by Means of two Altitudes of the Sun. 87 
curacy, to which, under similar circumstances, our process is 
liable. 
If we are desirous of knowing how much our conclusion is 
affected by substituting the tangent of the hour-angle for the 
tangent of the azimuth, it may be done with the greatest faci- 
lity. We have seen, that the area GC (fig. 1.) is to GB as one 
minute to the error in the assumed latitude. But our method 
supposes that^c (fig. 2.) is to gb as one minute to the correc- 
tion required ; and we must therefore estimate the difference 
betwixt these ratios, in order to ascertain how far the ap- 
proximation is inaccurate. Let EG — my FG ; and then, 
since GC may be considered as = GD ^ -- F ° x FG, and GB 
= GD+ . EB __ g£ + eb xm jp q t h e f orme r ratio will 
2 2 9 
GD 1 EB 
equal g D ^ Fc y m = (according to the notation employed 
above) m . 2 T t ~ y — m — m . n ~ - x nearly = the minutes 
contained in the computed error of latitude. Their difference 
will equal m . 
= m 
z 
T*. 
z = m . 
. i + T 1 - 1 + 1 * 
.z.— z . - 
T 1 — t z 
t . „ - „„ . — . ■■■ . L (—being 
substituted for its equal z) = the minutes contained in the 
error of our approximation. It will be more convenient, 
however, to express this difference independently of the 
azimuth. Now, preserving the notation before adopted, we 
S gb tybh tyb 
have T=- 4 - = 
Icc-d 
l y & — d A 
therefore, 
