Of an Obfervation, either of Sun or Star, what it is, how, or with what, and when it is taken, and finding the Latitude thereby. 1. AN Obfervation, is the finding either the Sun's or Star's Meridian Altitude (at Sea) with a Quadrant, or with a

Cross-staff.

2. Meridian Altitude, is the Height above the Horizon of the Sun, or Star, they being upon the Meridian of the Place of Ob. fervation; and that the Sun is, every Day at Noon, but the Stars at different Times, according to the Difference of their feveral Right Afcenfions from the Sun's Right Afcenfion.

3. A Quadrant is the Inftrument whereby only the Sun's Altitude (at Sea) is found; but by Hadley's Quadrant the Altitude of a Star may be determined.

4. A Cross-ftaff, or Fore-ftaff, is an Inftrument whereby Mariners find either the Sun's or Star's Altitude. The particular Description of Davis's Quadrant and the Crofs-ftaff I here omit, having done it largely in the Mariner's Compafs rectified, to which Book I refer the Learner, and will now fhew how to find the Latitude after you have obferved which is called working an Obfervation, and that in this one Propofition.

Propofition. The Meridian Altitude of any Heavenly Object, and it's Declination given; to find the Latitude of the Place of Obfervation.

In this Propofition are two Cafes.

Cafe 1. Where, or when the Object obferved doth both Rife and Set in 24 Hours. The Rules are thefe.

Rule 1. The Meridian Altitude, and Declination of one Kind; that is, both North, or both South; the Difference of the Zenith Distance, and the Declination, is the Latitude required?

Note; In the above Cafe, whe the Declination is greater than the Zenith Distance, the Latitude is of the fame Name; but it lefs, then of a contrary Name to the Declination.

Rule 2. The Meridian Altitude, and Declination of contrary Names; that is, one North, and the other South, the Sum of the Zenith Diftance and the Declination, is the Latitude required of the fame Name with the Declination.

Note 1. By Meridian Altitude South, I mean the Object obferved is to the Southward of the Obferver; and when North, then to the Northward of the Obferver.

By Zenith Diftance understand the Complement of the Meridian Altitude of the Object observed.

Example 1. On the 20th of May 1770, the Sun's Meridian Altitude 61d. 08m. South; and his Declination 20d. c8m. North, What is the Latitude of the Place of Observation? d. m.

The Sun's Zenith Distance
Sun's Declination

28 52 South

20 08 North

The Sum (by Rule 2) is the Lat. of the Place - 49 00 North Example 2. On the firft of July 1770, the Sun's Zenith Diftance being 11d. 50m. North, and his Declination 23d. 08m. North. What is the Latitude of the Place of Obfervation? d. m.

From the Sun's Declination

Subtract the Sun's Zenith Distance

The Rem. (by Rule 1.) is the Lat. of the Place

23 08 North

11 50 North

11 18 North

Example 3. On the 3d of June 1770 the Sun's Zenith Diftance being 29d. 15m. South, and his Declination then 22d. 23m. North. What is the Lat. of the Place of Obfervation?

To the Sun's Zenith Distance
Add his Declination

d. m.

29 15 South

22 23 North

The Sum (by Rule 2.) is the Lat. of the Place 51 38 North Example 4. On the 22d. of Auguft 1770, the Star Fomelhaut being obferved, and his Zenith Distance 20d. 17m. North, this Star's Declination (in Page 178) is 30d. 56m. South. What is the Latitude of the Place of Obfervation?

The Sum is the Latitude required 51 13 South Example 5. The 30th of September 1770, the Foot of the Crofiers (by fome called the Cock's Foot) a Star much used in Southern Voyages, being obferved, his Meridian Altitude was 48d. 06m. South; this Star's Declination (in Page 178) is 61d. 31m. 'South. What is the Latitude of the Place of Obfervation? d. m.

Cafe. 2. Where, or when the Object obferved doth neither

Rife nor Set in 24 Hours; that is, doth not in the Diurnal Motion move below or under the Horizon.

Note 1. To fome Parts of the Earth, both the Sun and Stars do not rife or fet, but are above the Horizon, and upon the Meridian of the fame Place twice in the Space of twenty-four Hours; and this lafteth but for fome Part of the Year with the Sun, but always with fome.Stars.

Note 2. When the Sun, or a Star doth not either rise or fet, and cometh upon the Meridian below or under the Pole, between the Pole and Horizon; it is then at the leaft Meridian Altitude.

Note 3. Such Stars as do not fet, come upon the Meridian both below, and also above the Pole, that is between the Zenith and the Pole, and their greateft Meridian Altitudes are when they appear above the Pole.

Note 4. Where a Star cometh upon the Meridian, both below, and also above the Pole, it is always to the Northward of the Zenith, both in it's leaft and greatest Meridian Altitude; or else always to the Southward.

Note 5. Again, there are fòme Stars which come upon the Meridian, to the Northward of the Zenith, and below the Pole; and to the Southward between the Zenith and the Equinoctial; and alfo to the Southward, and below the Pole; and to the Northward between the Zenith and the Equinoctial.

Nole 6. When the Sun cometh to the Meridian below, or a Star, both above and below the Pole, the Lajitude of that Place is of the fame Name with the Sun or Star's Declination: That is, if the Sun or Star's Declination be North, the Latitude of the Place is North; but South, when the Declination is South. Note 7. For thofe Stars which never come to the Meridian above the Pole, at their greatest Meridian Altitude, the former two Rules ferve for to find the Latitude.

Then to find the Latitude by the Sun under the Pole, or Stars, both under and above the Pole. The Rules are thefe.

Rule 3. The Object obferved, being on the Meridian below the Pole, the Sum of the Meridian Altitude, and Complement of the Declination, is the Latitude required, of the fame Name with the Declination.

Rule 4. The Object obferved, being on the Meridian above the Pole, the Difference of the Meridian Altitude, and the Complement of the Declination is the Latitude required, of the fame, Name with the Declination,