Which shews, that to those inhabitants who live at the equator, the sun will at this season appear to the north at noon, and their shadow will therefore be projected southwards.

But if you rectify the globe to the winter solstice, the south point being then the uppermost point at noon, the same persons will at noon have the sun on the south side of them, and will project their shadows northwards.

Thus they are amphiscii, projecting their shade both ways; which is the case of all the inhabitants within the tropics.

The artificial horizon remaining as before, rectify the globe to the times of the equinox, and you will. find that when this horizon is under the strong brass meridian, a line going vertically upwards will be perpendicular to it, and consequently the sun will be directly over the heads of the inhabitants, and they will be ascii, having no noon shade; their shadow is in the morning projected directly westward, in the evening directly eastward.

The same thing will also happen to all the inhabitants who live between the tropics of Cancer and Capricorn; so that they are not only ascii, but amphiscii also.

Those who live without the tropics are heteroscii; those in north latitude have the noon shade always directed to the north, while those in south latitude have it always projected to the south.

The inhabitants of the polar circles are called peris

cii; because, as the sun goes round them continually, their shade goes round them likewise.

OF ANCIENT DISTINCTIONS FROM SITUATIONS.

These terms being often mentioned by ancient geographical writers to express the different situation of parts of the globe, by the relation which the several inhabitants bore to one another, it will be necessary to take some notice of them.

The antoci are two nations which are in or near the same meridian; the one in north, the other in south latitude.

They have therefore the same longitude but not the same latitude: opposite seasons of the year, but the same hour of the year; the days of the one are equal to the nights of the other, and vice versa, when the days of the one are at the longest, they are shortest at the other.

When they look towards each other, the sun seems to rise on the right-hand of the one, but on the left of the other. They have different poles elevated; and the stars that never set to the one, are never seen by the other.

Perioci are also two opposite nations, situated on the same parallel of latitude.

They have therefore the same latitude, but differ 180 degrees in longitude; the same seasons of the year, but opposite hours of the day; for when it is twelve at night to the one, it is twelve at noon with

the other. On the equinoctial days, the sun is rising to one, when it is setting to the other.

Antipodes are two nations diametrically opposite, which have opposite seasons and latitude, opposite hours and longitude.

The sun and stars rise to the one, when they set to the other, and that during the whole year, for they have the same horizon.

The day of the one is the night of the other; and when the day is longest with the one, the other has its shortest day.

They have contrary seasons at the same time; different poles, but equally elevated; and those stars that are always above the horizon of one, are always under the horizon of the other.

PROBLEM XXII. To find the Antœci, the Perioci, and the Antipodes of any place.

Bring the given place to the strong brass meridian, then in the opposite hemisphere, and under the same degree of latitude with the given place, you will

find the Antœci.

The given place remaining under the meridian, set the horary index to XII; then turn the globe, till the other XII is under the index, then you will find the Pericci under the same degree of latitude with the given place.

Thus the inhabitants of the south part of Chili are Antœci to the people of New England, whose Pericci are those Tartars who dwell on the north bor

ders of China, which Tartars have the said inhabitants of Chili for their Antipodes.

This will become evident, by placing the globe in the position of a right sphere, and bringing those nations to the edge of the broad paper circle.

PROBLEM XXIII. The day of the month being given, to find all those places on the globe, over whose zenith the sun will pass on that day.

Rectify the terrestrial globe, by bringing the given day of the month on the back side of the strong brass meridian, to coincide with the plane of the broad paper circle: observe the of the brass meridian, which

given day of the month.

number of degrees

corresponds to the

This number of degrees, counted from the equator on the strong brass meridian, towards the elevated pole, is the point over which the sun is vertical; and all those places, which pass under this point, have the sun directly vertical on the given day.

Example. Bring the 11th of May to coincide with the plane of the broad paper circle, and the said plane will cut eighteen degrees for the elevation of the pole, which is equal to the sun's declination for that day, which being counted on the strong brass meridian towards the elevated pole, is the point over which the sun will be vertical; and all places that are under this degree, will have the sun on their zenith on the 11th of May.

Hence, when the sun's declination is equal to the latitude of any place in the torrid zone, the sun will be vertical to those inhabitants that day; which furnishes us with another method of solving this problem.

OF PROBLEMS PECULIAR TO THE SUN.

PROBLEM XXIV. To find the sun's place on the broad

in which you seek the

Consider whether the year

sun's place is bissextile, or whether it is the first, second or third

year after.

If it be the first year after bissextile, those divisions to which the numbers for the days of the months are affixed, are the divisions which are to be taken for the respective days of each month of that year at noon; opposite to which, in the circle of twelve signs, is the sun's place.

If it be the second year after bissextile, the first quarter of a day backwards or towards the left-hand, is the day of the month for that year, against which, as before, is the sun's place.

If it be the third year after bissextile, then three quarters of a day backwards is the day of the month for that year, opposite to which is the sun's place.

If the year in which you seek the sun's place be bissextile, then three quarters of a day backwards is the day of the month from the 1st of January to