170 
PRESTON. 
7 38 
fore HP of 5.05; both of these being equivalent to the first 
construction, viz., 7.38 X 0.505. 
In cases where the value of 20.05 cos a is represented by 
a line longer than ten units, extrapolation is avoided by 
plotting on a scale twice as large as that just used, which 
would make the point I fall at I'. I' is then to be projected 
to J', and the value of a' A is, as before, —3.74. If A is 
plotted on this scale nearly every value of 20.05 cos « will be 
shorter than the horizontal distance between 0 and the point 
to which I' is projected, or J', and the values of a' A will be 
vertical lines lying between J' and the center, so that the 
only extrapolation resorted to is that for values of a' between 
20.00 and 20.05; but no sensible error would be introduced 
by following the first construction. 
The scale at the left or right gives the result in correct 
units. This follows from the proportion 
H’JH' O: : L K : LO 
or HI' : H' O :: L K: F G, as previously given. 
Hence 
r V _HI'XFG= (0.505 X 20) (— 7.38) = - 0.505 X 7.38. 
H' O 20 
Second term .—To get V B = — sin ax B (see plate 8). 
In this case we make use of the inner quadrant or the one 
described with a radius 20. 
Find the right ascension in the quadrant marked {b and c). 
The sine for radius 20 is equal to M N or — 0.930 X 20. 
The value of B on June 9 is HP or — 8.35. Project P to Q. 
The intersection of the vertical line through IVwith the line 
O Q gives the point P, and the distance R S, read from the 
scale, gives 7.76, which is the value of sin ax B. 
In actual work the thread being held at Q and the point N 
being selected by inspection, the position of P and its value 
on the scale are read off at sight without either drawing 
