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Therefore, suppose the sun in the vernal equinox, rectify the globe for the latitude of London, and the place of the sun; then bring the vernal equinox, or sun's place, to the western edge of the horizon, and the hour index will point precisely to VI; at which time we will also suppose the moon to be in the autumnal equinox, and consequently at full and rising exactly at the time of

sun-set.

But on the following day, the sun, being advanced scarcely one degree in the ecliptic, will set again very nearly at the same time as before; but the moon will, at a mean rate, in the space of one day pass over 13 deg. in her orbit; and therefore, when the sun sets in the evening after the equinox, the moon will be below the horizon, and the globe must be turned about till 83 degrees of Libra come up to the edge of the horizon, and then the index will point to 7 h. 6 min. the time of the moon's rising, which is an hour and quarter after sun-set for dark night. The next day following there will be two hours and an half, and so on successively, with an increase of one hour and a quarter dark night each evening respectively, at this season of the year; all owing to the very great angle which the ecliptic makes with the horizon at the time of the moon's rising.

On the other hand, suppose the sun in the autumnal equinox, or beginning of Libra,and the moon opposite to it in the vernal equinox, then the globe, rectified as before, being turned about till the sun's

place comes to the western edge of the horizon, the index will point to VI, for the time of the setting and the rising of the full-moon on that equinoctial day. On the following day, the sun will set nearly at the same time; but the moon being advanced (in the 24 hours) 13 degrees in the ecliptic, the globe must be turned about till that arch of the ecliptic shall ascend the horizon; which motion of the globe will be very little, as the ecliptic now makes so small an angle with the horizon, as is evident by the index, which now points to VI h. 17 m. for the time of the moon's rising on the second day, which is about a quarter of an hour after sun-set. The third day, the moon will rise within half an hour; on the fourth, within three quarters of an hour, and so on; so that it will be near a week before the nights will be an hour without illumination and in greater latitudes this difference will be still greater, as you will easily find by varying the case, in the practice of this celebrated problem on the globe.

This phenomenon varies in different years; the moon's orbit being inclined to the ecliptic about five degrees, and the line of the nodes continually moving retrograde, the inclination of her orbit to the equator will be greater at some seasons than it is at others, which prevents her hastening to the northward, or descending southward, in each revolution, with an equal pace.

PROBLEM XLV. To find at what azimuth the moon is upon at any place when it is flood, or high water; and thence the high tide for any day of the moon's age at the same place.

Having observed the hour and minute of high water, about the time of new or full-moon, rectify the globe to the latitude and sun's place; find the moon's place and latitude in the ephemeris, to which set the artificial moon, or a patch representing the moon, and screw the quadrant of altitude in the zenith; turn the globe till the horary index points to the time of flood, and lay the quadrant over the centre of the artificial moon, and it will cut the horizon in the point of the compass upon which the moon was, and the degrees on the horizon contained between the strong brass meridian and the quadrant, will be the moon's azimuth from the south.

To find the time of high water at the same place.

Rectify the globe to the latitude and zenith, find the moon's place by an ephemeris for the given day of her age, or day of the month, and set the artificial moon to that place in the zodiac: put the quadrant of altitude to the azimuth before found, and turn the globe till the artificial moon is under its graduated edge, and the horary index will point to the time of the day on which it will be high water.

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THE USE OF THE CELESTIAL GLOBE IN THE SOLUTION OF PROBLEMS ASCERTAINING THE PLACES AND VISIBLE MOTIONS OR ORBITS OF COMETS.*

There is another class or species of planets, which are called comets. These move round the sun in regular and stated periods of times, in the same manner, and from the same cause, as the rest of the planets do; that is, by a centripetal force, every where decreasing as the squares of the distances increase, which is the general law of the whole planetary system. But this centripetal force in the comets being compounded with the projectile force, in a very different ratio from that which is found in the planets, causes their orbits to be much more elliptical than those of the planets, which are almost circular.

But, whatever may be the form of a comet's orbit in reality, their geocentric motions, or the apparent paths which they describe in the heavens among the fixed stars, will always be circular, and therefore may be shewn upon the surface of a celestial globe, as well as the motions and places of any of the rest of the planets.

To give an instance of the cometary praxis on the globe, we shall chuse that comet for the subject of these problems, which made its appearance

* Martin's Description and Use of the Globes.

at Boston, in New England, in the months of October and November, 1758, in its return to the sun; after which it approached so near the sun, as to set heliacally, or to be lost in its beams, for some time spent in passing the perihelion. Then afterwards emerging from the solar rays, it appeared retrograde in its course from the sun towards the latter end of March, and so continued the whole month of April and part of May, in the West Indies, particularly in Jamaica, whose latitude rendered it visible in those parts, when it was for the greatest part of the time invisible to us, by reason of its southern course through the heavens.

When two observations can be made of a comet, it will be very easy to assign its course, or mark it out upon the surface of the celestial globe. These, with regard to the above-mentioned comet, we have, and they are sufficient for our purpose in regard to the solution of cometary problems.

By an observation made at Jamaica on the 31st of March, 1759, at five o'clock in the morning, the comet's altitude was found to be 22 deg. 50 min. and its azimuth 71 deg. south-east. From hence we shall find its place on the surface of the globe by the following problem.