GRAPHIC REDUCTION OP STAR PLACES. 
165 
be stated as about 6 seconds for the right ascensions and 1J 
minutes for the declinations. With the above stated di¬ 
mensions the trigonometrical functions may be read off to 
three places, and the multiplication, by the graphical method, 
of these functions by the day numbers can be accomplished 
so that the greatest error will be only a few hundredths of a 
second of arc, which is abundantly sufficient for the reduc¬ 
tion of star places for the ordinary latitude observations with 
the zenith telescope. 
Concentric with the quadrant having a radius of 20 inches, 
another is drawn with a radius of 20.05 inches. This is for 
the purpose of finding 20.05 cos a. The two radii bounding 
the quadrants are subdivided into spaces of tenths of an inch. 
Each radius is therefore divided into 200 parts. Thus by 
estimating tenths of these divisions readings may be made 
to the two thousandth part of the radius. Through these 
points of division lines are drawn parallel to the radii, the 
result being that the entire surface is divided into small 
squares. 
The divisions of the quadrant are numbered for declina¬ 
tion in the center and for right ascension on either side. 
The degrees of declination are not indicated again on plates 
8 and 9, as these are only intended to illustrate the method 
by application to a special case. The trigonometrical func¬ 
tions for the declination are used, however, on these sheets 
as they would appear on plate 7. The hours for the last 
argument are so chosen that the lines representing the star 
numbers a, b, c, d will fall horizontally. This facilitates 
their multiplication by the day numbers A, B , G, D, which 
are all plotted vertically. On the margin is indicated the 
space in which the right ascensions must be sought for the 
different star numbers a, b, c, d. A negative sign before the 
hours indicates that the trigonometrical function is to be 
taken in this sense. 
The quantities A, B, C, D are plotted on the largest scale 
possible with the accompanying quadrant. This necessitates 
a slight change in the values of A, and they are laid down 
