86 Mr. Lax’s Method of finding the Latitude of a Place , 
an error of half an unit in each of the log. cosines whose dif- 
ference is equal to the area gc; and, of course, in some 
instances, an error of an unit in the area itself, upon any parti- 
cular supposition of latit. and declin. We have only to ascertain 
the ratio which this area bears to unity; for the same ratio 
will the correction of the latit. bear to the error in our re- 
sult. If the latit. for instance, be 50°, and the declin. io°, on 
the same side of the equator with the latit. then, radius being 
unity, z (the increment of the hour-angle) will equal 
= — g- = (g being the sine of the hour-angle, and a 
cos. 5 o°x Y 
the cos. of the altit. ^ — — - x ~ f =11 minutes nearly, 
when z is 5 0 ; and we have seen that, at any other dis- 
tance from the meridian, the incremental area will be of the 
same magnitude. Hence, subtracting the log. cosine of 5 0 
from that of 5 0 lT o", we get the difference equal to 1238; 
and, consequently, the error in our approximation will be to the 
error in the assumed latit. as 1 : 1238, when the log. cosines 
are carried to seven places of decimals. 
But, when the zenith distance of the sun, at his greatest 
altit. is very small, and there is moreover a considerable uncer- 
tainty with respect to the latit. this error will probably become 
of more importance, and we may find it necessary to guard 
against it. Now it is manifest that, by diminishing the mul- 
tiple which the area gb is of the area gc, exactly in the same 
proportion we shall diminish this error ; and I shall afterwards 
explain in what manner it may be accomplished. The same 
expedient is also calculated to prevent another species of inac- 
