1 08 Mr. Lax,’s Method of finding the Latitude of a Place , 
dently of the second incremental area, which I have demon- 
strated above can never be necessary, except when the zenith 
distance at noon is very small. The error of three seconds arises 
from a different cause, and might have been entirely excluded 
with the assistance of the 3d and 4th tables. We should, in 
fact, deduce from these tables an approximation of 22'; and, if 
we calculate the area gc with the lat. 54 0 32' o", it will be 
found equal to 34762, .ana consequently 
multi plied by 22, produces 17' 49", 64 for the correction, and 
the lat. is found = 54 0 27' 49", 64. 
It would have been still better, however, to have obtained a 
near value of the lat. in the first instance, by means of the 3d 
and 3th tables. The work might have been dispatched in 
rather less time, and the conclusion would have been as rigidly 
accurate. 
It is obvious that, if the time when the first observation was 
made could have been ascertained within two or three seconds, 
the area gb might have been immediately found by either of 
the two methods which have been explained, without the assist- 
ance of a second altitude, or of the first table ; and the latitude 
determined with much greater facility, and with sufficient ex- 
actness. When the azimuth indeed, as in the present case, 
does not exceed four or five degrees, an error of a second in 
time will not produce an error of more than a second in the 
result; and, as the azimuth decreases, the error in latitude, 
arising from a given error in time, will be diminished in the 
same proportion. In general, if z be the error in the assumed 
time, the error in the corrected latitude will be nearly equal to 
15 Tx&. 
