A line joining the oppofite angles of any parallelogram is called its diagonal or diameter. In every parallelogram, therefore, two diagonals may be drawn, which in the fquare and rectangle are equal to one another; and the diagonal divides every parallelogram into two equal parts.

A figure nearly refembling a rhombus is called a rhomboid: when the four fides are not equal, and none of them parallel to one another, a trapezium and trapezoid.

Every other right-lined figure, that has more fides than four, is called a polygon; according to the number of its fides, pentăgon, hexagon, heptagon, octagon, &c.: if the fides are equal to one another, a regular polygon.

Solid figures are fuch as have length, breadth, and thickness; and are bounded by one or more surfaces.

A folid body exactly round is called a globe or sphere; which we may conceive to be formed by the circumvolution of a femicircle round its diameter, fo that every part of its surface is equally diftant from a point within it called its centre.

A fpherical figure, not exactly round, is called a fpheroid. If we fuppofe a folid to be formed by the revolution of a right-angled parallelogram about one of its fides, it is called a cylinder or roller, and the ends of it are equal circles; but a folid, whofe ends are elliptical, is called a cylindroid, or flat roller. A folid body bounded by three or more plane fides, incli ning gradually from its base to a point, is called a pyramid.

A folid, whofe fides are parallelograms, and its ends two fimilar equal plane figures, parallel to one another, is called a prifm.

A folid bounded by fix equal squares, placed perpendicular to one another, is called a cube.

A folid body having a circle for its bafe, and its top terminated in a point or vertex, in the form of a fugar loaf, is called a cone; which may be conceived to be formed by the revolution of a right-angled triangle round one of its legs. When the fides are perfectly equal, or, as it is otherwife expreffed, when its axis is normal or perpendicular to its base, it is called a right cone; when its axis is inclined to its bafe, and its fides unequal, a fcalene cone.

Curve lines or figures formed by cutting a cone with a plane, are called CONIC SECTIONS; whence that part of geometry which treats of these curves and figures has got its name. The chief of them are the parabola, hyperbola, and ellipfis or ellipfe.

A knowledge of the properties of the ellipfe is particularly requifite for understanding the motion of the planets.

An ellipfe may be defcribed by fixing the ends of a thread to two points in a plane, or tying them to two pins stuck in a table; and then with a pencil keeping the thread stretched, and marking all around the line it defcribes; thus, A D a d. (See figure 3.)

The curved line is called the circumference of the ellipfe, and forms an oblong kind of circle; the two points F f are called the foci or focuses; a straight line paffing through them and produced both ways to the circumference, is called the greater axis or longeft diameter, as, A, a; a point upon this line in the middle between the foci, is the centre of the ellipfe, as, C; a line paffing through this point, and crofling the greater axis at right angles, is the forteft diameter or leffer axis, as, D d. . If an ellipfe is fuppofed to revolve on its longer axis, it will generate what is called an oblong period; if on its fhorter axis, an oblate period, fuch as is the figure of the earth,

T

Of the HEAVENLY BODIES,

O form a juft conception of the Heavenly Bodies we muft fuppofe them to be viewed from the fun. In this fituation the ftars would appear as fo many bright spots of dif ferent magnitude and fplendour fixed in a concave sphere, always remaining at the fame distance from one another: and the planets, as fo many lucid orbs, moving among the fixed stars with different degrees of velocity, and completing their revolutions in different periods; but each of them always in the fame fpace of time. The planets would alfo appear of very different bulks, and fome of them to be accompanied by smaller bodies always moving round them.

1. The PLANETS and their SATELLITES.

If we fuppofe a fpectator at the fun capable of discovering the diftances of the planets, they will appear to move in different orbits; thus, Mercury, Venus, the Earth attended by the moon, and Mars. (See fig. 4.)

Sa

So Jupiter, Saturn, and the Georgium fidus, in much larger circles; which will be better understood by means of a plane

tarium.

The orbits of the planets, however, are not exactly circular, nor in the fame plane, as they are usually reprefented in a diagram, or by a planetarium, but elliptical, and croffing each other obliquely in different parts of the heavens. So that if we take the plane of the earth's orbit or of the ecliptic, as a ftandard, and suppose it to be continued every way, the paths of the other planets will be differently inclined towards it.

The points where the orbit of any planet interfects the plane of the ecliptic are called its nodes; and a straight line be→ tween these points, the line of the nodes.

The orbits of all the planets are in fuch a pofition, that one of their foci coincides with the centre of the fun; thus, let the ellipfe A Dad (fee fig. 3.) represent the orbit of a planet, F will be the centre of the fun.

The diftance between the centre of the fun and the centre of the orbit, is called the ECCENTRICITY of the planet, as, F C. In every revolution the planet approaches once to the fun, and once recedes from it. The point in which it is at the greatest diftance, is called its APHELIUM or -on; as, a; the point in which it is at the leaft diftance, the PERIHELIUM: as, A. Thefe points at the ends of the greater axis are called the APSIDES or auges of the planet, and hence the greater axis is fometimes called the line of the apfides.

That diftance of a planet from the fun is called its mean dif tance, which is equally different from the greatest and the leaft; as, at D or d, the extremities of the fmailer axis.

Although the centre of the fun be commonly reckoned the point round which the planets revolve, yet that is not strictly true; for the fun himself not only turns on his axis, but is agitated by a small motion round what is called the centre of gravity of the whole system.

A planet moves with different degrees of velocity in different parts of its orbit. The nearer it is to the fun, the swifter is its motion. Thus the earth takes almost eight days more to run through the northern half of the ecliptic, when it is fartheft from the fun, than it does to pass through the fouthern; fo that our fummer is that much longer than the fummer of the other hemifphere, which, in the space of 4000 years, a mounts to more than 87 years. And hence alfo among other reasons, the temperature of places in the higher northern lati

tudes

tudes is much more mild than in the correfpondent fouthern

latitudes.

The more diftant the planets are from the fun, the flower they move in their orbits; fo that the periodical times of their revolutions are greater, both on account of the largeness of their orbit and the flowness of their motion.

By the obfervation of certain spots on the furface of planets, it has been discovered, that befides their motion round the fun each of them moves round its axis in the fame manner with the earth.

A ball whirled from the hand into the open air turns round upon a line within itself, while it moves forward; such a line as this is meant when we speak of the axis of a planet.

The earth and the other planets move round the fun as they do round their axis, from west to east.

None of the planets, in any part of their orbits, recede farther from the ecliptic on either fide than 8 degrees; fo that the breadth of the zodiac is only 16 degrees.

The axis of the earth is inclined 23 degrees to the plane of its orbit and confequently goes that far north and fouth of the equinoctial line: hence the obliquity of the ecliptic. This obliquity is found to be now above the third part of a degree lefs than it was in the time of Ptolemy, which is afcribed to the force of the attraction of the fun and alfo of the moon upon the earth.

The fame attraction of the fun and moon on the earth caufes it to be go feconds later every year of coming round to the fame point in the equator, or, as it is called, to the equinoctial point, than it did the year before. So that all the stars an nually fhift 50 feconds forward before the apparent place of the fun; which is called the PRECESSION OF THE EQUINOXES, the retrogradation of the folfiitial and equinoctial points, the progression or movement of the flars in longitude; and makes a degree in 72 years; about 31 degrees fince the time of Meton, the inventor of the cycle of the moon or the golden number, about 2224 years ago. Thus the conftellations, in which the fun at that time feemed to move at the vernal equinox, or at any other time of the year, have now got near 31 degrees forward; those which then were in Aries, are now in Taurus, &c. and the ftars, which fet at any particular season of the year in the time of Virgil, for inftance, now fet at a different time.

The annual motion of the earth round the fun makes the ftars appear to go round the earth in 23 hours, 56 minutes, 4 feconds; fo that if we obferve this night, when any ftar disappears

behind a chimney or corner of a houfe at a little distance, the fame ftar will disappear next night 3 minutes 56 seconds fooner, the fecond night 7 minutes 52 feconds fooner, and fo on through the year: fo that in 365 days, as measured by the return of the fun to the meridian, there are 366 days as measured by the ftars returning to it. The former are called folar days, and the latter fidereal. Hence in 365 days the earth turns 366 times round its axis; and therefore, as a turn of the earth on its axis completes a fidereal day, there must be one fidereal day more in a year than the number of solar days; one day being loft with refpect to the number of folar days in a year, by the planets going round the fun; just as it would be loft to a traveller, who in going round the earth would lofe one day by following the apparent diurnal motion of the fun; and confequently would reckon one day less at his return, than those who remained all the while at the place. from which he set out.

The earth's motion on its axis being perfectly uniform, and equal at all times of the year, the fidereal days are always precifely of an equal length; and fo would the folar or natural days alfo be, if the earth's orbit were a perfect circle, or its axis perpendicular to its orbit. But the earth's diurnal motion on an inclined axis, and its annual motion in an elliptic orbit, cause the fun's apparent motion in the heavens to be unequal. For fometimes he takes more than 24 hours to perform a revolution from the meridian to the meridian, and fometimes lefs, according to a well-regulated clock. So that time fhewn by an equally going clock and a true fun-dial is never the fame, but at four times of the year. From the 24th December till the 15th of April, the clock goes before the fun; from that time till the 16th June the fun will be before the clock; from thence till the 31st Auguft the clock will be before the fun, and from thence to the 24th December the fun will be faster than the clock.

The difference between the time fhewn by a well-regulated clock and a true fun-dial is called the equation of time.

When we speak of the fun as moving in the ecliptic, the diftance which he has gone at any time from his apogee, or farthest point from the earth, till he return to it again, is called his mean anomoly; and is reckoned in figns and degrees, allowing 30 degrees to a fign. When the fun's anomaly is lefs than 6 figns, the folar noon precedes the clock noon; and when more, the contrary.

Thus neither the days nor hours, as measured by the fun's apparent motion, are of an equal length; owing, 1ft, to the

unequal