ALLUSIONS IN ANCIENT WRITINGS.

357

Ancient familiar allusions to the Risings and Settings of particular Stars.

w" The Greeks seem early to have seen the superior accuracy and determinateness of the celestial phenomena. In the didactic poem of Hesiod, this mode of marking the times of navigation and of rural labours is frequently employed; and its use was retained by the country-folk of both Greece and Italy far into the time of the Roman empire. Those who wrote on rural subjects or natural history, employed it: we meet with it in Aristotle, as well as in Pliny and Columella."-Keightley's Edition of Ovid's Fasti. (Introduction, p. xiv.)

X" The (Latin) poets teem with allusions to them, so much so that many passages must be unintelligible without we know the times at which certain stars or constellations, more particularly Capella, Arcturus, the Pleiades, and Orion, rose and set heliacally and acronychally at those times and for those countries."-" Astronomy," Library of Useful Knowledge, p. 169.

Y *

*

*

"Rain, wind, and other aërial phenomena were held to be connected with the rising and setting of various signs; the times of their risings and settings, both apparent and real, were computed by Meton, Eudoxus, and other ancient astronomers. The tables thus constructed were cut on brass or marble, and fixed up (whence they were called Tapaжhyμara) in the several cities of Greece, and the peasant or sailor had only to look on one of these parapegmata, to know what sign was about to rise or set, and what weather might be expected. Without considering the difference of latitude and longitude, * the Romans borrowed the parapegmata, like every thing else, from the Greeks. The countryman, as we learn from Pliny (xviii. 60, 65), ceased to mark the stellar heavens ; a kalendarium rusticum siderale (Colum. ix. 14) taught him when the signs rose and set, and on what days he was to expect sacrifices and festivals."-Keightley's Ed. Ovid's Fasti. Introd.

* The longitude could make no difference.

COSMICAL, ACRONYCHAL, AND HELIACAL RISINGS AND SETTINGS.

z Stars are said to rise or set cosmically * when they rise or set at sun-rise.

Stars are said to rise or set acronychally † when they rise

or set at sun-set.

Those stars which, during the past month, have been visible above the western horizon each succeeding evening for a shorter time than its preceding one, will be said to set heliacally when, a few days hence, they first cease to be visible because of the sun's arriving into that part of the ecliptic from which, even as late as at their time of setting, his evening twilight can overpower them.

Stars are said to rise heliacally, when, after having hidden them in the splendour of his rays, the sun first gets so far eastward of them as that his morning twilight can no longer overpower them at their rising.

The Cosmic relates to the morn;

Acronych, to sun-set or first night;"

Heliac, at eve or at dawn

The horizon's condition in light.

KOσμos, the distribution or order of things--the world. † ȧkpóvvč, prima nox, the beginning (one end) of the night. † ἡλιακος, solar.

TIMES OF COSMICAL RISING, ETC.

359

PROBLEM N.

CELESTIAL GLOBE.

Given the latitude, to find the time of year at which a particular star now rises or sets cosmically, acronychally, or heliacally.

RULE.-Rectify the globe for the given latitude, and attach the quadrant to the declination in the zenith: Then,

I. With regard to a given star at its rising :

Bring the star to the eastern, or rising, edge of the horizon; and, keeping the globe from rotating,

1. Look for the degree of the Ecliptic rising with the star-this will shew the day on which (in the present age of the world) the star rises cosmically.

2. Find, by the quadrant, that degree of the Ecliptic which is only 12 * degrees below the eastern horizon :— this will shew the day on which the star rises heliacally.

3. Look for the degree of the Ecliptic coinciding with the western or setting edge of the horizon :- -this will shew the day on which the star rises acronychally.

II. With regard to a given star at its setting

Bring the given star to the western, or setting, edge of the horizon;-then, keeping the globe from rotating,

1. Find, by the quadrant, that degree of the Ecliptic which is 12* degrees below the western horizon :-this will shew the day on which the given star sets heliacally.

2. Look for the degree of the Ecliptic setting with the star :-this will shew the day on which the star sets acronychally.

3. Look for the degree of the Ecliptic in the eastern horizon :--this will shew the day on which the star sets cosmically.

* If the given star be only of the second magnitude, 13 degrees, &c. (see page 133).

Ex. 1. At what time of year does Aldebaran now rise cosmically, at what time heliacally, and at what time acronychally, at London?

Answer. Cosmically, 18° II (8th June)-heliacally, 15° (7th July)-acronychally, 17° ↑ (8th December).

Ex. 2. On what day of the year does Aldebaran now set heliacally, on what day does it set acronychally, and on what day cosmically, at London?

Answer. Heliacally, 14° 8-acronychally, 2° II - cosmically, 3o 7.

Ex. 3. On what days of the year does Sirius now rise at Rome (latitude 42°), cosmically, heliacally, and acrony chally?

Ex. 4. On what days do these several risings of Sirius take place at Alexandria (lat. 31°) ?

Ex. 5. On what three days does Spica (a of Virgo) set heliacally, acronychally, and cosmically, at Madrid?

Ex. 6. In the evening of what day might Antares be seen to set for the last time, in a clear horizon, in lat. 51 N.; and in the morning of what day will it first be seen in that latitude, after having been involved in the sun's rays? (See Z, p. 358.)

Ex. 7. For how many days longer is this star (Antares) visible in the evening at Madrid than in the latitude of

London?

Ex. 8. What are the cosmical and acronychal risings of Castor at Edinburgh and at Gibraltar ?

Ex. 9. On what day does (in Orion's girdle) rise cosmically at London; and how many days after will it be sufficiently removed from strong twilight to be seen at its rising, in the morning? (See note on last page.)

Ex. 10. On what day, at Greenwich, does & in the girdle of Orion rise at sunset; and at what altitude will it be when the sun on that evening becomes 13° depressed, and the whole constellation may be plainly discernible?

EXERCISES ON THE EFFECT OF PRECESSION. 361

Exercises concerning the effect of Precession on the places of the Stars in relation to the Equinoctial and its Poles, the Equinoxes, Solstices, &c.

I. With regard to their Longitudes :

Since the lines of celestial longitude (drawn from the ecliptic and converging in the pole of the ecliptic) all refer to the intersection at the first point of Aries, the consequence of the westward or retrograde shifting of this point is a westward shifting of each of these lines also; and, therefore, an apparently forward motion of the stars themselves along their several parallels of latitude; hence,

RULE. The number of degrees of any proposed change in a star's longitude multiplied by 72 (R, p. 355), will shew the number of years occupied in producing that change. Or,-If the time be given and the change demanded, the longitude will be 1° less for every 72 years elapsed, or 1° greater for every 72 years to come.

Ex. 1. How long is it (nearly) since the two remarkable stars in the Goat's head had longitude 10 signs passing through them; and how many years hence will their longitude become 10s. 5°?

Answer. Their longitude at present is 10 signs 110:-hence, on a celestial globe constructed 72 years × 1, or 108 years ago, these stars must have had longitude 10 signs passing through them; and in 72 yrs. X 3, or about 250 years hence, their longitude will be 10 signs 5o. The pupil may readily perceive that, when this time shall come, not only their times of culmination must be different, but that their declinations also will be a little less south, and their diurnal arcs, &c., consequently altered in any given latitude.

2. What is the present longitude of the chief of the Pleiades; and what will be its longitude in about seventytwo years?

Ex. 3. What was the longitude of 8 of Aries about 80 years ago; and what will be the longitude of a of Aries as laid down on a globe published about 36 years hence?

Ex. 4. How long is it since the star 8 of Aries had longitude 0, and the Equinoctial point r was consistent with its constellation?