106 Mr. Lax’s Method of finding the Latitude of a Place , 
to be applied are well known. We must find an approximate 
value of p (page 89) by means of the 3d and 4th tables, and 
compute an incremental area with the least, as well as with the 
greatest altitude. If this plan had been pursued, the latitude 
would have been ascertained within less than a second of the 
truth. Or, if the weather had been favourable, we might have 
prevented the error as effectually, by making the observations 
when the hour-angles were much less, and approached nearer 
to an equality. 
N. B. The log. sines and tangents of the declin. and lat. to be 
employed in all the operations should be taken out at the same 
time. But, when the first method of computing the incremen- 
tal area is adopted, we may avail ourselves, with considerable 
advantage, of the following expedient. Instead of taking the 
whole log. sine and tangent of the new lat. take the increments 
of each, or the difference betwixt their respective values in the 
two suppositions ; and find the increment of the log. tangent 
corresponding to the increment of the log. secant • This 
may readily be effected, when the log. tangent is deduced from 
the log. secant in the former process, by taking the rate of in- 
crease belonging to each, and thence inferring by an easy pro- 
portion the proper increment of the log. tangent in the latter 
case. The difference betwixt this increment and the increment 
of r is the value of the area gc. An instance of the method 
thus improved shall be given in the next example. 
