Example.-May 21st, 1890, at 10h. 12m. p.m. apparent time at ship; in long. 22° 30′ W.; the observed altitude of Polaris was 50° 18′ 10′′; height of eye 20 feet; index error +1′ 10′′; required the latitude. If any interpolation be necessary when taking out the Ist corr. it can be done at sight. Example.-October 26th, 1890, a.m. at ship; long. 175° 42′ E.; the observed altitude of Polaris was 58° 0′ 30′′; height of eye 27 feet; index error of sextant 1' 50" to subtract; time by chronometer 5h. 10m. 2s., which was 9m. 40s. slow on mean time at Greenwich; required the latitude. The small circle is the parallel of declination much exaggerated. The figure shows that when the star's hour angle is 6h. E. or W. there is practically no correction to apply, the true altitude being, for all practical purposes, the latitude. When the star is on the meridian above or below the pole, the star's polar distance is the correction, plus to true altitude when below the pole, minus to true altitude when above the pole. Examples for Practice Example 1.-September 6th, 1890, in long. 38° 30′ W., at 11h. 51m. p.m., apparent time at ship, suppose the altitude of the Polar star to be 30° 30′ 25", the height of the observer's eye being 22 feet, and the index error +2′ 20′′; required the latitude. Ans. 29° 24'7 North.-By N.A. Method, 29° 25′ 7′′ N. Example 2.-March 12th, 1890, in long. 45° 30′ E., at 3h. 30m. a.m., mean time at ship, suppose the altitude of the Polar star to be 70° 26′ 30′′, the height of the observer's eye being 18 feet, and index error -1′ 30′′; required the latitude. Ans. 71° 32′ North.—By N.A. Method, 71° 31′ 35′′ N. Example 3.-November 4th, 1890, in long. 150° 18′ E., at 10h. 23m., p.m., mean time at ship, the observed altitude of the Polar star was 53° 10' 20", height of eye 19 feet, index error +2' 10"; required the latitude. Ans. 51° 50'7 North.-By N.A. Method, 51° 51′ 8′′ N. Example 4.-At ship March 22nd, 1890, p.m., in long. 40° 30′ W.; the observed altitude of the Polar star was 48° 30′; height of eye 26 feet; time by chronometer March 22d. 10h. 4m. 30s., which was 8m. 10s. fast on mean time at Greenwich; required the latitude. Ans. 48° 24'-8 North.-By N.A. Method, 48° 24′ 28′′ N. Example 5-August 3rd, 1890, at 10h. 28m. 12s. p.m., mean time at ship; long. 35° 2' W.; the observed altitude of Polaris off the meridian was 35° 10' 15"; index error of sextant 1' 45" to subtract; height of eye 17 feet; required the latitude. Ans. By N.A. Method, 35° 3′ 52′′ N. Example 6.-November 23rd, 1890, a.m. at ship; long. 168° 44′ W.; mean time at Greenwich by chronometer (corrected for error and rate) was November 23d. oh. 11m. 36s.; the observed altitude of the Polar star off the meridian was 48° 15′; height of eye 25 feet; required the latitude. Ans. By N.A. Method, 47° 28′ 8′′ N. NOTE. The method of finding the latitude by the pole star, though confined to the northern latitudes, is very useful at sea, as it is available at all times when the star is visible, and the horizon is sufficiently distinct; it also does not require a more accurate knowledge of the time than is usually possessed on board ship. Consequently the chief error will depend on the capacity of the observer in taking an altitude, and the state of the weather, in conjunction with the visibility of the horizon. By using the Nautical Almanac method, the first correction always gives the latitude within 2' of accuracy. THE CORRECTIONS OF THE COMPASS BY AMPLITUDES, TIME-AZIMUTHS AND ALTITUDE-AZIMUTHS THE Compass needle points to the magnetic pole of the earth, which, not being coincident with the true pole, the result is a varying angle (according to locality), which is called the Variation of the Compass. Before the time of Columbus variation had not been recognised, but we now know there is a slow progressive alteration of the position of the needle with respect to the true meridian; it moves towards the west, until it arrives at its maximum on that side; it then returns, passes over the true meridian, and moves easterly, until it arrives at its maximum towards the east; it then returns as before. When first noticed in London, there was about a point of easterly variation; this had decreased to zero in 1657; the needle then moved westward until it attained a maximum of 24° W. in 1816; now (1914) it is less than 15°, progressing to eastward, and the line of no variation will in years to come again coincide with the true meridian-a complete cycle of changes through east and west occupying about 320 years. DEFINITIONS Variation of the compass is the angle which measures the difference between the true and magnetic meridians. Deviation of the compass is the deflection of the needle to the right or left caused by local attraction, generally in the ship or in the cargo. It measures the deflection of the needle from the magnetic meridian. Compass error is the combined effect of both variation and deviation, the algebraic sum of which is the error, and measures the total deflection of the needle from the true meridian. The methods of finding the true bearing of a celestial object are by— Amplitude, Altitude azimuth, Time azimuth. The elements required are Time, Latitude, Declination. The error of the compass can also be found by comparison with objects on land whose true bearing is known, and the deviation by comparing the magnetic and compass bearings. The true bearing of a point of land or any conspicuous object can be found in combination with a celestial object. AMPLITUDE The method by an amplitude consists in observing the compass bearing of the sun, or other heavenly body when its centre is in the true horizon; that is, at its rising or setting. Since the object can only be referred to the visible horizon, and being subject to vertical displacement due to refraction, parallax, and dip, an observation taken near the visible horizon requires a small correction. Refraction causes objects to appear in the horizon when, on an average, they are 33' below. A star, if you can really recognise it, may be taken when it is 33' plus the dip above the horizon. The moon, owing to its irregular disc and large horizontal parallax, is a very unfavourable object. You can find the true amplitude (bearing) of the sun without computing it, from Amplitude Table, which is accurate within a degree. The Observation. For the sun, which has an appreciable disc, no preparation is needed except being ready at the compass a few minutes in advance, and keeping the sight vanes (attached to the compass) pointed in the right direction. Then when it is estimated that the lower edge of the sun is about his semi-diameter above the horizon, observe the bearing. There should also be noted with this observation, as well as with all others for determining the error of the compass and the deviation, the ship's head by Standard Compass, and the angle of heel, if any, to starboard or port. RULE.-I. For the Greenwich Date, and the Declination of the heavenly body. With the time at ship and longitude, find the corresponding time at Greenwich; and to that Greenwich time reduce the object's declination, taken from the Nautical Almanac. 2. For the True Amplitude.-Under the latitude write the corrected declination; then, to the log. secant of the latitude add the log. sine of the declination; their sum (rejecting index 10) will be the log. sine of the true amplitude, which take out in degrees and minutes. The true Amplitude is to be named: From east if the object is rising, but from west if the object is setting. Towards N. for N. declination, towards S. for S. declination. If the declination is o, the true amplitude is true east at rising, true west at setting; no computation is required. For latitude o the declination is the true amplitude. 3. For the Error of the Compass.-Under the true amplitude write the observed amplitude, reckoned from E. or W. as the case may be. If both are N., or both S., take, their difference; if one is N. and the other S., take their sum; the result in each case will be the error of compass. Then looking from the centre of the compass in the direction of the observed amplitude Name error E. if the true is to the right of observed amplitude. 4. For the Deviation of the Compass.-Under the error of the compass write the variation taken from the chart, or as given in the question, thenError and variation, both E. or both W., take their difference. Error and variation, one E. and the other W., take their sum. The resulting deviation will be of the same name as the error of compass; unless the error has been subtracted from the variation, in which case the deviation will be E. when error is W., but W. when error is E. |