Improved Geometrical Plotting Quadrant, &c. 167 

 My solution to the last problem is inferior to the common 

 method of plotting the triangle on paper, and measuring the 

 angles with a protractor; but I have introduced it here to 

 show that my instrument is capable of solving this as well 

 as all other cases of obtuse-angled triangles, and might, by 

 extending: the arc to a semicircle, as shown by the dotted 

 lines on" the figure, solve any triangle. In the practical 

 problems in surveying, which follow, the triangles can al- 

 ways be taken right- or obtuse-angled, and the instrument 

 as at present constructed is fully competent. I might here 

 add, that a given line can readily, by my instrument, be di- 

 vided into any number of equal parts ; drawings might be 

 enlarged or diminished as readily as with the proportional 

 compasses, and many other equally useful purposes may be 

 effected thereby. 



First. — To measure an inaccessible Distance by a perpendi- 

 cular Line set off towards tlw right Hand, j'rum the Line 

 or Base between the Observer and Object. 

 Set the base line of the instrument in a line pointing to 

 the object, at the same time place a staff at any distance, at 

 pleasure, as a perpendicular (being [)0 degrees from the base). 

 On this perpendicular measure any distance (say 50 yards or 

 other measures) as a second station ; move the instrument 

 to this distance, and place it with its perpendicular in the 

 same line as before ; the instrument being so placed, set 

 the lower limb pointing to the object, and with the screw 

 make the same fast ; this done, the distance of the object 

 will be thus readily known. Raise the. moving perpendi- 

 cular of the instrument to the divsion 50 (as before sug- 

 gested), then with this height move the same, by means of 

 the nut, till the extremity intersects exactly the lower limb 

 before set, at which intersection the distance from the se- 

 cond station will be shown; and on the base line will also 

 at the same lime be seen the distance from the first station ; 

 this is a case of right-angled triangles. 



Note. As the divisions on the perpendicular arc denomi- 

 nated (either feet, yards, poles, or other measures), so will 

 the distances be indicated on the other limbs, and on the 



base of the instrument. 



L 4 Secondly. 



