42 A. W. Roberts.—Computation of Nov: 25. 
point of intersection of the tangents and the centre of the chord will 
also pass through the centre of the ellipse. 
As all the lines will not pass through one point, the central point of 
all their intersections will probably be the centre. 
The next step is to find the position of the Axis Major. In the 
case of Sirius, the form of the interpolating curve indicates that a 
portion of it lies on each side of this line. The line, therefore, from 
which opposite ordinates are equal, is the axis major. 
The axis major being drawn, and the centre having alrealy been 
found, the focus can be determined either from the equation, 
(Oe owe 
ye sia ae ae ii). 
or by trial with a pair of compasses. 
IJI.— TRANSFORMATION OF CO-ORDINATES. 
The following measures are then carefully taken with a pair of 
~ compasses : 
(1) Semi-axis major... —... ius ae 74S 
(2) Semi-axis minor... a be 5 te 5°27 
(3) Co-ordinate of centre of apparent ellipse along 
E. line (y) ie Be wee, 2 APL 
- (4) Co-ordinate along N. line (a) aos ere 0-"571 
(5) Inclination of Axis Major to Declination Circle 41°°30 
Let the cc-ordinates of the apparent ellipse be, referred to apparent 
centre, x and y’, , 
- Let the co-ordinates of the apparent ellipse, referred to Sirius, be 
xand y. 
Let co-ordinates (3) and (4) be (a) and (@). 
Let 9 = inclination of axis major to E. and W. line ; then 
x’ == cos 9 (a — a) — sin 9( y— 8B) 
y =sind <x — a) + cos? (y—R) 
b pa Ss 
But «= oie — y’ (remembering that @ is along N. axis), sub- 
stituting anil giving numerical values to the several constants we have : 
527 2 
(5°27)? — (663a—'749y + 2°7358)? = (°749x —*663y— 3°1844)? (=) 
Simplifying this equation we have : 
—°08152 x + °40828 y — ‘04736 a? + °038262 ay — 05138 y? + 1L=0 
As a check upon these values we make y = 0, © 
