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Given the Sun's apparent Altitude 18° 59', the Moon's 70° 44", the apparent Distance of their Centres 103° 30' 8", and the Moon's Horizontal Parallax 59′ 15′′. Required the true Distance?

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I fhall leave the working of the other Examples by this Method, to exercise the Learner, and proceed to fhew how to find the true Altitudes of the Sun, Moon, or a Star by Calculation,

To find the Sun's true Altitude,

It sometimes happens, that the Distance of the celestial Objects may be taken, but for Want of a good Horizon, or Affiftants, their Altitudes cannot be taken at the fame Time; to fupply fuch De ficiences, obferve the three following Cafes.

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The apparent Time, the Ship's Latitude, Longitude, and the Sun's Declination given, to find the true Altitude of his Centre.

RULE.

If the Ship's Co-Latitude and the Sun's Declination be both North or both South, their Sum; but if one be North and the other South, their Difference is the Sun's Meridian Altitude.

With the apparent Time from Noon, enter Table XVI. and from the Column of Rifing take out the Logarithm correfponding to it.

To this Logarithm, add the Log. Co-fine of the Latitude, and the Log. Co-fine of the Sun's Declination.

Their Sum, rejecting 20 in the Index, will be the Logarithm of a Natural Number, which being fubtracted from the Natural Sine of the Sun's Meridian Altitude, will leave the Natural Sine of his true Altitude at the given Time.

EXAMPLE.

Required the true Altitude of the Sun's Centre, in Lat. 49° 57′N. July 25, 1796, at 6 H. 56 M. 30 S. in the Morning?

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Co. Lat.

Mer, Alt.

59 29 Nat. Sine

Decl. at that Time 19 26

40 3 Reject 20 N. N. 45871-Log.=4,66154

Nat. Sine true Alt. 40277 23° 45′•

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86148

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What will be the true Altitude of the Sun's Centre at London, November 24, 1796, at 3 H. 21 M. 30 S. apparent Time in the Afternoon?

H. M. S:

App. Time from N. 3 21 39 Its Log in Col. of Rifing 4,55900 51° 32′ N. Log. Co-fine

Latitude

Decl. at that Time 20 49 S. Log. Co-fine

Co. Lat.

2,79383

9,97068

38 28 N. Nat. Num. 21062 Log.=4,32351

Mer. Alt.

17 39

Nat. Sine 30320

Nat. Sine true Alt. 5 19

Nat. Sine 09258

CASE II.

The apparent Time, the Latitude and Longitude given, to find the Altitude of any of the known fixed Stars.

RULE.

Turn the Longitude into Time, and add it to or fubtract it from the Time at the Ship, according as it is Eaft or West, the Sum or Difference will be the Time at Greenwich.

Take the Sun's Right Afcenfion from the Nautical Almanack, and proportion it to the Time at Greenwich, and add it to the apparent Time at the Ship, which will give the Right Afcenfion of the Meridian, or Mid-Heaven.

Find the Star's Right Ascension and Declination in Table XIII. and take the Difference between its Right Afcenfion and the Right Afcenfion of the Meridian, which will be the Distance of the Star from the Meridian.

Having the Star's Distance from the Meridian, with its Declination and the Ship's Latitude, the true Altitude is found in the fame Manner as has been fhewn in the laft Examples of finding the true Altitude of the Sun.

EXAMPLE.

What will be the true Altitude of Aldebaran at Edinburgh, April 11, 1796, at 5 H. 56 M. 20 S. apparent Time. H. M. S.

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H. M. S.

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Co. Lat.

34 2 N. Nat. Num. 17078 Log. 4,23245

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NOTE. As the Table is calculated only to 30", the Difference between the Log. of 3 H. 7 M. 30 S. and 3 H. 8 M. must be taken, which is 218: Then fay, As 30: 218: 22: 160, which being added to 4,50025 the Log. of 3 H. 7 M. 30 S. gives 4,50185, the Log. of 3 H. 7 M. 52 S. as above.

CASE III.

The apparent Time, the Latitude and Longitude of the Ship given, to find the true Altitude of the Moon's Centre.

RULE.

Turn the Longitude into Time, and if it be Weft add it to, but if it be Eaft fubtract it from the apparent Time at the Ship, and it will give the Time at Greenwich.

Take the Sun's Right Afcenfion out of the Nautical Almanack, and proportion it to Greenwich Time, which being added to the Time at the Ship, the Sum will be the Right Afcenfion of the Meridian or Mid Heaven.

Take out of the Nautical Almanack the Moon's Right Afcenfion and Declination, and proportion them to the Time at Greenwich. Turn the Moon's Right Ascension into Time, and take the Difference between it and the Right Afcenfion of the Mid Heaven, which will be the Distance in Time of the Moon from the Meridian.

Having the Ship's Latitude, together with the Moon's Declination and Distance from the Meridian, the true Altitude is found, in the fame Manner as has been fhewn in finding the true Altitude of the Sun and Star.

EXAMPLE.

What will be the Moon's true Altitude at 19 H. 16 M. 52 S. apparent Time, in Latitude 14° 45'S. and Longitude 167°E. on August 24, 1796 ?

App. Time at Ship
Long. 167° E. in Time

App. Time at Greenwich
Sun's Right Afcenfion
App. Time at Ship

H. M. S.

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N. Sine of Moon's true Alt. 44° 20' N. Sine 69892

In the laft Example proportional Parts are taken in finding the Right Afcenfion, Declination and Log. Rifing.

By the three laft Cafes the true Altitudes of the Objects are found, therefore if the apparent Altitudes be wanted, the Difference between the Sun's Parallax and Refraction must be added to the Sun's true Altitude, the Refraction must be added to the true Altitude of a Star, and the Difference between the Moon's Refraction and Parallax in Altitude must be fubtracted from the true Altitude of the Moon thus found, to obtain the respective apparent Altitudes of their Centres.

To find the Longitude by the Eclipfes of Jupiter's Satellites.

On the Day preceding the Evening on which it is proposed to obferve an Eclipfe, look for the Time when it will happen at Greenwich, in Page 3d of the Month in the Ephemeris. Find the Diff. of Longitude, either by a good Map, Sea Chart, or Dead Reckoning.

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