93 
by Means of two Altitudes of the Sun. 
latitude. Hence, if this difference be ten minutes, the error in 
the approximation will not be more than T r T th part of a second; 
and, if the difference be one degree, the error will only be six 
times greater than in the former case. It will therefore always 
be inconsiderable, except when the latitude and declination are 
nearly equal, and on the same side of the equator. 
But, if this cause should be likely to produce an effect of some 
importance, we may prevent it by computing an incremental 
area with the least altitude likewise, and the latitude increased 
or diminished by a minute, and then taking a mean betwixt 
them both for the magnitude of the area gc. Thus we 
shall generally obtain a conclusion sufficiently exact ; but, if 
we are desirous of rendering it perfectly so in every instance, 
we must divide the difference betwixt the real and apparent in- 
tervals, in such a manner that the areas assigned to the two 
observations may be to each other in the same ratio as their 
correspondent incremental areas. This division will be readily 
dispatched by making the difference betwixt the logarithms of 
the two first terms, in the proportion (taken from the ist table) 
equal to the difference betwixt the logarithms of the two last, 
which are given when either of the formulas tyi — . -^4-, 
o sym 3 
vm cos. of merid. alt. (u.) i , , . 1 r , - r 
or — x — c 0S ' of dec ' iin — TTp 1S em pl°y ec l ; but must be found, if 
the first method of computing the area gc be adopted. Suppose 
that a and b, representing the logs, of the areas gb and gb in 
the table, appear from inspection to exceed each other nearly 
as much as the logs, of the areas gc and gc ; let c and d be the 
two next terms in succession, and let m and n be the logs, of 
the quantities expressing the incremental areas; then will 
