by Means of two Altitudes of the Sun. 
azimuth is == which is known, and consequently the tangent 
may likewise be obtained. Having thus discovered a near value 
of p, or of the error in our first assumed latitude, we are enabled 
so far to correct it in our second hypothesis, and in a much 
greater degree to reduce the error in our conclusion. 
As it will sometimes, though not often, be necessary to have 
recourse to this expedient, two short tables might be added, in 
order to facilitate the operation. The first might contain the 
log. cosines to every degree from the 15th to the 90th of the 
quadrant; and be so contrived, as likewise to exhibit the log. 
sine of any arc, as far as the 75th degree, expressed in minutes 
and seconds of time ; that, by subtracting the log. cosine of the 
altitude from the log. sine of the hour-angle, (the cosine of de- 
clination being considered as equal to radius,) we might obtain 
the log. sine of the azimuth. This should be made one of the 
arguments of the second table ; the other being the cosine of the 
latitude to every five degrees of the first sixty of the quadrant ; 
and the table should give us the value of 15 x a T, which, mul- 
tiplied into the minutes contained in the error of time, would 
determine with sufficient exactness the quantity p. We might, 
indeed, with the same facility, compute the fourth table accord- 
ing to the mean value of the cosine of declination, if it could 
be supposed that such a degree of precision would ever be 
required. 
Perhaps it would be advisable for the mariner, in order to 
avoid all distinction of cases, to calculate, in every instance, his 
incremental area with the lat. varied ten minutes, instead of 
one; and then he would always be secure of a result sufficiently 
qorrect for his purpose. In the case supposed above, if the real 
MDCCXCIX. N 
