95 
by Means of two Altitudes of the Sun. 
hour-angle, the greater is the exactness with which the lat. is 
determined. Sometimes, however, it will be impossible to make 
both, or perhaps either of our observations within the distance 
which I have recommended; but, even in these cases, our 
rule may be conveniently applied. It has already been demon- 
strated that we can never be subject to any material error in 
consequence of the inequality of the areas gb and gb, except 
when the zenith-distance of the sun, at his meridian altitude, is 
very small ; and, for this case, an effectual remedy has been pro- 
vided. We need not, therefore, make any farther remarks 
upon this species of inaccuracy. 
But perhaps it will be imagined, that because we still continue 
to suppose the areas of the “ figura tangentium’ to represent 
the increments of the latitude, a considerable error will be in- 
troduced. We can easily prove, however, that in consequence 
of the increment of the time being so much diminished by 
increasing the distance from noon, this error will seldom be of 
moment enough to claim, our attention. Let T be the tangent 
of the azimuth, and r the tangent of the hour-angle at the ob- 
servation farthest from noon ; then it follows, from what has 
been demonstrated before, that the ratio of gb to gc will ex- 
ceed the ratio of GB to GC, and, consequently, the ratio of 
gb to gc, (supposed to be of a proper magnitude,) by m . — ~ . 
^ -r — V k- Hence it is evident that, by diminishing one of 
these ratios and increasing the other, as we are directed in the 
present case, till they become equal, we augment the latter by a 
portion of this difference expressed by 7^77, and, on this ac- 
count, it will be made too great by m . - n ~ 1 . T • 7 t~-- ^ 
