Altitude, croffing the Ecliptick in 29 d. of Taurus, where the Fig. Sun is 12 d. high, and is equal to the Complement of the Sun's XXXIII. Altitude 78 d. (3) An Arch of a Meridian (or Hour-Circle) Po, passing through 29 d. of Tturus, and croffing the Quadront of Altitude in 12 d. thereof, and is equal to the Complement of the Sun's Declination (or his Distance from the Pole) 70 d. So that the Three Sides of this Triangle are Given, and the Three Angles are Required.

The Canons for Calculation.

r. For the Sun's Azimuth, the AngleZP. By Cafe IX.
of O. A. S. T.

93 15

The Difference between the half Sum, and 70 d. P 23 45

Being thus prepared, the Proportions are,

(1.) As the Radius, Sine 90 d.

Ís to the Sine of ZP (one of the Sides containing the enquired Angle Z) 38 d. 30 m.

So is the Sine of Zo (the other Side containing the enquired

Angle Z) 78 d.

To the Sine of 37 d. 31 m. (2.) (2.) As this Sine of 37 d. 31 m.

Is to the Sine of the half Sum, 93 d. 15 m. (or 86 d. 45 m.) So is the Sine of the Difference, 23 d. 15 m.

To the Sine of 40 d. 20 m.

(3.) To this Sine of 40 d. 20 m. add the Radius, and it will be 19.811063; the half whereof 9.905531 is the Sine of 53 d. 34 m. Whose Complement 36 d. 26 m. doubled, makes 72 d. 52 m. And that is the Quantity of the Angle ZP: Or the Sun's Azimuth from the North Part of the Meridian. And that taken from 90 d. leaves 17 d. 8 m. for the Sun's Azimuth from the East or Weft. And that added to 90 d. gives 107 d. 8 m. for the Sun's Azimuth from the South.

Fig. XXXIII.

2. For the Hour, the Angle ZPO. By Cafe I. of O. A.

S. T.

As the Sine of the Side P (70 d.)

Is to the Sine of the Angle

ZP, (72 d. 52 m.)

So is the Sine of the Side Z (78 d.)

To the Sine of the Angle ZPO, (84 d. 7 m.)

And that is the Hour, counted from the North Part of the
Meridian (which in Time is 5 h. 36 m. that is, 36 m.

after 5 in the Morning, or 95 d. 53 m. (or 6 h. 24 m.)
from the South.

3. For the Angle ZOP, the Angle of Pofition. By Cafe

I. of O. A. S. T.

As the Sine of the Side P, (70_d.)

Is to the Sine of the Angle

ZP, (72 d. 52 m.)

So is the Sine of Z P, (38 d. 30 m.)

To the Sine of the Angle ZOP, 39 d. 16 m.
Which is the Angle of the Sun's Position.

PROB. Χ.

To find the Longitude and Latitude of any Star.

THE HE Longitude Longitude of any Star is an Arch of the Ecliptick, contained between the beginning of Aries, and the Interse&ion of an Arch of a great Circle, which passeth through both the Poles of the Ecliptick, and also through the Body of that

Star.

The Latitude of a Star is that Part of an Arch of a great Circle, which passeth through both the Poles of the Ecliptick, and through the Body of the Star, and is contained between the Ecliptick Line and that Star.

I. For the Longitude, Skrew the Quadrant of Altitude over that Pole of the Ecliptick which is nearest to the Star, whose Longitude you seek. Then laying the Quadrant just over the Centre of the Star, look what Degrees of the Ecliptick, are cut by the (counting them from the beginning of Aries) Quadrant of Altitude, and those Degrees are the Degrees of the Star's Longitude. So the Quadrant of Altitude skrewed over the North Pole of the Ecliptick, and laid upon the bright Star Capella,the Quadrant shall cut 77 d. 16 m. of

the

the Ecliptick Circle, counted from the beginning of Aries; and Fig. that is that Star's Longitude.

Note, That the Poles of the Ecliptick are diftant from the Poles of the World 23 d. on either fide.

For the Latitude, the Quadrant fitted as before, and laid over the Centre of Capella, the Star shall cut 22 d. 50 m. of the Quadrant of Altitude; and such is the Latitude of that Star, North, for that it lyes on the North Side of the Ecliptick Line. This needs no Trigonometrical Calculation.

T

PROB. ΧΙ.

To find the Right Afcenfion and Declination of a Star.

HE Right Afcenfion of a

Star

is that Arch of the Equinodial, which is contained between the beginning of Aries, and that Point which comes to the Meridian with that Star. The Declination of a Star is an Arch of the Meridian contained between the Equinoctial and any Star.

For the Right Afcenfion, (the Globe being rectified) bring Capella to the Meridian, and then shall you find 73 d. 7 m. of the Equinoctial contained between the beginning of Aries and the Meridian; and that is the Right Afcenfion of Capella.

For the Declination, bring Capella to the Meridian, so shall you find 45 d. 37 m. of the Meridian contained between the EquinoFial and Capella; and that is the Declination of that Star. And in this manner you may find the Longitude, Latitude, Right Afcenfion, and Declination, of any other Star upon the Calestial Globe, as in this following Table of the principal Fixed Stars of the first Magnitude you shall find.

This needs no Trigonometrical Calculation.

XXXIII.

1

Fig. XXXIII.

1.

PROB. XII.

To find the Distance of Two Stars.

F the Two Stars be both of them under the fame Meri

I I dian, Bring them under the General (or Brass) Meridian,

and fee what Degrees of the Meridian are contained between them, for that is their Distance.

2. If they lye not under the fame Meridian, but have the fame Declination, or lye in the fame Parallel, Bring one of them to the Meridian, and fee what Degrees of the Aquinoctial are cut thereby: Then bring the other Star to the Meridian, and count what Degrees of the Equinoctial are contained between the Meridian and the Degrees before found; for that is the Distance of those Two Stars.

3. If the Two Stars do neither lye under the fame Meridian, nor in the same Parallel, Then lay the Quadrant of Altitude (it being loose) to both the Stars, and the Degrees of the Quadrant contained between the Two Stars is their Distance And if the Quadrant be too short, you may use the Circle of Pofition, or take their Distance with a pair of Calope-Compaffes, and measure their Distance upon the Equinoctial, or any other great Circle.

Thus,