FINDING THE LOCUS OF GEOGRAPHICAL POSITION. 237 
tial body be laid 
off at M along a 
meridian making 
an angle with the 
bounding merid¬ 
ian equal to the 
hour-angle of the 
observed celestial 
body, an astro¬ 
nomical triangle 
will be formed in 
which the known 
parts are the two 
sides PL and PM, 
representing re¬ 
spectively the co¬ 
latitude and co- 
declination, and their included angle LPM, which is the 
hour-angle of the observed celestial body. Two of the un¬ 
known parts of this triangle are the azimuth, PLM, and the 
co-altitude, LM, of the observed celestial body. If the tri¬ 
angle, PLM, were revolved about the central point of the 
projection, with the side, PL, kept in coincidence with the 
bounding meridian until the point L is brought to the posi¬ 
tion of the point P, the latter would then occupy the position 
P', and the point M would fall at M', so that the unknown 
side of the triangle, representing the co-altitude, would lie 
along some meridian, and could be measured from the grad¬ 
uation of the projection, and the unknown angle, repre¬ 
senting the azimuth, would become an included angle be¬ 
tween two meridians, wdiich could likewise be measured from 
the graduations of the projection ; and thus the altitude and 
azimuth of any observed celestial body could be simultane¬ 
ously determined from the diagram with any degree of pre¬ 
cision that the scale of the projection might permit. To 
obviate the necessity for actual revolution of the triangle, as 
described above, a series of equally spaced concentric cir- 
P 
S 
Figure 2. 
