Of the Phænomena of the Planets

Thus the Moon at N is enlighten’d by the Sun, and reflects to us the solar Beams in the Direction of LO from the Surface LMI, and tho’ her Globe scarcely bears any Proportion to that of the Sun in Bulk, yet being so very far remote from him, the shadowy Part is almost equal to the lucid one. Consequently the light Side being always towards the Sun, and turn’d from us as at Q, the dark Part must very near if not quite obscure it, and her Globe, to the earth at Z, in that Position be invisible; but as the dark Part of the Moon is always something less than the refulgent Part, there will even be in this Position, a bright silver Verge round the Moon, like an illuminated Atmosphere. But as this can never be seen, but in the exact Syzygia with the Sun, we must never expect to be Eye-witness of it, but in very total Eclipses of the Sun, such as of the Year 1715, at which Time such a Phænomena did appear, and was by many attributed to the Rays of Light in the Moon’s Atmosphere. But notwithstanding this might have been occasioned some small Resemblance of this lucid Ring, yet we have stronger Reasons to induce us to believe she has no such Thing as an Atmosphere.

At Y the Moon still keeping her light Side q, t, r, towards the Sun, part of her dark Side qs will be turn’d away from the Earth; in this Case, a similar Part of her Light tr will be seen, and she will appear horn’d; and increasing with her back towards the West, at X one half will appear enlighten’d, but as being only one Quarter of her Globe, it is called the first Quarter of the Moon; at W she will appear gibbose; the Part ac being only wanting now to make her imperfect Disk edb complete to e.

At U the dark Side is quite removed from an Eye at the Earth, and the same Side appears to the Earth, as is seen from the Sun; in this Position the Moon is always full-faced with Light, and continues so in absolute Plenilunam for some time, at least an Hour, but the exact mean Duration of the Moon’s full-face is 1^h. 3^m. 5^2ds. the light Hemisphere being more than half her Globe; at V she shews the same Face as at W, but is here decreasing on the opposite Side of her Body; hg is equal to ae and similar to fi.

At T she is again bisected as at X, and this is called the last Quarter; at R she shews the same Quantity of Light as at Y, cut off by the Angle of Appearance mznqs, being here equal to ci, and also equal to mp, her Back as here declining is always to the East.

How to project the Quantity of Light at any Time, and represent the Moon’s general Phases. See the Figure at M, where BE shews the Limits of Light, as received from the Sun; AB the Portion cut off from the Earth by the Line AC; ABDH the Field of Light, and GA and ED the first and last extream Rays reflected to the Earth.

Now as a Circle view’d obliquely, has always the Appearance of an Ellipse, the Moon’s Light will always be form’d by joining the two Curves in opposite Points, according to the Obliquity of the Plain, dividing the Hemisphere of Light and Shade to that of the Disk, as HDI to HAI, or HCI, in I and H. DC, &c. being always as the Sine Complement of the Moon’s Distance from the Sun.

As the Moon is perpetually changing and producing new Phases to the Earth, so in like Manner all the inferior Planets perform the same Diversity of Appearance to the superior Planets.

Thus Mercury and Venus are ever changing their Faces to the Earth, the Earth to Mars, &c.

But the Planets to one another, do not only change their Phases, but also vary very sensibly their apparent Magnitudes, for Venus appears much the largest to the Earth, when she affords it the least Light, as is plain from her apparent Disk at O, P and Q; and Mercury the same. Since therefore it appears, that we are deprived of much by the greatest Share of their respective Light, the most useful Thing to us, it is a strong Argument that they were not made for our Use alone, at least in this Respect, and may vary possibly be inhabited Worlds themselves.

Mercury at A, to the Earth at B, appears horn’d, and at the same Time to Mars at H, he would appear as the Change; at N he would appear gibbose; and M to E with a full Face. Venus at B to the Earth at E would also appear gibbose; and at F, to Mars in I, she would seem bisected, but at the same Time to the Earth gibbose; at D Venus would appear like a half Moon to the Earth at E, but Mercury at M gibbose. The superior Planets never appear to the inferior ones horn’d or bisected; but the most neighbouring Ones, sometimes, when near their Quadratures, appear gibbose, as Mars at C, will show to the Earth at E, and the Earth in C to Mercury and Venus at D and M.

The Quantity of Light at G cut off from the Eye at E, is ns, but to the Eye at C it is oy, z being common to both, and jx, ow their Supplements. At A, gh form all the Light to E, ig being the visible Hemisphere, and k the obscure one.

At B, cdb is all the apparent Light to E, aec being dark, and its similar Part invisible; at C, mosu cut off the Light to D, and qop what is seen from M.

A total Eclipse of the Sun, is when all the Sun’s Body is obscured by the Moon, as at B; and a total Eclipse of the Moon, is when all the Moon’s Body is enveloped in the Earth’s Shadow; as at BCD and L, of which there are two kinds, viz. Total with Continuance, as through ABCDE, and KLMN; and total without Continuance in the Direction of HBG.

A partial Eclipse of the Sun or Moon; is when the Whole cannot be obscur’d, such as I, F and M, in the Positions HK, HE, and GH; and F and D of AG and EC.

A central Eclipse of the Moon, is when the Moon passes thro’ the Center of Earth’s Shadow as at C, and a central Eclipse of the Sun, is when the Centers of the Sun and Moon are perfectly conjoin’d in absolute Syzygia as at B, of which there ar two Kinds, viz. first, central and total with or without Continuance; and secondly, central, not total, called Annual, at which Time all the Moon’s Body appears upon the Sun’s Disk, and encompass’d with a Ring of Light, and at R to the Earth at L, and in this Case the Moon’s Shadow does not reach the Earth.

But the Moon being less than the Earth, and the Sun greater, her Shadow can never cover the whole Globe, only a Part of it, and total Darkness is but to those Inhabitants, on whom the Shadow falls. The circumjacent Places will be illustrated with some of the Sun Beams, call’d the Penumbra, or a lucid partial Shadow, as EO, which will have different Degrees of Illumination, according to the Distance from the Center or Surface of the real one. Without this Penumbra all the Sun’s Disk will be seen at the same Time, and no Eclipse perceived at all.

Let S represent the Sun; E the Earth; I the Moon, and C her Shadow; draw the Line aKN and buD, and then KDN will be the penumbral Cone. Now it is plain, while the Moon is in the Line SIE, there will be atotal Eclipse to the Earth at L; but without the Points D and N there will be not Eclipse at all. But if the Moon were either at F or H, (which here may represent the Beginning and End of an Eclipse in I) the Sun might be totally eclipsed to N or D, but in both which Positions to the Earth at L, the Sun would be free from Obscuration.

Hence the Radius of the Penumbra, is always equal to the Sum of the Semidiameters of the Sun and Moon, and is represented at T. And if no Part of this Penumbra falls upon the Earth’s apparent Disk of the Moon’s Orbit, as R, which si found by substracting the Sun’s horizontal Parallax ZWS, from the Moon’s horizontal Parallax gwR, there can be no Eclipse in that Part of the Moon’s Orbit.

But if the Sum of the Semidiameters of the Disk and Penumbra, be greater than the Moon’s true Latitude; then an Eclipse to some Part of the World must unavoidably happen. And if the Moon’s Latitude be less than the Semidiameter of the Disk, the Eclipse will be central, and may be total.

In like Manner from the Moon’s Diameter, Latitude and Radius of the Earth’s Shadow in the Moon’s Orbit, (which is found from substracting the Semi-Angle of the Cone kXi out of the Moon’s horizontal Parallax kXM) we determine when an Eclipse of the Moon will happen.

For if at any Time the Sum of the Semidiameters of the Moon and Shadow exceeds the Moon’s true Latitude, as at M, that full Moon will be eclipsed. And if their Difference be more than the said Latitude, it will be total.

But the Moon, altho’ deprived of the direct solar Beams, is not absolutely hid from us at the same Time, because the Rays of Light passing thro’ our Atmosphere are refracted, and thrown obliquely into the real Shadow, as from w to ☾, and thereby faintly illuminates the whole Cone.

A Transit is the apparent Passage of an inferior Planet over the Sun’s, or any superior Planet’s Disk.

Let A represent the Earth, B the Sun, and FL and MG respectively, the Orbits of Mercury and Venus; then to an Observer upon the Earth at H, I will be a Transit of Mercury, and K a like visible Conjunction of Venus in her Passage over the Sun; and such will always happen in every Conjunction, when the Planet’s Latitude is less than the Sun’s Semidiameter.

The Position of the Line of Direction over the Disk, with respect to the Horizon, depends upon the Planet’s Altitude and Distance from the Nonagesimal Degree, and may be either as RTXV, WTS, or ZXS, &c.

An Occultation, is the disappearing of any Planet or Star when conjoin’d with the Moon, in a Space opposite to the Eye, such as E and C; the Moon passing betwixt us and it, as at D seems to cover it; by which Means it becomes invisible to us, and remains hid from our Sight all the Time the Moon is passing thro’ the Spaces E or C.

N and P represent each Immersion, and Q and O the Emersions. The various Positions of these Appulses is shewn by the Immersions f, b, h, and a, and their respective Emersions e, d, c, &c.

Occultations happen to almost all the Stars in the Zodiac, that are within the Limits of the Moon’s Orbit, in every Revolution of the Moon’s Node, and always at such a Time, when their Latitude from the Orbit is less than the Moon’s Semidiameter. Which how to calculate, as also Transits. See the Doctrine of Eclipses abovementioned.