FINDING THE LOCUS OF GEOGRAPHICAL POSITION. 243 
-~= — 2'.45 %. 0.389m 
? = — 3° 40' sec. 0.001 
— — \— 188°.5 &?. sec. 0.005m 
= _ 1140.5 i g , cosec . o.041m 
log (d A)..#_..... 0.43671 
Having performed this computation, we find the value of 
dx to be —2'.7, which applied to —32° 34', the longitude 
of the assumed geographical position, becomes 32° 36'.7, 
which is the longitude of a point of the horizon-free line of 
position. The latitude of this point is the same as the lati¬ 
tude of the assumed or estimated geographical position. 
The coordinates of the required point of the line of position 
are therefore <p = — 3° 40', X = — 32° 36'.7. The azimuth 
of this line of position will be the mean of the azimuths of 
the two observed stars, which in this case is 188°.5, counting 
from north through east, south, and west. 
Obviously, if the two differences of altitude be measured— 
i. e. f if three different stars have been observed in quick suc¬ 
cession—two lines of position will be obtained, and their 
intersection is the true geographical position of the observer. 
The formula that has been employed for reducing the 
estimated geographical position of the observer to the line 
of position or locus of constant difference of altitude, by 
computing the difference of longitude between the two 
points, is most appropriate in all cases in which the mean 
A _i_ A 
azimuth — i ~ -— l - lies between 315° and 45° and between 
Jj 
135° and 225°. 
When the mean azimuth lies outside these limits, or, in 
other words, when it lies between 45° and 135° and between 
225° and 315°, it is better to reduce the estimated geograph¬ 
ical position to a point on the required line of position by 
