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Chambers, Ephraim, 1680 (ca.)-1740 / Cyclopædia, or, An universal dictionary of arts and sciences : containing the definitions of the terms, and accounts of the things signify'd thereby, in the several arts, both liberal and mechanical, and the several sciences, human and divine : the figures, kinds, properties, productions, preparations, and uses, of things natural and artificial : the rise, progress, and state of things ecclesiastical, civil, military, and commercial : with the several systems, sects, opinions, &c : among philosophers, divines, mathematicians, physicians, antiquaries, criticks, &c : the whole intended as a course of antient and modern learning

Miserere - Moon,   pp. 560-579 PDF (18.6 MB)

Page 577

6. Nor is the Apogee of the Moon without an Irregularity;
being found to move forwards, when it coincides with the
Line of Syzygies, and backwards, when it cuts the Line
at right Angles. See APOG EE: Nor is this Progrefs and
'Regrefs in any meafure equal: in the ConjunaiZ, or Op-
pofition, it goes briskly forwards; and in the Quadratures,
moves either flowly forwards, flands ftill, or goes back-
ward. See SYZYGIES.
7. The Motion of the Nodes is not uniform; but when
the Line of the Nodes coincides with that of the Syzygies,
they fhand fiill; when the Nodes are in the Quadratures,
i. e. when their Line cuts that o- the Syzygies at right An
gles, they go backwards, from Eart to Well; and this,
Sir J.Newion {hews, with the Velocity of 16", i)"', 24"",
in an Hour. See NODE.
The only equable Motion the Moon has, is that where-
with Ihe turns round her Axis exaffly in the fame fpace of
Time, in which fhe revolves round us in her Orbit; whence
it happens, that lhe always turns the fame Face towards
For, as the Moon's Motion round its Axis is equal, and
yet its Motion or Velocity in its Orbit is unequal; it fol-
lows, that when the Moon is in its Perigee, where it moves
fwiftefr in its Orbit, that part of its Surface, which, on ac-
count of its Motion in the Orbit, would be turn'd from the
Earth, is not fo, entirely; by reafon of its Motion round
its Axis : Thus, forne Parts in the Limb, or Margin of
the Moon, fometimes recede from the Center of the Disk,
and fometimes approach towards it, and fome Parts, that
were before invifible, become confpicuous: which is call'd
the Moon's Libration.
Yet this Equability cf Rotation occafions an apparent
Irregularity; for the Axis of the Moon, not being perpen-
dicular to the Plane of its Orbit, but a little inclined to it:
and this Axis maintaining its Parallelifm, in its Motion
round the Earth ; it mufi neceffarily change its Situation,
in refpedl of an Obferver on the Earth; to whom, fome-
times the one, and fometimes the other Pole of the Moon,
becomes vifible. Whence it appears to have a kind of
Libration. See LIBRATION and Axis.
Pbyfical Laws of the MooN's Motion.
Thus much for the Lunar Phbnomena: It remains that
we affign the Phy/ical Cabfe thereof. The Mcon, we have
obferved, moves round the Earth, by the fame Laws, and
in the fame Manner, as the Earth round the Sun and o-
ther Planets. The Solution therefore of the Lunar Mo-
tion, in gent'ral, comes under thofe of the Earth, and other
Planets. See PLANET and EARTH.
As for the particular Irregularities in the Moon's Motion,
to which the Earth, and other Planets, are not fubject,
they arife from the Sun, which acis on, and difturbs her
in her ordinary Progrefs thro her Orbit.; and are all me-
chanically deducible from the famne great Law, whereby
her general Motion is direded, viz. the Law of Graviration
or 4ttraffion. See GRAVITATION.
Other fecondary Planets, v., the Satellites of lupiter
and Saturn, are doubtlefs fubjec& to the like Irregularities
with the Moon; as being expofed to the fame perturbating
or diflurbing Force of the Sun; but their Difiance fecures
them from our Obfervation. See SATrELLITE and Di-
The Laws of the feveral Irregularities in the Syzygies)
Quadratures, Uec. fee under SYZYGIES, QUADRATURES,
The fronomy of the MOON.
i. To determine the Period of the Moon's Revolution
round the Earth, or the Periodical Monrbh; and the Time
between one Oppofit ion and another, or theSynodical Montb:
fince, in the middle- of a Lunar Eclipfe, the. Moon is
oppofite to the Sun:   (See ECLIPSE.) Compute the
time between two Eclipfes, or Oppofitions ; and divide
this, by the number of Lunations, that have pafled in the
mean time: the Quotient will be the Quantity of the Sy-
nodical Month.-Compute the Sun's mean Motion du-
ring the time of the Synodical Month, and add this to the
entire Circle defcribed by the Moon: Then, as the Sum
is to 36oQ, fo is the Quantity of the Synodical Month
to the Periodical.
Thus, Co ernicus in the Year i 5c0, Noveml-er 6. at i2 at
Night, ob ferved an Eclipfe of the Moon at Rome; and At-
gufi 1, 1553, at 4h. a5', another at Cracow: hence, the
Quantity of the Synodical Month is thus determined;
Obf.t A. 5 23d. 237h. 4.25'
Obf.   A. i5ood. 31oh.'
Interval of Time A     zkzd. 191 h. 1.5.
And the        Days            S
Exa& Interval  A. 2ad. 297h. 1.5'
QLr 't99liC5c
77)                  Moo
Which divided by 8a2 Months elapfed, in the mean time,
gives the Quantity of the Synodical Month 42521', 9", 9"'
that is, 29 days, i! hours, 41 minutes.
From  two other Obfervations of Eclipfes, the one at
Cracowu, the other at Babylon, the fame Author determines
more accurately the Quantity of the Synodical Month to
be                     425241- 3'. 10"'. 9''
That is z9 d. i r h.
The Sun's Motion in the time 29. 6. 24 13
The Moon's Motion        389. 6. 24.18
Quantity of the Periodical Month 2I d. 7 h. 43  5.
hence, x. The Quantity of the Periodical Month being
given; by the Rule of Three we may find the Moon's di-
urnal and hourly Motion, Wc. And thus may Tables of
the mean Motion of the Moon he confirucled. See TA-
BLES; fee alfo DiURNAL and HORARY.
2. If the Sun's mean diurnal Motion be fubfilraaed from
the Moon's mean diurnal Motion 3 the Remainder will give
the Moon's diurnal Motion from the Sun: and thus may a
Table of Latitudes be conflruaed, fuch as thofe of ulflial-
3. Since in the middle of a total Eclipfe, the Moon is in
the Node; if the Sun's Place be found for that time, and
to this be added fix Signs, the Sum will give the Place pf
tbh Node. See NODE.
4. From comparing the antient Obfervations with the
modern, it appears that the Nodes have a Motion, and
that they proceed in Antecedentia, i. e. from Taurus to Iriesi
from A, ies to Fifces, Tic. If then to the Moon's mean di-
urnal Motion, be added the diurnal Motion of the Nodes;
the fame will be the Motion of the Latitude; and thence,
by the Rule of Three, may be found in what titne the
Moon goes 36of from the Dragon's Head, or in what time
She goes from, and returns to it: That is the Quantity of
the Dracontic Month.
5. If the Motion of the diurnal Apogee be fubflraaed
from the mean Motion of the Moon, the Remainder will
be the Moon's mean Motion from the Apogee: and thence,
by the Rule of Three, is determin'd the Quantity of the
lnomaliJlic Montb.
According to the Obfervations of Kepler, the mean Sy-
nodical Month is a9d. sz h. 44% 3,'. a2'. Her Periodical
Month 27d.- 7 h. 43'. 8". The Place of the Apogee for
the Year 1700, Yanuary r. Old Stile, was I I S. 8'. 5 7' ! /'-
The Plane of the Nodes 4 S. 2 7 Q. 39'. 17 ". Mean diurnal
Motion of the Moon 13g. IO'. 35". Diurnal Motion of the
Apogee 6'. 41". Diurnal Motion of the Nodes 3'. it".
Lailly, the Eccentricity 4362 Parts, fuch, whereof the
Diameter of the Eccentrice is 1o000: and therefore the
diurnal Motion of the Latitude is 130. 13'. 46"1i 'and the
diurnal Motion from the Apogee I3'. 3'. 54".
Theory of the LUNAR Motions and Irregularities.
The Tables of Equation, which ferve to folve the Irre-
gularities of the Sun, do likewife ferve for thofe of the
But then thefe Equations mufl be correcfed for the
Moon; otherwife they will not exhibit the true Motions in
the Syzygies. The Method is thus: Suppofe the Moon's
Place in the Zodiac, required in Longitude, for any given
time; here, we firft find, in the Tables, the place where
it would be, fuppofing its Motion uniform, which we call
mean, and which is Sometimes fafler, and fometimes flower
than the true Motion: then, to find where the true Motion
will place her, which is alfo the apparent, we are to find
in another Table at what Diflance it is from its Apogee ;
for, according to this Diflance, the Difference between her'
true and mean Motion, and the two Places which correfpond
thereto, is the greater. The true Place thus found, is not
yet the true Place; but varies from it, as the Moon is more,
or lefs remote both from the Sun, and the Sun's Apogee:
which Variation refpeaing, at the fame time, thofe twq
different Diflances, they are to be both confidered and
combined together, as in a Table apart. Which Table
gives the Correction tod be made of the true Places firft
found: That Place thus correaed, is not yet the true
Place, unlefs the Moon be either in Conjunaion, or Oppo-
fition: If She be out of thefe, there muft be another
Correalion, which depends on two, things taken together,
and compared, viz. the Diflance of the Moon's correcied
Place from the Sun; and of that at which Ihe is with re-
gard to her own Apogee;i this lail Diflance having been.
changed by the firI Correc~ion.
By all thefe Operations and Correclions, we at length
arrive at the Moon's true Place for that inflant. In this it
muff be owned, occur prodigious difficulties: The Lurar
Inequalities are fo many, that it was in vain the Aro-
nomers laboured to bring 'em under any Rule, before thel
Great Sir If. Newton ; to whom we are indebted both for
ihe mechanical Caufes of thefe Inequalities, and for the
Method of computing and afcertaining them: So that he
7         'at

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