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TABLE XXI.

Error of Observation, arising from a deviation of one Minute, of the Plane of the

central Mirror of the circular Instrument, from the Perpendicular

64

TABLE XXII.

Error of Observation, arising from an Error in the Line of Collimation

65

TABLE XXIII.

For computing Part First of the Equation of equal Altitudes

68

TABLE XXIV.

For computing Part Second of the Equation of equal Altitudes

69

TABLE XXV.

Altitude to be observed in order to ascertain the Apparent Time with the greatest

accuracy

70

TABLE XXVI.

Correction of the observed Altitude for the Spheroidal Figure of the Earth

71

TABLE XXVII.

For computing the Apparent Time from an Observation of the Altitude of an Object 72

TABLE XXVIII.

For computing the Apparent Time, &c.

74

TABLE XXIX.

For computing the Apparent Time, &c.

76

TABLE XXX.

To find the Augmentation of the Moon's Semidiameter, by the Altitude of the

Nonagesimal, and the Apparent Distance of the Moon therefrom

79

TABLE XXXI.

Augmentation of the Moon's Semidiameter

TABLE XXXII.

Contraction of the Semidiameters of the Sun and Moon

ib.

TABLE XXXIII.

Reduction of the Moon's Equatorial Horizontal Parallax

ib.

TABLE XXXIV.

Correction of the Moon's Parallax in Latitude

ib.

TABLE XXXV.

Greatest Effect of the Moon's Parallax in Longitude

ib.

TABLE XXXVI.

Reduction of the Latitude of the Place of Observation

ib.

TABLE XXXVII.

Equation of Second Difference

TABLE XXXVIII,

Correction of Approximate Time, answering to the Equation of Second Difference

TABLE XXXIX.

Equatorial Semidiameter of the Moon in Time

ib.

TABLE XL,

Increase of the Moon's Semidiameter in Time

TABLE XLI.

Natural Versed Sines, to every Tenth Second of the Quadrant

TABLE XLII.

218

TABLE XLIII.

Correction of the Logarithmic Difference, when the Moon's Distance from the Sun

is observed

TABLE XLIV.

Correction of the Logarithmic Difference, when the Moon's Distance from a Star

is observed

ib.

TABLE XLV.

Logarithms of Numbers

ib.

TABLE XLVI.

Logarithmic Sines to every Tenth Second of the Quadrant

TABLE XLVII.

Logarithmic Tangents to every Tenth Second of the Quadrant

TABLE XLVIII,

Half Elapsed Time

326

TABLE XLIX.

Middle Time

329

TABLE L.

Rising

TABLE LI.

Proportional Logarithms

TABLE LII.

The mean right Ascensions and Declinations of 183 principal fixed Stars, adapted to

the beginning of the Year 1810

349

TABLE LIII.

Part First of the Precession in right Ascension, for complete Years

TABLE LIV.

For computing Part Second of the Precession in right Ascension, and to find the
Precession in Declination, for complete years

ib.

TABLE LV.

Decimal Numbers for multiplying the Annual Precession of a Star in right

Ascension

353

TABLE LVI.

Semi-annual Solar Equation of Northern Stars in Declination

ib.

TABLES LVII, LVIII, AND LIX.

For computing the Nutation or Deviation of a Star in right Ascension, and

Declination

354

TABLES LX, LXI, AND LXII.

For computing the Aberration of a Star in right Ascension and Declination

TABLE LXIII.

The mean Longitudes and Latitudes of 122 fixed Stars, chiefly Zodiacal, adapted

to the beginning of the Year 1810

356

TABLE LXIV.

Precession of the Equinoctial Points in Longitude, for complete Years

TABLE LXV.

Precession of the Equinoctial Points in Longitude, for Months and Days

ib.

TABLE LXVI.

Secular Variation of the fixed Stars

ib.

TABLE LXVII.

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LXVI

THR

TIIEORY AND PRACÍICE

OF FINDING THE

LONGITUDE AT SEA OR LAND).

EXPLANATION OF THE TABLES.

TABLES

1. AND II.

For converting Longitude into Time, and conversely.

TABLE I. is intended to facilitate Proh. I. page 104, and is constructed according to the principles there delivered. Column first contains hours, and the second column the degrees answering thereto ; the third contains either minutes, seconds, or thirds; and the fourth column the corresponding degrees and minutes, minutes and seconds, or seconds and thirds: the fifth and sixth columns are a continuation of the two former. Table 11. being the converse of Table 1. requires no farther explanation,

EXAMPLES

I.

Required the degrees, &c. answering to 3h. 18' 56" ? 3 hours in col. first, Tab. l. = 45° 0' in col. second. 18 minutes in col. third

4 30 in col. fourth. 36 seconds in col. fifth

14 in col, sixth,

49 44

Hence 3h. 18' 56'

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What time answers to 76° 50' 45"? 70 degrees in col, fifth, Table 11. = 4h. 40' 0" in col. sixth. 6 degrees in col. first

24 O in col. second. 50 minutes in col. third

320 in col. fourth. 45 seconds in col. third

3 in col. fourth.

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III. AND IV.

Depression or Dip of the Horizon. The dip of the horizon is the vertical angle contained between a horizontal plane passing through the eye of an observer, and a line joining the eye and the visible horizon.

The first of these tables contains the dip, answering to a free, or unobstructed horizon: it is calculated by the rule given in page 84 ; each number is diminished by one tenth, for the effect of terrestrial refraction; and wrote out to the nearest tenth of a minute, which is sufficiently accurate for any purpose to which it can be applied at sea; especially since altitudes observed from the horizon of the sea are commonly taken to the nearest minute, and as there is still a little. uncertainty as to the quantity of the terrestrial refraction. The numbers in this, as well as those in the other table, corresponding to the height of the eye, are to be subtracted from the observed altitude, when the fore observation is used; but added thereto in the back observation.

If the land intervenes, or the horizon is obscured by a fog, and the ship, therefore, nearer to it, than to the visible horizon when unconfined ; and if the Sun's. limb is brought into contact with the line of separation of the sea and land; the dip will be considerably greater than in Table11t. and will increase as the distance of the ship from the land diminishes. In this case, therefore, the distance of the ship from the land is to be found, and the dip answering thereto, and to the height of the eye above the water is to be taken from Table iv. Or, the dip.may be found independent of the table, by the rule given in vol. 1. Book vi. Chap. I.

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Correction of the Sun in Altitude. The numbers in this table are the differences between the refraction and the Sun's parallax in altitude. These numbers are expressed in minutes and tenths of a minute, which is sufficiently accurate in computations for the latitude or apparent time. When greater accuracy is required, the difference between the numbers in the two following

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