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For computing Part Second of the Precession in right Ascension, and to find the
TABLES LX, LXI, AND LXII.
APPENDIX, No. I.
TIIEORY AND PRACÍICE
OF FINDING THE
LONGITUDE AT SEA OR LAND).
EXPLANATION OF THE 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,
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,
Hence 3h. 18' 56'
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.
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.
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