GRAPHIC REDUCTION OF STAR PLACES. 
169 
— 3.74, agreeing with the logarithmic computation previ¬ 
ously given. This follows from the proportion 
or 
Hence 
h J: h 0 :: L K: L 0 
HI: 10 :: L K: F G. 
L K = 
HIX FG 
10 
which gives L K in correct units, since the value of A, or 
0.507, was plotted on a scale 10 times its true value. 
When a number of stars are to be reduced for the same 
date, the point J applies to all, and the values of a'A for the 
separate stars are the vertical lines included between the 
axis of abscissas and the line J O. The lines are, of course, 
vertically under the points on the arc corresponding to the 
right ascensions. 
For the sake of uniformity in the process of multiplication, 
the day numbers A, B , C, D are always projected to the ver¬ 
tical scale at the right when finding the products a' A , b' B, 
c' C, d' D. It is evident that the same result would ensue 
by projecting the star numbers a', b ', c', d' to the horizontal 
scale at the top, drawing the radial line and measuring the 
intercept obtained by projecting the day numbers to the left. 
For example, if G is projected to m" and m" O is drawn it 
will intersect the line //prolonged, in K", giving L" K" = 
— 3.74, as before. The algebraic proportions may be written 
out similarly to those above. If G is projected to m' and 
the line m' O is drawn it will intersect the line J f I' pro¬ 
longed, in K' giving L' K' = — 3.74, as before. To avoid 
confusion with lines already given in the figure G m' and 
m' O are not drawn. 
Without writing out the proportions it is quite evident 
that in the triangle 
so that it is equal to 
L’ K' O the line U K' is ^ of L’ 0, 
of (2 X 5.05). Likewise in the tri- 
angle L” K” O the line L" K" is O ,and is there. 
