by Means of tzvo Altitudes of the Sun. 99 
distance from the meridian. The error in the assumed latitude 
will, in this case, be equal to the whole increase of the altitude 
betwixt the time of observation and noon ; and from this consi- 
deration we may be enabled, in any particular instance, to dis- 
cover at what distance from the meridian this plan may be safely 
adopted. We can extend it also to any number of observations 
that happen to be made within the proper limits, by connecting 
them successively with one on the opposite side of the meridian, 
and thus determining the areas gb corresponding to each. Hav- 
ing afterwards calculated an incremental area with any of the 
assumed latitudes varied one minute, we must subtract its loga- 
rithm from the logarithmic value of each of the areas gb, and we 
shall discover, by means of the second table, the correction to be 
applied to each of the supposed latitudes. 
But the method which has just been explained might always 
be safely adopted, within the limits prescribed to the former 
rule, if, in computing the incremental area, we were to employ 
the latitude obtained by means either of the 3d and 4th, or of 
the 3d and 5th tables. This precaution would entirely prevent 
the error which might arise from the inequality of the ratios 
of GC to GB, and gc to gb, when the difference betwixt the 
real and the assumed latitude was very considerable. The 
error which is occasioned by the disparity of the hour-angles, 
might be obviated by the same means that were practised in the 
first method. There is only one objection, indeed, to this rule’s 
being exclusively adopted, when either of the altitudes is taken 
within the distance at first recommended. It would be neces- 
sary, in that case, to extend the table much farther than we 
are obliged to do, if we adhere to the former rule ; but the 
labour is so much abridged by this plan, that I am doubtful 
O 2 
