166 
PRESTON. 
on a scale ten times their real value; for example, the value 
on June 9 is 0.507, but is plotted as 5.07. 
B may range from about + 9" to — 9", so the marginal 
numbers are used, and the correct value of this quantity 
multiplied by any of the trigonometrical functions will be 
given by reading the result from the scale at the left. 
C and D range from about + 20" to — 20". They are 
plotted so that the radial value would be 20. Since both 
are symmetrical with reference to the horizontal line pass¬ 
ing through the center, all values are plotted above the 
horizontal radius, and negative values in all day numbers 
are made apparent by using a curve in which dots are made 
for each individual day. The scale of dates is laid off in the 
middle of the sheet, and the value of any of the day numbers 
at a specified time may be found at the intersection of the 
corresponding curve, with the vertical line through the 
given date. By means of the horizontal lines the values of 
A, B y Gy D may be transferred visually to the margin. For 
example, on June 9 we have the values 
A = + 5.07, B = — 8.35, O = — 3.57, D = - 20.07. 
Referring now to plate 8, we shall show the construction, 
i. e n the graphic computation of the quantities 
a? A = 20.05 cos a x A. 
V B = — sin o. x B. 
c' C = (tan oj cos d — sin a sin 5) X O. 
d! D— cos a sin d X D. 
It should be borne in mind, however, that in actual prac- 
, tice the method is very much shorter than would appear 
from the lines drawn in plate 8. For example, in finding 
the value of a' A, when.we have once located the position 
of the right ascension, 16 h 33 m .5 on the quadrant, it is seen 
by mere inspection that the quantity 20.05 cos a is equal 
to — 7.38. In fact it is not necessary to know the numeri¬ 
cal value of this quantity, since it is to be multiplied by A, 
and it is only the final product that we care to determine. 
