VARIATION OF COMPASS.] NAVIGATION N A UTICAL ASTRONOMY. 



1091 



semi-diameter, the altitude of the sun's lower limb should 

 be about 17 + dip. 



Examples. 



1. In January, 1830, in latitude 27 30' N., the rising 

 amplitude of Aldebaran was observed, by compass, to be 

 E. 23 30 N. Required the variation of the compass. 



By the A'autical Almanac the declination of Alde- 

 baran was 16 9' 37' N. ; and since by right-angled 

 triangles, we have 



sin. declination = sin. amplitude X cos. latitude ; 



ein. declination 

 therefore, sin. amplitude= cos . latitude 



so that the logarithmic computation is as follows : 



10 



sin. declination 16 9' 37 ... 9 '44455 

 cos. latitude 27 36' 0* . . .-9-94753 



sin. amplitude 18 18' 16' 

 Magnetic amplitude 23 30' 0" 



9-49702 



5 11' 44" 



As the star is thus farther by 5 11' 44" from the mag- 

 netic east towards the north than from the true east, 

 the magnetic east has therefore receded thus much to- 

 wards the south, and consequently the magnetic north to- 

 wards the east, hence the variation of the compass is 5 11' 

 44 E. But the following directions will serve for all cases- 



When the object is rising, the true amplitude is al- 

 ways estimated from the east, and when it is setting, 

 fnmi the west, and towards the north or south, according 

 as the declination is north or south. 



If the true amplitude, and that by compass, 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, easterly when the true amplitude is to 

 the right, and westerly when it is to the left of the 

 observed amplitude. 



2. On Feb. loth, 1841, in latitude 43 36' N., and 

 longitude 20 W., the setting amplitude of the sun's 

 centre was observed to be W. 6 45' N., at Ch. 52m. P.M., 

 apparent time. Required the variation of the compass. 



Time at ship . . . 6h. 52m. 

 Long, in time . . . Hi. 20m. W. 



Time at Greenwich . 8h. 12m. 



Sun's dec. at noon, Kaut. Aim. 12 37' 18' 8. 

 Correction for 8h. 12m. . -6' 49" 



Sun's dec. at time of obs. 



sin. declination 12 30' 8. 

 cos. latitude 43 30' 



in. amplitude W. 17 23' S. 

 Magnetic amplitude W. 45' N. 



12 30- 29 S. 



10 



. 9-33534 

 .- 9-85984 



. 9-47550 



Variation 



24 



8' West, the true amplitude 

 being to the left of the 

 magnetic. 



The true amplitude is always of the same name north 

 or south, as the declination, as is obvious. 



3. In latitude 21 14 N., when the sun's declination 

 reduced to the time at ship, was 19 18' 6* S., its mag- 

 netic amplitude at rising was E. 35 20' S. Required 

 the variation of the compass. 



Ans. Variation, 14 34' West. 



4. In latitude 20 22 N., and longitude 79 W., the 

 sun's centre was observed to set W. 4 17' S. ; the time 

 at the ship was about Oh. P.M. : the sun's declination at 

 noon Greenwich time, was 30', and the hourly increase 

 of declination 1'. Required the variation of the compass. 



Ans. Variation, 3 31 E. 



5. In latitude 48" 20" N. the star Rigel was observed 

 to set 9 50' to the northward of the west point of the 



compass : the star's declination was 8 25' S. Required 

 the variation of the compass. 



Ans. Variation, 22 33' W. 



VARIATION OF THE COMPASS FROM AN AZIMUTH. The 

 computation of the azimuth of a celestial object requires 

 the solution of an oblique-angled spherical triangle, the 

 three sides being given to find an angle. The three sides 

 are the co-latitude, the co-declination, and the zenith 

 distance, or co-altitude of the object : the azimuth is 

 measured by the angle at the zenith, or that of which 

 the sides are the co-latitude and the co-altitude ; in 

 other words, it is the angle at the zenith between the 

 meridian and the vertical circle through the object, 

 agreeably to the definitions (page 1074). In north lati- 

 tude, the true azimuth is reckoned from the south point 

 of the horizon ; and in the south latitude, from the north 

 point, towards the east, when the altitude is increasing, 

 and towards the west when the altitude is decreasing. 



The observed or magnetic azimuth being reckoned 

 from the same point as the true azimuth, if both are east 

 or both west, their difference will be the variation ; but if 

 one is east and the other west, their sum will be the vari- 

 ation. The variation is east or west, according as the 

 true azimuth is to the right or to the left of the observed 

 azimuth. 



Examples. 



1. On June 9, 1853, at about 5h. 50m. A.M., in lati- 

 tude 50 47' N. and longitude 99 45' W., the bearing of 

 the sun by compass was S. 92 36' E. ; when the altitude 

 of his lower limb was 18 35' 20', the index correction was 

 + 3' 10', and the height of eye 19 feet Required the 

 variation of the compass. 



1. For the Co-declinition and the Co-altitude. 

 Time at ship, June 8 . . 17h. 50m. 

 Long. 99 45' W. in time . . Oh. 39m. 



Time at Greenwich, June 9 . Oh. 29m. 



Sun's dec. June 9, at noon, Gr. time 22' 57 30" 

 Hourly var.+ 11* -8 .'.cor. for 29m. + 6" 



Dec. at time of observation 



Co-declination . 



22 57' 42" 

 90 



67 



18" 



Obs. alt. . 

 Index cor. 



Dip 4' 17" ) 

 Semi 15' 46" ) 



18 35' 20" 

 + 3' 10" 



18 38' 30" 

 + 11' 29" 



App. alt. . 

 Ref. and par. 



True alt 



18 49' 59" 

 2f 41" 



18 47' 18" 

 90 



Co-alt. . ... 7112 / 42" 



2. For the true Azimuth. 

 Co-declination 67 2" 18" 



Sin. co-alt. . 71 12' 42" Arith. Comp. -0238109 

 Sin. co-lat. . 39 13' 0" Arith. Comp. -1991079 



2) 177 28' 0" 



Sin. 88 44' 0" 

 Sin. (88 44' 



codec.) 21 41' 42" 



Cos. 



51 52' 4" 



2 



9-9998939 

 9-5678091 

 9-7900218 



True azimuth S. 103 44' 8" E. 

 Observed azl S. 92 36' 0' E. 



Variation . . 11 



8' 8" W., the true azimuth being 

 to the loft of the observed. 



