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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

(1728)

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

Page 577

Moo 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 us. 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- STURBING Force. The Laws of the feveral Irregularities in the Syzygies) Quadratures, Uec. fee under SYZYGIES, QUADRATURES, bc. 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. z.ao' 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- dus. See LATITUDES. 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 Moon. See EQUATION. 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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