Chapter X. The periodital Divisions of Time（续 2）

time, or méasurement of the arcs of direction, is also treated of, in reference to the 16th canon of Placidus, which is as follows :—

“ To equate the Arc of Direction. Add the arc of direction to the “ right ascension of the natal Sun; look for this sum in the table of “‘ right ascensions under the ecliptic, and take the degree and minute “ of longitude corresponding with that sum; then, in the best ephe- “‘ meris, reckon in how many days and hours the Sun, from the day * and hour of birth, has arrived at that-degree and minute. The num- “ber of days indicate as many years; every two hours over, reckon “amonth.” (Ibid. p. 55.) ® Whether general or annual.

Chap. X.] . PTOLEMY’S TETRABIBLOS., _ 211

It is in this method, which preserves a natural order and succession, that times and seasons require to be contemplated.

And now, in adverting to the scope allotted to this work in its commencement, all further adaptation of the forms of events liable to take effect at particular times will here be relinquished ; because the operative influences which the stars exercise in all events, whether general or particular, may be arranged in proper order, if care be taken that the causes set forth by the Rules of Science, and the causes arising from any existing commixture, be duly combined and blended together.

thi an! Ger ~ asm ee. are eh = oon henge ues ec ad

THE vattous constellations of the fited stats having now - beens duly described, theit aspects remain to be investlgated.

independently of the stedfast and ‘amitatte aspects which the said stars preserve among themselves, either rectilinearly, | or triangularly, or by other similar forms*, they have also _ certain aspects considered as referring exclusively to the planets and the Sun and Moon, or parts of the zodiac ; certain’ others to the earth only ; and others, again, to the earth, the planets and the Sun and Moon, or parts of the zodiac, combined.

With regard to the planets only, and parts of the zodiac, . aspects are properly considered as made to them by the fixed stars, when the said planets and fixed stars may be posited on one and the same of those circles which are drawn . through the poles of the zodiac ; or, also, if they be posited on different circles, provided a trinal or sextile distance be--

tween them may be preserved ; that. is to say, a distance © |

equal te.a right angle and a third part more, or a distance equal to two thirds of a right angle; and provided,’ also, that the fixed stars be on such parts of the -circle as are liable to be transited by any orie of the planets. These parts are

* That is to say, by the opposition, trine, &c.

situated within the latitude of the soiliac, which circumscribes the planetary motions. And as far as the five planets are concerned, the aspects of the fixed stars depend upon the visible mutual conjunctions, or configurations, made in the - forms above prescribed 5 but, with respect to the Sun and Moon, they depend on occultations, conjunctions, and suc- _ cedent risings of the stars. Occultation is when a star becomes invisible by being carried under the rays of the lucninary 3 conjunction, when it is placed under the lumi-+ nary’s ceitre; and succedent fising, when it dam to ree appear on issuing out beyond the rays.

In regard to the earth only, the aspects of the fixed stars are four ta number, and are known by the common term of angles; to speak, however, more particularly; they are the oriental horizon, the meridian of mid-heaven above the ¢arth, the occidental horizon, and the. meridian or mid+- “heaven below the earth. And in that part of the earth where " the equator is in the zenith, the whole of the fixed stars

'” ‘are found to rise and set, and to be aboye as well as below the

_ earthy‘once in each revolutions because the situation of the . poles f ‘the equator, being in this manner on the plane of the

~~ horizon, thereby preverits the constant visibility or invisibility

‘of any one of thé parallel circles, But in other parts of the ‘ earth, where the pole of the equator is in the zenith, the "fixed stars ‘cah never set nor rise 3 because the equator itself . is.¢hen on the plane of the horizon, and. circumscribes the | two hemispheres (which it thus creates, one above and the ethet below the earth) in such a manner, thzt in one revolu- _féon every star tust twice traziait: the meridian, some of | them above, others below the earth, In other declinations,

fhowever, béetween these extreme positions of the equator, as

. just mendtioued, there are certain of ilve circles always visible,

= and othets never visible ; ‘consequently, the stars intercepted _

between the first of sisch nce and :the poles can neither rise nor set, but saust, in the course of one revolution,’ twice

transit the meridian ; above the earth, if the said stars be on a circle always visible ; but below the earth, if on a circle never visible. The other stars, however, situated on the greater parallels, both rise and set, and are found in each revolution once on the meridian above the earth, and once on that below the earth.—lIn all these cases, the time occnpied in proceeding round from any one angle to the same again, must be everywhere equal in its duration, for it is marked by one sensible revolution; and the time occupied in passing from either meridianal angle to the angle diametrically opposite, is also everywhere equal ; because it is marked by the half of one revolution. So, also, the passage from either horizontal angle to its opposite angle is again effected in the same equal portion of time, wherever the equator may be in the zenith, for it is then likewise marked by the half of an entire revolution ; because on such

.a position of the equator, all the parallels are then divided,

as well by the horizon as by the meridian, into two equal parts. But in all other declinations, the time of passage of a semicircle above the earth is not equal to that of its passage below the earth, except only in the case of the equinoctial circle itself, which, in an oblique sphere, is the only one divided by the horizon into two equal parts, all others (its parallels) being bisected into dissimilar and unequal arcs. It follows, accordingly, that the time contained in the space between rising or setting, and either meridian, must be equal to the time between the same meridian and rising or setting; because the meridian divides equally such portions of the parallels as are above or under the earth. But in proceeding in an oblique sphere, from rising or setting to either meridian, the time occupied must be unequal ; and in a right sphere, equal, because the entire portions above the earth are, in a right sphere only, equal to those below the earth ; whence, for instance, in a right sphere, whatever stars may . be together on the meridian must also all rise and set ‘to-

gether, until their progress becomes perceptible by the poles of the zodiac; while, on the other hand, in an oblique sphere, whatever stars may be together on the meridian can neither all rise together nor set together; for the more southern stars must always rise later than those which are more northern, and set earlier*.

- The aspects. made by the fixed stars, in regard to the planets or parts of -the zodiac, and the earth combined, are, considered, in a general manner, by the rising, or meridianal

_ position, or setting of the said fixed stars in conjunction with any planet or part of the zodiac ; but their aspects are properly distinguishable, by means of the Sun, in the nine following modes :—

1.. The first is called matutine subsolar, when the star is found together with the Sun in the oriental horizon. Of this aspect, one species is called the oriental, invisible, and succedent rising ; when the star, at the commencement of its occultation, rises immediately after the Sun: another is called the precise oriental co-rising ; when the star is found in partile conjunction with the Sun in the oriental horizon : another is the oriental, precedent, and visible rising; when the star, beginning to appear, rises before the Sun.