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PRESTON. 
This follows from the proportion 
q U:q 0::XY :XO 
or MN:q 0 :: X Y: T V. 
Hence 
y y _M N X T V __ sin a sin d (— 0.930 X 20) (0.800 X 20) 
qO ~ qO | 20 
= — 0.744 X 20 = —14.88. 
We now find the first term of c' =■ tan w cos d. The co¬ 
sine of * is X For + 0.600 X 20 = 12.00. Project V to W; 
draw O W. Where this intersects the horizontal line through 
Z determines the distance Z E, which is 
tan o) cos d or + 0.260 X 20 = + 5.20. 
The sum of the two terms of c' is therefore (5.20 + 14.88) or 
1.004 X 20 = 20.08. The distance Z O is 20 times the natural 
tangent of the obliquity of the ecliptic, and the line through 
Z is drawn once for all, as it is common to all the stars. In 
order to have the two terms of c' on the same scale, Z is 
taken at a distance from the axis of X of 20 X 0.434 = 8.68. 
So that we have the proportion 
q W : q O : : ZE : ZO 
or X V : q O : : Z E : tan w X 20. 
Hence 
Z E = X Vtan - - — = ( Q,60Q x 20 - > (tanco X 20) 
q O 20 
= 0.600 X 0.434 X 20 
== 0.260 X 20. 
The value of Z E is laid off on the prolongation of X Y y 
giving the point A, where 
XA = X F+ YA = (0.260 + 0.744) X 20 = +1.004 X 20; 
the first term of the value c'C being positive and the second 
