84 Mr. Lax’s Method of finding the Latitude of a Place, 
posed latitude, rejecting thrice the log. radius. But, if ■ - r ■ ” 1 
be greater than radius, which must necessarily be the case 
when the azimuth is greater than a right angle, we must then 
consider-^ rr? as the square of the tangent of the arc 
whose secant is 
Sy 
observing in other respects the direc- 
tions before given. The quantities r and s are both employed 
in the first computation, from the result of which we also ob- 
tain y\ and, consequently, this operation will not be attended 
with much trouble. 
The above instructions, it is manifest, are given upon the 
supposition of r and s having the same sign ; but, if the declin. 
and latit. should not be of a similar denomination, then will 
our expression become m 1 + LUL . JLL and we must consider 
m % -f as the square of the secant whose corresponding 
5n i 
tangent is 1 ■ With this exception, the process will be 
the same as when the tangents r and s are both affirmative. 
The preceding formula naturally suggests to us another 
method of finding the log. area gc ; and, as some perhaps^ 
may think this more eligible than either of the former, I shall 
take the liberty of explaining it. When the latit. is given, the 
area GC, it is obvious, must invariably preserve the same mag- 
nitude at all distances from the meridian ; and, consequently, 
the area gc, which is proportional to it, must likewise remain 
constant. If, therefore, we can ascertain this area when the 
hour-angle is supposed to vanish, we may employ it when 
the sun is at any distance from noon. Let us now conceive 
the declin. to be equal to nothing; then will our expression 
