Ball — On the Binary Star 5 Ursae Majoris, 
321 
^^0. 22 of Table II. In all, sixty-four mean results of observation 
are employed. 
Ordinates are then erected on the scale of one millimeter to each 
of the angles of position. 
All the points thus constructed would, if the observations vrere 
perfect, lie upon a curve. The next task is, therefore, to draw among 
all the points the curve which, on the whole, coincides most nearly 
with the observations. The abundance of points in the lower portion 
of this curve renders its form in that neighbourhood a matter of but 
little uncertainty ; this will enable the form of the curve in the ear- 
lier portions to be corrected, where there are but few points to guide 
the hand in its formation. It should be remembered, in setting up 
the ordinates, that the positions of 1781-97, 1802-09, 1804-08 are 
each to be increased by 360°, as otherwise the curve would be dis- 
continuous. 
The curve, having been completed, is now submitted with this 
communication to the Academy. (Plate XXII., Science). 
Ordinates are read off upon this curve, for every five years. The 
angles of position, thus interpolated, are given in the third column of 
Table III. 
TABLE III. 
The Angles of Position and the Distances in the Projected Ellipse, 
deduced from the Corresponding Epochs ly the Interpolating Curve. 
No. 
Epocli. 
t 
Interpolated 
Angle of 
Position. 
6> 
Distance. 
1 
1785 
136° -0 
84-5 
2 
1790 
123 -0 
95-1 
3 
1795 
112 -5 
97-1 
4 
1800 
101 -5 
92-6 
5 
1805 
88 -5 
77-8 
6 
1810 
69 -0 
40-4 
7 
1815 
328 -0 
39-1 
8 
1820 
280 -0 
51-2 
9 
1825 
245 -5 
54-1 
10 
1830 
212 -0 
52-0 
11 
1835 
181 -0 
56*4 
12 
1840 
153 -5 
65-1 
13 
1845 
137 -5 
82-5 
14 
1850 
126 -0 
98-2 
15 
1855 
115 -5 
91-8 
16 
1860 
104 -6 
93-1 
17 
1865 
91 -3 
79-6 
18 
1870 
64 -0 
50-1 
19 
1872-28 
24 -2 
28-8 
R. I. A. PROC. — vol. I., SER. II., SCIENCE. 2 T 
