MATHEMATICAL INSTRUMENTS. 23 



movable in a hollow canal cut through the greater part of 

 their length. To this centre, on each side, is affixed a slid- 

 ing piece of a small length, with a fine line drawn on it, 

 serving as an index, to be set against other lines or divisions 

 placed upon the compasses. Thus, by placing the index 

 against 1, and screwing it fast, if you open the compasses 

 then the distance between the points at each end will be 

 equal. If you place the index against 2, and open the com- 

 passes, the distance between the points of the longer legs 

 will be twice the distance between the shorter ones; and 

 thus a line is bisected, or divided, into two equal parts. If 

 the index be placed against 3, and the compasses opened, 

 the distance between the points will be as 3 to 1, and so a line 



Fig. 24. 



Fig. 22. 



