282 ON FINDING THE LONGITUDE &C. 



EXAMPLE II. 



October 7th, 1805, at the Forest plantation, latitude 31° 27' 

 48", observed the apparent double altitude of the moon's lower 

 limb (greatest) near the meridian, 1330 u . 14 " 



The index error being subtractive, add the lesser contact of 7 i< "0 



the sun with his image taken immediately after observation. 5 



2)133 26 44 

 Lat. 31" 27' 48'' . Apparent altitude of the 3's centre. 66 43 22 

 'iolat. 58 32 12 . Parallax and refraction. . . + 22 41 75 



True altitude of the 2>'s centre. . 67 6 3 75 

 Correction per formula. . —11 43 



True alt. of 3's centre on the mer. 67 5 52 32 



Colatitude 58 32 12 



h 



3's declination when on the meridian. 8 33 40 32 



Appt. time at Greenwich when the 3 had this declination by even proportion 17 43 52 18 

 Correction by the equation of second difference. . — 2 12 47 



Appt. time at Greenwich, when the 3 was on the mer. of place of observation. 17 41 39 71 

 /Vppt. time corrected, when the 3 was on the meridian of Greenwich. . 11 24 18 15 



Difference of apparent time 6 17 21 56 



Correct for the equation of time -J- 4 39 



Difference in mean time, of the 3 passing the two meridians. . . . 6 17 25 95 

 Difference of A. R. of the 3 and ©, gained during the interval. . . —12 5 



Longitude of the place of observation 6 5 20 95 



Mr. EUicott has made 30 calculations, on which he seems to rely for the longitude of 

 the Natchez, (others were rejected,) his extreme results are 6' 1 4' 27" to 6 k 6' 41", and 

 a mean of the whole is 6'" 5' 49". The position of the Forest plantation is about 2i miles 

 east of Natchez, i. e. 9" in time, which being added to the above result, gives 6 h 5' 30"" 

 for the longitude of Natchez, differing from the mean of Mr. Ellicott's observations 19" 

 or 4j miles. 



An immersion of Jupiter's 1st satellite was taken just before 

 his opposition, and an emersion of the same soon after, and as 

 they were probably both affected by the near vicinity of the 

 light of Jupiter's disk, but acting in contrary directions, a mean 

 of the two results may be supposed near to the truth, subject to 

 the correction which the Greenwich calculations may require. 



June 11th. By an immersion of Jupiter's 1st satellite. . . 6>> 5' 41" 4 



July 6th an emersion of ditto. . . . . .. 6 5 12 19 



Mean longitude . 6 5 26 8 



The mean differs only 5" 8, nearly 1 J,mile from the result of the meridian altitude. 



CjPIn the above method of finding tbjj longitude, as a small error in the meridian altitude of 

 the moon, will produce a considerable one in the longitude, a correction ought to be applied 

 on account of the spheroidal figure of the earth Edit. 



