To find the apparent Time by the Altitúde of a fixed Star.

Correct the Obf. Altitude for the Dip and Refraction.

Find the Ship's Lat. by Account at the Time of Observation. Find the Star's Right Afcenfion and Declination in Table XIII. Then add together

Zenith Distance,

Co. Latitude, and

Polar Dift. into one Sum.

From half this Sum fubtract the Zenith Dift. noting the half Sum and Remainder.

Then add together

Log. Co. Sec. of Complement of the Lat. Rejecting their
Log. Co. Sec. of Polar Distance,

Log. Sine half the Sum, and the

Log. Sine Remainder into one Sum.

Indexes.

Half the Sum of thefe four Logarithms will be the Log. Co. Sine of half Hour Angle.

Turn this Hour Angle into Time, and apply it to the Star's Right Afcenfion, by fubtracting it when the Star is Eaft of the Meridian, or adding it when it is Weft of the Meridian, their Sum or Difference will be the Right Afcenfion of the Meridian or Mid Heaven.

From the Right Afcenfion of the Meridian (increased by 24 if neceffary) fubtract the Sun's Right Afcenfion the preceding Noon at Greenwich, taken from Page 2d of the Month in the Nautical Almanack, the Remainder will be the apparent Time at Ship nearly.

To this Time apply the Long. of the Ship from Greenwich turned into Time, by adding it when it is Weft, or fubtracting it when it is East, the Sum or Difference will be the apparent Time of the Observation nearly by the Meridian of Greenwich.

Then fay, as 24 Hours is to the daily Variation of Sun's Right Afcenfion, fo is this Time to a Number of Minutes and Seconds, which fubtracted from the above Time, leaves the correct apparent Time at Ship.

Suppofe on Sept 7th, 1796, in Lat. 7° 45′ South, and Long. 35° 18' Eaft of Greenwich, the Alt. of the Star Procyon, being then Eaft of the Meridian, fhould be 28° 16', and the Eye 18 Feet above the Surface of the Sea. Required the true Time?"

Then fay, as 24 H.: 3M. 36S.:: 14 H. 18 M. 50 S.: 2 M. 9 S. which fubtracted from 16 H. 20 M. 2 S. the Time at Ship nearly, leaves 16 H. 17 M. 53 S. the true Time at Ship after Noon, or 4 H. 17 M. 53 S. after Midnight.

Refrac. 2′ 18′′

Suppofe on April 14, 1796, in Lat. 48° 56' N. Long. 66° W. the Obf. Alt. of Aldeberan, when Weft of the Meridian, should be 22° 24', the Height of the Obferver's Eye 21 Feet above the Surface of the Sea. Required the true apparent Time at Ship.

Log. Co. Sec. 0,01736
Log. Co. Sec. 0,18248

3 41

Then say, as 24 H.: 3 M. 41 S.:: 12 H. 12 M. 4 S.: 1 M. 52 S. which fubtracted from 7 H. 48 M. 4 S. the apparent Time at Ship nearly, leaves H. 46 M. 12 S. the corrrect app. Time at Ship.

NOTE. This Method of finding the Time is certain, could a good Horizon be obtained in the Night; but as that is not always the Cafe, it is beft to regulate the Watch by the Sun.

By the above Method the true Time is generally found at Sea, though fome make Use of the following, it being somewhat fhorter. When the Sun or Star's Declination, and Complement of Lat. are both North or both South, their Sum*, but if one be North and the other South, their Difference is the Meridian Altitude.

From the Natural Sine of the Sun or Star's Mer. Alt. fubtract the Natural Sine of the true Altitude.

Then add together

'

The Log. Co. Sec. of the Comp. of the Lat. Rejecting their
The Log. Sec. of the Sun or Star's Decl. and} Indexes.

The Log. of the Diff. of the Natural Sines into one Sum. The Sum of thefe three Logarithms, being found in the Column of Rifing, the Hours, Minutes and Seconds correfponding to it, will be the true Time from the Noon when the Altitude was taken.

The four last Examples may be worked by the above Method. *If the Sum exceeds 90° fubtract it from 130, and the Remainder will be the Meridian Altitude.

EXAMPLE

I..

In Col. of Rifing gives true Time 5 H. 33′ 30′′

4,94683

Diff. of Nat. Sines

28718 Its Log. 4,45815

In Col. of Rifing gives true Time 3H, 50' 30"

466717

Here we find the Time found by this Method differs 2 Seconds

from that found by the former, but it may be found to the newmit

Second by taking Proportional Parts.

Thus, the Difference between the Log. of 3 H. 50' 30" and 3 H, 51 is 172, and the Difference between the Log. of 3 H. 50' 30" and that in the Calculation is 15.

Now as 172 30′′ :: 15 : 2", which being added to 3 H. 50 30", gives 3 H. 50' 32", the fame as that found by the former Method.

Having found the Hour Angle, proceed to find the true Time by the Stars, as has been fhewn in the two laft Examples, worked by the former Method.

It fometimes happens, that for Want of a Map of the Stars, or a Celestial Globe, many are at a Lofs to know whether they have obferved by the right Star or not, as there may some other Stars come to the Meridian nearly at the fame Time. But this may be eafily proved, by finding the Star's Meridian Altitude as above; and if it nearly agrees with that on the Quadrant, it must certainly be the right Star, otherwise not. The fame may be obferved of any of the

Planets.

To know when any Star comes to the Meridian, or what Star will be on the Meridian at any given Time, fee the Explanation following Table XIII. and for their Rifing and Setting, with that of the Moon and Planets, fee the Directions following Table XV. in this Book.

NOTE 1.

If an Obfervation of the Sun has not been taken the preceding Noon, or two Altitudes to find the Latitude, it may be