Centre. This Equation at a mean distance of the Moon from the Earth, is as the Sine of the Angle contain'd between the right Line D F, and a right Line drawn from the Point F to the Moon, nearly; and when greatest, amounts to 2′, 25″. Now the Angle comprehended be tween the right Line D F and a Line from the Point D, is found either by substracting the Angle E DE from the mean Anomaly of the Moon, or by adding the Moon's distance from the Sun to the distance of the Moon's Apogee from the Apogee of the Sun. And as Radius is to the Sine of the Angle thus found, so is 2′, 25″ to the second Equation of the Centre, which is to be added, if that Sine be less than a Semi-circle, and substracted if greater: Thus we have its Longitude in the very Syzygies of the Luminaries.
If a very accurate Computation be required, the Moon's Place thus found muſt be corrected by a second Variation. The first and principal Variation we have already consider'd, and have observ'd it to be greatest in the Octants. The second is greatest in the Quadrants, and arises from the different Action of the Sun on the Moon's Orbit, according to the different Position of the Moon's Apogee to the Sun, and is thus computed: As Radius is to the versed Sine of the distance of the Moon's Apogee from the Sun's Perigee, in consequentia so is a certain Angle P to a fourth Proportional. And as Radius is to the Sine of the Moon's distance from the Sun, so is the Sine of this fourth Proportional and another Angle Q to the second Variation, which is to be subtracted, if the Moon's Light be increasing; and added, if diminishing.
Thus we have the Moon's true Place in her Orbit; and by reduction of this Place to the Ecliptic, the Moon's Longitude. The Angles P and Q are to be determined by observation: in the mean time, if for P be assumed 2′, and for Q 1′, we shall be near the truth.
Nature of the Moon.
1. From the various Phases of the Moon: From her only shewing a little part illumined, when following the Sun ready to ser: From that Part's increasing as she re- ceeds from the Sun, till at the distance of 80° she shines with a full Face and again wains as she re-approaches that Luminary, and loses all er Light when she meets him : From the lucid Part's being constantly turn'd towards the West, while the Moon increases; and towards the East when she decreases; it is evident, that only that part shines on which the Sun's Rays fall: And from the Phænomena of Eclipses, happening when the Moon should shine with a full face, viz. when she is 180° distant from the Sun; and the darkned Parts appearing the fame in all Places, it is evident fhe has no Light of her own, but borrows whatever Light she has from the Sun. See PHASES, ECLIPSE, and SUN.
2. The Moon sometimes disappears in the clear Heaven, so as not to be discoverable by the best Glasses; little Stars of the fifth and sixth Magnitude all the time remaining visible. This Phænomenon Kepler observed twice Anno 1580, and 1583; and Hevelins in 1620. Riccioli, and other Jesuits at Bononia, and many People throughout Holland observed the like April 14, 1642. yet at Venice and Vienna she was all the time conspicuous. December 23, 1703, there was another total Obscuration: At Arles she first appear'd of a yellowish brown; at Avignon ruddy and transparent, as if the Sun had shone through at Marseilles, one part was reddish, the other very dusky; and, at length, tho' in a clear Sky, wholly disappear'd. Here it is evident, that the Colours appearing different at the same time, do not belong to the Moon; that they are occasion'd by an Atmosphere around her variously disposed in this and that Place, for refracting of these or those coloured Rays.
3. The Eye, either naked, or arm'd with a Telescope, sees some parts in the Moon's Face darker than others, which are call'd Maculæ, or Spots. Through the Telescope, while the Moon is either increasing or decreasing, the illumined parts in the Macula appear evenly terminated; but in the bright Parts, the Bound of the Light appears jagged and uneven, composed of dissimilar Arches, convex and concave. (see Tab. ASTRONOMY, Fig. 18.) There are also observed lucid Parts dispersed among the darker; and illumined Parts seen beyond the limits of Illumination; other intermediate ones remaining still in darkness; and near the Macula, and even in 'em, are frequently seen such lucid Specks. Beside the Maculæ observed by the Antients, there are other variable ones invisible by the naked Eye, call'd New Maculæ, always opposite to the Sun; and which are hence found among those parts which are the soonest illumined in the increasing Moon, and in the decreasing Moon lose their Light later than the intermediate ones; running round, and appearing sometimes larger, sometimes smaller.
Hence, (1.) As all parts are equally illumined by the Sun, in as much as they are equally distant from him: if some appear brighter, and others darker; some reflect the Sun's Rays more copiously than others; and therefore they are heterogeoeous. And, (2.) Since the Boundary of the illumined Part is very smooth and equable in the Maculæ, their Surface must be so too. (3.) The parts illumined by the Sun sooner, and deserted later than others that are nearer, are higher than the rest, i. e. stand up above the other Surface of the Moon. (4) The New Maculæ answer perfectly to the Shadows of terrestrial Bodies.
4. Hevelius writes, that he has several times found, in Skies perfectly clear, when even Stars of the 6th and 7th Magnitude were conspicuous, at the same Altitude of the Moon, and the same Elongation from the Earth, and with one and the same excellent Telescope; that the Moon and its Macule do not appear equally lucid, clear, and perspicuous, at all times; but are much brighter, purer, and more distinct at one time than another. From the Circumstances of the Observation, 'tis evident, the reason of the Phænomenon is not either in our Air, in the Tube, in the Moon, nor in the Spectator's Eye; but must be look'd for in something existing about the Moon.
5. Cassini frequently observ'd Saturn, Jupiter, and the fix'd Stars, when hid by the Moon, near her Limb, whether the illumined or dark one, to have their circular Figure changed into an oval one; and in other Occultations found no alteration of Figure at all. In like manner, the Sun and Moon rising and setting in a vaporous Horizon, do not appear Circular, but Elliptic. Hence, as we know, by sure Experience, that the Circular Figure of the Sun and Moon is only changed into an Elliptic one by means of the Refraction in the vapoury Atmospherer; 'tis pretty apparent, chat at the time when the circular Figure of the Stars is thus changed by the Moon, there is a dense Matter incompassing the Moon, where- in the Rays emitted from the Stars are refracted; and that at other times, when there was no change of Figure, this Marter was wanting.
This Phænomenon is well illustrated by the following Experiment: To the inner bottom of any Vessel, either Plane, Convex, or Concave, with Wax fasten a Circle of Paper; then pouring in Water, that the Rays reflected from the Circle into the Air may be refracted before they reach the Eye; viewing the Circle obliquely, the circular Figure will appear changed into an Elliplis.
6. The Moon is a dense opake Body, beset with Mountains, Valleys, and Seas. That the Moon is dense, and impervious to the Light, has been shewn but some parts sink below, and others rise above the Surface; and that considerably, in as much as they are visible at so great a distance of the Earth from the Sun: in the Moon therefore are huge Mountains, and very deep Valleys. Ricciolus measured the height of one of the Mountains, call'd St. Catherine, and found it nine Miles high. Again, in the Moon are spacious Tracts, having smooth even Surfaces, and those reflecting less Light than the rest: Hence, as the Surface of fluid Bodies is naturally even, and as when transparent, they transmit a great part of the Rays of Light, and reflect very little; the Lunar Spots are fluid, transparent Bodies: and as they continue constantly the fame, are Seas. In the Moon, therefore, are Mountains, Valleys, and Seas.— Hence again, the lucid parts of the Spots are Islands and Peninsula's.
And since in the Maculæ, and near their Limbs, are seen some parts higher than others, in the Lunar Seas are Rocks and Promontories.
And since the new Spots are contiguous to the Mountains, and in all respects like the Shadows of Bodies on our Earth; no doubt they are the Shadows of the Lunar Mountains: Whence also appears the Matter of the Moon is opake.
Note, This Reasoning will be put past doubt by viewing the sensible Horizon from some Eminence : Where it passes over a Plain, the Line will appear smooth and even; where a-cross Mountains and Valleys, irregular and winding; smooth, but dark, &c.
7. The Moon is incompass'd with an heavy and elastic Atmosphere, wherein Vapours and other Exhalations arise, and whence they return in form of Dew and Rain.
In a total Eclipse of the Sun, we find the Moon incircled with a lucid Ring parallel to her Periphery.
Of this, we have too many Observations to doubt: In the great Eclipse of 1713, the Ring was very conspicuous at London, and elsewhere. Kepler observes the same of an Eclipse in 1605, at Naples and Antwerp; and Wolfins of another in 1606 at Leipsic, described at large in the Acta Eruditorum, with this notable Circumstance, that the part next the Moon was visibly brighter, than that furthest from it; which is confirmed by the Observations of the French Astronomers in the Memoires de l'Academie, &c. 1706. Hence about the Moon is some Fluid, which corresponds to her Figure, and which both reflects and refracts the Sun's Rays. And hence also, this Fluid is denser below,near
