24 GEOGRAPHIC TABLES AND FORMULAS. [bull. 234. 
Table 3 gives for various hour angles, expressed in mean solar time 
and for even degrees of latitude from 30 to 50 degrees, the azimuths 
of Polaris for eight years, computed for average values of the north 
polar distance of the star, the arguments being the hour angle (or 23'' 
56"M minus the hour angle when tlie latter exceeds 11^ 58'"), which 
is termed the time argument, " and the latitude of the place of obser- 
vation. The table is so extended that azimuths may be taken out by 
inspection and all interpolation avoided, except such as can be per- 
formed mentally. 
The hours of the "time arguments '' are placed in the columns headed 
"hours," on the left of each page. The minutes of the time argu- 
ments will be found in the columns marked "m," under the years for 
which they are computed, and the}^ are included between the same 
heavy zigzag lines which inclose the hours to which they belong. 
The time arguments are given to the nearest half minute; the occur- 
rence of a period after the minutes of any one of them indicates that 
its value is 0"\5 greater than printed, the table being so arranged 
to economize space. 
The table will be used as follows: Find the hours of the time argu- 
ment in the left-hand column of either page; then, between the heavy 
lines which inclose the hours, tind the mimdes in the column marked 
at the top with the current year. On the same horizontal line with 
the minutes the azimuth will be found under the given latitude, which 
is marked at the top of the right-hand half of each page. Thus, for 
1904, time argument 0^ 43"^, latitude 36°, find 0" on left-hand page, 
and under 1904 find 43'" on tenth line from the top, and on same line 
with the minutes, under latitude 36'^, is the azimuth 0° 17'. For 1908, 
time argument 9*' 33^*", latitude 48°, the azimuth is 1° 1^', found on the 
twenty-first line from the top of right-hand page. 
If the exact time argument is not found in the table, the azimuth 
should l)e proportioned to the difference between the given and tabu- 
lar values of said argument. 
The table has been arranged to give the azimuths by simple inspec- 
tion. No written arithmetical work is required, all being performed 
mentally. It will always be sufficient to take the nearest whole degree 
of latitude and use it as above directed, except for a few values near 
the top of either page where the difference of azimuths for 2'^ differ- 
ence of latitude amounts to four or five minutes of arc. 
a The vertical diameter SS', fig. 6, divides tlie apparent path of Polaris into two equal parts, and for 
the star at any point Sq on the east side is a corresponding point Si on the west side of the meridian, 
for which azimuth Nw is equal to the azimuth Ne. The arc, Ssi S'sq, taken from the entire circle (or 
23h 56m.i), leaves the arc Sso, and its equal Ssj, expressed in time, may be used to find, from table 3, 
the azimuth Nw, which is equal to Ne. 
The hour angles entered in table 3 include only those of the west half of the circle ending at S, 
and when an hour angle greater than ll^ 58™ results from observation it will be subtracted from 23'> 
56™. 1, and the remainder will be used as the " time argument" for the table. The surveyor should 
not confound these two quantities. The hour angle itself always decides the direction of the azimuth 
and defines the place of the star with reference to the pole and meridian, as noted at top of table 3, 
See examples. 
