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zenith, and turn the globe till the hour index points to the given hour, and set the quadrant of altitude to the given azimuth; then the star that cuts the quadrant in the given altitude, will be the star sought.

Though two stars, that have different right ascensions, will not come to the meridian at the same time, yet it is possible that in a certain latitude they may come to the same vertical circle at the same time; and that consideration gives the following

PROBLEM XXX. The latitude of the place, the sun's place, and two stars that have the same azi.. muth, being given, to find the hour of the night.

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Rectify the globe for the latitude, the zenith, and the sun's place; then turn the globe, and also the quadrant about, till both the stars coincide with its edge; the hour index will shew the hour of the night, and the place where the quadrant cuts the horizon, will be the common azimuth of both stars.

On the 15th of March, at London, the star Betelgeule, in the shoulder of Orion, and Regel, in the heel of Orion, were observed to have the same azimuth ; on working the problem, you will find the time to be 8 hours 47 minutes.

What hath been observed above, of two stars that have the same azimuth, will hold good likewise of two stars that have the same altitude; from whence we have the following

PROBLEM Xxxt. The latitude of the place, the sun's place, and two stars, that have the same altitude, being given, to find the hour of the night.

Rectify the globe for the latitude of the place, the zenith, and the sun's place; turn the globe, so that the same degree on the quadrant shall cut both stars, then the hour index will shew the hour of the night.

In the former propositions, the latitude of the place is supposed to be given, or known; but as it is frequently necessary to find the latitude of the place, especially at sea, how this may be found, in a rude manner at least, having the time given by a good clock or watch, will be seen in the following

PROBLEM XXXII. The sun's place, the hour of the night, and two stars, that have the same azimuth or altitude, being given, to find the latitude of the place.

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Rectify the globe for the sun's place, and turn it till the index points to the given hour of the night; keep the globe from turning, and move it up

and down in the notches, till the two given stars have the same azimuth, or altitude; then the brass meridian will shew the height of the pole, and consequently the latitude of the place.

PROBLEM XXXIII. Two stars being given, one on the meridian, and the other on the east or west part of the horizon, to find the latitude of the place.

Bring the star observed on the meridian to the me. ridian of the globe; then, keeping the globe from turning round its axis, slide the meridian up and down in the notches, till the other star is brought to the east or west part of the horizon, and that elevation of the pole will be the latitude of the place sought.

OBSERVATION. From what hath been said, it appears, that of these five things, 1. the latitude of the place; 2. the sun's place in the ecliptic; 3. the hour of the night; 4. the common azimuth of two known fixed stars; 5. the equal altitude of two known fixed stars ;--any three of them being given, the remaining two will easily be found.

There are three sorts of risings and settings of the fixed stars, taken notice of by the ancient authors, and commonly called poetical risings and settings, because mostly taken notice of by the poets.

These are the cosmical, achronical, and heliacal.

They are to be found in most authors that treat on the doctrine of the sphere, and are now chiefly used in comparing and understanding passages in the ancient writers ; such as Hesiod, Virgil, Colu

* Costard's History of Astronomy.

mella, Ovid, Pliny, &c. How they are to be found by calculation, may be seen in Petavius's Uranologion, and Dr. Gregory's Astronoiny.

DEFINITION. When a star rises or sets at sunrising, it is said to rise or set cosmically.

From whence we shall have the following

PROBLEM XXXIV. The latitude of the place being given, to find, by the globe, the time of the year when a given star rises or sets cosmically.

· Let the given place be Rome, whose latitude is 42 deg. 8 m. north ; and let the given star be the Lucida Pleiadum. Rectify the globe for the latitude of the place; bring the star to the edge of the eastern horizon, and mark the point of the ecliptic rising along with it'; that will be found to be Taurus, 18 deg. opposite to which, on the horizon, will be found May the 8th The Lucida Pleiadum, there. fore, rises cosmically May the sth.

If the globe continue rectified as before, and the Lucida Pleiadum be brought to the edge of the western horizon, the point of the ecliptic, which is the sun's place, then rising on the eastern side of the horizon, will be Scorpio, 29 deg. opposite to which, on the horizon, will be found November the 21st. The Lucida Pleiadum, therefore, sets cosmically November the 21st.

In the same manner, in the latitude of London, Sirius will be found to rise cosmically Aug. the 10th, and to set cosmically Nov. the 10th.

It is of the cosmical setting of the Pleiades, that Virgil is to be understood in this line,

Ante tibi Eoz Atlantides abseondantur,*

and not of their setting in the east, as some have imagined, where stars rise, but never set.

DEFINITION. When a star rises or sets at sun setting, it is said to rise or set achronically.

Hence, likewise, we have the following

PROBLEM XXXV. The latitude of the place being given, to find the time of the year when a given star will rise or set achronically.

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Let the given place be Athens, whose latitude is 37 degrees north, and let the given star be Arcturus.

Rectify the globe for the latitude of the place, and bringing Arcturus to the eastern side of the horizon, mark the point of the ecliptic then setting on the western side; that will be found Aries, 12 deg. opposite to which, on the horizon, will be found April the 2d. Therefore Arcturus rises at Athens achroni. cally April the 2d.

* Georg. I. i. v. 221.

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