VARIATION OF THE COMPASS. It was many years after the discovery of the compass, before it was suspected that the magnetic needle did not point accurately to the north pole of the world; but, about the middle of the sixteenth century, observations were made in England and France, which fully proved that the needle pointed to the eastward of the true north. This difference is called the variation of the compass, and is named east when the north point of the compass (or magnetic north) is to the eastward of the true north, but west when the north point of the compass is to the westward of the true north. The quantity of the variation may be found by observing, with a compass, the bearing of any celestial object when in the horizon, (or, as it is called, the magnetic amplitude ;) the difference between this and the true amplitude, found by calculation, will be the variation. The same may be obtained by observing the magnetic azimuth of any celestial object, (that is, its bearing by a compass when elevated above the horizon;) the difference between this and the true azimuth, found by calculation, will be the variation. Some years after the discovery of the variation, it was found that it did not remain constant; for the easterly variation, observed in England, gradually decreased till the needle pointed to the true north, and then increased to the westward, and is now above two points. As all the courses steered by a compass must be corrected for the variation, to obtain the true courses, it is of great importance to the navigator to know how to find the variation at any time. To do this, it is necessary to find the magnetic amplitude or azimuth of a celestial object, which may be done as follows: To observe an amplitude by an azimuth compass.* When the centre of the sun is about one of his diameters above the horizon, turn the compass round in the box, until the centre of the sun is seen through the narrow slit which is in one of the sight-vanes, exactly on the thread which bisects the slit in the other: at that instant push the stop, which is in the side of the box, against the edge of the card, and the degree and parts of a degree which stand against the middle line on the top, will be the magnetic amplitude of the sun at that time, which is generally reckoned from the east or west point of the compass. To observe an azimuth by an azimuth compass. Turn the compass round in the box until the centre of the sun is seen through the narrow slit which is in one of the sight vanes, exactly on the thread which bisects the slit on the other, or until the shadow of the thread falls directly along the line of the horizontal bar; the card is then to he stopped, and the degree and parts of a degree which stand against the middle line of the stop, will be the magnetic azimuth of the sun at that time, which is generally reckoned from the north in north latitude, and from the south in south latitude. § At the time of making this observation, you must also observe the altitude of the sun, in order to obtain the true azimuth. What is here said of the sun, is alike applicable to the moon, planets, and stars. *The figure of an azimuth compass, furnished with sight-vanes, is given in Plate VI., figure 5. The card of this compass is similar to that of a common compass. The observation is to be taken at that altitude on account of the dip, refraction, and parallax, the correction of altitude depending on these causes being, in general, nearly equal to the sun's diameter. If the instrument is furnished with a magnifying glass fixed to one of the vanes, you may (instead of proceeding as above) turn the compass box until the vane is directed towards the sun, and when the bright speck (or rays of the sun collected by the magnifying glass) falls upon the slit of the other vane, or upon the line in the horizontal bar, the card is to be stopped, and the divisions read off as above. To find the true amplitude. RULE. BY LOGARITHMS.-To the log. secant of the latitude (rejecting 10 in the index) add the log. sine of the sun's declination ;* the sum will be the log. sine of the true amplitude, or distance of the sun from the east or west point, towards the north in north declination, but towards the south in south declination. BY INSPECTION.-Find the declination at the top of Table VII., and the latitude in the side column; under the former, and opposite the latter, will be the true amplitude. When great accuracy is required, you may proportion for the minutes of latitude and decli nation. EXAMPLE 1. Required the sun's true amplitude, at rising, in the latitude of 39° 0′ N., on the 22d of December, 1848 when his declination was 23° 28′. Hence the true bearing or amplitude of the sun at rising is E. 30° 49' S., and a setting it is W. 30° 49′ S. EXAMPLE II. Required the moon's true amplitude at setting, in the latitude of 35° 8′ N., when her declination is 13° N. BY LOGARITHMS. Latitude 35° 8' Log. Sec. 0.08734 BY INSPECTION. Under the declination 13°, and opposite the latitude 35°, stands 15° 56', which is nearly the true amplitude; the exact value may be found by finding the amplitude for 36° latitude, and proportioning the difference for the miles in the latitude. Hence the true amplitude at setting is W. 15° 58′ N., and at rising E. 15° 58′ N. EXAMPLE III. Required the sun's true amplitude in the latitude of 42° 30′ N., when his declination was 20° S. Hence the amplitude at setting is W. 27° 38′ S., and at rising E. 27° 38′ S. To find the true azimuth at any time. At the time of observing the magnetic azimuth, you must also observe the altitude of the object; this altitude must be corrected as usual for the dip, parallax, refraction,† &c., in order to obtain the true altitude; you must also find the declination of the to accuracy to take several azimuths and altitudes, and to take the mean of all the azimuths and all the altitudes, and work the observation with the mean azimuth and altitude. The same is to be observed in taking an amplitude. The declination of the sun at noon is given in the Nautical Almanac, and in Table IV., and must be corrected for the longitude of the ship and the hour of the day, by means of Table V. In observations of the altitude of the sun's lower limb by a fore observation, it is usual to add 12 for the effect of dip, parallax, and semi-diameter. The refraction is to be subtracted from the sum and he remainder will be the true altitude, nearly. * object, and the latitude of the place of observation, and then the true azimuth may be calculated by the following rule:— RULE. Add together the polar distance, the latitude, and the true altitude; take the difference between the half-sum and the polar distance, and note the remainder. Then add together the log. secant of the latitude, the log. secant of the altitude, (rejecting 10 in each index,) the log. cosine of the half-sum, and the log. cosine of the remainder; half the sum of these four logarithms will be the log cosine of half the true azimuth, which, being doubled, will give the true azimuth, reckoned from the north in north latitude, but from the south in south latitude. EXAMPLE 1. In latitude 51° 32′ N., the sun's true altitude was found to be 39° 28, his declination being then 16° 38′ N.; required the true azimuth? The logarithm 9.72347 of this example is also the cosine of 121° 56', which, being doubled, gives another azimuth 243° 52′, the former being 116° 8'. One of these corresponds to an observation in the forenoon, the other to an afternoon observation. EXAMPLE II. In latitude 42° 16' S., the sun's true altitude was found to be 18° 40', his declination being then 7° 38′ N.; required the true azimuth. Question I. Given the sun's altitude, corrected for dip, refraction, &c., 20° 46', his declination 17° 10′ S., and the latitude of the place 40° 38′ N.; required the true azimuth. Answer. 137° 50' from the north. The declination is to be found according to the directions in the note in the last page. The polar distance of the sun, moon, or star, is the distance from the elevated pole, and is found by subtracting the declination of the object from 90° when the latitude and declination are of the same Quest. 11. What is the sun's azimuth in the atitude of 26° 30' N. in the forenoor when his correct central altitude is 24° 28′, and his declination 22° 40′ N.? Ans. 75° 44' from the north. Quest. III. At the island of St. Helena, the sun's true central altitude was found to be 30° 23′ in the forenoon, his declination being then 22° 58′ S.; required the azimuth at that time. Ans. 72° 21' from the south. Quest. IV. What point of the compass did the star Aldebaran bear on, in the latitude of 34° 23′ S., on January 1, 1836, when the correct altitude of that star was 22° 26'? Ans. 130° 23′ from the south. Having the true and the magnetic amplitude or azimuth, to find the variation. Having found the true and magnetic amplitude or azimuth, the variation may be easily deduced therefrom by the following rule, in which the amplitude is reckoned from the east or west point of the horizon, and is called north when to the northward of those points, but south when to the southward. The azimuth is reckoned from the north in north latitudes, but from the south in south latitudes, and is named east when falling on the east side of the meridiau, otherwise west. If the observed and true amplitudes be both north or both south, their difference will be the variation; but if one be north and the other south, their sum will be the variation. If the true and observed azimuths be both east or both west, their difference will be the variation, otherwise their sum; and the variation will be easterly when the point representing the true bearing is to the right hand of the point representing the magnetic bearing, but westerly when to the left hand; the observer being supposed to look directly towards the point representing the magnetic bearing. EXAMPLE I. Suppose the sun's magnetic amplitude at rising is E. 26° 12′ N., and the true amplitude E. 14° 20′ N.; required the variation. The variation in this example is easterly, because the true amplitude falls to the right of the magnetic. To calculate the variation by observing the sun's azimuth when at equal altitudes in the forenoon and afternoon. The variation of the compass may also be determined by observing the magnetic azimuths of the sun, in the morning and evening, when at the same altitude, the observer being supposed to be at the same place at both observations; for it is evident that if the declination of the sun do not vary during the time elapsed between the observations, the middle point of the compass between the two bearings will be the bearing of the true north or south point of the horizon, at the place of observation, and the difference between that bearing and the north or south point of the compass will be the variation. In this kind of observations, it will be convenient always to estimate the magnetic azimuths from the south point of the compass, calling them east or west, as before directed; and this method is supposed to be made use of in the following rule. Then, if one azimuth be east and the other west, half their difference will be the variation, otherwise their half-sum, and the variation will be of the same name as their greater azimuth, excepting, however, where the half-sum is taken and exceeds 90°, in which case its supplement will be the variation, of a different name from the azimuth; the variation being always supposed less than 90°. If the declination of the sun varies during the elapsed time between the observations (as is generally the case), an allowance may be made for that variation by applying a correction to the afternoon azimuth, calculated by the following rule:— RULE. Find, from Table IV., the daily variation of the sun's declination on the day of observation. Then to the constant logarithm 9.1249 add the log, cosine of the latitude of the place, the log. sine corresponding to the elapsed time between the observations found in the column P. M., the Prop. Log. of the daily variation of the sun's declination, and the Prop. Log. of the elapsed time, estimating hours and minutes as minutes and seconds; the sum, rejecting 30 in the index, will be the Prop. Log. of the correction to be applied to the western azimuth, by subtracting when the sun is approaching towards the northern hemisphere, otherwise by adding.+ The azimuth, thus corrected, is to be used in estimating the variation instead of the observed azimuth. It is not necessary, in this calculation, to find the latitude or declination to any great degree of accuracy, which is the greatest advantage of the method; another of the advantages consists in being able to take a great number of observations, and applying the correction at one operation to the variation deduced from the mean of all the observations, so that, when great accuracy is required (as in taking observations ashore), this method may be used with success; and it is evident that it is alike applicable to the moon or any heavenly body; but the observations must be taken in the same place, as it would increase the calculation considerably to make an allowance for the change of place, as well as for the change of declination; and it would be better, in this case, to calculate each observation separately by the rules before given. EXAMPLE Suppose that, on the 10th of April, 1864, in the latitude of 42° 29′ N., longitude 50° W., the sun's morning azimuth is observed to be S. 54° 24' F., and in the evening, when the sun is at the same altitude, is S. 39° 46′ W., the elapsed time between the observations being 6h 20m; required the variation. Daily variation of declination 22′ P. L....... .9128 Corr. western azimuth 11' nearly P. L.... 1.2266 Corrected azimuth S. 39 35 Difference........ S. 14 49 W. E. The half of which, 7° 24', is the variation, which is easterly, because the greater azimuth S. 54° 24′ E. is easterly. The elapsed time may be determined by any common watch; but if none be used in the observa. tions, it may be determined as follows-If one of the observed azimuths be east and the other west, take half their sum, otherwise half their difference, and to the log. sine of this half-sum (or half-difference) add the log. secant of the sun's declination, and the log, cosine of the sun's correct altitude at the time of taking the azimuth; the sum, rejecting 20 in the index, will be the log, sine to be used in the above calculation, and this logarithm will correspond to the elapsed time marked in the column P. M. of Table XXVII. |