MATHEMATICAL 
best finish, duly tempered, and fitted with 
scrupulous exactness; the hinges in every 
part should fit close and firmly ; having 
screw-pivots, in order that they may be 
taken to pieces on occasion. The screws 
ought to fit into female sockets of steel ; 
those of brass being extremely liable to wear 
out in the thread, or worm, and to cause 
the parts that depend on their motion to be 
lax and uncertain. The protractor and 
sector should be of very fine clear ivory, 
and the parallel ruler may be of the same, 
or of ebony : but which ever it may be 
made of, the utmost care must be taken to 
preserve it from warping, while its edges, 
as well as those of the other flat instru- 
ments, ought to be guarded from injury. 
The protractor especially should never be 
touched by a knife, or by any sharp or 
hard instrument, when drawing lines along 
its edge. When describing its uses, the 
reader will collect proper ideas regarding 
the absolute necessity for preserving its 
edges from the smallest diminution or irre- 
gularity ; since the most trivial defect there- 
in could not fail to render the whole of its 
operations precarious. 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 
being 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 formed, 
we shall detail the uses and proportion 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 surface of the lead should, when 
cut, appear very smooth and glossy, with- 
out any flaws, or resemblance of antimony : 
the mark left on paper should be perfectly 
superficial, and exempt from any impression 
or scratch, which bad pencils invariably 
make, and which cannot be erased or de- 
faced without giving the paper a rough sur- 
face, and a disposition to absorb ; so as to 
shew blotty when colours are used. Some 
judgment is required 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 inferior 
kind are made of black-lead dust, cement- 
ed with glue, gum, starch, linseed-tea, and 
a variety of such adhesive matters, accord- 
ing to the degree of hardness the composi- 
INSTRUMENTS. 
tion is intended to bear. When we see 
“ hard lead,’’ and “ soft lead,” impressed on 
the cedar casings of black-lead pencils, we 
may generally suspect 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 re- 
tailers according to their fancy, or to the 
predilection shewn by their respective cus- 
tomers. We, therefore, recommend to per- 
sons 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 drawing line are sold 
in perfection. In tapering a pencil to a fine 
point, it is necessary, after the sliape may 
have been 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 sui'ported, and may, when the lead 
is very good, be made to taper beautifully, 
without danger of being broken by the 
operation. 
The compasses given in a complete case 
vary, being intended for various different 
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 relaxed too much at the joint 
they should be tightened, by means of 
two little apertures 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 sepa- 
rate the two limbs, by turning against the 
sun. If the points of compasses are not 
duly tempered, they will prove very trou- 
blesome ; when too brittle, they will be per- 
petually snapping ; and when too soft, they 
will be subject to bend. The mathemati- 
cian will occasionally have to work on sub- 
stances harder titan paper ; therefore the 
temper of his points is a matter of some 
importance. If too highly tempered, he 
should heat them near the flame of a can- 
dle until they change to a straw colour ; 
when they ought to be instantly plunged 
into a lump of soap, or of tallow, 6cc. 
When too soft, let the points be heated to 
a bright red, and then be suddenly immer- 
sed in water in which salt-petre htts been 
