. 72 ] - 
times very conveniently applied upon this occafion j 
for if, through any two given objects, we defcribe fe- 
veral fegments of circles, in which thofe objeds (hall 
fubtend the angles of * 120°, 90°, 8c°, yo", &c. 
refpedively, we fhall then know immediately, upon 
finding the two objeds fubtend any one of thefe 
angles, that we are fmiated fomewhere in the cir- 
cumference of the correfponding fegment ; and, the 
bearing alfo from one of the objeds being known, 
our precife fituation will be determined with great 
accuracy. 
The manner of deferibing thefe fegments, through 
two given points, may be performed in the following 
manner. Let B and C [Tab. II. fig. i.] be the given 
points : then, joining thefe two points, bifed the 
line B C in A, and draw the indefinite right line 
DE, perpendicular to B C, through the point of bi- 
fedion. Upon BC, at the point C conftitul'e the 
angles DCB, F C B, G C B, H C B, &c. refpec- 
tively equal to the difference between the angles, 
which correfpond to the feveral intended fegments 
and 90'’; and on the oppo-fite or fame fide of the 
line C B with thofe fegments, accordingly as they 
exceed or fall diort of 90°. Then will the points 
D, F, G, FI, &c. where the lines CD, C F, C G, 
C H, &c. interfed the line D E, be the centres of 
* The number and frequency of thefe fegments, as well as 
the magnitude of their , rel'peftive angles, muft be determined, 
according to the particular circumflances of the occafion, upon 
which they are appli^^d : I have mentioned no greater angle, 
than 120 °, as there are few cafes, in which this v.nll not be 
fiifficicnt ; and indeed it is the greateft, that Hadley’s quadrant, 
tile only inflrument fit for this purpofc, will eafily admit, accord- 
ing to the prefent conftruiSlion of it. 
I the 
