MATHEMATICAL INSTRUMENTS. 



the purpose of being- replaced by a brass 

 limb, with a port-crayon, a dotting-leg, 

 &c. The former has a pair of clasp-springs, 

 acted upon by a ring 1 of the same metal, 

 to secure a piece of fine black-lead pencil, 

 which should be cut to a fine point, ex- 

 actly level with the other leg of the com- 

 pass. This is meant for drawing circular 

 lines. The dotting-leg is for making dots 

 in circular figures, and bears a small 

 brass graduated wheel between two side- 

 pieces, from which it derives its supply 

 of ink. The dotting- leg is, however, best 

 used dry ; when the marks made by the 

 impression of the gradations on the wheel 

 may be followed by a pen- The wheel is 

 apt to let the ink fall, and to make sad 

 blotted work. A third limb is likewise 

 applicable in this instance, viz. a drawing 

 pen, intended to make ink lines in circular 

 figures ; the sides of this are two steel 

 slips, bending towards each other at their 

 ends, which are finished so as not to cut 

 the paper, but to make a line of any 

 strength, according as the ink may be 

 allowed to pass, more or less freely, by 

 the expansion or contraction of their 

 points, as acted upon by a small screw 

 about the middle of their bend. 



There is also a neat small pair of com- 

 passes intended for drawing circles, &c. 

 of a small diameter ; in tliese there is only 

 a fixed drawing limb, in lieu of a plain 

 steel leg : they are highly convenient when 

 the longer compasses are in use for dot- 

 ting', and are capable of doing the work, 

 which comes within a small radius, to 

 great nicety; not being so apt to jump as 

 those of a longer size, when the circles 

 are very small. The inventor of this in- 

 strument was named Bowes, whence it 

 bears that designation ; though some 

 have vulgarly corrupted it to " bow-com- 

 passes." t 



The proportional compasses consist of 

 two flat brass limbs, both of which bear 

 steel points ; a screw, sliding in a 

 groove, connects them ; and by being 

 tightened at pleasure enables the operator 

 to slide the bridge along so as to be fixed 

 at an}' point on the lateral tables. When 

 closed, the two limbs, and their respec- 

 tive points, appear but as one piece, and 

 are kept to that position by a small stud 

 in one, which fits into the other half. This 

 instrument must be perfectly closed be- 

 fore the bridge is moved, else the chan- 

 nels of the two limbs will not lay in a 

 right line. Four tables are engraved on 

 these compasses, viz. on one side a table 

 of circles, on the other side (of the same 

 face) a table of lines. By applying the 



index on the bridge to the several lines, 

 as numbered in the former table, the ra- 

 dius of a circle being taken between the 

 long points, at one end of the compasses, 

 the shorter points, at the other end, will 

 give such part of the circumference as the 

 bridge may be placed against : thus, if 

 the seventh part of a circle be required, 

 close the compasses and slide the bridge, 

 bringing the mark on it into an exact line 

 with the mark at 7 in the table of circles ; 

 then screw rather tight, and open the 

 long points equal to the radius of the cir- 

 cle ; the other points will give a measure- 

 ment, between their points, equal to a se- 

 venth part of that circle's circumference ; 

 and give the face of a regular polygon of 

 seven sides. 



The proportional parts of lines are as- 

 certained in the same manner, by setting 

 the index to that table, the long points 

 measuring the whole line, and the short 

 ones giving t lie part required, according to 

 the figure against which the index on the 

 bridge is set. 



The line of planes, or of squares, shews 

 the areas under the different figures : 

 thus, set the index to four, the measure 

 between the long points will give a square 

 four times as large (in contents) as a 

 square made with the measure between 

 the small points on one of its sides : thus, 

 if the square made on the latter contained 

 six square inches, that made on the former 

 would give an area equal to twenty-four 

 square inches. 



The line of solids shews, in the same 

 manner, the difference between the solid 

 contents of bodies of a regular figure; in 

 this case, however, the bodies must be 

 similarly quadrangular, such as cubes ; or 

 spherical, as balls, globes, &c. ; then, by 

 taking their diameter, the table will indi- 

 cate the difference of their solid contents ; 

 the small points being considered as im- 

 plying unity. 



Triangle-compasses are made for the 

 purpose of ascertaining three points, in 

 the same manner as the common biped- 

 compasses ascertain only two. This is 

 effected by a third leg, which may be 

 taken off at pleasure, working like a gin 

 for raising weights ; or like the legs of a 

 theodolite-stand, and having a hinge at 

 right angles with that where it joins the 

 top of the compasses. By this simple con- 

 trivance the added leg may be made to 

 incline to the right or left of the direction- 

 given by the upper hinge. 



Where work is to be executed on a 

 large scale, viz. projecting meridians in 

 maps, it is necessary to have a very 



