is to be found: C.de
notes ý Center or Place where | Ý Pin C P. is set up: C.S&Cs
denote y two shades of ý Pin. B. denotes y middle point of
the Arch S.B.S;
A
.
MS
Of Placing DIA L S.
31
duly placed. Namely, if, when the Chap.
Side HN of the ſaid Inſtrument be
ap-
V.
plied to the Horizontal Dial, the String w
falls exactly on the perpendicular Line
PP, then the Dial is placed Horizon-
tally, or truly Level ; otherwiſe it is
not, but muſt be altered, till the Spring
does exactly fall on the ſaid Perpendi-
cular. In like manner, if, when the
Side ZN or ZH be applied to a Verti-
cal Dial, the String exactly falls on the
Perpendicular PP, then the Dial is
placed Vertically, or truly Upright ;
otherwiſe it is not, but muſt be altered
till the String does ſo fall.
Again, an Horizontal Dial muſt be
placed not only Horizontally in
gene-
And 2dly,
ral, but alſo ſo, as that the four Car-nal Points
dinal Points of the Dial may reſpectively of the Di-
anſwer the like Cardinal Points of the
al-plane
muſtanſwer
Horizon. In like manner Vertical Di- to the Car-
als muſt be placed, not only in general
Points of
Vertically, but alſo fo, as that the its reſpec-
Plane of each Vertical Dial may be
tive Cele-
pa-
tial Plane.
rallel or anſwer to the Plane of that
Vertical Circle in the Heavens, which it
particularly has reſpect to. Thus the
Plane of a Direct South or North Dial
muſt be fo placed, as that it may be pa-
rallel
2.
The Cardi.
dinal
32
Of Placing DIAL s.
CHAP. rallel to the Plane of the Prime Verti
V. cal, which it repreſents, and that it may
W reſpectively anſwer to the ſouth or
north Side of the ſaid Plane of the
Prime Vertical. In like manner, the
Plane of a Direct Eaſt or Weſt Dial
muſt be ſo placed, as that it may be
parallel to, or fall in with the Plane of
The Meridian, which it repreſents; and
that it may reſpectively anſwer to the
eaſt or weſt side of the ſaid Meridian
Plane.
3. Now in Order thus to place aright
To find the any of the fore-mentioned Dials, it
is requiſite to find where the Meri-
any Plane dian croſſes the Place, on which you
would put the Dial. And this may
be done ſeveral Ways. The moſt
eaſy is by the Help of what is cal-
led) the Mariners Needle, ſuppoſing
it has none, or but little Variation in
the Place where you are. For then
the Meridian runs over, or parallel to
the Length of the ſaid Needle. Ano-
ther Way is by holding up a String,
when the Sun is in its Meridian Alti.
tude, (which is to be found by the
Quadrant,) for then the Shade of the
String will repreſent the Meridian Line
of
Line of
or Place
of Placing DIAL S.
33
:
of the place where you are. Another CHAP.
Way, ſomewhat longer, but much furer, V.
is this : Any Time in the Morning, m
when the Sun ſhines, erect any Pin or
ſtraight piece of Iron or Wood, and
mark where the End of its Shade falls.
See Fig. 11.
Then on the Point, where the Pin
was erected, as on a Center, draw a
Circle paſſing through the other Point,
where the End of the Pin's Shade fell.
After which erecting the Pin again
where it was, wait till the End of the
Pin's Shade touches the Circle in ſome
other Point. The Arch between the
two Points of the Circle, on which
the End of the Pin's Shade fell at the
two ſeveral Times, being biſected or
divided exadly in Half, a right Line
drawn from the Center of the ſaid Cir-
cle (i. e. from the point where the Pin
was erected ) through the Point of Bi-
ſection will be the Meridian Line of the
Place where you are.
The Meridian Line of the Place
4.
where you are, being thus found out to place a-
by one or more of the fore-mentioned right an
Ways, an Horizontal Dial is truly tal Dial.
placed,
..
34
Of Placing DIA L s.
Chap.placed, (ſo as that its Cardinal Points
V. Thall anſwer the like Points of the
wHorizon,) by placing the Meridian
Line (or which is the ſame, the 12
a Clock Line) of the ſaid Horizontal
Dial exactly upon, or parallel to the
Meridian Line of the place where
you
are. For the Meridian Line of the
Dial being thus placed upon, or paral-
lel to the Meridian Line of the Place,
the North and South Points of the Ho-
rizontal Dial, being no other than
the North and South Ends of the Me-
ridian Line of the Dial, will anſwer
to the North and South Points of the
Horizon of the Place, theſe directly
anſwering to the North and South
Ends of the Meridian Line of the Place.
And the North and South Points of
the Dial being thus placed fo, as to
anſwer to the ſaid Points of the Hori-
zon; the Eaſt and Weſt Points of the
Dial (if rightly drawn ) will likewiſe
anſwer to the Eaſt and Weſt Points of
the Horizon.
The Method of placing aright a
5.
to place Direct North or South, Eaſt or Weſt
aright * (as well as of an Horizontal) Dial
does likewiſe depend on the Meridi-
Direet
Eaſt or
Of Placing DIAL S.
35
an Line of the Place. For having CHAP.
found this by one or more of the V.
Ways above-mentioned, in order to
place aright a direct Eaſt or Weſt
Dial, all that is to be done, is only
this, viz. directly upon or parallel to the
ſaid Meridian Line of your Place, you
muſt erect the Dial with the Face of it
Eaſtward, if it be a direct Eaſt Dial;
or Weſtward, if it be a direct Weſt
Dial.
In order to place arighe a direct 6.
North or South Dial a little more is to place
aright a
to be done. Namely, having found Direct
the Meridian Line of your Place, you North
muſt draw another Line croſſing the Dial
former perpendicularly, which will
be the Prime Vertical Line of the
Place. Upon which therefore direct-
ly, or parallel to it, muſt be placed
the Dial with the Face of it ſouth-
ward, if it be a direct South Dial; or
northward, if it be a direct North
Dial.
Hitherto we have conſidered Dials,
7.
as drawn on Moveable
Moveable Planes, or of Un-
Planes not already Fixed.
ſuch as are uſually drawn Horizontal al-planes.
Dials. But Vertical Dials, (whether
Direct
South or
movable or
And on Fixed Din
36
Of Placing DIAL $.
n
:
To know
::
when a
Wallis
Direet
.
CHAP. Direct or Declining) are more uſu-
V.
ally drawn on Unmoveable or Fixed
Planes, hamely, on the sides of ſome
Wall. Wherefore in order to draw
a Vertical Dial on a Wall, it is re-
quiſite firſt to know, whether the
Wall be a direct Eaſt or Weſt, North
or South Wall, or a Declining Wall ;
and if the latter, how great its Decli-
nation is.
Now there are ſeveral Ways de-
8.
livered in Treatiſes of Dialling for to
do this; but ſuch as require, ei-
ther a peculiar Inſtrument called from
Eaſt or its Uſe a Declinatory, or elſe the
WA, North Sun's Azimuth to be taken, or both.
Wherefore I think the following Me
thod is to be preferred before any
ocher, on Account of its Eaſineſs,
and withal Exactneſs. To the Wall,
whoſe Situation you would know,
adjoin a Board ſo, as that one of its
Sides may touch the Wall, and the
Surface of the Board may lie Hori-
zontally, and faſt. Upon the Board
thus prepared find the Meridian by
the laſt of the three Ways above-
mentioned, and draw a Line on the
Board repreſenting the ſame, which
therefore
3
or South
..
}
.
:
'.:
..
:
Dual Plate z
M
- Direct South 85
IN
North
wall
W
$
A
Fig. 12
30
Place this facing Pag. 37.
09
90
LI
D / North wall deck.
A South wall decline
D A North wall decl. s Eastuurd 26 Degr
South Wall - $dech weſtw. 20 Degr
М.
W---
Eastward 20 Degr
weſtward 20 Degr: 18
E
W
SA
30
Fig. 15
c
Fig. 13
09
60
go
30
L
M
&
M
M
.
W-.
W-:
-E
Trg. 14
00
A North will declin
A North wall decl. Westw N ard 20 Degr.
D
A south wall declin. Iafts ward 20 Degr
.
n weſtw. 20 Degr
South wall declins Eaftw.20 Degr
A
Eig. 16.
30
30
60
90
H
H
Of Placing DIAL S.
37
:
,
therefore we call the Meridian Line. CHAP.
or runs parallel to your Wall, then mm
it is a direct Eaſt or Weſt Wall. If
not ſo, then lay a Quadrant flat upon
the faid Board, with one of its Sides
or Edges applied to the Wall, and
its Center at the ſame Time on the
Meridian Line. If the other Side
falls upon the Meridian Line drawn
on the Board, then the Wallis a
direct North and South Wall, i. e.
that Side of the Wall which is to-
ward the Sun and you, directly Faces
the South; and the other Side of it
conſequently Faces directly the North.
See Fig. 12.
But if when one side of the Qua- 9.
drant is applied to the Wall as afore, To know
the other Side does not fall upon the wall de-
Meridian Line on the Board, then it clines.
is a declining Wall. And if when
the right side or Edge of the Qua-
drant 'is applied to the Wall, the Mea
ridian Line of the Board is beyond,
or without the other Side of the Qua-
drant, then the Wall in reſpect of
its fouch Side declines Eaſtward, in
reſpect of its north Side Weſtward,
(as
.
.
38
Of Placing DIAĽ S.
CH A P. (as Fig. 14.) but if the Meridian
V.
Line of the Board be within the left
Side of the Quadrant, then the Wall
in reſpect of its fouth Side declines
Weſtward, in reſpect of its north
Side Eaſtward, as Fig. 13. On the
contrary, if the left side or Edge of
the Quadrant be applied to the Wall,
and the Meridian Line on the Board
be without the right side of the Qua-
drant, then the Declination of the
Wall in reſpect of its fouth Side is
Weſtward, in reſpect of its north Side
Eaſtward (as Fig. 15.): but if the
ſaid Meridian Line be within the
right Side of the Quadrant, then the
Declination of the Wall in reſpect
of its fouth Side is Eaſtward, and in
reſpect of its north Side Weſtward, as
Fig. 16.
Having thus found, whether the
To find the Wall declines Eaſtward or Weſtward,
Degrees of it remains to find, how great its .
Declination is. Now, as when, one
Side of the Quadranc being duly ap-
plied (as afore ) to the Wall, the o
ther Side falls exactly upon the Me-
ridian Line of the Board, the Wall
has no Declination; ſo when the
other
IO.
Declina-
tion.
..
ww
Of finding the Situation of Walls.
39
other Side of the Quadrant does not CHAP.
fall exactly upon the ſaid Meridian V.
Line, then the Number of Degrees con- w
tained in the Angle made by the faid
other Side of the Quadrant, and the
ſaid Meridian Line is the Meaſure of the
Declination. Wherefore as often as the
faid Meridian Line falls within the
Quadrant, the Number of Degrees in-
tercepted between the ſaid Meridian
Line, and that Side or Edge of the
Quadrant which is not applied to the
Wall, is the Meaſure of the Wall's De-
clination. But if the Meridian Line
falls without the Quadrant, then having
drawn on the Board a Circle, with a
Ray equal to that of the Quadrant, and
upon that Point of the Meridian Line
whereon you place the Center of the
Quadrant, as the Center of the ſaid
Circle, thereupon take with the Com-
paſſes the Diſtance between the Meria
dian, and that Edge of the Quadrant,
which is not applied to the Wall: The
ſaid Diſtance applied to the Diviſion
of the Quadrant into 90 Degrees, will
thereby ſhew the Meaſure of the Wall's
Declination.
U
All
40
Of finding the
CHAP. All that has been aforeſaid, is illur-
V. trated by (*) Fig. 12, 13, 14, 15, and
um 16. In each of which the Line ML
11. denotes the Meridian Line; the Line
illufra. EW denotes the Plane of the Prime
rion by Ex-
amples. Vertical, or ( which comes to the fame)
the Plane of a direct South Wall or
Dial; and conſequently E denotes the
true Eaſt Point, W the true Weſt
Point, ESW the South Side of the
Plane of the Prime Vertical, or a direct
South Wall; ENW the north Side
of the Plane of the Prime Vertical,
or a direct North Wall : the Line
DC denotes a declining Wall. Where-
fore it is evident, that in Fig. 12.
one Edge of the Quadrant being duly
applied to E W the Wall, on the ſouth
Side of it ES W, the other will fall
upon the Meridian Line, ML drawn
on the Board ; and thereby ſhew, that
the ſaid Wall EW has no Declina-
tion. But in Fig. 13. the right Edge
(*) From all theſe Figures it is evident, that the De-
clination of a Wall or Dial, is the Arch WD or EC of
the Horizon intercepted between the Plane of the Primc
Vertical, and of the Wall or Dial.
of
Declination of WALI S. 41
of the Quadrant being applied to DC CHAP
the declining Wall, and the Meridian V.
Line ML falling within the other mm
Side of the Quadrant, thereby is ſhewn,
that the Wall declines weſtward, and
alſo that the Meaſure of the Decli-
nation is 20 Degrees, this being the
Number of the Degrees intercepted
between the left side of the Quadrant,
and the Meridian Line ML. In Fig.
14. the right Edge of the Quadrant
being applied to DC the Wall, and
the Meridian Line M L falling with-
out the left Edge of the Quadrant, I
take with my Compaſſes, on a Circle
deſcribed as above directed, the Di-
ſtance between ML the Meridian
Line, and the left Edge of my Qua-
drant, and applying the ſame to the
Diviſion of the Quadrant into go De-
grees,
I find the Meaſure of the ſaid
Diſtance to be 20 Degrees ; which con-
fequently is the Meature of the Decli-
nation of the Wall DC eaſtward. And
after the ſame Manner, the fore-menci-
oned Method of finding the Declina-
tion of a Wall may be illuſtrated in
all ocher Reſpects.
:
U 2
Ha-
42 of finding the Declination, &c.
CHAP. Having thus ſhewn how to find
V. the Declination of a Wall, it re-
numains only to ſhew how to draw
a Dial upon a declining Plane or
Wall.
22
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A Dial declining West ward 20 Degrees
W
Dial. Plate 8.
C:
Fig. 17
D
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Place this
facing p. 43
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CH A P. VI.
Of drawing a DecLINING Dial.
T
m
I.
HE principal Difficulty in draw-CHAP.
ing a Declining Dial, is in find VI.
ing the Diſtance of the Subſtyle from
the Meridian or 12 a Clock Line, and
the Height of the Style above the Sub-The chief
ſtyle. Now to remove this Difficulty, in drawing
there is adjoined to the End of this a Decli-
Chapter, a Table ſhewing the faid Par-ning Dial.
ticulars, anſwerable to any Degree of
Declination, and which will ſerve for
moſt parts of England.
Having then drawn ( as in a Direct
South or Norch Dial) two Lines croſ-
Subſtyle
fing each other perpendicularly, one and Style
ZN repreſenting the Meridian, the of a Decli-
other E W repreſenting the Prime by Dialling
Vertical ; if you work by Dialling-
Tables, turn to the faid Table (viz.
Tab. III.) and ſee what is the Sub-
ſtyle's Diſtance from the Meridian
anſwerable to the Declination of
the
2.
To find the
U 3
44
Of Declining DIAL S.
CHAP. the Wall, which, ſuppoſing the De-
VI. clination 20 Degrees, will be 15 De-
grees, 5 Minutes. Then draw an Arch
from Z N to EW, on the Weſt Side
of ZN, if the Declination be eaſt-
ward; and on the eaſt Side, if the
Declination be weſtward. On the ſaid
Arch fer off from ZN the found Di-
ſtance of the Subſtyle, viz. at S in
Fig. 17. and 18. The Line CS,
drawn from C (the Interſection of
ZN and EW, and the Center of the
Dial) to S, will be the Subſtyle.
Then in the Table ſee what is the Style's
Height anſwerable to the Declination,
V. g. of 20 Degrees, and it is 35 De-
grees, 34 Minutes. Set this off from
Sto P, and draw the Line CP, which
will ſhew the Style.
3. Having found the Subſtyle and
To draw
the Style, draw (as afore in an
and direct South
Liges.
North Dial ) the Contingent Line
croſſing the Subſtyle at right An-
gles in any
in any Point Q: only the
Subſtyle CS being here different
from the Meridian ZN, mark the
Pointm of the Meridian where
it
14
the Hour- Horizontal,
Or
olen ser
2:
Pag. 44.
A Dial declining East ward 20 Degrees
W
E
Fig. 18
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Of Declining DI AL S.
45
of an
it is croffed by the Contingent. CHAP
Then taking ( as afore in the other VI.
Dials ) the Point Æ in the Sub-m
ſtyle fot the Center of an Equi-
noctial Dial, draw a (*) Semicir-
cle ; one Half of it being on one
Side of the Subſtyle, and the other
Half on the other Side. After which
draw the Line ÆM cutting the E-
quinoctial Semicircle
in M. The
Line ÆM will be the Meridian
of the Equinoctial Dial, from which
you are to begin to divide on each side
the Equinoctial Semicircle into Hours,
or ſix equal Parts. Lines drawn from
Æ through the ſaid Diviſions to the
Contingent will be the Equinoctial
(*) It is to be obſerved, that in Declining Dials the
entire Semicircle muſt be drawn; and it is not ſuffici-
ent to draw only one Half of the Semicircle as in Direct
South and North Dials, foraſmuch as the Meridian or 12
a Clock Line of the Equator, not falling in with the
Meridian or '12 a Clock Line of the Declining Dial, (as
it does in Direct North and South Dials,) hence the Di-
viſions on each side the 12 a Clock Line of the Equinoc-
tial, will not cut the Contingent at equal reſpective Di.
ſtances, as in Direct North and South Dials.
U 4
Hours
.
46
Of Declining DIAL S.
}
CHAP. Hours. And conſequently Lines drawn
VI. from C the Center of the declining
WDial
Dial to the fame Points of the Con-
tingent, whereon the Equino&tial Hour-
lines fall, will be the Hour-lines for
the declining Dial, ( as afore in an
Horizontal and Direct North or South
Dial,) and ſo the Dial will be finiſhed.
See Fig. 17 and 18.
And thus I have gone through
4.
The Core thoſe Elements of Dialling, which
cluſion. I judge moſt requiſite to be known
by Young Gentlemen, at leaſt at
their firſt Inſtitution in the ſaid Art
or Science. What follows, are ſuch
Dialling Tables as are requiſite to
this Treatiſe ; which though cal-
culated indeed for the Latitude of
Oxford, (viz. 51 Degrees, 45 Mi-
nutes, ) yet will ſerve without
any
ſenſible Difference for moſt Parts
of England. The Dialling Scales, or
rather the Way of drawing Dial-
ling Scales, viz. the Lines or Scales
of Latitude and of Hours, (both
mentioned and made uſe of in this
Treatiſe ) as alſo of Inclination of
Meridians,
:
Dial. Plate 9.
The Geometrical way of drawing Lines or Scales of Hours, L atitudes, Declination or Chords
Fig. 19
Place this facing pag. 47.
Scale,
127.7
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1171
20
A Scäir ar Line lof Latitudes.
/
larger Line or
=;
...........
+
30
or Scale
3
o
301
of Hours
40
50
/
60
170
go
*
of Hours
22
5
3
A Line oi Scale of Chords or of Declinati on
The Geom, way of drawing a Scale of Inclination of Meridians & Chords
10
Fig. 20.
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20
30
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Of Declining DIAL S.
47
Meridians, and of Declination (not CHAP
mentioned in this Treatiſe, but pur into VI.
all Dialling Scales) is repreſented Fig.
19. and 20.
.
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TAB.
.:
48
00
:
I 02
I
I
II.
2 14
2/ 18
3 2 1
3) 16.
TAB. I
T A B. II.
Shewing what Angle e-Shewing the like Angles
very Hour-line, (as al-
in a Direct South or
ſo Quarter, Half, and North Dial.
three Quarters of an
Hour) makes with the
Meridian or twelve a
Clock Line, in an Ho-
rizontal Dial.
Hours. Degrees. Minutes. Hours. Degrees. Minutes.
I 2 00 OO
I 2
00
57
02
19
2 02
54
21 04 40
3 08 . 52
31_07. 01.
II.
II
53
Il 09
25
I 14 55
II. 52
OL
23
10
16. 58
21 24
40
127 41
22
2 31. 04
21 25
24
3 34 33
9.
31 38
09 9.
31 31
I! 41 . 51
I 35 13
40
2 38 54
3 49
49. 36
31 42 49.
4 53
40
8
41 47 OO
Il 57. 53
Il 51 27
21 62.
II
2
13
3
37
61. 15
7. 5 71. 09 7. 5
5/ 66
.
Il 75. 38
1 72 :
II
80.
29.
·
00
31 85 14
3 83 58
6.
00.
6.
00.
T AB.
10
23
IO.
2 19
1
28
3 28
28. 30
46
245
8.
56.
66.
3) 61
36
2
21 77
6 go
:
1
49
TA B. III.
Shewing the Diſtance of the Subſtyle
from the Meridian, and the Height
of the Style above the Subſtyle, an
fwerable to the ſeveral Degrees of
Declination.
Decli- Subſtyle's
38
Dif-Style's Height a.
tance from the bove the Sub-
nation.
Meridian. style.
Degrees. Degrees . Minutes. Degrees. Minutes.
I
O. 47
14
2
I.
34
13
3
2 I
II
4 3
8
8
5 3 55
5
6
4 42
7 5
28
37: 55
8 6.
14 37 49
9 7
37 .
42
10
7.
37. 34
38
38
38
38
38
NO
48
Decli.
.
50
Declina-/Subſtyle's
48
36.
36
36
36
36.
15.
T A B. III.
Dir-Style's Height a-
tance from the bove the Sub-
tion.
Meridian. ſtyle.
Degrees. Degrees. Minutes. Degrees. Minutes.
II
8.
33 37 .
26
I2
9
18
37.
16
13 IO
2 37.
6
14
IO
55
15 II
32
43
16
I 2 . 15
31
17 I 2. 59
18
18
13
41
2
19 14 24
35.
50
20
5 35.
34
21 15 47 35. 19
22 16.
27 35.
2
23 17 7
34.
44
24 17.
47
34 26
25
15 34
8
26
19.
33. 49
27
41 33.
29
20 19 33.
8
29
20. 55 32 47
30 21. 31 32. 25
31
22. 6
32.
32 22 40 31 :
33 23 14 31. 17
34 23 47 30. 53
35 24. 19 30.
28
Decli.
18.
19.
28
tow
51
36
38
26.
TAB. III,
Subſtyle's Dif-'Style's Height a-
Decli-
tance from the bove the Sub-
nation. .
Meridian.
ſtyle.
Degrees. Degrees. Minutes. Degrees. Minutes.
24.
52 30. 3
37
25.
23
29.
36
25 53 29
39
26.
23
28
4.5
40
26.
52
28. 18
41 27
21 27. 51
42 27. 4.9 27. 23
43
28 16 26.
55
44
28
42
26
45 29.
8
25. 57
46 29 33 25 29
47 29
24.
58
30
22 24
49 30 45 23
. 8
23 27
51 31. 30 22 56
52 31. 51 22. 24
53 32 I 2 21.
52
54 32 32 21
55 32 51
48
56 33.
57 33. 28
19 42
58
33
19 9
59 34. 3
18
35
60
34.
18. 2
Declic
58
48
28
58
50
31
20.
20.
15
46
19
52
Declina. Subſtyle's
61
63
64
65
46
58
36.
36
I 2.
T A B. IIÍ.
Dif-|Style's Height a-
tance from the bove the Sub-
tion.
Meridian. ſtyle.
Degrees. Degrees.
Minutes. Degrees.
Minutes
34. 35 17 .
28
62
34. 50
16.
54
35 5
16. 19
35 19 15 45
35.
32 15. IO
66
35.
14
35
67
35
14.
68
10 13. 44
69
6.
21
49
70
32
I 2 13
71
42
72
51
II.
2
73 37. I
26
74 37 9 9. 34
75 37 17 9 13
-76 37. 25
8
37
77 37. 22
8
9
78
37 . 37
79 37. 44
6. 47
80
37. 50
6.
IO
37 54 5 4.1
82
37. 59 4 57
2
4
19
6
3 43
9 3 5
Declic
36.
36.
36
II.
38
10.
مأم
g
.
24
7:
81
83
38
84
85
38
38.
TAB. III.
Subſtyle's Dif-Style's Height a-
Decli.
tance from the bove the Sub-
Ination.
Meridian. ſtyle.
Degrees. Degrees.
Minutes. Degrees. Minutes.
86
II
2
29
87
13
I 52
88
14
I
89
14 O 37
90
15
38
38
38
38
38
A CATALOGUE of the ſeveral
Draughts of Dials, and other Cutts
belonging to this Treatiſe.
Fig 1.
AN
N Horizontal Dial drawn by
the Help of the Equinoctial
Dial.
2. An Horizontal Dial drawn by the
Help of dialling Scales.
3. An Horizontal Dial drawn hy the
Help of Dialling Tables.
4. A Direct Souch Dial drawn by the
Help of the Equinoctial Dial.
5. A
:
4
54
A CATALOGUE, &c.
5. A Direct South Dial drawn by
the Help of Scales.
6. A Direct South Dial drawn by the
Help of Tables.
7. A Direct North Dial.
8. A Direct Eaſt Dial.
9. A Direct Weſt Dial.
10. The Draught of an Inſtrument,
whereby to find, whether a Dial-plane
be truly Horizontal, or Erect.
11. The Draught of the moſt exa&t
Method for finding the Meridian of a
Place or Dial-plane.
12, 13, 14, 15, 16. Several Draughts
repreſenting the Method to find whether
a Wall be Director Declining; and if de-
clining, how many Degrees it bas of
Declination.
17. A Dial declining Weſtward 20
Degrees.
18. A Dial declining Eaſtward 20
Degrees.
19. The Geometrical Way of drawing
Lines, or Scales of Hours, of Latitudes,
and alſo of Declination, or (which comes
to the fame) of Chords.
20. The Geometrical Way of drawing
a Line or Scale of the Inclination of
Meridians.
F I N I S.
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