GRAPHIC REDUCTION OF STAR PLACES. 
173 
term negative, their difference is + 20.08. This is to be 
multiplied by the value of C on June 9, which is —-3.57 ; 
project B to C; draw C 0. Where the vertical line through 
A meets C 0 prolonged gives the point D and the line D D' 
is the product c' C or (tan <o cosd — sin « sin <?) X C or —3.59. 
This follows from the proportion 
H f Q : H’ 0 : : D' D : U 0 
or HE : H' 0 : : D' D : XA. 
Hence 
ry n HB X X A —3.57 (1.004 X 20) Q KQ 
D D ~ H’ 0 ~~ 20 “ 
If sin a sin $ is positive, the value of Z E is laid off to the 
left of Y, the construction being otherwise the same. 
Fourth term. —To find d! D = cos a sin d X D (see plate 8). 
Seeking the right ascension in the quadrant marked (a and 
d) we find cos a for radius 20 to be f g or — 0.368 X 20. This 
must not be confounded with — 0.369 X 20, which is on the 
same scale the value of 20.05 cos a and which is measured on 
the outer circle. The sine of d is TV or 0.800 X 20. Project 
g to m. Where the line m O intersects the line X V already 
drawn, determines the point n. X n is then the value of 
cos a sin o or — 0.294 X 20 = — 5.88. 
We have 
qm : q 0 :: Xn: X 0 
or / g : q O :: X n : T V 
Hence 
jr _fgXTV_(- 0.368 X 20) (+ 0.800 X 20) _ 
qO 20 
-0.368 X 16.00= —5.88. 
The line Xn is now to be multiplied by — 20.07, the value 
of D on June 9, which we find equal to the line Hp. 
