Prob. XLV. To find the place of any Planet upon the globe; and so by that means, to find its place in the Heavens: Also to find at what Hour any Planet will rise or set, or be on the meridian at any one Day in the Year.
You must first seek in an Ephemeris (White’s Ephemeris will do well enough) for the place of the Planet proposed on that day; then mark that point of the ecliptic, either with chalk, or by sticking on a little black patch; and then for that night you may perform any problem, as before, by a Fixed Star.
Let it be required to find the situation of Jupiter among the Fixed Stars in the heavens, and also what time he rises and sets, and comes to the meridian on the 19th of May, 1757, N. S. at London.
Looking for the 19th of May, 1757, in White’s Ephemeris, I find that Jupiter’s place at that time is in about 12 degrees of ♏; latitude about 1¼ degree North. Then looking for that point upon the Celestial globe, I find that ♃ is then nearly in conjunction with the bright Star in the Southern Balance, and about 1 degree North of it.
To find when he rises and sets, and comes to the meridian: Having put a little black patch on the place of Jupiter, elevate the globe according to the latitude, and having brought the Sun’s place to the meridian, set the hour index to 12 at noon; then turn the mark which was made for Jupiter, to the Eastern part of the horizon, I find ♃ will rise somewhat more than half an hour after three in the afternoon; and turning the globe about, I find it comes to the meridian a little before eleven at night; and sets almost a quarter past six next morning.
This example being understood, it will be easy to find when either of the other two superior Planets, viz. Mars and Saturn, rise, set, and come to the meridian.
I shall conclude this subject about the Globes with the following problems.
Prob. XLVI. To find all that space upon the Earth, where an Eclipse of one of the Satellites of Jupiter will be visible.
Having found that place upon the Earth, in which the Sun is vertical at the time of the eclipse, by [Prob. 13], elevate the globe according to the latitude of the said place; then bring the place to the meridian, and set the hour index to 12 at noon. If Jupiter be in consequence of the Sun, draw a line with black lead, or the like, along the Eastern side of the horizon, which line, will pass over all those places where the Sun is setting at that time; then count the difference betwixt the right ascension of the Sun, and that of Jupiter, and turn the globe Westward, ’till the hour index points to this difference; then keep the globe from turning round its axis, and elevate the meridian, according to the declination of Jupiter. The globe being in this position, draw a line along the Eastern side of the horizon; then the space between this line, and the line before drawn, will comprehend all those places of the Earth where Jupiter will be visible, from the setting of the Sun, to the setting of Jupiter.