318 Proceedings of the Royal Irish Academy. 
TABLE I. 
Elements of the Orhit of the Binary Star ^ Ursae Majoris. 
Semi axis 
Major. 
Eccentri- 
city. 
Position 
of Node. 
Inclina- 
tion. 
Angle between 
Maj or Axis 
and Line of 
Nodes. 
Period in 
Years. 
Perihelion 
Passage, 
A. D. 
Authority. 
a 
3".857 
e 
0-41640 
95"-37 
y 
59^-67 
X 
13r-63 
F 
58-262 
£ 
1817-25 
Savary. 
3 -278 
0-37770 
97 -78 
56 -10 
134 -37 
60-720 
1816-73 
Herschel II. 
2 -417 
0-41350 
98 -87 
54 -93 
130 -80 
61-464 
1816-44 
Madler. 
2 -439 
0-43148 
95 -83 
52 -82 
128 -95 
61-676 
1816-86 
Villarceau. 
For a definition of the meaning of the elements, reference may- 
be made to Sir John Herschel' s beautiful memoir already referred 
to (p. 172). 
We next proceed to compare these orbits with the observations. 
Amid the multitude of observations available for this purpose, 
twenty-two have been selected, distributed fairly over the ninety 
years during which the star has been observed ; and, wherever a choice 
has been possible, the results which have the greatest weight have 
been adopted. The selection has principally been made from Dawes' 
Catalogue of Micrometrical Measurements" already referred to ; other 
observations have been supplied by the kindness of Dr. Briinnow. 
The comparison has only been instituted between the observed 
and computed angles of position, as the angle of position is susceptible 
of much more precise measurement than the distance. The result of 
the comparison is shown in Table II. The first column contains the 
number of the observation ; the second, the observer on whose authority 
the angle of position is given ; the third contains the epoch, expressed 
in years A. D., and decimals of a year ; the fourth contains the ob- 
served position ; the fifth contains the positions computed from Savary' s 
elements; the sixth contains the difi'erence between the positions 
computed from Savary' s elements and the observed positions. 
The remaining columns contain the computed positions and dif- 
ferences for the elements determined by the three other astronomers 
referred to. 
