Ball — On the Binary Star ^ Ursae 3fajoris. 323 
"We have now to deduce the real ellipse from the projected ellipse. 
By measurement we find — 
CA = 
62-6 
= a 
CD = 
57-7 
= 
cs = 
23-7 
nSA = 
312'' 
— a 
nSx = 
70" 
= ^. 
S is the focus of the real ellipse, C the projection of the centre 
of the real ellipse ; AM is therefore the projection of the major axis 
of the real ellipse, whose eccentricity must be 
^= 0-3786. 
CA 
a 1 
The ratio y = , = I'OSO, 
a' 
and = = 1-085. 
If Q be the angle between the intersection of the real and the 
projected ellipses and the line Sn, and if 7 be the inclination of the 
planes of the two ellipses, 
then [a'\^ . ^ /^V • 00 
^-j sm2a+ (^-j sin2^. 
tan 2 a 
y 1 cos 2a + ( - J cos 2y3. 
cos 7 = ^ - tan (Q - a), tan (Q - /3). 
Whence we deduce 
n = lor -28 
7 - 53« -07, 
X is the angle between the line drawn from S through perihelion in 
the real ellipse and the line of nodes. We have 
tan (a - 12) 
*^^^ = -'"tan(^-Q), 
whence, 
X = 135° -32. 
