and confirmed by other obfervations on the light of the fixed stars *, that the eclipfes happen later when the Earth is at E than when at F, because the light must in the latter case pass through a space as much greater as the line JE exceeds J F.

CHA P. VIII.

OF THE MOON.

THAT the Moon revolves round the Earth, is x proved from its apparent diameter, which continues at all times, and in all pofitions, nearly of the fame magnitude, whence it may be easily inferred, that its diftance from the Earth is nearly at all times the fame. Its horizontal parallax, which at a medium is about 57', fhews that it is very much nearer to us than the reft of the celeftial bodies.

The most remarkable appearance in the Moon is Y the continual change of figure to which it is fubject. Sometimes it appears perfectly full or circular, at other times half-illuminated, and at other times more or less than half; changing through a very great variety of figures. These changes being always the fame at the fame elongation from the Sun, are a proof that it receives its light from that luminary: for the Moon is enlightened only on the fide that faces the Sun; and a greater or lefs quantity of that enlightened part is vifible to us, according to our

* The aberration of the fixed ftars arifing from the progreffive motion of light, will be explained in Book II. Se&. I.

pofition.

pofition. This cannot be better illustrated than by an ivory ball, which being held in the Sun in various pofitions, will prefent a greater or less part of its illuminated fide to the view of the obferver. If it be held nearly in oppofition, fo that the eye of the observer may be almoft immediately between it and the Sun, the greatest part of the enlightened fide will be feen. But if it be moved in a circular orbit towards the Sun, the visible enlightened part will gradually decrease, and at last disappear when the ball is held directly towards the Sun. Or, to apply the experiment more immediately to our prefent purpofe; if the ball at any time, when the Sun and Moon are both visible, be held directly between the eye of the observer and the Moon, that part of the ball on which the Sun fhines will appear exactly of the fame figure as the Moon itself.

The Moon's path or orbit is inclined to the plane of the ecliptic, in an angle of about five degrees and A a quarter. Its periodical revolution is performed in twenty-feven days, feven hours, forty-three minutes, eleven feconds and a half; but because, during that time the Sun, by its apparent motion, advances confiderably in the ecliptic, a space of about two days and a quarter is required by the B Moon to overtake it. When the Moon is as nearly in a line between the Earth and the Sun as the inclination of its orbit will allow, it is called the New c Moon; and when the Earth is in like manner between the Moon and the Sun, the Moon is said to

be

be full. The time between two fucceeding full D moons is called the fynodical revolution, and exceeds the periodical revolution, for the reafon already given, it being performed in twenty-nine days, twelve hours, forty-four minutes, and, three feconds. If the new or full Moon happen near the E node, an eclipfe takes place; at the new Moon, the Moon being interpofed between the Sun and Earth, occafions an eclipfe of the Sun; at the full, the Moon entering into the fhadow of the Earth, is deprived of the Sun's light, the Earth being interpofed between it and the Sun: which phenomenon is called a lunar eclipfe, or eclipse of the Moon. At other times, that is, when the new or full Moon happens at a distance from the node, the Moon passes too far to the northward or fouthward of the ecliptic, either to intercept the Sun's light from the Earth, or to enter the Earth's fhadow, and confequently no eclipse happens.

It is determined from obfervations of angular F velocity, parallax and apparent diameter, that the Moon revolves round the Earth in an elliptical orbit, in the focus of which the Earth is placed: and that its velocity is such, that a radius joining its center with that of the Earth does very nearly defcribe equal areas in equal times.

The line of the apfides, or principal diameter G of the Moon's orbit, is not fixed or stationary, but revolves with an irregular or libratory motion from weft to east completing one revolution in almost nine years.

The

H

The line of the nodes is alfo fubject to a like irregular motion from east to west, which is completed in almost nineteen years.

I The variation of the Moon's motion in any part of its orbit is the difference between its real motion and that which it would have had, provided it had described equal areas in equal times. This is governed chiefly by its elongation from the Sun. During the first quarter its velocity is diminished; in the fecond quarter, from the quadrature to the oppofition or full Moon, it is increased; in the third quarter, from the oppofition to the last quadrature, the velocity is again diminifhed; and from that quadrature to the conjunction, its velocity is again increased. The quantity of angular motion loft exceeds the quantity gained: therefore the whole periodical revolution is performed in a longer time than would have been employed if the Moon were subject to no fuch variation, but defcribed equal areas in equal times.

K

This variation, and confequently the retardation of the periodical time, is greater when the Earth is in the perihelium, and lefs when the Earth is in the aphelium: whence it comes to pass, that all the Moon's revolutions are not equal, but are performed in lefs time in the latter fituation than in the former.

L On all thefe, as well as other accounts, the determination of the Moon's place in the heavens for a given instant of time has ever been a pro

blem

blem of great difficulty, which till of late years has not been folved to any confiderable degree of exactness. Within the laft twenty years the. commiffioners, appointed by the English government for the discovery of the longitude, have particularly attended to this branch of astronomy, and by publishing almanacs in which the Moon's elongation from the Sun, and from certain fixed ftars, is afcertained for every three hours, have enabled navigators to determine the fituation of ships at fea in general within thirty miles of the truth. This is an advantage of fingular use in long voyages, and is at present much used in the royal navy, and East India Company's fhips.

CHA P. IX.

CONCERNING THE ECLIPSES OF THE SUN AND MOON.

WE have feen in what manner the periodical revolutions of the celeftial bodies, together with the figure, magnitude, and pofition of their orbits, may be respectively determined by obfervations made on their apparent motions and fituations. From the properties of the ellipfis, and the cftablished law of their velocities (121, K), or otherwife, more immediately from the confideration of gravity (98, w, x), astronomical tables are computed, by which the places of the heavenly bodies may be found for any inftant of time. The conVOL. I ftruction

L