476] 
ORBIT OE A PLANET FROM THREE OBSERVATIONS. 
447 
94. I annex a specimen; the characteristics of the logarithms are omitted. 
o 
o 
II 
o 
o 
- 6° 34' 
+ 46° 34' 
02701 
56107 
00286 
06113 
16272 
02376 
76144 
65052 
06247 
65052 
06247 
32251 
65338 
12360 
81324 
08623 
a\ = 1-06418 
y 1 = -21014 
a? a = --45017 
•92367 
x 3 = — *65049 
•92367 
32251 
02701 
•01329 
•12196 
02701 
00830 
y-2 == + 
•91038 
2/3 = 
•80171 
29950 
03531 
log = 
•95922 
log 2/3 = 
90402 
</>, = 11° 10' 
n = 1-0847 
95922 
95922 
90402 
90402 
65338 
04752 
81324 
10980 
30584 
00674 
09078 
01382 
</> 2 (= 63° 41') = 116° 19', r 2 = 1-0157 <¿3 (= 50° 57') = 230° 57', r 3 = 1 0323. 
The calculation of the equation of the orbit is then as follows : 
A = -36397 
log = 56107 
12214 
A 2 = -13248 
A, 2 — 3 = — 2-86752 
log = 45750 
log R, = 03531 
R 1 = 1-0847 
A + 2 = 2-36397 
log = 37364 
logr 2 = 00674 
38038 
log \/l + A 2 = 02701 
77815 
log 6 VT+Ä 2 = 80516 (a) 
45750 
30103 
log 2 (A 2 - 3) = 75853 (c) 
23856 
B 2 = + 2-4010 
A - 2 = - 1-63603 
log = 21378 
log t3 = 01382 
22760 
R 3 = - 1-6889 
log 2 V3 (A 2 - 3) = 99709 (b)