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end of the quadrant to coincide with that degree of declination at which the reckoning ends.

Then bring the first meridian under the graduated edge of the strong brass meridian, which strong meridian will serve as the horary index.

Now turn the globe westward, and observe the degrees cut in the quadrant of altitude by the first meridian, while the hours XI, X, IX, &c. in the forenoon, pass successively under the brazen one; and the degrees thus cut on the quadrant by the first meridian are the respective distances of the forenoon hours, from XII on the plane of the quadrant.

For the afternoon hours, turn the quadrant of altitude round the zenith, until it comes to the degree in the horizon, opposite to that where it was placed before, namely, as far from the west towards the south, and turn the globe' eastward ; and as the hours I, II, III, &c. passes under the strony brazen meridian, the first meridian will cut on the quadrant of altitude the number of degrees from the zenith that each of the hours is from XII on the dial.

When the first meridian goes off the quadrant, at the horizon, in the forenoon, the hour index will shew the time when the sun comes upon this dial ; and when it goes off the quadrant in the afternoon, it points to the time when the sun leaves the dial.

Having thus found all the hour distances from XII, lay them down upon your dial-plane, either by dividing a semicircle into two quadrants, or by the line of chords.

In all declining dials, the line on which the gno

mon stands, makes an angle with the twelve o'clock line, and falls among the forenoon hour-lines, if the dial declines towards the east; and among the afternoon hour-lines, when the dial declines towards the west ; that is, to the left-hand from the twelve o'clock line in the former case, and to the right-hand from it in the latter.

To find the distance of this line from that of twelve. This may be considered, 1. If the dial declines from the south towards the east, then count the degrees of that declination in the horizon, from the east point towards the north, and bring the lower end of the quadrant to that degree of declination where the reckoning ends; then turn the globe, until the first meridian cuts the horizon in the like number of degrees, counted from the south point towards the east, and the quadrant and first meridian will cross one another at right angles, and the number of degrees of the quadrant, which are intercepted between the first meridian and the zenith, is equal to the distance of this line from the twelve o'clock line.

The numbers of the first meridian, which are intercepted between the quadrant and the north pole, is equal to the elevation of the style above the plane of the dial.

The second case is, when the dial declines westward from the south.

Count the declination from the east point of the horizon towards the south, and bring the quadrant of altitude to the degree in the horizon at which the


reckoning ends, both for finding the forenoon hours and the distance of the substyle, or gnomon line, from the meridian; and for the afternoon hours, bring the quadrant to the opposite degrees in the horizon, namely, as far from the west towards the north, and then proceed in all respects as before.

It is presumed, that the foregoing instances will be suthcient to illustrate the general principles of dialling, and to give the pupil a general idea of that pleasing science: for accurate and expeditious methods of constructing dials, we must refer him to treatises written expressly on that subject.

Note. For a simple and easy method of constructing, instrumentally, sun dials, see my edition of our Author's Geomctrical and Graphical Essays, page 33, 3d edition, 1803.

Well's Art of Shadows, Svo. and Leadbetter's Art of Dialling, 8vo. are among the best treatises, for learners, on the subject.





NAVIGATION is the art of guiding a ship at sea, from one place to another, in the safest and nost convenient manner. In order to attain this, four things are particularly necessary.

1. To know the situation and distances of places.

2. To know at all times the points of the compass.

3. To know the line in which the ship is to be directed from one place to the other.

4. To know, in any part of the voyage, what point of the globe the ship is upon.

The knowledge of the distance and situation of places, between which a voyage is to be made, implies not only a general knowledge of geography, but of several other particulars, as the rocks, sands, straits, rivers, &c. near which we are to sail; the bending out or running in of the shores, the knowledge of the times that particular winds set in, the seasons when storms and hurricanes are to be expected, but especially the tides ; these, and many other similar circumstances are to be learned from

sea-charts, journals, &c. but chiefly by observation and experience.

The second particular to be attained, is the knowledge at all times of the points of the compass

where the ship is. The ancients, to whom the polarity of the loadstone was unknown, found, in the day-time, the east or west, by the rising or setting of the sun ; and at night, the north, by the polar star. We have the advantage of the mariner's compass, by which, at any time in the wide ocean, and the darkest night, we know where the north is, and consequently the rest of the points of the compass.

Indeed, before the invention of the mariner's compass, the voyages

of the Europeans were principally confined to coasting; but this fortunate discovery has enabled the mariner to explore new seas, and discover new countries, which, without this valuable acquisition, would probably have remained for ever unknown.

The third thing required to be known, is the line which a ship describes upon the globe of the earth, in going from one place to another.

The shortest way from one place to another is an arc of a great circle drawn through the two places.

The most convenient way for a ship, is that by which we may sail from one place to another, directing the ship all the while towards the same point of the compass.

i A ship is guided by steering or directing her towards some points of the compass: the line wherein

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