go Mr. Lax’s Method of folding the Latitude of a Place , 
were to differ from the assumed latitude 30 minutes, the error 
in his conclusion would not exceed the fourth part of a second. 
We must observe, that if n (the approximate value of p, thus 
deduced) be the minutes by which the first assumed lat. is 
varied in our second hypothesis, we ought to multiply the cor- 
rection, after it is taken from the 2d table, by this quantity; 
but, as n is always supposed to be a whole number, the addi- 
tional trouble arising from this process can never be an 
object of the smallest consideration. The 2d table, however, 
may be as conveniently applied to the case, where the lat. is 
varied ten minutes, as where it is varied only one. The loga- 
rithms which form the argument are the same in both cases, 
except that the index in the former is less by unity than in the 
latter. 
Another species of inaccuracy originates in our conceiving 
the fluxion of the lat. to vary as Tz, instead of x Tz; and it 
may be useful to ascertain how much our conclusion is affected 
by this circumstance. We suppose, in fact, that the incre- 
ments of the lat. corresponding to the finite times gf and ge 
are to each other as the areas gc and gb drawn into the co- 
sine of the first lat. ; whereas, in strict propriety, they are to 
each other as the sum of all the elements of these areas drawn 
into the cosines of the latitudes belonging to each, i. e. (i { ge 
= m y.gf) we consider these increments as being in the ratio 
of gc x X : gb x X, instead of gc x 
gb. 2 * + m '* 
g c - 
2A-J-X 
:gb 
2 x -f m a 
Hence 
2 X + A 
g° 
m . 
* =m . ^i f5 L(rad.= ij 
