GRAPHIC REDUCTION OP STAR PLACES. 171 
lines or writing figures. This advantage, of course, applies 
to all determinations by this method. 
We have the proportion 
or 
H' Q : H' 0 : : S R : S 0 
HP: H 0 : : SR: M N. 
Hence 
qj? _HPX MN _ (— 8.35) (—0.930 X 20) _ , 7 
WO 20 + Mb - 
The value of b' B is then — 7.76. 
As in the case of a' A, all reductions for stars on June 9 
have one point in common (here Q)> and the values of 
sin a X B will appear as vertical lines included between the 
line Q 0 and the axis of X. 
In giving the values of the trigonometrical functions the 
factor 20 is always written, as that is the number of units 
in the radius. The natural value of the function is, of 
course, the first factor. 
Third term. — To find c C= ( tan o> cos d — sin a sin S') O, (see 
plate 8). 
Here oj = 23° 27'== obliquity of ecliptic 
and tan a> = 0.434 
We first find the second term of the parenthesis. By the 
same construction as was used for b f B the sine of « is 
— 0.930 X 20 = MN. The sine of 9 is T For +0.800 X 20. 
These quantities must be multiplied in such a way that the 
product is a horizontal line, viz., by projecting N to U and 
noting the point where the line U O intersects the horizon¬ 
tal line through V. The line X Y is equal to —14.88 or 
— 0.744X20. We therefore have for the second term of the 
parenthesis on the actual scale 
sin a sin d — —0.744 X 20= —14.88. 
24—Bull. Phil. Soc., Wash., Vol. 13. 
