Chapter X. The periodital Divisions of Time（续 3）

_ 2. The second aspect is termed matutine location in the mid-heaven ; when the star is found on the meridian, either € above or. below the earth, while the Sun is on the oriental horizon. And of this:aspect, one species is called a succedent and oriental: location in the mid-heaven, invisible;

. when, immediately after the Sun’s rising, the star shall be found on the meridian : another is the precise oriental location in the mid-heaven ; when, exactly as the Sun rises, the star is at the same time on the meridian; another is the ori- _ ental precedent location in the mid-heaven ; when the star. first shall come to the meridian above the earth, and the Sun may then immediately rise. |

3. The third, called matutine setting, ia when the Sun may be actually ia the oriental horizon, but the star in the -eecidental. One of the forms of this aspeet is talled the _ oriental, suecedent setting, invisible; when the star sets immediately after the Sun’s rising: another is the precise oriental co-setting, when the star sets at the moment of the ‘Sun’s rising: epother is the oriental, precedent, and visible setting, when the Sun dogs not rise until immediately after the setting of the star.

4. The fourth aspect is named meridianal subsalar, and takes place when the Sun is actually op the meridian, but

the ster on the oriental horizon. Of this, one is diurnal and:

invisible ; when the star rises while the Sun is posited on the meridian -aboye the earth; another is nocturnal and visible ; when the star rises while the Sun is placed on was meridian below the earth.

5, The fifth is called meridianal location in the mid- —

heayen ; when the Sun, as well as the star, may be at the game time on the meridian. Of this aspect, two sorts are diarnal and invisible; when the star is on the meridjan

ahowe the earth, together with the Sun, or on that below the

. - earth, diametrically opposite to the Sun. Two also are noctuma], and of these, one 3s invisibles when the star is on the meridian under the earth, together with the Sunt the ‘other, however, is visible; when ths star is on-the meridian above the earth, diametrically opposite to the Gun.

6. The-sjxth is meridianal setting 5 when the star is found en the accidental bomzon, while the Sun is on the meridian. Of cubis, one species is diurnal and invisible ; when the star sets while the Hun is above the earth on the meridian: the other is nocturnal and visible; when the star sets while the Sua is on the meridian below the earth.

7. The seventh aspect is called vespertine subsolars whea the star is found on the oriental horizon, while the Sun is posited on the occjdental horizon, One form of this aspect

is the vespertine succedent rising, visible ; when the star rises immediately after sunset: another is the precise vespertine _ co-rising ; when the star rises and the Sun sets at one and ‘the same time: another is the precedent, vespertine rising, invisible ; when the star rises immediately before the Sun “sets, -

8. The eighth is _—e vespertine location in the midheaven; when the star is on the meridian, either above or below the earth, while the Sun is placed on the occidental horizon. Of this aspect, one kind is called a visible vespertine location in the mid-heaven; when the star is found there immediately after sunset: another is the precise vespertine location in the mid-heaven; when the star is found there at the moment of sunset : aaoiher is the vespertine precedent location in the mid-heaven, invisible ; when the Star arrives there inamediately before sunset.

9. The ninth aspect is called vespertine setting ; when the star, together with the Sun, is on the occidental horizon. One form of this aspect is the vespertine, succedent and visible setting ; when the star, at the commencement of its occultation, sets immediately after the Sun: another is the precise vespertine setting ; when the star sets at the same moment with the Sun: another is the precedent, invisible setting; when the star, before it emerges from its occultation, sets before the Sun.

ALMAGEST; Book II. Exrract From Cuap. IX. Of Circumstances regulated by Ascensions.

—IN any climate whatever, the magnitude of a given day or

night is to be computed by the number of ascensional times

proper to that particular climate. For example, the mag- FF

nitude of the day will be ascertained by numbering the times between the Sun’s zodiacal degree and the degrce diametri- ‘cally opposite, in the succession of the signs; and that of the night, by numbering the times, from the: degree diametrically opposite to the Sun, onwards, in the order of the signs, to the degree actually occupied by the Sun: because, by dividing the respective amounts of these times so obtained, by fifteen, the number of equatorial hours. belonging - to each space will be exhibited ;, and if the division be made by twelve, instead of fifteen, the result will shew the num- - bers of degrees equivalent to one temporal hour of either of the said spaces respectively*. ‘The magnitude of any temporal hour may be, however, more easily found by referring to the annexed Table of As-' censions, and taking the difference between the respective aggregate numbers, inserted therein under the heads of the equinoctial parallel or right sphere, and: of any. particular climate for which the magnitude of the temporal hour is required ; and, if the said hour be a diurnal hour, the ag-- gregate times as stated against the zodiacal degree occupied by the Sun; but, if nocturnal, those stated against the degree diametrically opposite, are to be compared; and the sixth part of the difference between them is to be added, if rn * Thus (according to the Table inscrted at p. 223), in the climate or latitude of Lower Egypt, the times of ascension between the first point of Gemini and the first point of Sagittarius, diametrically opposite, are 205° 18’, which, being divided by 15, give 13 hours 41'minutes and a fraction of equatoriat‘time, as the length of:the day of the first point of Gemini. And the same number of times of aseension, divided by 12, give 17° 6’ and a fraction of the equator, as the length of the diurnal temporal hour. ‘In the latitude of Southern Britain, the times of ascension between the same points as abovementioned are 236° 2’, which, divided by 15, give 15 hours 44 minutes and a fraction of equatorial time as the length of the day of the first point of Gemini; and, if divided by 12, they produce 19° 40’ and a fraction of the cquator, as the length of the diurnal femporal hour.

the said degtee be in the northern signs, to the fifteen times of an equatorial hour; but subtracted therefrom, if in the southern signs. The amountthus obtained will be the required number of degrees of the temporal hour in question*. And if it-be required to reduce the temporal hours of any -given day or night, in a certain climate, into equatorial ‘hours, they must be multiplied by their proper horary times, whether diurnal or nocturnal, as the case may be; the pro- .duct is then to be divided by fifteen, and the quotient will necessarily be the number of equatorial hours in the climate - in question, on the given day or nightt. On the other

* Thus, the aggregate times of ascension, in a right sphere, of the first point of Gemini are 57° 44’; and, in the climate of Lower Z:gypt, 45° 5’: the sixth part of the difference between them is 2° 6' and a fraction, which, added.to 15°, again makes the diurnal temporal hour of the first point of Gemini equal to 17° 6’ and a fraction of the equator. In the climate of Southern Britain, the aggregate times of ascension of the first point of Gemini are 29° 43’: the sixth part of the difference between that sum and 57° 44’ of right ascension is 4° 40 and a fraction, which, added to 15°, makes the diurnal temporal hour of the first point of Gemini, in South Britain, equal to 19° 40’ and a fraction of the equator, as before shewn.

+t For example, \ Diurnal horary times of the first point of Gemini, in the latitude of Alexandria - = © «= «= 17°. & $0"