32(3 On the Problem of the Three Points in Surveying. [Oct. 



In military sketching, also, this problem maybe applied with consi- 

 derable advantage, when amongst hills, or on ground with points suffi- 

 ciently strongly marked. Let B, E, D, F, Fig. 4, be four points 



about twenty miles distant from each other, the situation of which 

 has been ascertained with any of the common instruments, and it 

 is intended to sketch in accurately the country adjoining them. Let 

 these points be laid down on the scale of one mile to an inch upon 

 drawing paper, mounted on cloth like a pocket map. Draw the occult 

 lines BC, BF, FD, and DC, bisect them and draw in ink perpendi- 

 cular to them H I and K L &c. &c. Then, with the radii of half the 

 occult line, lay of the tangents of 5° 10° 15° to 40°, and mark them as 

 shewn in the Fig. 85° 80° 75° &c. 



Let A be the place of a station required to be found, from which the 

 points B and E subtend an angle of 115|° and the points E and D an 

 angle off* 97° j these angles being greater than 90° their supplements 

 must be taken, namely, 641 and 83°, then the leg of a pair of compasses 



