her fruits pine away as children at the withered breafts of their mother, no longer able to yield them relief; what would become of man himself, whom all thofe things do now ferve? And how would he look back on those benefits, for which, when they were daily poured upon him in boundless profufion, he forgot to be thankful?

LECTURE

LECTURE XXXIX.

AN EXPLANATION OF THE PHENOMENA OF THE PLANETS, ACCORDING TO THE COPERNICAN SYSTEM.

I

SHALL here define again fome words which I have already explained, and recal your attention to fome circumftances which I have mentioned in a former Lecture. Thefe repetitions will not, I hope, be an object of complaint, as they will render this Lecture more perfect, and anfwer the beneficial purpose of grounding you more firmly in the fcience we are now treating.

The line that a planet describes round the fun is called it's orbit; the motion of all the planets in their orbits is from weft by the fouth to the eaft; this is called their annual motion.

The orbits of the planets are not all in the fame plane, but in planes inclined to each other, or interfecting each other at different angles. The orbit of the earth is taken as a ftandard, from whence their refpective inclinations are computed.

The planes of the feveral orbits of the planets produced to the fixed ftars, mark the feveral circles which each planet would appear to defcribe in the fphere of the heaven to a fpectator placed in the fun; thefe circles may be called the beliocentric orbits of the planets.

The heliocentric orbit of the earth is the ecliptic: to a fpectator in the fun, the earth will ap

pear

pear to go round the fun in the ecliptic caftward in twelve months.

We may fuppofe as many great circles as we please to be defcribed upon the fphere of the heavens, interfecting one another at the poles of the ecliptic, and cutting it at right angles; these are termed fecondaries of the ecliptic, and circles of latitude. The latitude of a planet or flar is it's dif tance from the ecliptic, measured in degrees, &c. upon a circle of latitude paffing through the ftar or planet.

The latitude a planet would appear to have, when viewed from the fun, is it's heliocentric latitude; that which it appears to have to an inhabitant of the earth, is called it's geocentric latitude.

By the place of a planet is meant the place of it's center; it's geocentric place is that where it appears to an inhabitant of the earth.

The two points where the ecliptic is cut by the heliocentric orbit of a planet, are the nodes of the planet. The afcending node 8, is the point where the ecliptic is cut by the planet, before it deviates northward therefrom. The defcending node 8, is the point where the planet cuts the ecliptic before it deviates fouthward.

When any planet has paffed it's afcending node, it deviates more and more northward till it is got ninety degrees from the node, then it is at it's utmoft heliocentric northern latitude, or northern limit; from thence it continually approaches the ecliptic till it comes to g, after paffing which it deviates more and more fouthward, till it is go degrees from this node, when it is at it's fouthern limit, or utmost fouthern heliocentric latitude, which from thence continually decreases till the planet returns again to the afcending node. A planet feen from the earth, only appears in the ecliptic, when it is in one of it's nodes.

VOL. IV.

The

The equator cuts the ecliptic in two oppofite points when the fun appears in one of these points, it is our vernal; when in the other, it is our autumnal equinox. The point of the vernal equinox is counted the first point of the ecliptic, becaufe fpring begins the aftronomical year; this point is marked Aries.

The longitude of a celeftial object is the number of degrees, &c. contained upon the ecliptic, reckoning from Y eastward, to the point where a circle of latitude drawn through the object cuts the ecliptic. The longitude and latitude of an object being given, it's place in the sphere of the heavens is known; and it's place is ufually expreffed, by faying it is in fuch a degree and minute of fuch a fign, and in fuch latitude.

A planet is faid to be in conjunction with the fun, when it's geocentric place is very near the geocentric place of the fun; that is, when the fun is between our earth and the planet, or when the planet is between the earth and the fun.

A planet is faid to be in oppofition, when it's geocentric place is oppofite to the geocentric place of the fun; that is, when the earth is between the fun and the planet.

An exact or central conjunction or oppofition can happen only when a planet is in one of it's nodes; it is, however, ufual to term it a conjunction or oppofition, when the fame fecondary of the ecliptic paffes through the fun or any planet, though the planet has latitude.

When the geocentric place of a planet is a quarter of a circle diftant from the geocentric place of the fun, the planet is faid to be in quadrature.

A planet is faid to be direct, when it's geocentric motion is eastward; retrograde, when weftward; flationary, when it's geocentric place continues the fame for fome time.

The

The distance an inferior planet seen from the earth appears to be from the fun, is called it's elongation.

OF THE CONJUNCTIONS AND ELONGATIONS OF THE INFERIOR PLANETS, MERCURY AND VENUS.

There are two different fituations, in which an inferior planet will appear in conjunction with the fun; one when the planet is between the fun and the earth, the other when the fun is between the earth and the planet.

Let A, fig. 2, pl. 6, be the earth in it's orbit, E the place of Venus in EHG her orbit, S the fun, FVPQRTD an arc in the starry heaven.

In the fituation of things represented in this diagram, the fun and Venus will appear in the fame point of the heavens, and fo be in conjunction. If Venus be at G, there will alfo be a conjunction. When the planet is at E, nearer to the earth than the fun, it is called it's inferior conjunction; but when the planet is at G, farther from the earth than the fun, it is termed the Juperior conjunction of the planet.

When the planet is either at E or G, it has no elongation; but as the planet moves from E to y, it's elongation increafes; for when it is at y, it appears in the line Ay P, while the fun appears in the line ASQ; fo that PAQ will be the angular measure of it's elongation or distance from the fun. When the planet arrives at x, it appears in the line AxV, which is a tangent to it's orbit, and then VAQ is the angular measure of it's elongation; which is the greatest that can be on that fide the fun, for after this the elongation decreases. When the planet is at K, it's elongation is PAQ; when at G, it is nothing, because it is then in its fuperior conjunction; as the planet moves on from

G2

G1