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It is of this rising of Arcturus that Hesiod speaks in his Opera and Dies.*
When from the solstice sixty wint'ry days
If the globe continues rectified to the latitude of the place, as before, and Arcturus be brought to the western side of the horizon, the point of the ecliptic setting along with it will be Sagittary, 7 degrees opposite to which, on the horizon, will be found November the 29th. At Athens, therefore, Arcturus sets achronically November the 29th.
In the same manner Aldebaran, or the Bull's Eye, will be found to rise achronically May the 22d, and to set achronically December the 19th.
DEFINITION. When a star becomes visible in a morning, after it hath been so near the sun as to be hid by the splendour of his rays, it is said to rise heliacally.
But for this there is required some certain depression of the sun below the horizon, more or less, according to the magnitude of the star. A star of the first magnitude is commonly supposed to require that the sun be depressed 12 degrees perpendicularly below the horizon.
This being premised, we have the following
* Lib j. ver. 285.
PROBLEM XXXVI. The latitude of the place being given, to find the time of the year when a given star will rise heliacally.
Let the given place be Rome, whose latitude is 42 degrees north, and let the given star be the bright star in the Bull's Horn.
Rectify the globe for the latitude of the place, screw.on the brass quadrant of altitude in its zenith, and turn it to the western side of the horizon. Bring the star to the eastern side of the horizon, and mark what degree of the ecliptic is cut by 12 degrees, marked on the quadrant of altitude; that will be found to be Capricorn, 3 deg. the point opposite to which is Cancer, 3 deg. and opposite to this will be found on the horizon, June 25th. The bright star, therefore, in the Bull's Horn, in the latitude of Rome, rises heliacally June 25th.
These kinds of risings and settings are not only mentioned by the poets, but likewise by the ancient physicians and historians.
Thus Hippocrates, in his book De Ære, says, “ One ought to observe the heliacal risings and settings of the stars, especially the Dog-Star, and Arcturus ; likewise the cosmical setting of the Pleiades.”
And Polybius, speaking of the loss of the Roman fleet, in the first Punic war, says, “ It was not so much owing to fortune, as to obstinacy of the consuls, in not hearkening to their pilots, who dissuaded them from putting to sea at that season of
the year, which was between the rising of Orion and the Dog-star; it being always dangerous, and subject to storms."*
DEFINITION, When a star is first immersed in the evening, or hid by the sun's rays, it is said to set heliacally.
And this again is said to be, when a star of the first magnitude comes within twelve 'degrees of the sun, reckoned in the perpendicular.
Hence, again, we have the following
PROBLEM XXXVII. The latitude of the place being given, to find the time of the year when a given stur sets heliacally.
Let the given place be Rome, in latitude 42 deg. north, and let the given star be the bright star in the Bull's Horn. Rectify the globe for the latitude of the place, and bring the star to the edge of the western horizon ; turn the quadrant of altitude, till 12 deg. cut the ecliptic on the eastern side of the meridian. This will be found to be 7 deg. of Sagittary, the point opposite to which, in the ecliptic, is 7 deg. of Gemini; and opposite to that, on the horizon, is May the 28th, the time of the year when that sets heliacally in the latitude of Rome.
OF THE CORRESPONDENCE OF THE CELESTIAL AND
That the reader may thoroughly understand what is meant by the correspondence between the two spheres, let him imagine the celestial globe to be delineated upon glass, or any other transparent matter, which shall invest or surround the terrestrial globe, but in such a manner, that either may be turned about upon the poles of the globe, while the other remains fixed, and suppose the first point of Aries, on the investing globe, to be placed on the first point of Aries, on the terrestrial globe (which point is in the meridian of London), then every star in the celestial sphere will be directly over those places to which it is a correspondent. Each star will then have the degree of its right ascension directly upon the corresponding degree of terrestrial longitude; their declination will also be the same with the latitude of the places to which they answer; or, in other words, when the declination of a star is equal to the latitude of a place, such star, within the space hours, will pass vertically over that place, and all others that have the same latitude.
If we conceive the celestial investing globe to be fixed, and the terrestrial globe to be gradually turned from west to east, it is clear, that as the meridian of London passes from one degree to another,
* Allams's Trcatise on the Globes.
under the investing sphere, every star in the celestial sphere becomes correspondent to another place upon the earth, and so on, until the earth has completed one diurnal revolution; or till all the stars, by their apparent daily motion, have passed over every meridian of the terrestrial globe. From this view of the subject, an amazing variety, uniting in wonderful and astonishing harmony, presents itself to the attentive reader; and future ages will find it difficult to investigate the reasons that should induce the present race of astronomers to neglect a subject so highly interesting to science, even in a practical view, but which in theory would lead them into more sublime speculations, than any that ever yet presented themselves to their minds,
A GENERAL DESCRIPTION OF THE PASSAGE OF THE
STAR MARKED Y IN THE HEAD OF THE CONSTEL
LATION DRACO, OVER THE PARALLEL OF LONDON,
The stary, in the head of the constellation Draco, having 51 deg. 32 min. north declination, equal to the latitude of London, is the correspondent star " thereto. To find the places which it passes over, bring London to the graduated side of the brass meridian,
will find that the degree of the meridian over London, and the representative of the star, passes over from London, the road to Bristol, crosses the Severn, the Bristol channel, the counties of Cork and Kerry, in Ireland; the north part of the Atlan