Page:Newton's Principia (1846).djvu/484

 {|align=center cellspacing="0"
 * colspan="8" |The Comet's
 * |||Dist. from sun.|||Longitude computed.|||Latitud. compu- ted.|||Longitude observed.|||Latitude observed|||Dif Lo.|||Dif. Lat.
 * Dec. 12|||2792|||♑  6°.32′||| 8°.18½|||♑  6° 31½||| 8°.26|||+1||− 7½
 * 29|||8403|||♓ 13.13⅔|||28.00|||♓ 13.11¾|||28.10$1/12$|||+2||−10$1/12$
 * Feb.  5|||16669|||♉ 17.00|||15.29⅔|||♉ 16.59⅞|||15.27⅖|||+0|| 2¼
 * Mar.  5|||21737||| 29.19¾|||12.4||| 29.20$6/7$|||12. 3½|||−1||  ½
 * }
 * 29|||8403|||♓ 13.13⅔|||28.00|||♓ 13.11¾|||28.10⇭⇭⇭|||+2||−10⇭⇭⇭
 * Feb.  5|||16669|||♉ 17.00|||15.29⅔|||♉ 16.59⅞|||15.27⅖|||+0|| 2¼
 * Mar.  5|||21737||| 29.19¾|||12.4||| 29.20⇭⇭⇭|||12. 3½|||−1||  ½
 * }
 * Mar.  5|||21737||| 29.19¾|||12.4||| 29.20⇭⇭⇭|||12. 3½|||−1||  ½
 * }

But afterwards Dr. Halley did determine the orbit to a greater accuracy by an arithmetical calculus than could be done by linear descriptions; and, retaining the place of the nodes in ♋ and ♑ 1° 53′, and the inclination of the plane of the orbit to the ecliptic 61° 20⅓′, as well as the time of the comet's being in perihelio, Dec. 8d.00h.04′, he found the distance of the perihelion from the ascending node measured in the comet's orbit 9° 20′, and the latus rectum of the parabola 2430 parts, supposing the mean distance of the sun from the earth to be 100000 parts; and from these data, by an accurate arithmetical calculus, he computed the places of the comet to the times of the observations as follows:—

This comet also appeared in the November before, and at Coburg, in Saxony, was observed by Mr. Gottfried Kirch, on the 4th of that month, on the 6th and 11th O. S.; from its positions to the nearest fixed stars observed with sufficient accuracy, sometimes with a two feet, and sometimes with a ten feet telescope; from the difference of longitudes of Coburg and London, 11°; and from the places of the fixed stars observed by Mr. Pound, Dr. Halley has determined the places of the comet as follows:—