8 3 
by Means of two Altitudes of the Sun . 
d \ *a 
ing the succeeding value of x) = - j- x 
~ a \ + dl\ 
A A 1 
d A 1 * — aliydPx 
FTTa 1 
</aa 
TTx* 
tf— Z A 
X TT 
Sx 
(taking x positive instead of negative, as it ought to be when l is 
positive) y r —. -£r ; and, consequently,-^- = 1 -y * -£r, 
-, when radius is m. 
r m* 
sy 
A 1 m a 
when radius is unity, but == rrC 
Now — ma y be considered as the increment of the hyperbolic 
log. of y, and therefore, with its proper modulus, may represent 
the area which is the object of our investigation. We may sup- 
pose the other side of the equation to be the square of the co- 
sine of the arc whose sine is ~ m h x 9 . into the increment of 
the hyperbolic log. of x 1 , divided by the square of the radius ; 
and if, instead of taking this log. with the hyperbolic, we take 
it with Briggs’s modulus, we must then consider — as the in- 
v 
crement of the log. of y, according to the same system. But 
~ being equal to ■— (when L is only one minute), it will vary 
as s; and, therefore, if its value be determined according to 
Briggs’s system, when s is equal to radius, and be denominated 
v , its value in any other case will be expressed by ~L m 
Hence, to obtain the log. of the area gc, the quantity with 
which we are immediately concerned, we must find the log. 
value of and divide it by 2 ; we must then take out the 
log. cosine of the arc whose log. sine is equal to the quotient ; 
and, having multiplied it by 2, we must add the product to the 
constant log. of v (3,1015), and the log. tangent of the sup- 
M 2 
