gulated by a certain, unchangeable_and_conftant Lecture Law, which none of them tranfgrefs; for every XVI. Planet moves in the Perimeter of his own Ellipfe, fo that the Line or Ray paffing from its Center to the Center of the Sun, does always defcribe or fweep an Elliptick Space or Area proportional to the Time; or, which is the fame Thing, in equal Time it sweeps an equal Area. Hence the Planets must move more flowly in their Aphelia, and quicker in their Perihelia: And thefe Aphelia are not like the Apogeon of the Moon; but they are either at Reft without Motion, or, if they have any, it is fo flow, that it is not easily perceived in the Time of a Man's Age. And here it is to be obferved, that of all the Planets, Mercury has the moft Excentrick Orbit; for therein the Excentricity is to the mean Distance as 2051 to 10000.

Of the Motions of the three fuperior Planets, Mars, Jupiter and Saturn, and the Appearances arifing from them.

W

Sun.

E have now dwelt long enough on Thefe fuperithe Explications of the Motions of or Planets. may have the two inferior Planets; let us next any Pofition contemplate the Superiors. For or Aspect in which Purpose let ABCT be the respect of the Orbit of the Earth, and let Saturn, Plate XIV. Jupiter and Mars, turn round the Fig. 1. Sun in different Orbits at their proper Distances, and perform their Circulations, each in its proper Period; and let P QV be a Portion of the Zodiack in which thefe Planets are obferved to perform

their

Lecture their Motions: Firft, It is plain that all these Planets, XVI. feen from the Sun, may be observed either in Conjunction with the Earth, or in Oppofition to it. Thus Saturn may be in h, when the Earth is in M, in the Line which joins the Centers of the Sun and Saturn; in which Cafe the Earth and Saturn from the Sun are seen in Conjunction: But the Earth may likewife be in the fame Right Line produced the contrary Way, as in B, where from the Sun these two Planets will be seen in Oppofition to each other. But in this Situation, the Sun feen from the Earth, will appear to be in Conjunction with Saturn. Secondly, It is evident, that these Planets, seen from the Earth, may have any Afpect, or obtain any Pofition in respect to the Sun, and may have any defired Elongation from him; which cannot be in the inferior Planets, who are always confined to the Neighbourhood of the Sun. For from the Earth T, there may be drawn a Line T P, which will cut all the Orbits of the fuperior Planets, and may make, with TS the Line which joins the Sun and Earth, any Angle required, as STP. And therefore, when the Earth is in T, Saturn may be in F, whofe Elongation from the Sun will then be the Angle STF. Moreover, when the Earth and any fuperior Planet are feen from the Sun in Conjunction together, that Planet, obferved from the Earth, will appear in Oppofition to the Sun; and an Inhabitant of our terraqueous Globe will fee the Sun and it, in oppofite Parts of the Heavens.

Conjuncti

LET now any fuperior Planet, as for Example, Saturn, be feen from the Sun in Conjunction with The Times the Earth: After Conjunction the Earth having a between two quicker angular Motion than Saturn, an Inhabions, or two tant or Spectator in the Sun will fee the Earth Oppofitions, daily to recede more and more from Saturn. And in the fuperi- becaufe the Earth, according to its mean Motion, ar Planets. does every Day defcribe an Arch of the Ecliptick

of 59 Minutes 8 Seconds, and Saturn moves only 2 Minutes in a Day, the Earth will appear from the Sun, to recede every Day from Saturn the Space

of

of an Arch of 57 Minutes 8 Seconds. If we fay Lecture then, As 57 Minutes 8 Seconds is to 360 Degrees, XVI. or to 21600 Minutes, fo is one Day to a fourth Quantity; we fhall have the Number of Days in which the Earth will be again obferved from the Sun, to be in Conjunction with Saturn, which is 378 Days. But when the Earth and Saturn are feen from the Sun in Conjunction, the Sun and Saturn from the Earth appear in Oppofition. And therefore the Time between two Oppofitions of the Sun and Saturn, immediately following one another, computed according to their middle Motions, is 378 Days, or 1 Year and 13 Days. And there is the fame Time between two Conjunctions of Saturn and the Sun feen from the Earth, or between any two fimilar Afpects or Elongations from the Sun. And the Time between the Oppofition and Conjunction of Saturn with the Sun, is the half of this Time, or 189 Days.

By the fame Method we fhall find, that the Time between two Conjunctions or Oppofitions of Jupiter and the Sun confifts of 398 Days, or a Year and 33 Days. But Mars, after an Oppofition, does not again come into the fame Situation, till after two Years and 50 Days.

WHEN the Planets are in Oppofition to the Sun, they rife when the Sun fets, and fet when he rifes; and then, after their Departure from the Oppofition to the Sun, they remain to the Eastward of the Sun; and after Sun-set they are to be seen.. in the Evening, till they come in Conjunction with him, when they fet and rife together. Afterwards, as they recede from the Sun, they become more Wefterly than he, and are then only to be seen in the Morning before the Sun is up; for in the Evening they fet before the Sun, till they at laft come to be oppofite to the Sun, when again they rise at Sun-fet.

As in the inferior Planets, fo the fuperior have The Planes not their Orbits in the Plane of the Ecliptick; of their Orfor the Planes of all their Orbits cut the Plane of bits are inthe Ecliptick in Lines which pafs through the Ecliptick

Sun,

clined to the

Lecture Sun, which are called, the Lines of the Planets XVI. Nodes: And the Points where thefe Lines meet

with the Ecliptick, are called the Nodes. And therefore the fuperior Planets are never precifely in the Ecliptick, but when they are in the Nodes : In all the other Points of their Orbits they are further or nearer to the Ecliptick, according to their Distance from the Nodes; and their Distances are greatest, when they are at equal Distances from both Nodes; which Points are called the Limits, where the greatest Heliocentrick Latitudes, which measure the Inclinations of the Orbits to the Ecliptick, are as follow: Saturn's greateft Heliocentrick Latitude is 2 Degrees 30 Minutes; Jupiter's is 1 Degree 20 Minutes; and that of Mars is 1 Degree 52 Minutes.

The Helio- HAVING the Place of a Planet in its Orbit, centrick and Or, which is the fame Thing, its Distance from the Geocentrick Node, by the fame Method we find out its Helio

Latitudes.

centrick Latitude, as we did in the inferior Planets Mercury and Venus. But the Geocentrick Latitudes, or the Distances of the Planets from the Ecliptick, as they are feen from the Earth, depend much upon the Pofition and Distance of the Earth. For where the Heliocentrick Latitude continues the fame, yet according to the various Pofitions the Earth may have, the visible Latitude of a Planet feen from thence, will be various. For let Tt be the Orbit of the Earth; and the OrPlate XIV. bit of any fuperior Planet, as for Example, that Fig. 2. of Mars, fuppofe to be M, whofe Plane is inclined to the Ecliptick, and cuts it in the Line of Nodes n N. Let Mars be in ♂ and the Earth in T, fo as Mars may be obferved in Oppofition to the Sun; and from let fall on the Plane of the Ecliptick the Perpendicular & E; this Line will fubtend the Angle which measures the Geocentrick Latitude. And therefore, when the Earth is in T, the visible Latitude is measured by the Angle

TE. But if the Earth was in t, fo that Mars was feen in Conjunction with the Sun, its visible Latitude will be the Arch which measures the

Angle

Angle

E, which is much less than the Angle Lecture TE, and is nearly lefs in the fame Proportion

as the Distance T is lefs than the Distance t When the Earth is in T, the Geocentrick Latitude of Mars is greater than its Heliocentrick; but when it is in t, the Heliocentrick is greater than the Geocentrick; and according to the various Pofitions of Mars and the Earth, his vifible Latitude will be changeable; fo that all other Things being alike, the Latitude is greater, the nearer he comes to the Oppofition of the Sun; and the lefs, as he approaches to a Conjunction with the fame.

It is also evident, that none of the fuperior Planets can be seen from the Earth in the Sun's Disk, as the inferior Mercury and Venus are; but yet they may be all of them covered by the Sun, and lie behind him, when they come in Conjunction with him, and are near their Nodes.

XVI.

Saturn bave

always a

SINCE the Faces of all the Planets which are Jupiter and turned towards the Sun, fhine only with a reflected and borrowed Light; and because the round full Earth, feen from Jupiter or Saturn, is always to Face. be obferved near the Sun's Body; the Faces of these Planets which are turned towards the Sun, will alfo be towards the Earth; whence the Inhabitants of our Globe do always behold thefe Planets thining in full Orbs or Circles. But Mars having an Orbit which lies very near the Earth, its Face, which is towards the Sun, will not always be totally turned towards the Earth; but when in Mars in bis his Quadrature, or when there is about a fourth Quadrature, Part of the Ecliptick between the Sun and him, as gibbofe. fuppofe the Earth in M or B, and Mars in N or Fig. 1. R, then fome Part of the illuminated Face will be turned from the Earth; and therefore Mars will not appear in a complete Circle, but will be feen as deficient or gibbofe; but when he comes to be in Conjunction or Oppofition, he then re-affumes his round Figure, his illuminated Face being totally turned towards the Earth; and particularly, when, in Oppofition to the Sun, he looks brightest and biggest.

FOR

Plate XIV.