Note. The correction of a star's approximate time of transit may be readily found by means of Table XV., in the same manner, precisely, as if it were the proportional part of the sun's right ascension that was under consideration. See explanation, page 25, and examples, pages 26 and

28.

PROBLEM XIII.

To find what Stars will be on, or nearest to, the Meridian at any given

Time.
RULE.

To the sun's right ascension, at noon of the given day, add the apparent time at ship, and the sum will be the right ascension of the meridian or mid-heaven; with which enter Table XLIV., and find what stars' right ascensions correspond with, or come nearest thereto, and they will be the stars required.

If much accuracy be required, the sun's right ascension at noon of the given day must be previously reduced to the given time and place, by Problem V., page 298; at sea, however, this reduction may be dispensed with.

Example 1.

What star will be nearest to the meridian, April 6th, 1825, at 9:40 20: apparent time?

Sun's right ascension at noon of the given day = 10*24:
Given apparent time at ship or place =

9.40.20

Right ascension of the meridian or mid-heaven-10:40" 44:

Now, this being looked for among the right ascensions of the stars, in

* See Note, page 318.

Table XLIV., it will be found that the star's right ascension corresponding nearest thereto, is that of Argûs Navis; which, therefore, is the star required, or the one nearest to the meridian at the given time.

n

Example 2.

What star will be nearest to the meridian, December 31st, 1825, at 10:1241 apparent time?

Sun's right ascension at noon of the given day- 18:41:49:
Given apparent time at ship or place =

10. 12. 41

Right ascension of the meridian or mid-heaven=4*54"*30:

Now, this being looked for among the right ascensions of the stars, in Table XLIV., it will be found that the star's right ascension corresponding nearest thereto, is that of ß Eridani; which, therefore, is the star required, or the one nearest to the meridian at the given time.

Note. When the sum of the sun's right ascension and the apparent time exceeds 24 hours, let 24 hours be subtracted therefrom; and the remainder will be the right ascension of the meridian, as in the last example.

PROBLEM XIV.

Given the observed Altitude of the lower or upper Limb of the Sun, to find the true Altitude of its Centre.

RULE.

For the Fore Observation.

and the dip

To the observed altitude of the sun's lower limb (corrected for index error, if any,) add the difference between its semi-diameter of the horizon; and the sum will be the apparent altitude of the sun's centre: or, from the corrected observed altitude of the sun's upper limb subtract the sum of the semi-diameter * and the dip of the horizon† ; and the remainder will be the apparent central altitude.

For the Back Observation.

From the observed altitude of the sun's lower limb subtract the differ

*

Page III. of the month in the Nautical Almanac.

↑ Table II.

ence between its semidiameter and the dip of the horizon: or, to the observed altitude of its upper limb add the sum of the semi- diameter and the dip of the horizon, and the sun's apparent central altitude will be obtained.

Now, from the apparent altitude of the sun's centre, thus found, subtract the difference between the refraction* corresponding thereto, and the parallax in altitudet, and the remainder will be the true altitude of the sun's centre.

Example 1.

Let the observed altitude of the sun's lower limb, by a fore observation, be 16:29, the height of the eye above the level of the sea 24 feet, and the sun's semi-diameter 16:18"; required the sun's true central altitude?

Observed altitude of the sun's lower limb = 16:29: 0

Let the observed altitude of the sun's upper limb, by a fore observation, be 18:37, the height of the eye above the surface of the water 30 feet, and the sun's semi-diameter 15:46"; required the true central altitude?

Let the observed altitude of the sun's lower limb, by a back observation, be 20:10, the height of the eye above the level of the sea 25 feet, and the sun's semi-diameter 15.55"; required the true central altitude?

Let the observed altitude of the sun's upper limb, by a back observation, be 25:31, the height of the eye above the surface of the water 27 feet, and the sun's semi-diameter 15:49"; required the true central altitude?

Remark. I think it my duty, in this place, to caution the mariner against the mistaken rule for the back observation, given in some treatises on Navigation ;-because, if that rule be adopted, the ship's place will, most assuredly, be affected by an error in latitude equal to the full measure of the sun's diameter, or about 32 miles: and this, to a ship approaching or drawing in with the land, becomes an object of the most serious consideration, since it so very materially affects the lives and interests of those concerned. To set the mariner right in this matter, I will here work an

Example.

December 25th, 1825, in longitude 35: W., the meridian altitude of the sun's lower limb, by a back observation, was 16:28 south, the height of the eye being 20 feet; required the latitude?

By the old rule, the latitude is only 49:50. north, which is evidently erroneous, it being 32 miles and 20 seconds less than the truth.

PROBLEM XV.

Given the observed Altitude of the upper or lower Limb of the Moon, to find the true central Altitude.

RULE.

Turn the longitude into time, and add it to the apparent time of observation if it be west, or subtract it therefrom if east, and it will give the corresponding time at Greenwich.

To this time let the moon's semi-diameter and horizontal parallax be reduced, by Problem VI., page 302, (or by Table XVI., as explained in pages 30 and 33,) and let the reduced semi-diameter be increased by the correction contained in Table IV., answering to it and the observed altitude; then,

To the observed altitude of the moon's lower limb (corrected for index error, if any), add the difference between the true semi-diameter and the dip of the horizon; or, from the observed altitude of the upper limb subtract the sum of the semi-diameter and dip, and the apparent central altitude of the moon will be obtained; to which let the correction (Table XVIII.) answering to the moon's reduced horizontal parallax and apparent central altitude be added, and the sum will be the altitude of the moon's

centre.

Example 1.

In a certain latitude, March 10th, 1825, at 3:40 20: apparent time,