GRAPHIC REDUCTION OF STAR PLACES. 
175 
Star No. 1381 .—Catalogue of Stars for Observations of Latitude. 
(Report of U. S. Coast and Geodetic Survey for 1876, Appendix No. 7.) 
Reduction from mean to apparent right ascension. 
Log. N 
a = 16 h 33 m 41 s = 248° 25 / 
sin a — 9.9684n = — 0.930 
d = 53° 7 / 
cos a - 9.5657n = — 0.368 
tan $ = 0.1247 = + 1.33 
» 
sec £ = 0.2217 = + 1.67 
Terms 
a 
3 8 .073 + 1.337 
X sin a tan d 
b 
cos a tan d 
c 
cos a sec d 
d 
sin a sec 8 
15 
15 
15 
Log 1.337. 
0.1261 
“ sin a.... . 
9.9684n 
“ tan d . 
0.1247 
Sum logs. 
0.2192n 
No. 
—1.656 
No . 
3.073 
8.8239 
8.8239 
8.8239 
sum. 
1.417 
9.5657n 
9.5657n 
9.9684n 
0.1247 
0.2217 
0.2217 
Logs a b c d .. 
0.1514 
8.5143n 
8.6113n 
9.0140n 
“ A,B,C,D . 
9.7055 
0.9215n 
0.5521n 
1.3026n 
“ a A, b B, c C, d D .. 
9.8569 
9.4358n 
9.1634 
0.3166 
Nos. “ “ “ “ .. 
+ 0.719 
+ 0.273 
f 0.146 
+ 2.073 
A B C D . 
+ 0.507 
— 8.35 
— 3.57 
—20.07 
Construction of Auxiliary Lines .—In order to find the tan¬ 
gents from 0° to 45° the lineup is used. These values may 
be reduced either graphically or mentally. For values of 
the declination between 45° and 87° the tangents are read 
from the lines t, t', t", t"', and t iv of plate 7. The method 
of construction enables us to find the values for every min¬ 
ute of arc. The curve t applies to declinations from 45° to 
50° ; t' extends from 50° to 60°, etc. The units in the degrees 
are given by the vertical scale, and each small square repre¬ 
sents vertically 6 minutes of arc. The tangents are the hori¬ 
zontal lines included between the axis of ordinates and the 
