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

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478
the mathematical principles
[Book III.
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°.10112 +2 −10112
Feb.  5 16669 ♉ 17°.00 15.°29⅔ ♉ 16°.59⅞ 15°.27⅖ +0 + 2¼
Mar.  5 21737 29°.19¾ 12.°04 29°.2067 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:—

The Comet's

True time. Dist from
the sun.
Longitude
computed.
Latitude
computed.
Errors in
Long.     Lat.
d.   h.   ′ ″
Dec. 12.4.46.  
21.6.37.  
24.6.18.  
26.5.20.  
29.8. 3.  
30.8.10.  
Jan. 5.3.1.½
9.7. 0.  
10.6. 6.  
13.7. 9.  
25.7.59.  
30.8.22.  
Feb. 2.6.35.  
5.7.4.½
25.8.41.  
Mar. 5.11.39.   

28028
61076
70008
75576
84021
86661
101440
110959
113162
120000
145370
155303
160951
166686
202570
216205
°   ′   ″
♑ 6.29.25
♒ 5.6.30
18.48.20
28.22.45
♓ 13.12.40
17.40.5
♈ 8.49.49
18.44.36
20.41.0
26.0.21
♉ 9.33.40
13.17.41
15.11.11
16.58.55
26.15.46
29.18.35
°   ′   ″
8.26.0 bor.
21.43.20
25.22.40
27.1.36
28.10.10
28.11.20
26.15.15
24.12.54
23.44.10
22.17.30
17.57.55
16.42.7
16.4.15
15.29.13
12.48.0
15.5.40
′   ″
-3.5
-1.42
-1.3
-1.28
+1.59
+1.45
+0.56
+0.32
+0.10
+0.33
-1.20
-2.10
-2.42
-0.41
-2.49
+0.35
′   ″
-2.0
+1.7
-0.25
+0.44
+0.12
-0.33
+0.8
+0.58
+0.18
+0.2
+1.25
-0.11
+0.14
+2.0
+1.10
+2.14

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:—