the observed altitude of the moon's lower limb was 20:10:40%, and the height of the eye above the level of the sea 24 feet; required the true altitude of the moon's centre, the longitude of the place of observation being 35:40: west ?

Observed altitude of moon's lower limb = 20:10:40"
Moon's true semi-diam. = 15'46"

Dip of the horiz. for 24 feet=4.42 } Diff.= +11. 4

Apparent altitude of the moon's centre = 20:21:44"
Correction to altitude 20:21:44", and

horiz. parallax 57:32", Table XVIII.= +51.24

In a certain latitude, March 26th, 1825, at 13047 apparent time, the observed altitude of the moon's upper limb was 30:17:30, and the height of the eye above the level of the sea 30 feet; required the true altitude of the moon's centre, the longitude of the place of observation being 94:15:30" east?

Greenwich time past midnight, March 25th=713"45!

Observed altitude of moon's upper limb 30:17:30:

Moon's true semi-diam. = 15:31?
Dip of the horiz. for 30 feet 5. 15

} Sum= -20.46

Apparent altitude of moon's centre = 29:56:44"
Correction to altitude 29:56:44", and

horiz. parallax 56:26%, Table XVIII. = +47.16

Note. In the above examples, the altitudes are supposed to be taken by the fore observation; and since this mode of observing is not only the most natural, but, also, the most simple, it will, therefore, be constantly made use of throughout the subsequent parts of this work. Hence the necessity of making constant reference to the particular mode of observation may, in future, be dispensed with.

PROBLEM XVI.

Given the observed Altitude of a Planet's Centre, to find its true Altitude.

RULE.

From the planet's observed central altitude (corrected for index error, if any,) subtract the dip of the horizon, and the remainder will be the apparent central altitude.

Find the difference between the planet's parallax in altitude (Table VI.) and its refraction in altitude (Table VIII.); now, this difference being applied by addition to the apparent central altitude when the parallax is greater than the refraction, but by subtraction when it is less, the sum or remainder will be the true central altitude of the planet.

Example 1.

Let the observed central altitude of Venus be 16:40', the index error 2:30 subtractive, and the height of the eye above the level of the sea 28 feet; required the true altitude of that planet, allowing her horizontal parallax to be 31 seconds?

Let the observed central altitude of Mars be 17:29:40", the index error 3:45 additive, and the height of the eye above the surface of the water 26 feet; required the true central altitude of that planet, allowing his horizontal parallax to be 17 seconds?

True Apparent central altitude of Mars = 17:25:50%

Remark. In taking the altitude of a planet, its centre should be brought down to the horizon. Neither the semi-diameters nor the horizontal parallaxes of the planets are given in the Nautical Almanac, but it is to be hoped that they soon will be. If the parallaxes of the planets be determined by means of a comparison of their respective distances (from the earth's centre) with the earth's semi-diameter, they will be found to be as follows, very nearly; viz.,

Venus' greatest horizontal parallax, about 32 seconds; and her least parallax about 5 seconds.

Mars' greatest horizontal parallax, about 17 seconds; and his least parallax, about 3 seconds.

Jupiter's mean horizontal parallax, about 2 seconds; and that of Saturn about 1 second.

The parallaxes of the two last planets are subject to very little alteration, because the distances at which those objects are placed from the earth's centre are so exceedingly great as to render any variations in their parallaxes almost insensible.

PROBLEM XVII.

Given the observed Altitude of a fixed Star, to find the true Altitude.

RULE.

To the observed altitude of the star apply the index error, if any; from which subtract the dip of the horizon, and the remainder will be the star's apparent altitude.

From the apparent altitude, thus found, let the refraction corresponding thereto be subtracted, and the remainder will be the true altitude of the star.

Example 1.

Let the observed altitude of Spica Virginis be 18:30, the index error 3:20 subtractive, and the height of the eye above the level of the water 18 feet; required the true altitude of that star?

Observed altitude of Spica Virginis = 18:30: 0%
Index error =

3.20

4. 4

Apparent altitude of Spica Virginis = 18:22:36%

Let the observed altitude of Regulus be 20:43, the index error 1:47" additive, and the height of the eye above the level of the sea 20 feet; required the true altitude of that star?

Note.-The fixed stars do not exhibit any apparent semi-diameter, nor any sensible parallax; because the immense and inconceivable distance at which they are placed from the earth's surface causes them to appear, at all times, as so many mere luminous indivisible points in the heavens.

SOLUTION OF PROBLEMS RELATIVE TO THE LATITUDE.

The Latitude of any place on the earth is expressed by the distance of such place from the equator, either north or south, and is measured by an arc of the meridian intercepted between the said place and the equator.— Or,

The Latitude of any place on the earth is equal to the elevation of the pole of the equator above the horizon of such place; or (which amounts to the same), it is equal to the distance of the zenith of the place from the equinoctial in the heavens. The complement of the latitude is the distance of the zenith of any place from the pole of the equator, and is expressed by what the latitude wants of 90 degrees. The latitude is named north or south, according as the place is situate with respect to the equator.

PROBLEM I.

Given the Sun's Meridian Altitude, to find the Latitude of the Place of Observation.

RULE.

Find the true altitude of the sun's centre, by Problem XIV., page 320, and call it north or south, according as that object may be situate with respect to the observer at the time of observation; which, subtracted from 90%, will give the sun's meridional zenith distance of a contrary denomination to that of its altitude.

Reduce the sun's declination to the meridian of the place of observation, by Problem V., page 298, or, more readily, by Table XV. Then, if the meridional zenith distance and the declination are both north or both south, their sum will be the latitude of the place of observation; but if one be north and the other south, their difference will be the latitude, and always of the same name with the greater term.*

* The principles upon which this rule is founded may be seen by referring to "The Young Navigator's Guide to the Sidereal and Planetary Parts of Nautical Astronomy," page 98; reading, however, the word sun instead of star.