Wherefore, firft obferved Altitude 28° 30′ — 17′ = 28° 13′ the first correct Altitude to be used in the Operation. N. S. Lat. by Ac. 48° 0' 0,17449 47281 Declin. 13 17 0,01178 2 58 20 16 50 0,18627 Ela. T. 2 26 40 Diff. N. S. 18322 Its Log. 4,26297 it 13 17 48 3 N. And as it differs but three Miles from the Latitude by Account, may be taken as the true Latitude. Questions for Exercise. Ift. Being at Sea in Latitude by Account 39° 28'N. when the Sun's Declin. was 20° 41'N. at 11 H. 30 M. 15 S. A. M. per Watch, the Altitude of the Sun's lower Limb was obferved to be 68° 18′ 45 and at 12 H. 26 M. 28 S. P. M. it was 70° 58', the Height of the Eye being 21 Feet above the Surface of the Sea; Required the true Lat. of the Ship? Anfwer, 39° 28'N. 2d. Being at Sea in Lat. 50° 40'N. by Account, at 10 H. 17 M. 30 S. A. M. per Watch, the Altitude of the Sun's lower Limb was obferved to be 17° 4' 4, and at 11 H. 17 M. 30 S. it was 19° 31', the Declination being then 20° N. and Height of the Eye 21 Feet above the Sea. Required the Latitude in ? Anfwer, 50° oʻN. M. 3d. Suppofe a Ship at Sea in Lat. 47° 34'N. by Account, at 9 H. 55 M. 30 S. by Watch, the Altitude of the Sun's lower Limb was 17° 24', Bearing by Compafs S. by E. E. and at 12 H. 54 10 S. his Altitude was 21° 45', the Declination being then 19° 30'S. the Height of the Eye 20 Feet above the Sea, and the Ship's Courfe by Compafs was E. S. at the Rate of 7 Knots per Hour. What was the true Latitude ? 4th. At 11 H. 28 M. 20 S. A. M. per Watch, the Altitude of the Sun's lower Limb was 28° 18', the Sun bearing then S. by W. by Compafs. At 2 H. 58 M. 20 S. P. M. his Altitude was 16° 40′, the Height of the Eye 20 Feet, his Declination being then 13° 17'N. and the Latitude then by Account 47° 50'N. the Ship's Course during the Elapfed Time was N. E. with her Larboard Tacks on Board, failing at the Rate of fix Knots, and made half a Point Leeway. What Latitude was the in when the last Altitude was taken? Anfwer, 48° 9'N. By the Ship's Course per Compass is to be understood, its Course made good, Leeway, if any, being first allowed, or the Course, by Compafs, corrected for the Lee-way only, but not for the Variation. Had the Variation of the Compaís been applied, both to the Ship's Course and the Sun's Bearing, it would not have made any Difference in the Operation or Result, as the Angle formed by them will always be the fame, whether they are both estimated by the Compass, or when the Variation is allowed on both. This Method of finding the Latitude is of excellent Ufe, fince there are so many Circumftances at Sea, which deny the Opportunity of having the Sun's Meridian Altitude; and as the knowing the true Latitude is of the greatest Confequence, efpecially in coming into the English Channel, &c. where there are frequent Obstructions of Clouds, every Seaman ought to be ready at determining his Lati→ tude, by this Method, whenever an Opportunity offers, left he fhould not fee the Sun upon the Meridian. NOTE. The nearer to Noon the Observations are taken, the better; provided the elapsed Time be not much less than Half the Interval of Time, when they are both taken on the fame Side of Noon, nor much greater than Once and Half the greater Interval, when taken on different Sides of Noon. To find the Latitude by the Meridian Altitude of the Moon. IN N Page 6th of the Month in the Nautical Almanack, find the Time of the Moon's paffing over the Meridian of Greenwich. Turn the Longitude into Time, by Table XVIII. and add it to the above Time, if it be Weft, but fubtract it, if it be Eaft: The Sum, or Difference, will be nearly the Time of her Paffage over the Meridian of the Place of Obfervation; which call Reduced Time. In Page 7th of the Month in the Almanack, find the Moon's Şemidiameter and Horizontal Parallax, at the Reduced Time. Take the Difference between the Moon's Semidiameter and Dip, and add it to the obferved Altitude, if the lower Limb was observed, but fubtract it, if the upper Limb was obferved: The Sum or Difference will be the apparent Altitude of her Center. From the Proportional Logarithm of the Moon's Horizontal Parallax, found in Table XIX. increafing its Index by 10, fubtract the Log. Co-fine of the Moon's apparent Alt. the Remainder will be the Prop. Log. of the Moon's Parallax in Altitude, from which take her Refraction, the Difference will be a Correction, which being added to the apparent Altitude, will give the true Altitude of her Center: Hence the Zenith Distance, to which apply her Declination, and you will have the Latitude. NOTE. The Moon's Declination is fet down in Page the 6th of the Month for every Noon and Midnight in the Nautical Almanack. Therefore find the Declination for the nearest Noon and Midnight both before and after the reduced Time, and take the Diffe rence. Then as 12 Hours: is to the Difference in 12 Hours :: fo is the reduced Time to a proportional Part; which being added to, or fubtracted from the Declination the Noon or Midnight before the reduced Time, according as it is increasing or decreafing, will give the Declination at the Time and Place of Observation. Suppofe on Sept. 21, 1796, in Long. 45° Weft, the Altitude of the Moon's lower Limb, when on the Meridian South of the Ob→ ferver, should be 67° 43′, the Eye being 23 Feet above the Sea, Required the Latitude? By the Almanack, the Moon paffes over the Meridian of Greenwich that Day at 16 H. 10 M. Afternoon, and the 45° Weft turned into Time, and added to it, gives 19 H. 10 M. that is, 7 H. 10 M. paft Midnight, the Time the paffes the Meridian of the Place of Obfervation. Hor. Par. 59' 15" Prop. Log. 10,4826 Moon's obf. Alt. 67° 43′ 30′′ Prop. L. of M's P. in Alt. 22' 16" 9075 ނ II 34 23 Dip 4 34 67 55 4 21 53 Correct. of Moon's Alt. 21 53 Sept. 21ft, Moon's Decl. at Midnight 15° 37′ 17 37 M's tr. Alt. 68 16 57 Moon's Dec. 90, NOTE. If the nearest Minutes are taken and the Seconds rejected, it will be fufficiently exact for the Purpose of finding the Latitude. Zen. Dift. 21 43 3S Decl. 18 40 ON Lat. in 40 23 3N Suppofe on Dec. 13, 1796, in Long. 30° Eaft, the Alt. of the Moon's upper Limb fhould be obferved when on the Meridian, being then South 56° 15', the Eye 20 Feet above the Sea. Required the Latitude? The Moon paffes over the Meridian of Greenwich that Day, by the Almanack, at 11 H. 23 M. Afternoon. The Long. in Time 2 H. fubtracted from 11 H. 23 M. leaves 9 H. 23 M. for the Time the paffes the Meridian at the Place of Obfervation. At this Time the Moon's Semi-diameter is found to be 16' 41", and her Horizontal Parallax 61' 10". To find the Latitude by the Meridian Altitude of a Planet. In Page 4th of the Month in the Nautical Almanack are given the Declinations and Times of the Planets Paffage over the Meridian of Greenwich every 6 Days. Reduce the Longitude into Time, and add it to, or fubtract it from, the Times of their Paffages over the Meridian of Greenwich, according as their Longitude is Eaft or Weft: The Sum or Difference will be the Time they pass the Meridian of the Place of Obfervation: Correct the obferved Altitude for the Dip and Refraction, with this correct Altitude and Declination find the Latitude; as for EXAMPLE. Suppofe in Longitude 45°W. on October 1, 1796, the Meridian Altitude of Jupiter, when South of the Obferver, fhould be 41° 30', the Eye 22 Feet above the Sea, and the Latitude be required? By By the Almanack Jupiter paffes the Meridian of Greenwich that Day at 9 H. 53 M. Afternoon; and 3 H. the Long. in Time, added to it, gives 53 M. after 12 at Night, when he paffes over the Meridian of the Place of Obfervation. 37 23 32N. The Declination of the Planets are fet down for every 6 Days, but may be found for intermediate Days by taking Proportional Parts. OF THE PARALLAX. PAR ARALLAX is the Difference between the Altitude of the Sun, Moon, or Star, and the Altitude of the fame Object seen at the fame Time from the Earth's Surface; or it is the Angle the Earth's Semi-diameter would appear under by an Obferver placed at the Sun, Moon, or Star. The Parallax of the Heavenly Bodies are greateft when in the Horizon, hence called the Horizontal Parallax; that of the Moon's is fet down in the Nautical Almanacks for every Noon and Midnight, and lies between 54' and 62'; the Parallax diminishes according to the Altitude of the Object until it comes to the Zenith, where it is nothing; the Difference of the Elevation of Objects is called the Parallax in Altitude, and it is eafy calculated by faying, as Radius is to the Horizontal Parallax, fo is the Co-fine of the Altitude to the Parallax in Altitude: Now, as all Objects are depreffed by their Parallax, fo they are elevated above their true Altitudes by Refraction. Let |