GRAPHIC REDUCTION OF STAR PLACES. 
167 
We need only know that the value of a' is the line F G. 
This factor enters the computation as a line without reference 
to its numerical value. A fine thread being attached at the 
center 0, and the other end being held by the hand at J, 
the intersection of this thread with the vertical line through 
the point of right ascension, G, gives at once the value of 
a' A, or — 3.74. No lines are actually drawn, but the final 
products are found by projecting selected points, with the 
eye, either horizontally or vertically until they meet the 
line of the thread. This visual projection is rendered easy 
and accurate by the small spaces into which the sheet is 
divided. Moreover, on the regular working sheet both the 
quadrants indicating right ascensions and declinations and 
the curves for the day numbers are drawn. The diagrams 
are separated for illustration and to avoid confusion in the 
construction lines, which in the regular work are never 
drawn. For comparison, the logarithmic computation, em¬ 
ploying Bessel’s numbers, is given on the following page for 
the apparent declination of star No. 1381. 
GRAPHIC DETERMINATIONS. 
Reductions in Declination. —Proceeding now to determine 
the quantities a' A, b' B, c' C, d' D for star No. 1381, we shall 
indicate data and final results by full lines. Construction 
lines are dot'ted. Partial results, which are intermediate be¬ 
tween the data and final results, such as the values of tan oj 
cos sin « sin <5, etc., are shown in broken lines. The reduc¬ 
tion is made from the mean place on January 0, 1895, to its 
apparent place on June 9, 1895. 
The position of the star is (taking the nearest half minute 
in «): 
Right ascension — a = 16 h 33 m .5. 
Declination = S = 53° 7'. 
First term. —To get a' A = 20T05 cos a x A (see plate 8). 
We seek the value of a in the quadrant marked (a and d) and 
read at once the value of 20.05 cos « or F G on the outer one 
