97 
by Means of two Altitudes of the Sun. 
the incremental areas. Let us suppose, for instance, the difference 
betwixt the intervals to be q, and the quantities deduced from the 
4 th table to be a and b ; then will = the minutes by which 
the former latitude is to be varied. 
If, however, there be any considerable uncertainty respecting 
the latitude, I would recommend the following method of ob- 
taining an approximate value of it, before we begin the process 
for investigating its real magnitude. This will effectually pre- 
clude, in almost every instance, the various errors that have 
been described. The increment of the altitude is equal to xSz, 
and, therefore, when the azimuth is so small that its sine varies 
nearly as the arc, the whole increase of the altitude, whilst the 
sun is moving to the meridian, will be xz x — the 
sine of the hour-angle being considered as equal to the arc itself. 
Now the first of the two tables which have just been explained, 
will enable us to find the value of by subtracting the log. 
cosine of the altitude from twice the log. sine of the hour-angle; 
and a third table might be added, to furnish us with the whole 
expression ~ g 2 , (according to the mean value of <5j) one of its 
arguments being the quantity AL— already determined, and thq 
other the supposed latitude. It might, perhaps, be advisable to 
add another column to the first of these tables, containing twice 
the logarithmic sine of the hour-angle, as this would in some 
measure abridge the operation. We should find it more conve- 
nient too, if the last table were to give us the complement of the 
arc whose value is rather than the arc itself ; because it 
o 
MDCCXCIX. 
