by Means of two Altitudes of the Sun . 
logarithmic values of gb. Having then added them all toge- 
ther, and taken a mean betwixt them, we have only to com- 
pute a single incremental area gc with any of the altitudes 
and the lat. varied one minute, and, subtracting its log. from 
the mean log. value of gb, we shall obtain a very accurate cor- 
rection of the assumed latitude. But, if there be more obser- 
vations on one side of the meridian than on the other, when all 
the pairs have been united, and the areas resulting from them 
found, we may combine the supernumerary observations on 
either side with any of those which are made on the opposite 
side. The properest, however, for this purpose, is the observa- 
tion which is made at the least distance from the meridian. 
I should hope, moreover, the practical astronomer will think 
it a circumstance of some moment, that the principal part of 
the work consists in finding the time, an operation which he is 
obliged so frequently to perform. Any of the three methods 
which are usually adopted upon this occasion might easily be 
applied to the tables which have been described; but I will 
venture to recommend a different rule, which I conceive to be 
better adapted to our purpose than any of the others, and to 
which the directions before given had a particular reference. 
Let a be the sine of the altitude ; y the cosine of the hour- 
angle ; d the sine, l the cosine, and r the tangent of declina- 
tion ; l the sine, x the cosine, and s the tangent of the latitude. 
when radius is unity, but = — nC . when radius is m 
== d-L. x 9 . into the square of the tangent of the arc whose se- 
Hence we deduce the following rule for deter- 
M 
MDCCXCIX. 
