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Then Dr B+ BYA=DYA = 78° 21', Then fay;

78 21 C. A. 0.6947934

As the Co-fine of DYA
To the Co-fine of DYB = 54 52
So is the Tangent of BY = 29 54
To the Tangent of YA = 58 36

Whence the with the Star is Place about the required.

9.7600311 9.7596871

10.2145116

Point A in the Ecliptic which rifeth 28° 36'; and the Sun being in this 9th of May, fhews that is the Time

PROBLEM XXXIII.

Given the Latitude of the Place, and the Oblique Defcenfion of a Star or Planet, to find the Time of its Cofmical Setting.

Practice.

Admit the Oblique Defcenfion of the Star Fomabant be 2920 32', I demand the Time of his Cofmical Setting at Chichester, Lati-H tude 50° 56 ?

The Scheme being drawn, there is formed the Oblique Triangle B AY, "in

which there is given

P

E

Æ

D

the Angle at Y= 23o 29'; the Angle at B = 39° 04; and the Side B Y= 67° 28', the Distance of

the

the Oblique Defcenfion from the Point Aries V; to find the Side Ar; which by letting fall the Perpendicular YD, is performed thus;

As Radius

To the Co-fine of BY 67° 28'
=
So is the Tangent of DBY= 39° 04′

To the Co-tangent of DYB = 72° 43'

10.0000000

72° 43'

9.5834491 9.9094022 9.4928513

Then fay

49

14 C. A. 0.1851001

9.4728985

10.3820615

As the Co-fine of DYA

Is to the Co-fine of DYB = 72 43
So is the Tangent of BY = 67 28
To the Tangent of AY = 47

38

That is in the Ecliptic, fhort of Aries 1

to which add fix Signs

and fubftract the Sum

from twelve Signs

there remains the Afcendant

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17 38

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that is 12° 22' of the Sign Leo, in which Point the Sun is, about the 25th Day of July; and that is the Time required.

PROBLEM XXXIV.

Given the Latitude of the Place, and the Oblique Afcenfion and Defcenfion of a Star or Planet, to find the Time of its Rifing Achronically; and alfo of its Achronical Setting.

Practice.

Practice.

The Solution of this Problem is deduced from the two foregoing ones; for fince a Star rifes achronically when the Sun fets the Moment it riteth, therefore find the Point of the Ecliptic which rifeth with the Oblique Afcenfion of the Star, and its oppofite Point will be that which is fought.

Thus the Point of the Ecliptic which rifeth with the Oblique Afcenfion of Fomabant is 28° 36′, whofe oppofite Point is m 28° 36', to which Place the Sun arrives about the Tenth Day of November, and that is the Time when this Star rifeth achronically.

The Achronical Setting of a Star, is when it fetteth with the Sun; therefore that Point of the Ecliptic which defcends with the Oblique Defcenfion of a Star is the Point fought.

Thus the Point of the Ecliptic which defcends with the Oblique Defcenfion of Fomabant is 12° 22', by the laft Problem.

Now the Sun comes to this Point about the 21ft of January; and then will this Star fet achronically, as required.

PROBLEM XXXV.

Given the Latitude of the Place, the Depreffion of the Star below the Horizon, and the Time of its Cof mical Rifing, to find the Time of its Helical Rifing,

Practice.

The Helical Rifing of the fixt Stars and Planets, is only their getting out of the Sun Beams fo far as to VOL. II. M m

appear

appear visible; but as the Magnitude and Splendor of the Stars is greater and less, so there is required a lefs or greater Distance from the Sun, in order to their Vifibility. With regard to the Horizon, the Stars and Planets become vifible according to their Magnitudes, and require a particular Depreffion of the Sun below the Horizon, as is hereunder fet down.

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Now let it be required to find the Heliacal Rifing of the Star Fomabant of the firft Magnitude, at Chichefter, Lat. 50° 56', where he rifeth Cofmically when the Sun enters 289 36'?

Let:

Let the Scheme be conftructed as in

H

Prob. 32; draw the Parallel of 12° Depreffion (for Foma- E bant is a Star of the firft Magnitude) and thro' the Point of Interfection with the Ecliptic at D, defcribe the Azimuth ZDN; fo fhall there be constitu

ted the Right-angled

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Triangle ABD, in which calculate the Angle at A by Prob. 28, which you will find to be 21° 36', the Altitude of the Nonagefima Degree; befides which there is given the Side B D 12°, the Depreffion, or Arch of Vifion; by which to find the Side A D, the Distance of the Sun in D from the Cofmical Place at A, to do which fay;

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That is in the Ecliptic

To which add his Cofmical Place in

The Sum is the Heliacal Place in

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Which Place the Sun occupies June the Thirteenth, and that is the Day fought; for then will this Star be vifible at his Rifing in the Morning.

VOL. II.

M m 2

PRO

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