MATHEMATICAL INSTRUMENTS. 



large pair, such as are known at the 

 makers by the designation of beam-com- 

 passes : these may be had in separate 

 cases, with covers sliding in grooves, 

 and to the extent of full two feet in 

 length. In some professions such are in- 

 dispensable, but it is far more convenient 

 to have a branch, or elbow-joint, to the 

 shifting compasses ; the upper part fitting 

 into the socket made for receiving the 

 several limbs, and its lower end being 

 socketed in the same manner ; so that one 

 leg of the compasses may be made, to 

 any extent, longer than the other. As 

 all the additional joints have a hinge, 

 the excess of length may be made sub- 

 servient to any direction, by being bent 

 downwards, so as to stand at right an- 

 gles with the paper ; as in such case 

 the other leg ought also, in order to 

 prevent its shifting, or cutting the sur- 

 face. The elbow joint is often given in 

 a flat case of instruments. 



The drawing-pen is ordinarily about 

 six inches in length, and is made on the 

 same principle as that intended for cir- 

 cular operations ; in general, this un- 

 screws in the centre, and disengages the 

 upper part of the handle, to which a fine 

 steel needle is attached, the use of which 

 is to mark down, by the slightest punc- 

 ture, those points that require peculiar 

 delicacy. The small flat steel turn-screw 

 has one end narrowed, that it may fit the 

 screw-heads in the hinges of compass 

 limbs ; while the other, by means of two 

 studs that fit into corresponding holes 

 on the side of the joint connecting the 

 two limbs of the compass, serves to 

 tighten or to relax them at pleasure. 



The common parallel rules made to 

 fit into cases, consist of two slips, mov- 

 ing upon four pivots ; i. e. one at each 

 end of two metal plates, whereby the 

 slips are always kept at a perfect paral- 

 lel. This chiefly depends on the perfect 

 equality of lengths in the metal slips, and 

 theii being placed at exactly the same an- 

 gle, at points equidistant from the edges 

 of the slips. Some parallels have a third 

 piece, which fold* between the two above 

 described, and requiring an additional pair 

 of metal hinges, which meet on them as a 

 centre. This is certainly a very great 

 convenience, inasmuch as it extends the 

 scope of the instrument, and gives a third 

 parallel ; but the slightness of the middle 

 piece subjects it to warp ; and, at all 

 events, demands great care in using, so 

 as not to wrench the pivots, or to bend 

 them into an improper direction, where- 

 by the whole work would be falsified. In 



drawing lines with this ruler, observe the 

 following instructions. When a parallel 

 is to be made above the line to which you 

 apply the ruler, let the limbs be closed, 

 then press firmly on the bottom slip, by 

 two fingers placed at least two inches 

 apart, and clear of the hinges ; slide the 

 upper limb gently from you, by means of 

 the meta! stud in its centre, until you 

 bring it up to the point through which 

 the parallel is to be drawn. When you 

 would make a parallel below any given 

 line, the slips should be separated (keep- 

 ing the upper limb well pressed by two 

 fingers) until you bring the upper or lower 

 edge of the other limb, as may prove 

 most convenient, to the point through 

 which the parallel is to be made. Or you 

 may open your ruler to its full extent; 

 first, placing its upper thin edge along 

 the original line, and pressing on the 

 lower limb, then draw the upper one 

 down to the desired point. Both the 

 edges of this ruler are chamfered on. 

 one side only ; whence one edge lays 

 very flat to the paper, so as to guide 

 with great exactness, and serving excel- 

 lently for pencilled lines ; while the other, 

 being raised from the paper, gives 

 greater security from blotting when ink 

 is used, but requires a very steady hand, 

 and a no less accurate eye. 



Parallel rulers are sometimes made to 

 move on wheels, with graduated edges, 

 shewing the parts of inches over which 

 they pass. The theory is .excellent, but 

 we find in this many practical inconve- 

 niences ; such rulers being easily turned 

 out of their proper directions, by any 

 little inequality on the surface of paper, 

 or by the smallest deviation from per- 

 fectly even propulsion, or retraction. Be- 

 sides, the axis being necessarily made 

 loose, so as to allow greut freedom of mo- 

 tion, it is obvious the wheels cannot al- 

 ways preserve an exact level ; whence 

 the instrument must move as though of 

 a conical form, and give concentrating, 

 instead of parallel lines. Hence such 

 rulers aie deservedly discarded in most 

 instances ; though, for work requiring 

 more celerity than accuracy, they may be 

 found to answer. 



Protractors are chiefly made of ivory, 

 in the form of a thin flat scale, or ruler, 

 of which one side is plain, excepting a 

 very small nick, or mark, that points out 

 its'exact centre, and corresponds with a 

 line, perpendicular to it, on the opposite 

 edge, marked 90, dividing the instrument 

 into two equal and similar portions. The 

 edges on three sides of the protractor are 



