PROBLEM L.

To find the angles that the hour lines of a horizontal dial make with the horizon, and hence the means and method of constructing one for any given latitude.*

Rectify the globe for the latitude given, (then the pole will have the same elevation above the horizon as the gnomon, or stile of the dial must have above the

*From the following method and elements to construct a horizontal dial. Draw (on a piece of paper, board, stone, brass, &c. which is designed for the plane of the dial) a circle with the chord of 60° taken from the plane scale, suppose Gunter's, cross this circle at right angles, with two lines passing through its centre; one of which will represent the meridian north and south line, or twelve o'clock line, the other the east and west, or six and six-hour line; divide this circle for the hours, if for the latitude of London, as in the following table, viz. take in a pair of compasses (from the same line that the chord of 60° was taken from) 11° 51', and with one point in the north end of the twelve o'clock line, mark off on both sides of it the 11° 51' taken between its points; through which, from the centre of the circle, draw lines, which will represent the eleven and one o'clock hours, then take 24° 19′ from the same scale, and apply as before; through which likewise draw lines from the centre to represent the ten and two o'clock hour lines, proceed in this manner to the number of hours necessary for the latitude, which for London, (the longest day being less than seventeen hours)

plane thereof, which must always be equal to the latitude given), bring the equinoctial colure to the brass meridian, set the index to the upper XII, thus the meridian represents the twelve o'clock line, turn the globe until the index points to a quarter past twelve, look what degree the colure cuts on the horizon, which is equal to the angle made by it; proceed to turn the globe until the index points to half past twelve, three quarters, one o'clock, &c. to six, marking at each time the angle made on the horizon, reckoning from the south point; and the distance that any hour, or part of an hour, is from twelve in the afternoon, the same distance, or angle, any time equally distant from noon, will be in the forenoon; or the colure may be brought back to the meridian, and the problem repeated on the eastern hemisphere for the hours in the forenoon. Ob

from four in the morning to eight in the evening, will be sufficient; the quarters, &c. may be found from the globe and applied progressively, or placed after the hours are determined. The gnomon must be placed in the meridian line, its elevated part towards the north, if for north latitude, and the contrary for south latitude, its slant side rising from the centre of the dial, and its height above the plane of the dial, or the angle that it makes with the meridian, must always be equal to the latitude of the place, which, for the above, is, 51° 30'; which dial will answer quite round the earth on that parallel, and likewise on the same parallel south.

serve likewise, that the angle made by the five o'clock line in the afternoon, from the south, will be equal to the angle made by the seven o'clock line, in the afternoon, from the north; and the four o'clock line equal to the eight o'clock line in the evening, &c. Also that the seven, eight, &c. hour-lines in the afternoon will make the same angles, from the north, as the five, four, &c. hour-lines in the morning.

Globes that have the meridians drawn for every 15° will, at one position, show the angles that the hour-lines make with the horizon, if the colure is brought to the meridian, and will appear as in the following table, for the latitude of London.

12......... 0. Q

1.........11 51 › dist. from the 12 o'clock

2.........24 19

3.........38 3

4.........53 36

line, or from the south

point of the horizon.

...

5.........71 6

CHAP. IV.

The Rise and Progress of Astronomy; with an Account of the various Systems that have been introduced into the world, &c.

THE origin of this science has afforded much contention among the learned of different nations, each setting up their prior claim, as the Babylonians, Egyptians, Grecians,* &c.

The Babylonians were the first who made observations on the stars, by whom, according to Struyk's catalogue, an eclipse of the moon was observed 721 years before Christ; and it appears from history, that the Egyptians had their first knowledge of astronomy from the Babylonians.

The Greeks had their astronomical knowledge from Egypt; for Thales,† Pythagoras, Eudoxus, and others were instructed in this science in Egypt.

* The Chinese, according to their records, understood the phenomena of the celestial objects at a much earlier date than the Babylonians, as they have an account of an eclipse that happened 2155 years before the Christian era; but how far their history can be depended on is doubtful.

+ Thales flourished in Greece about 600 years before Christ.

Pythagoras, who lived in society with the Egyptian priests, who, at that time, were men of the most pro- found learning, was initiated into their religion and science, and carried home from thence the true system of the world, (about 450 years before Christ). This system taught, that the earth and planets turned round the sun, which was fixed in the centre, and that the diurnal motion of the sun and stars were not real, but apparent, arising from the motion of the earth on its axis.

The sciences were, however, much neglected by suc ceeding philosophers, particularly astronomy, so that of all the observations of eclipses, for the space of nearly two thousand years, that were sent from Babylon by Callisthenes, Ptolemy could recover but very few.

But although astronomy was not generally understood, yet it was received and cultivated by some; and the Pythagorean sect more particularly flourished in Italy many years.

The Ptolemies, kings of Egypt, were great patrons of learning; under them an academy for astronomy was established at Alexandria, which produced many great men, of whom was Hipparchus, who calculated the eclipses of the sun and moon that were to happen for six hundred years.