Example 2. March 10th, 1825, in latitude 42:41 S., and longitude 14895 E., at 19:25 per watch, the observed altitude of the sun's lower limb was 18:3, and the bearing of his centre, by azimuth compass, S.108:37:30 E.; the height of the eye above the level of the sea was 19 feet; required the variation? Observed altitude of the sun's lower limb-18: 3: 0% magnetic azimuth is to the left hand of the true azimuth. Note.-After this manner may the variation be deduced from the true altitude and magnetic bearing of a fixed star, a planet, or the moon, as will be seen by referring to "The Young Navigator's Guide to the Sidereal and Planetary Parts of Nautical Astronomy," page 263; where the principles of this method are familiarly explained by a stereographic projection. A new Method of computing the true Azimuth of a celestial Object, and, thence, finding the Variation of the Compass. RULE. From the natural versed sine supplement of the sum of the latitude and the true altitude, subtract the natural versed sine of the object's polar distance to the logarithm of the remainder add the logarithmic secants. of the latitude, and the true altitude: the sum of these three logarithms, rejecting 20 from the index, will be the logarithm of the natural versed sine supplement of the true azimuth; to be reckoned from the north in north latitude, but from the south in south latitude; the difference between which and the magnetic azimuth will be the variation of the compass, as before. Example 1. October 17th, 1825, in latitude 42:10: N., and longitude 14:30 W, at 32 per watch, the mean of several observed altitudes of the sun's lower limb was 23:39:34", and the mean of an equal number of his central bearings, by azimuth compass, N. 109:28:56" W.; the height of the eye above the level of the horizon was 17 feet; required the variation of the compass? Sum = 65:59:41 N.V.S.sup.-1.406821 Sun's N. polar dist. 99. 18. 58 Nat.V. sine 1. 161881 Remainder. 244940 Log. 5.389060 True azimuth N.129:41.53′′W. N.V. S. sup.361259 Log.=5.557819 Magnetic do. N.109. 28.56 W. 20:12.57%; which is west, because the magnetic azimuth is to the right hand of the true or computed azimuth. Example 2. December 9th, 1825, in latitude 19:40 N., the true altitude of the star Capella was 20:10, and his bearing, by azimuth compass, N. 41:0. E.; required the variation? Sum = · 39:50 0N.V.S. sup.-1.767911 Capella's N. pol. dis. 44. 11. 24 N.V. sine = .282968 Remainder 1.484943 Log. 6. 171710 True azimuth N. 47: 9:45′′E. N.V. S.sup.1.679922Log. 6. 225289 Magnetic do. N. 41. 0. 0 E. Variation = 6: 9:45"; which is east, because the magnetic azimuth is to the left hand of the true or computed azimuth. Remark. Instead of finding the natural versed sine supplement of the sum of the three logarithms, that sum may be considered as a logarithmic rising. In this case, if the supplement of the time corresponding thereto be taken from Table XXXII., and converted into degrees, by Table I. or otherwise, the result will be the true azimuth. Thus, in the last example, the sum of the three logarithms is 6.225289; the time corresponding to this, in the Table of Logarithmic Rising, is 8:5121, which, taken from 12 hours, leaves 3:8:39; and this, being converted into time, gives 47:9.45% for the true azimuth, which is precisely the same as above. PROBLEM III. To find the Variation of the Compass by Observations of a circumpolar Star. From the log. co-sine of the star's declination, (the index being increased by 10,) subtract the logarithmic co-sine of the latitude: the remainder will be the logarithmic sine of the star's greatest eastern or western azimuth (according as it may be situated with respect to the meridian); to be reckoned from the north in north latitude, but from the south in south latitude. Then, From the logarithmic sine of the latitude, (the index being increased by 10,) subtract the logarithmic sine of the star's declination, and the remainder will be the logarithmic sine of the star's true altitude when at its greatest eastern or western azimuth. Set the index of the quadrant to this altitude, and, when the står has attained it, let its bearing be taken by the azimuth compass; the difference between which and the computed azimuth, when they are of the same name, or their sum when of contrary names, will be the variation; which will be east, if the observed or magnetic azimuth be to the left of the computed azimuth; otherwise, west. Example 1. January 1st, 1825, in latitude 41:53: S., the greatest eastern azimuth of the star Canopus, by azimuth compass, was S. 72:50. E.; required the variation of the compass? To find the Star's Altitude when at its greatest Azimuth : Latitude of the place of observ. 41:53 0 S. Reduced declination of Canopus 52.36. 10 S. Star's alt. at greatest azimuth = 57:10:40% Log. sine 9. 824527 Log. sine 9, 924464 To find the Star's greatest eastern Azimuth :— 9.783430 Reduced declination of Canopus=52:36:10 S. Log. co-sine magnetic azimuth is to the left hand of the computed azimuth. Example 2. December 31st, 1825, in latitude 43:45 N., the greatest western azimuth of the star Dubhe, by azimuth compass, was N. 16:56′ W.; required the variation of the compass? To find the Star's Altitude when at its greatest Azimuth: Latitude of the place of observ. = 43:45′ 0′′N. 62.41..19 N. Log. sine 9.839800 Star's altitude at greatest azimuth=51: 6 8 Log. sine 9. 891130 To find the Star's greatest western Azimuth : : Reduced declination of Dubhe = 62:41:19′′N. Log. co-sine=9.661648 Lat. of the place of observation=43.45. 0 N. Log. co-sine 9.858756 Greatest western azimuth = Magnetic azimuth = Variation = N. 39:25:58 W. Log, sine = 9.802892 22:29:58"; which is west, because the magnetic azimuth is to the right hand of the true or computed azimuth. Remarks. In the above method of finding the variation of the compass, the star's declination must be greater than the latitude of the place of observation, and of the same name. A star, or other celestial object is said to be circumpolar when its distance from the elevated pole is less than the latitude of the given place (the declination and latitude being of the same name); because, under |