28 ' GEOGRAPHIC TABLES AND FORMULAS. [bull. 234. 
Table 4. — Azimuth and Apparent Altitude of Polaris at Different Hour Angles. 
[From U. S. Coast and Geodetic Survey Report for 1895.] 
The accompanying tables are intended for field use, to facilitate 
placing an instrument in the meridian. They are also suitable for 
determining the approximate latitude or meridian. They contain the 
azimuth of Polaris at intervals of fifteen minutes in hour angle for 
each degree of north latitude from 30*^ to 60°, and the apparent alti- 
tude at the same intervals and for each fifth degree of latitude.^ The 
tables are computed for the declination of Polaris 88° 46', but the rate 
of change in both azimuth and altitude is given with the argument 1' 
increase in declination.^ The tables are intended to be used in (con- 
nection with the American Ephemeris, where are given the apparent 
right ascension and declination of Polaris for each day in the year. 
The approximate local time will in general be known with sufficient 
accuracy from standard time and the approximate longitude of the 
place. The following example explains the use of the tables and the 
derivation of the hour angle of Polaris: 
Position, latitude 36° 20^ N., longitude 5"^ 20"' 30^ W. of Greenwich. 
h. m. s. 
Time of observation, July 10, 1895, standard (75th mer. ) mean time 8 52 40 p. m. 
Reduction to local time — 20 30 
Local mean time 
Reduction to sidereal time (Table III, Amer. Ephem. ) 
Sidereal time mean noon, Greenwich, July 10, 1895 
Correction for longitude, 5" 20"' 30^ (Table III, Amer. Ephem.) 
Local sidereal time 
Apparent right ascension of Polaris, July 10, 1895 
Hour angle before upper culmination 9 33 13 
8 
32 
10 
+ 
1 
24 
7 
12 
38 
+ 

53 
15 
47 
05 
1 
20 
18 
«The tables were computed with the following formulas: 
sin t 
an a = ^^^ ^ ^^^ ^ _ ^j^^ ^ ^^^ ^. 
sin h = sin <p sin 5 + cos 9 cos 6 cos t, 
cos 6 
cos 4= cot 3 tan q>; 
where o ^ azimuth from true north, 
t ^ hour angle, 
cp = latitude, 
6 = declination, 
h — true altitude, 
rte = azim.uth at elongation, 
/„ = hour angle at elongation. 
?' As the corrections are given with proper sign for increase in declination over 88° 40', they are to 
be applied with reversed sign while the declination is less than 88° 46', as it will be until near the 
close of the century. 
