will evidently be greater than its altitude observed from the surface, since the observer brings the image of the body down to his horizon, which is lower than the horizon seen from the surface of the sea immediately below him. The difference of altitude from this cause expressed in minutes and seconds, is called the dip of the sea horizon. Let a tangent at B, the point on the surface beneath the spectator supposed to be at T, meet the celestial concave at H, and through T draw the tangent т H, touching the earth at R; then, if м be the place of a heavenly body, the arc M H is its altitude observed at B, and the altitude observed by the spectator at T: the arc н н, is the dip due to the height в T of the spectator above the surface of the sea, and is evidently subtractive, to get the true altitude. This correction is found in all collections of nautical tables.

R

T

B

M H,

The use of the preceding corrections and reductions will be best seen in the following examples.

Rule XXIII.

Given, a star's observed altitude, to find its true altitude.

The stars are such a distance from the spectator that (excepting probably a few) the earth's orbit subtends no angle at the star: hence a star is considered to have no parallax and the only corrections used for reducing the observed altitude to the true are the index correction (the correction of the quadrant or sextant used) the dip, and refraction. Hence this rule.

:

1. To the observed altitude apply the index correction with its proper sign.

2. Subtract the dip (taken from table of dip of horizon). 3. Subtract the refraction (taken from table of refraction). 4. The result is the true altitude of star.

EXAMPLE.

The observed altitude of Arcturus was 36° 10′ 20′′, index correction + 2′ 42′′, and height of eye above the sea was 20 feet, required the true altitude.

(83.) The observed altitude of Aldebaran was 13° 4′ 30′′, index correction - 10′ 40′′, and height of eye above the sea was 16 feet; required the true altitude.

Ans., 12° 45' 43". (84.) The observed altitude of y Tauri was 62° 42′ 15′′, index correction + 0′ 40′′, and height of eye above the sea was 20 feet: required the true altitude.

Ans., 62° 38' 1". (85.) The observed altitude of a Canis Majoris (Sirius) was 32° 42' 30", index correction was 3′ 30′′, and height of eye above the sea was 12 feet: required true altitude. Ans., 32° 34' 0".

Rule XXIV.

Given, a planet's observed altitude, to find its true altitude.

The effect of parallax on the true altitude of a heavenly body is to diminish it (p. 102): the correction of parallax in altitude must therefore be added to the observed, to get the true altitude. Hence this rule.

Correct the observed altitude for index correction, dip, and refraction, as in (1), (2), (3), p. 106.

(4.) To the result add the parallax in altitude (taken out of the table of parallax in altitude of sun and planets). (5.) The result is the true altitude of the planet.

EXAMPLE.

January 4th, 1848, the observed altitude of Mars was 21° 41' 10", index correction 24 feet: horizontal parallax in Nautical Almanac being 101: required the true altitude.

(86.) Jan. 24, 1848, the observed altitude of Mars was 9° 8' 30", index correction 3′ 45′′, and height of eye above the sea 16 feet: required the true altitude. The horizontal parallax from Nautical Almanac was 8"-3.

Ans., 8° 55' 3".

(87.) Feb. 3, 1848, the observed altitude of Venus was 25° 8' 30", index correction 10′ 50′′, and height of eye above the sea 12 feet, required the true altitude. The horizontal parallax from Nautical Almanac, was 8′′-1. Ans., 24° 52′ 17′′.

(88.) Jan. 30, 1848, the observed altitude of Jupiter was 10° 20′ 10′′, the index correction was +0′ 14′′, and height of eye above the sea 18 feet: required the true altitude, the horizontal parallax in Nautical Almanac being 2′′0. Ans., 10° 11′ 0′′.

Rule XXV.

Given, the sun's observed altitude, to find the true altitude.

A1

Co

A

The true altitude of the sun's centre c H is found by observing the altitude of either the upper or lower limb a' H or ▲ H, and then subtracting or adding the semidiameter CA taken from the Nautical Almanac; the other corrections, namely, for the instrument, dip, refraction, and parallax, being made as in the preceding rules. In some of the nautical tables, the two corrections for refraction and parallax of the sun are combined in one table, and called the "correction in altitude of the sun.'

Hence this rule.

1. Correct the observed altitude for index correction and dip, as in article (1), (2), p. 106.

2. To this add the sun's semidiameter, if the altitude of the lower limb is observed; but subtract if the upper limb is observed: the result is the apparent altitude of the sun's

centre.

3. Subtract the refraction and add the parallax taken from the proper tables: or rather take out the "correction in altitude of the sun," and subtract it.

4. The remainder is the sun's true altitude.

EXAMPLE.

The observed altitude of the sun's lower limb (L. L.) was 47° 32′ 15′′", the index correction was + 2′ 10′′, and the height of the eye above the sea 15 feet: required the true altitude of the sun's centre: the semidiameter in Nautical Almanac being 15′ 49′′.

(89.) The observed altitude of the sun's L. L. was 48° 30′ 15′′, index correction 2' 50", and height of eye above the sea 15 feet: required the true altitude, the semidiameter being 15′ 55′′. Ans., 48° 38′ 46′′.

(90.) The observed altitude of the sun's L. L. was 40° 42′ 16′′, index correction + 5' 10", and height of eye above the sea 20 feet: required the true altitude, the semidiameter being 16' 4". Ans., 40° 58′ 6′′. (91.) The observed altitude of the sun's upper limb (U. L.) was 55° 57′ 42′′, index correction - 3' 40", height of eye above the sea 19 feet: required the true altitude, the semidiameter being 16' 6". Ans., 55° 33′ 4′′.

(92.) The observed altitude of the sun's L. L. was 39° 25′ 15′′, index correction-3′ 15", height of eye above the sea was 15 feet: required the true altitude, the semidiameter being 16' 3". Ans., 39° 33′ 11′′.

Rule XXVI.

Given, the moon's observed altitude, to find the true altitude.

The moon's horizontal parallax and semidiameter change so perceptibly that they cannot be considered (as in the corresponding case of the sun) to be constant for 24 hours. The parallax and semidiameter taken out of the Nautical Almanac must therefore be corrected for the Greenwich date in order to find the horizontal parallax and horizontal semidiameter at the time of the observation. Moreover