every nation, and whatsoever has rendered it worthy of public notice in the world.

There are many books extant in the world on this subject; some of lesser size, such as Gordon's Geographical Grammar, Chamberlain's Geography; and larger, viz. Moden's Geogra phy Rectified, in quarto, Thesaurus Geographicus, Moll's Geography, in folio, &c.

The second or special part of astronomy is called the theory of the heavens, or the sun and planets, which will lead us into the knowledge of a thousand beautiful and entertaining truths concerning the system of the world, the various appearances of the heavenly bodies, and the reasons of those appearances, viz. a more particular and exact account of the day and night, and of the several seasons of the year, spring, summer, autumn, and winter, of the length and shortness of the days. Why in the winter the sun is nearer to us than it is in the summer, and why the winter half-year is seven or eight days shorter than the summer half-year. Whence come the eclipses of the sun and moon, both total and partial; why the moon is only eclipsed when she is full, and the Sun only when she is new: Whence proceed the different phases of the moon, as the new or horned moon, the half-moon, the full, &c. Why the two lower planets Mercury and Venus always keep near the sun, and never move so far as two whole signs from it: Why Venus is horned, halved and full as the moon is. Why the three superior planets Mars, Jupiter and Saturn, appear at all distances from the sun, and are sometimes quite opposite to it. Why both the upper and lower planets sometimes appear swifter, sometimes slower; why they seem sometimes to move directly or forward, sometimes retrogade or backward, sometimes are stationary, or seem to stand still. Why they are sometimes nearer to the earth, which is called their perigeum, and sometimes farther from the earth, which is called their apogeum, and by this means appear greater or less. Why they are nigher to or farther from the sun, which is called their perihelion and aphelion; and in what part of their orbits this difference falls out. How it comes to pass that they seem higher in the horizon than really they are by refraction, and how again they seem lower than they really are by the parallax.

In this part of astronomy it is proper to shew the different schemes or hypotheses that have been invented to solve or explain all these appearances of the heavenly bodies. Here the Ptolematic or ancient system should have the first place, to represent how the ancients placed the earth in the centre of the world, and supposed the sun to move round it amongst the other planets as it appears to the vulgar eye; and what tedious and bungling work they made by their contrivance of solid transparent spheres

of different thickness, placed in eccentric order and assisted by their little epicycles. What infinite embarrassments and difficulties attend this rude and ill adjusted contrivance, and how impossible it is to solve all the appearances of nature by this bypothesis.

Then the modern or copernican scheme should be represented, which makes the heaven all void, or at least filled only with very fine ethereal matter; which places the sun in the centre of our world with all the planets whirling round it; which makes the earth a planet, turning daily round its own axis (which is the axis of the equator) to form day and night; and also carried yearly round the sun in the ecliptic between the orbits of Venus and Mars to form summer and winter. This scheme also makes the moon a secondary planet rolling monthly round the earth, and carried with it in its yearly course round the sun, whereby all the variety of appearances of the sun and moon, and of all the planets; as well as the differences of day and night, summer and winter, are resolved and explained with the greatest ease, and in the most natural and simple manner.

Here also it should be shewn that as the moon is but a secondary planet, because it moves round the earth which is itself a planet So Jupiter, because it moves round the sun has also four secondary planets or moons moving round it, which are sometimes called his satellites or life-guards. Saturn also has five such moons, all which keep their certain periodical revolutions: And beside these, Saturn is encompassed with a large flat ring 21000 miles broad, whose edges stand inward toward the globe of Saturn, (like a wooden horizon round a globe) at about 21000 miles distance from it, which is the most amazing appearance among all the heavenly bodies: But these secondary planets which belong to Jupiter and Saturn together with this admirable ring are visible only by the assistance of telescopes: And yet mathematicians are arrived at so great an exactness in adjusting the periods and distances of these secondary planets, that by the motions and eclipses of the moons of Jupiter they find not only the true swiftness of the motion of light or sun-beams; but they find also the difference of longitude between two places on the earth.

It may be manifested here also that several of the planets have their revolutions round their own axis in certain periods of time, as the earth has in 24 hours; and that they are vast bulky dark bodies, some of them much bigger than our earth, and consequently fitted for the dwelling of some creatures; so that it is probable they are all habitable worlds furnished with rich variety of inhabitants to the praise of their great Creator. Nor is there wanting some proofs of this from the scripture itself.― For when the prophet Isaiah tells us, that God who formed the

earth, created it not in vain, because he formed it to be inhabited; Isa. xlv. 18. He thereby insinuates, that had such a globe as the earth never been inhabited, it had been created in vain. Now the same way of reasoning may be applied to the other planetary worlds, some of which are so much bigger than the earth is, and their situations or motions seem to render them as convenient dwellings for creatures of some animal and intellectual kind.

Many of these things have been performed by ingenious men with great exactness, for the use of persons learned in the mathematics; but I know not any short, plain and intelligible account of them fitted for the use of the unlearned world, except among Dr. Wells' volumes, entitled Mathematics for a Young Gentleman: Yet I persuade myself, that some parts of it might be performed with greater ease and clearness, in a more natural method, and to much greater perfection, if some person of peculiar skill in these sciences and of equal condescension would undertake the work.

SECT. XIX. Problems relating to Geography and Astronomy to be performed by the Globe.

AS theorems in mathematic science are certain propositions declaring some mathematical truth: So a problem is a mathematical question proposed to be resolved, or some practice to be performed. Because this problematic part will require the recollection of a great many things in the former sections, I think it may not be improper to give a short summary of definitions of the chief subjects of discourse in the doctrine of the sphere, and set them in one view.

DEFINITIONS.-The latitude of a place on the earthly globe, is the distance of the zenith of that place from the equator toward the north or south pole measured by the degrees of the meridian.

The elevation of the pole is the height of the pole above the horizon of that place measured on the meridian: And it is always the same number of degrees as the latitude.

The longitude of a place is the distance of it toward the east or west from some first meridian, and it is measured on the equator.

The declination of the sun or any star or planet is its distance northward or southward from the equator measured on the meridian. It is the same thing as latitude on the earthly globe.

The right ascension of the sun is its distance from that meridian that cuts the point aries measured eastward on the equator; it is much the same with longitude on the earthly globe.

The hour of the sun is its distance from noon or the meridian of the place measured on the equator by 15 degrees, for every 15 degrees on the equator make an hour. Or it may be reckoned from the opposite meridian or midnight. Note, The right ascension is reckoned either in degrees or in hours.

The latitude of a star or planet is its distance northward or southward from the ecliptic: Note, The sun has no latitude be; cause it is always in the ecliptic.

The longitude of the sun or star is its distance from the point aries eastward measured on the ecliptic. But with regard to the sun or a planet, this is usually called the place of the sun, or planet, for any particular day, i. e. its place in the Zodiac, or the degree of the sign in which it is at that time.

The altitude or height of the sun or a star is its distance from and above the horizon, measured on the quadrant of altitudes. The depression of the sun or star is its distance from and below the horizon, The azimuth of the sun or a star is its disstance from the cardinal points of east, west, north or south, measured on the horizon. The sun or star's meridian altitude is its altitude or height when it is on the meridian or at the south.

The vertical altitude of the sun is used by some writers for its height above the horizon when it is in the azimuth or vertical circle of east or west. But the sun is said to be vertical at any place when it is in the zenith of that place at noon.

The amplitude of the sun or a star is its azimuth or distance from east or west at rising or setting.

The ascensional difference is the time of the sun or star's rising or setting before or after six o'clock: Or it is the difference between the sun or star's semidiurnal arc and a quadrant or 90 degrees, as some persons express it, because 90 degrees or a quadrant reaches from 6 o'clock to 12.

PROBLEMS.

Problem I. "To find the longitude and latitude of any place on the earthly globe."

Turn the globe about till the place come just under the side of the brazen meridian on which the figures are, which is called its graduated edge, then the degree marked on the meridian just over the place shews the latitude either north or south: And the globe so standing, that degree of the equator, which is cut by the meridian shews the true longitude of the place. So London will appear to have 51 degrees of north latitude, and near 18 degrees of longitude, counting the first meridian at Teneriff. So Rome has 414 degrees of north latitude, and about 13 degrees of lougitude, eastward from London, or almost 31 degrees from Teneriff