Had this Example been worked to seconds, the latitudes would have been 37′29′′ and 1° 23'3". NOTE. By the preceding method, the latitude may be found by two observed altitudes of a star; but in this case it will be necessary to reduce the interval between the observations, as measured in mean solar time by a watch or chronometer, to sidereal time by Table XXXVII., as explained in the use of that Table. EXAMPLES FOR EXERCISE. 1. October 20, 1854, in latitude by account 50° 10' N., at 0h. 34m. P. M. the sun's true altitude was 29° 15', and at 2h. 46m. P. M. it was 20° 3': required the true latitude. Answer. 50° 4' North. 2. February 25, 1854, in latitude 49° 36' N. by account, at Oh. 33m. P. M. the observed altitude of the sun's lower limb was 28° 53′, and at 2h. 43m. P. M. it was 19° 44', the height of the observer's eye being 14 feet: required the true latitude. Answer. 51° 23′ North. 3. July 7, 1854, in latitude 58° 25' N. by account, and longitude 99° 0 W., at 11h. 2m. A. M. per watch, the altitude of the sun's lower limb was 52° 53', and at 1h. 25m. P. M. the altitude was 52° 44′, the sun at that time bearing S. W. by W. by compass; the height of the observer's eye being 20 feet, and the ship's course during the elapsed time S. S. W. W., sailing at the rate of 8 knots per hour: required the ship's true latitude at the time when the greater altitude was observed. Answer. 57° 23′ North. 4. August 30, 1854, in latitude 12° 43' S. by account, and longitude 24° 15′ W., at 11h. 13m. 30s. A.M., the altitude of the sun's lower limb was 66° 9′ 30′′, and at 1h. 15m. 12s. P. M. it was 620° 0′15′′, bearing at that time N. W. W.: during the elapsed time the ship was sailing S. W. by W. at the rate of 4 knots per hour, and the height of the observer's eye was 28 feet: required the true latitude at the time of taking the greater altitude. Answer. 11° 37' South. To find the Latitude by an Altitude of the Sun taken near the Meridian ; having the Apparent Time from Noon, the Latitude by Account, and the Sun's Declination at the Time of Observation. RULE 1. From the observed altitude, find the sun's true altitude, and reduce the declination, taken from Page I. of the month in the Nautical Almanac, to the apparent time of observation by Table XXI. or XXXIII. 2. Add together the log. rising of the time from noon (XXIX.) the log. co-sine of the latitude (XXV.) and the log. co-sine of the declination; the natural number corresponding to the sum of these three logarithms natural sine (XXVI.) of the true altitude, will give the natural co-sine of the meridian zenith distance, to which apply the declination, as before, and the result will be the latitude. Should the latitude thus found, differ materially from the latitude by account, it will be advisable to repeat the operation, using that latitude instead of the latitude by account. NOTE. The apparent time at the ship when the altitude is taken, may be ascertained by altitudes observed when the sun is at a proper distance from the meridian, as shewn hereafter, and the error it then had, applied to the time shewn by the same watch when the altitude is taken; and should the ship have changed her meridian since the error of the watch was ascertained, the difference of longitude made, must be reduced into time by Table XIX., and added thereto, if east, or subtracted from it, if west. Or, the apparent time at the ship may be obtained by means of a chronometer shewing mean time at Greenwich, by applying to that time the equation taken from Page II. of the month in the Nautical Almanac, in order to reduce it to apparent time at Greenwich to this add the longitude of the ship (reduced into time by Table XIX.), if it be east, or subtract it, if west, and the result will be the apparent time at the ship. The observations should be taken within the following limits, viz. the number of the minutes in the time from noon should not exceed the number of degrees of the sun's meridian zenith distance. (See Note at the bottom of Page 192.) EXAMPLE I. October 11, 1854, in latitude by account 46° 8' N., and longitude 127 30 E., suppose the altitude of the sun's lower limb to be 36° 33′ 00′′ at Oh. 28m. 10s. P. M., ship time by a watch previously regulated; the height of the observer's eye being 18 feet: required the ship's true latitude. Sun's declination, October 10, (by p. I. N. A.)......... & 37 31 8. Sun's declination at Greenwich time 0 / 1 36 33 00 4 4 36 28 56 1 10 36 27 46 +16 4 36 43 50 +15 9* 6 52 40 S. 2.87753 9.84072 9.99686 519......Log.... 2.71511 59809 Nat. co-sine... 60328 6 53 S.............Co-sine Nat. number... Or thus, if corrected by Table XXI., the corr. for 16h. will be 15′ 6′′. EXAMPLE II. July 3, 1854, in latitude by account 26° 13' S., and longitude 166° 15′ W. at 11h. 48m. 40s. A.M., by a watch, whose error had been previously found to be 7m. 30s. fast for apparent time at ship, suppose the altitude of the sun's upper limb was 41° 2' 10" N., the height of the observer's eye being 20 feet, and the ship having made 38 miles of longitude to the eastward since the watch was regulated: required the true latitude of the place of observation. Latitude by account h. m. s. 0 16 18......... ..Rising 2.40265 ............Co-sine 9.95286 Sun's declination......... 22 57 N........................................................................ September 22, 1854, in latitude by account 50° 10' N., and longitude 20° 36′ W., the altitude of the sun's lower limb being 40° 12' 15" S., when a chronometer shewed 2h. 1m. 44s. mean time at Greenwich; the error of the instrument 1' 20" to add, and the height of the observer's eye 20 feet: By repeating the operation, with the latitude as above, the true latitude comes out 48° 53′ N. EXAMPLES FOR EXERCISE. 1. May 10, 1854 (civil time), in latitude by account 38°26′ S., and longitude 22° 40′ E., the altitude of the sun's upper limb was 33° 21′ 30′′ N., when a watch, previously regulated, shewed 11h. 10m. 15s. A. M., the height of the observer's eye being 24 feet, and the error of the instrument +2' 15" required the true latitude. Answer. 38° 10 South. 2. November 10, 1854, in latitude by account 60° 12′ N., and longitude 32° 30′ W., at 0h. 56m.. 12s. P. M., by a watch whose error had been previously found to be 4m. 18s. too slow for apparent time at ship, the altitude of the sun's lower limb was 11° 48′ 45′′ South of the zenith, the height of the observer's eye being 18 feet, and the ship having made 24 miles of longitude to the westward since the error of the watch was found: required the true latitude. Answer. 59° 57′ North. 8. March 15, 1854 (civil time), in latitude by account 47° 42′ S., and longitude 168° 20' E., the altitude of the sun's lower limb was 44° 6' 15" N., when a chronometer shewed 12h. 25m. 55s. mean time at Greenwich, March 14, the error of the instrument being - 2′0′′, and the height of the observer's eye 12 feet: required the true latitude. Answer. 47° 36' South. ON THE VARIATION OF THE COMPASS. THE VARIATION OF THE COMPASS is the deviation of the points of the Mariner's Compass from the corresponding points of the horizon, and is termed east or west variation, according as the magnetic needle, or north point of the compass, is inclined to the eastward or westward of the true north point of the horizon. For many years after the discovery of the compass, it was supposed that the needle exactly coincided with the plane of the meridian, and consequently that all the points of the compass agreed with the correspondent points of the horizon. In the year 1492, Columbus first observed that the needle deviated from the north and south points of the horizon; but still imagined this deviation was constantly the same: however, in 1634, Mr. Edward Gillibrand, Professor of Astronomy in Gresham College, discovered, from a comparison of his own observations with those of his predecessors, that the variation was not always the same at the same place; for in that year he found that the variation of the compass at Deptford was 4° 4' East, which, compared with the same as observed by Mr. Burrows, in 1580, at Limehouse, who had found it to be 11° 15' E., plainly shewed, that in the course of 54 years the variation had diminished more than 7 degrees. In 1657, according to Mr. Bond's observations, there was no variation of the compass at London: since that time the needle has been declining westward, and is at present about 24° 10' West.* It likewise appears, from observations made in various parts of the world, that in different places the variation differs both as to its quantity and denomination, being west in some places and east in others: thus, off the South Coast of Ireland the variation is at present about 30° West; but near Cape Horn, in South America, it is 22° East. But besides the deviation of the needle from the plane of the true meridian, which it acquires after being touched with a magnet, it obtains another property called the dip; that is, although the needle be properly balanced beforehand, it will now lose its horizontal position, and one end will incline below the horizon, while the other will be elevated, so that it will be necessary to attach a weight to the elevated end, in order to restore it to a horizontal position when supported on the central pin. The angle that it makes with the horizon is called the dip of the needle. Near the equator it inclines but little from the horizontal plane; but one end is depressed the more as we advance towards the poles-the north end in the northern hemisphere, and the south end in the southern hemisphere. The needle is also subject to a local attraction, resulting principally from the masses of iron on board ship, by which it will be drawn more o less from the magnetic meridian, according as the disturbing cause is According to the accurate observations of the late Colonel Beaufoy, made near London. the variation of the needle had arrived at its maximum in March 1819, when it was at noon 24° 41′ 42′′ West; the needle has since that time been retrograding, the magnetic north |