236 
LITTLEHALES. 
• • • ( 1 ) 
in which x — an auxiliary angle, 
t — the hour-angle, 
L — the latitude, 
d — the declination, 
and z = the zenith distance ; 
and the true bearing, or angle opposite the side of the astro¬ 
nomical triangle representing the polar distance, is computed 
from the formula: 
sin Az . — sin t cos d cosec z (2). 
There are superior qualities attached to this method of 
finding the Sumner line, because it may be used in any cir¬ 
cumstances so long as the altitude of the observed celestial 
body*does not greatly exceed 80°, and the results obtained 
have been demonstrated to possess an enhanced probability 
of accuracy. The present purpose, however, is not to dis¬ 
cuss these advantages which have been expounded by writers 
upon the subject of the new navigation, but to disclose a 
short and simple process of finding the zenith distance and 
azimuth without the aid of the extended computations indi¬ 
cated by the formulse just referred to, and so to provide for 
the practice of a method of finding the line of position and 
the compass error by inspection, 
Figure 2 represents a stereographic projection of the celes¬ 
tial sphere on the plane of the meridian. 
If the latitude of the observer be laid off along the bound¬ 
ing meridian at L, and the declination of the observed celes- 
,V,2 
t 
sin* y = s ^ n2 ~2 cos L cos d sec (L — 
cos z = cos (L — d) cos x 
