9 * 
by Means of tzvo Altitudes of the Sun. 
= m . 5 - . — = the minutes contained in the error pro- 
2 IOOOOO 
ceeding from this cause. When the real latitude, for instance, 
is 52 0 , and the assumed 51 0 50', this error will scarcely amount 
to a single second. But, if either the cosine of the latitude 
should be so small, or the difference betwixt the supposed and 
true latitude so great, as to render this error of any importance, 
we may prevent it by the same means that were recommended 
in the preceding case. In computing the incremental area gc, 
we must correct our first hypothesis respecting the latitude 
with the assistance of the third and fourth tables ; and, for the 
reasons assigned above, the cause of this inaccuracy will be 
removed. 
There is still another part of our process, which will some- 
times be the source of a small error. We are directed to dis- 
tribute the whole increment of the time betwixt the two obser- 
vations, by equalizing the areas corresponding to each in the 
“figura tangentium;” whereas they can only be considered as 
perfectly equal in the original curve whose ordinates are the tan- 
gents of the azimuth. It is supposed, in reality, that gc bears 
to GC the same ratio which gc bears to GC; or (which is 
nearly the same thing) that gd is to GD as gd to GD: we 
must therefore estimate the difference betwixt these ratios, and 
we shall easily deduce the amount of this error. Let us retain 
the notation employed above, and moreover let r represent the 
cosine, and r the tangent of the hour-angle at the observation 
farthest from noon ; A the difference betwixt the hour-angles, 
and y the excess of y above r : then, from what has already 
been demonstrated, we have = -- y d * , and = l ~~ dx • 
Ns 
