102 LECTURE X. 



ed to difterent parts of its concavitj' : it would, however, be more simple and 

 accurate to employ only one screw, in the middle of the arc, and to make 

 the flexible ruler, or bow, every where of such a thickness, as to assume a cir- 

 cular form in its utmost state of flexure: it would then retain the circular 

 form, without a sensible error, in every other position. (Plate VI. Fig. 

 82 . . 85.) 



For drawing a line perpendicular to another, we often employ a square ; 

 and if we use a rectangular drawing board, there is an additional convenience 

 in making the square to slide on its margin. Rulers also, of various descrip- 

 tions, are commonly made rectangular, in order to answer occasionally the 

 same purpose. 



Triangular compasses are sometimes used, for laying down a triangle equal 

 to a given triangle; and by repeating the operation, any figure, which can be 

 divided into triangles, may be copied without the intersection of arcs: but the 

 same end is more commonly obtained, by pricking off the figure with a steel 

 point. (Plate VI. Fig. 86.) 



Various properties of parallel lines are employed in constructing parallel 

 rulers: a parallelogram with jointed angles is the most commonly used; two 

 equal rulers being united by equal cross bars placed in an oblique position, 

 and turning on pins fixed in the rulers: the instrument is much improved by 

 adding a third ruler, similarly united to the second, for then the oblifjuity of 

 one of the two motions may be made to correct that of the other. A simple 

 cyhnder, or a round ruler, answers the purpose in a rough manner, and two, 

 small rollers, fixed on the same axis, are also sometimes attached to a flat 

 ruler, and cause it to move so as to be always in parallel positions. A very 

 useful instrument for drawing parallel lines, at any given distances, is now 

 generally known by the name of Marquois's scales, although it is by no means 

 of late invention ; by sliding a triangle along a graduated ruler, we read off 

 the divisions on an amplified scale with great accuracy; but where the dis- 

 tances of the lines are great, the obliquity of this motion is a considerable 

 inconvenience. The ruler or square of the drawing board affords us lines 

 parallel to each other, in a certain position; and if it be made with a joint, 

 ,or as the workmen call it, bevilledj it may be employed for the same purpose, 



