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1903.] DOOLITTLE—ORBIT OF DOUBLE STAR ~ 518. 171 
the two stars of a binary system revolve in elliptic orbits about 
their common center of gravity. The first method for determining 
the orbit of the companion star about its primary was given by 
Savary in 1827, who applied his method to the binary ¢ Urse 
Majoris. This was thus the first double star of which an orbit was 
computed. 
In the method of Savary, the elements of the orbit were derived 
from the least possible number of measures which would theoreti- 
cally determine them. It was thus but very poorly adapted to 
secure good results, since all double star measures are liable to 
errors which are very large in proportion to the quantities ‘to be 
determined from them. The method was improved by Encke, 
and other methods were subsequently devised by Sir John Herschel, 
Villarceau, Thiele and others; but in all of these the development 
was from the point of view of the pure mathematician, rather than 
from that of the practical astronomer. 
The astronomer who essays to compute the orbit of a double star 
_ will find that he has at hand a great mass of measures, which, 
having been made by observers of varying experience and with 
instruments of all degrees of perfection, are more or less discord- 
ant. Each one of these measures consists of a determination at a 
given time of the distance and direction of the companion star 
from its primary. 
If now these measures be plotted, by taking a point on the paper 
to represent the principal star and laying off from this, point each 
measured distance and direction to the companion star, a series of 
other points will be obtained which will represent to the eye the 
path which the companion has pursued about its primary. Were 
the measures free from error, the points which indicate the position 
of the companion would lie accurately upon the perimeter of an 
ellipse ; but practically they are very far from doing so, especially 
if the double star is very close and difficult of measurement. 
The ellipse which the companion appears to describe does not 
represent the true orbit of the body in space, since the true orbit 
is viewed more or less obliquely. It is evidently the projection of 
the true orbit on a plane tangent to the celestial sphere at the point 
at which the double star is situated. While the true orbit in space 
is an ellipse of which the principal star occupies the focus, the 
apparent or projected orbit, though also necessarily an ellipse, will 
not have its focus at the principal star. Nevertheless, Kepler’s 
