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PROBLEM XLVIII. To find the latitude, longitude,
declination, and right ascension of the comets.
In the circles of latitude contained in the zodiac, you will find the latitude of the comet to be about 30 deg. 30 min. from the ecliptic; the same circle of latitude reduces its place to the ecliptic in 26 deg. 30 min. of menwhich is its longitude sought. Then bring the cometary patch to the brazen meridian, and its declination will be shewn to be 9 deg. 15 min. south. At the same time, its right ascension will be 227 deg. 30 min.
PROBLEM XLIX. To shew the time of the comets, rising, southing, setting, and amplitude, for the day of the observation at Jamaica.
Bring the place of the comet into the eastern semicircle of the horizon, (the globe being rectified as directed) the index will point to III hours 15 min. which is the time of its rising in the morning at Jamaica, the amplitude 10 deg. very nearly to the south. The patch being brought to the meridian, the index points to IX o'clock 10 min. for the time of culminating, or being south to them. Lastly, bring the patch to touch the western meridian, and the index will point to III in the afternoon, for the time of the comet's setting, with 10 degrees of southern amplitude, of course.
PROBLEM L. From the comet's place being given, to find the time of its rising in the horizon of London, on the 31st day of March, 1759.
purpose you need only rectify the globe for the given latitude of London, and bring the cometary patch to the eastern horizon, and the index points to III hours 45 min. for the time of its rising at London, with about 14 deg. of south amplitude ; then turn the patch to the western horizon, and the index points to II h. 25 min. the time of its setting.
N.B. From hence it appears, the comet rose soon enough that morning to have been observed at London, had the heavens been clear, and the astronomers been before-hand apprized of such a phenomenon.
PROBLEM LI. To determine another place of the same comet, from an observation made at London on the 6th day of May, at ten in the evening.
On the 6th day of May, 1759, at ten at night, the place of the comet was observed, and its distance measured with a micrometer, from two fixed stars, marked v and v, in the constellation called Hydra, and its altitude was found to be 16 deg. and its azimuth 37 deg, south-west; from whence its place on the surface of the globe is exactly determined as in Problem xlvii, and having stuck a patch thereon, you will have the two places of the comet on the surface of the globe, for the two distant days and places of observation, as required,
From two given places of a comet, to assign its apparent path among the fixed stars in the heavens.
The two places of the comet being determined by the observations on the 31st of March, 1758, and the 6th of May following, and denoted by two patches respectively, you must move the globe up and down, in the notches of the horizon, till such time as you bring both the patches to coincide with the horizon; then will the arch of the horizon be. tween the two patches shew, upon the celestial globe, the apparent place of the comet in the interval between the two observations, and by drawing a line with a black-lead pencil along by the frame of the horizon, its path on the surface of the globe will be delineated, as required. And here it may be observed, that its apparent path lies through the following southern constellations, viz. the tail of Capricorn, the tail of Piscis Australis, by the head of Indus, the neck and hody of Pavo, through the neck of Apus, below Triangulum Australe, above Musca, by the lowermost of the Crosiers, across the hind legs and through the tail of Centaurus, from thence between the two stars in the back of the Hydra be. fore-mentioned ; after this, it passed on to Sextans Uraniæ, and then to the ecliptic near Cor Leonis, soon after which it totally disappeared.
PROBLEM LIII. To estimate the apparent velocity of a comet, two places thereof being given by observation.
Let one place be ascertained near the beginning of its appearance, and the other towards the end thereof; then bring these two places to the horizon, and count the number of degrees intersected between them, which being the space apparently described in a given time, will be the ve locity required. Thus, in the case of the above-mentioned comet, you will find that it described more than 150 deg. in the space of 36 days, which is more than four deg. per day,
PROBLEM LIV. To represent the general phenomenon
of the comet for any given latitude. Bring the visible path of the comet to coincide with the horizon, by which it was drawn, and then observe what degree of the meridian is in the north point of the horizon, which, in the case of the foregoing comet, will be the 23d deg. This will shew the greatest latitude in which the whole path can be visible in any latitude less than this, as that of Jamaica; where, for instance, the most southern part of the path will be elevated more than five deg. above the horizon, and the comet visible through the whole time of its apparition. But rectifying the globe for the latitude of London, the path of the said comet will be for the most part invisible, or below the horizon; and therefore it could not have been seen in
our latitude, but at times very near the beginning and end of its appearance ; because, by bringing the comet's path on one part to the south point of the horizon, it will immediately appear in what part the comet ceases to be visible; and then bringing the other part of the path to the point, it will appear in what part it will again become visible.
After this manner may the problems relating to any other comets be performed; and thus the paths of the several comets, which have hitherto been observed, may be severally delineated on the celestial globe, and their various phenomena in different latitudes be thereby shewn.
Note. A much more remarkable comet than the one of 1807, and which I noticed at page 166 of this work, made its first appearance in our northern hemisphere at the end of August last, and has continued till the present time (25th Dec. 1811), traversing among the northern constellations, with superior brilliancy, extent of coma and duration, to all other comets observed in the last century. It is now nearly at its extreme diminution of appearance, or at the vanishing distance.
It was only first observed about its recess from the perihelion, or the sun, and the following is the best summary of its paths and elements, that could be collected from various correct observations, on clear nights : 1811. Right Ascension,
North Declination. Aug. 21 147° 18'
0' 32° 53' 0" Sept. 1 155
39 19 12