MATHEMATICAL INSTRUMENTS. 



along its edge. When describing its 

 uses, the- reader will collect proper ideas 

 regarding the absolute necessity for pre- 

 serving its edges from the smallest di- 

 minution or irregularity ; since the most 

 trivial defect therein could not fail to 

 render the whole of its operations pre- 

 carious. We are disposed to think that 

 the flat instruments are usually made 

 rather too thin, whence they are easily 

 warped by change of weather, or by be- 

 ing kept in too warm a situation ; leaving 

 them exposed to a hot sun is extremely 

 injudicious. 



Having said thus much respecting the 

 materials of which they should be form- 

 ed, we shall detail the uses and propor- 

 tion of each instrument separately. The 

 pencil ought to be of very pure lead, 

 such as is free from ore, and that cuts 

 to a fine point without offering too 

 much resistance to the knife; the sur- 

 face of the lead should, when cut, appear 

 very smooth and glossy, without any 

 flaws, or resemblance of antimony : the 

 mark left on paper should be perfectly 

 superficial, and exempt from any impres- 

 sion or scratch, which bad pe'ncils in- 

 variably make, and which cannot be 

 erased or defaced without giving the pa- 

 per a rough surface, and a disposition 

 to absorb ; so as to shew blotty when 

 colours are used. Some judgment is re- 

 quired to distinguish the fine pencils, 

 made of solid lead ore, from those which 

 are vended by Jews, and, indeed, by 

 some who call themselves respectable 

 manufacturers of this article. The infe- 

 rior kind are made of black-lead dust, 

 cemented with glue, gum, starch, lin- 

 seed-tea, and a variety of such adhesive 

 matters, according to the degree of hard- 

 ness the composition is intended to bear. 

 When we see " hard lead," and " soft 

 lead," impressed on the cedar casings of 

 black-lead pencils, we may generally sus- 

 pect their quality ; for though the best 

 makers occasionally make a distinction in 

 regard to the hardness or softness of the 

 lead, they usually sort such into different 

 chests, and vend to the retailers accord- 

 ing to their fancy, or to the predilection 

 shewn by their respective customers. 

 We, therefore, recommend to persons 

 wishing to obtain good black-lead pen- 

 cils, that they purchase by the gross, 

 from the most eminent makers ; or that 

 they give a good price for them at those 

 warehouses where articles in the draw- 

 ing line are sold in perfection. In ta- 

 pering a pencil to a fine point> it is ne- 



cessary, after the shape may have beeis 

 generally given, to hold the point against 

 the inside of the tip of the fore-finger 

 of the left hand, cutting from you very 

 carefully, and turning the pencil round, 

 as may be necessary. By this means the 

 point is supported, and may, when the 

 lead is very good, be made to taper beau- 

 tifully, without danger of being broken by 

 the operation. 



The compasses given in a complete 

 case vary, being intended for various dif- 

 ferent purposes. First, a pair of hair- 

 compasses, so called, because, by means 

 of a screw near the middle of one limb, 

 a spring, which unites with the steel leg, 

 may be acted upon so gradually, as to 

 cause the points to give the most precise 

 measurements. When compasses are re- 

 laxed too much at the joint, they should 

 be tightened by means of two little aper- 

 tures that are on each side of the pivot- 

 head. In these the two small studs that 

 appear on the turnscrew are applied, 

 either to pinch tighter, by turning with 

 the sun ; or to relax, and even to separate 

 the two limbs, by turning against the sun. 

 If the points of compasses are not duly 

 tempered, they will prove very trouble- 

 some ; when too brittle, they will be per- 

 petually snapping; and when too soft, 

 they will be subject to bend. The mathe- 

 matician will occasionally have to work 

 on substances harder than paper ; there- 

 fore the temper of his points is a 

 matter of some importance. If too 

 highly tempered, he should heat them 

 near the flame of a candle until they 

 change to a straw colour, when they 

 ought to be instantly plunged into a lump 

 of soap, or of tallow, &c. When too soft, 

 let the points be heated to a bright red, 

 and then be suddenly immersed in water 

 in which salt-petre has been dissolved. 

 The points of compasses ought to be very 

 even, and the two sides that lay together, 

 when they are closed, should never be 

 ground, or rubbed, except to take ofT the 

 rough point sometimes occasioned by set- 

 ting the two other sides of each point. 

 The puncture made by compasses ought 

 to be barely visible; consequently the points 

 should be extremely fine : hence also we 

 see the necessity for avoiding to press up- 

 on compasses while measuring on paper, 

 &c. as their own weight will, generally, 

 cause them to leave a sufficient impression 

 for mathematical purposes. 



Besides the hair compasses, there is 

 usually a rather longer pair, of which one 

 of the steel legs draws out altogether, for 



