329 EXPLANATION AND USE OF THE TABLES. TABLE I. Difference of Latitude and Departure for Points and Quarters. ̧ The points and quarters under four points are found on the top of the table, and those above are found at bottom, to the distance of 300. TABLE II. Difference of Latitude to every Degree of the Quadrant. The explanation and use of Tables I and II. have examples in every Question in Plane, Middle Latitude, and Mercator Sailing, &c. TABLE III. Logarithmic Sines, Tangents, and Secants, to every Point and Quarter of the Compass. The points and quarters are contained in the first and last columns, and the log. sines, tangents, and secants, in the intermediate columns. TABLE IV. Contains the logarithms of natural numbers from 1 to 10,000, and to 5 decimal places of figures: the index is always one less than the number of integral figures in the natural number. See page 19. TABLE V. Log. Sines, Tangents, and Secants. This table contains the log. sine, tangent, and secant, to every miRute of the quadrant. See page the 26. TABLE VI. Meridional Parts. The meridional parts are to be taken out with the degrees of latitude at the top or bottom, and for the miles or minutes on either side. TABLE VII. Mean Refraction Is always to be added to the zenith distance, or subtracted from the observed altitude. TABLE VIII. The number opposite the height of the eye above the surface of the sea, is to be subtracted from the observed altitude. The number of minutes opposite the observed altitude is to be added to the observed altitude. TABLE X. Moon's Augmentation. The number answering to the moon's altitude is to be added to the moon's horizontal semidiameter. TABLE XI. Dip at different Distances from the Observer. The number opposite the distance, and under the height of the eye, is to be subtracted from the observed altitude. TABLE XII. Under the year and month, and opposite to the day of the month, which stands in the left-hand column, stands the declination for that day at noon at Greenwich, which you are to observe whether it is north or south. TABLE XIII. Variation of the Sun's Declination. For reducing the Sun's Declination to any Meridian, and to any Time under that Meridian. The first and second page contain the proportional parts of the sun's declination to every hour in the day, and to every 15 degrees of longitude, and to every minute and every six seconds of the daily variation of the sun's declination. The third page contains four proportional parts of the declination of the sun to every five minutes of time, and every degree and 15 minutes of longitude; and to every minute and every six seconds of the daily variation of the sun's declination. Er. 1. I demand the proportional part answering to six hours (or 90° of W. longitude) when the sun's daily variation in declination is 13 miles, or minutes, 24 seconds. Under six hours (or 90°) and opposite 13' in left hand col. is 3′ 15′′ Do. do. 24" Answer 3 21. Ex. 2. What is the proportional part answering to eight hours 40' (or 130° of W. longitude) when the sun's daily variation in declination is 18′ 42′′? Under 8 hours and opposite to 18' is Do. do. do. 42" Under 40 minutes and opposite to 18' is Do. 6' 0,0 0 14,0 0 30,0 To be added or subtracted according as the declination is either increasing or decreasing; but if the time is before noon or east longitude, the application of the sum is reverse to the former. TABLE XIV. Sun's Right Ascension. This table is sufficiently exact for finding when any star comes to the meridian, in order to obtain a latitude; but for all cases and calculations for determining apparent time, the sun's right ascension must be taken out of the Nautical Almanack for the given year. TABLE XV. The Right Ascension and Declination of the principal fixed Stars. Beneath the table is a note, showing how to correct the stars to any time before or after the year 1808. TABLE XVI. For turning Degrees and Minutes into Time, and the contrary. The manner of using this table, is plain from the following examples. To reduce the Time of the Moon's Passage over the Meridian of Greenwich, to the Time of its Passage over any other Meridian. This table is to be entered with the daily variation at the top (which is found page 6, in the Naut. Alm.) and the longitude of the place on the left-hand side column, the minutes corresponding, are to be added to the time of the moon's passage over the meridian of Greenwich, if the longitude be west, or subtracted, if east. Er. At what time will the moon pass the meridian of Cape Horn, in longitude 68° 13′ W. on the 5th of December 1810? Moon's passage over the meridian of Greenwich, Dec. 5, by Correction corresponding to daily var. 48 m. and long. 68° 13' W. + 8h 0 0 Time of the moon's passing the mer. of Cape Horn, Dec. 5. 8 TABLE XVIII. Decimals to every Minute in Twelve Hours. The use of the table is at the bottom of table XVII. 9 TABLE XIX. Of Amplitudes. This table is used in finding the variation of the compass. See page 154. TABLE XX. To find the Time of the Sun's Rising, Setting, and the Length of the Day and Night. First, Find the sun's declination at the top of the table (marked with the degrees of declination), and the latitudes in the right or left-hand columns (marked lat.), and in the common angle of meeting is the time of sun-setting, if the sun has north declination, but the time of sunrising, if the sun has south declination. Ex. 1. Let it be required to find the time of the sun's rising and setting, with the length of the day and night, in latitude 51° north, the 19th of July, 1810. I first seek the sun's declination for the given day, and find it 20 57' north, which I here call 21°, then under the declination 21, and against the latitude 51, stands 7 h. 53 m. the time the sun sets on the given day, in lat. 51 north, which being doubled, gives 15 h. 46 m. the length of the day; and if 7 h. 53 m. the time of the sun's setting, be subtracted from 12 h. the remainder 4 h. 7 m. gives the time of the sun's rising, which being doubled, gives 8 h. 14 m. length of the night. But, when the sun has 21° south declination in this latitude, the time of sun-setting becomes the time of sun-rising, and the length of the day will then become the length of the night. Thus, the 26th of November, 1810, the sun's declination will be 20% 54' south, or 21°, then the time of sun-rising is 7 h. 53 m. his setting 4 h. 7 m. and the length of the night 15 h. 46 m. and day S h. 14 m. When a greater degree of accuracy is required, proportional parts may be taken for degrees and minutes of latitude and declination. To find the Rising and Setting of the Stars. By this table the rising and setting of any star may be found, whose declination does not exceed 23° 28' north or south, in the following manner: If you are in north latitude and the star has north declination, look for the declination at the top, and the latitude in the right or lefthand columns, in the angle of meeting, is half the time of the star's continuance above the horizon in that latitude, or the time it takes in ascending from the eastern side of the horizon to the meridian, and descending from the meridian to the western part of the horizon, Therefore, if these hours and minutes be subtracted from the time of the star's coming to the meridian, the remainder will be the time of the star's rising, and if added, the sum will be the time of the star's setting. For finding when the star comes on the meridian, see page 213. Er. 1. Required when the star Arcturus rises and sets, December 1, 1810, in latitude 51 degrees North. The time of the star's coming to the meridian, or southing in the morning, page 213 ..... 9.39 Then under star's declination 20' 11', or 20° N. and against latitude 51 stands .... 7 47 When the latitude is north, and the star has south declination, or the latitude south, and the star has north declination, find the latitude in the side columns as before, against which, and under the degrees of declination, stands half the time the star is under the horizon, which being subtracted from 12, the remainder will be half the time the star will be above the horizon in that latitude. Example. What time will the star Virgin's spike, rise and set at London, June 7, 1810. ...... Under the declination 10° 10′ S. and against latitude 51° 32′ or 52 stands .... Half the time the star is above the horizon The star comes to the meridian in the evening, at Which subtracted, shows that the star rises 5 at minutes after 3 in the evening .................... Added, shows the time the star sets in the morning 12.0 652 5 9 8 13 1 21 In like manner may the rising and setting of the planets be found when their declination does not exceed 23°, and the time of ther passage over the meridian is known, which is found in page 4th of the Nautical Almanack. Suppose it were required to find the moon's rising and setting Ar 26, 1811, in latitude 52° north. In the Nautical Almanack (page 6th), I find that the moon passes |