174 
PRESTON. 
Project p to a; draw a 0. The intersection of a 0 with a 
vertical line through n gives the point t, and we have r t 
equal to cos « sin d X D or to + 5.91. 
We have 
H' a : H f 0 :: r t : r 0 
or H p : H' 0 :: rt : Xn. 
Hence 
r f Hp X Xn (— 20.07) ( — 0.294 X 20) , K Q1 
rt - WO 20-- + b - yl - 
Reductions in Right Ascension (see plate 9). In the reduc¬ 
tions for right ascension the curves for the day numbers 
A B CD are used as already plotted, and the star numbers 
are so constructed that the lines representing a, b, c, d, fall 
horizontally. 
This may be readily effected, since they all depend on at 
least three quantities, and these may be multiplied in such 
a way as to give the resulting line either desired direction. 
The inner quadrant already drawn holds good for the 
right ascensions, as already used for declinations. In seek¬ 
ing the trigonometrical functions of d, however, the degrees 
count in the opposite direction ; to facilitate this, each de¬ 
gree has its complement written opposite. 
In finding the values of a and b, it is necessary to use the 
value of tan d. This is obtained, where the declination is 
less than 45°, from the horizontal line at a distance of 10 
units from the origin. A line drawn from the given degree 
to the point O intersects it at a vertical distance from the 
origin equal to ten times the natural tangent of the angle. 
This construction gives us three units in the value. We 
may now proceed to the final result by using this value, or 
two units may be employed and the construction carried 
forward on the scale used for arcs beyond 45°. Both these 
methods will be indicated later. 
For comparison, the usual logarithmic computation is 
here given. 
