MATHEMATICAL INSTRUMENTS, 
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 nibbed, except to take 
off the rough point sometimes occasioned 
by setting the two other sides of each point. 
The puncture made by compasses ought to 
be barely visibh ; consequently the points 
should be. extremely tine: hence also we 
see the necessity for avoiding to press upon 
compasses while measnrinir on paper, A^c. 
as their own weight will, general!y, cause 
them to leave a sufficient impression for 
mathematical purposes. 
Besides the li.iir compasses, there is usu- 
ally arather longer pair, of which one of the 
steel leas draws out altogether, for the pur- 
pose of being replaced by a brass limb, with 
a por' -crayon, a dotting- leg, &c. The for- 
mer has a pair of clasp-«prings, acted upon 
by a ring of the same metal, to secure a 
piece of fine black-lead pencil, which should 
be cut to a fine point, exactly level with 
the othfr leg of the compass. This is meant 
for draw’ing circular lines. The doiting-leg 
is for making dots in circular figures, and 
bears a small brass graduated wheel be- 
tween two side pieces, fi'om which it de- 
rives 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 si ps, 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 these 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 dotting, 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 instrument was named 
Bowes, whence it bears tliat designation ; 
though some have vulgarly corrupted it to 
“ bow-compasses.” 
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 any point 
on the lateral tables. When closed the two 
limbs, and their respective points, appear 
but as one piece, and are kept to that posi- 
tion by a small stud in one, which fits into 
the other half. This instrument must be 
perfectly clos( d befoi e the bridge is moved, 
else the channels of the two limbs will not 
lay in a right line. Four tables are engrav- 
ed on the.se 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 radius 
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 com- 
passes 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 circle ; the other points 
will give a measurement, between their 
points, equal to a seventh part of that 
circle’s circumference ; and givq the face 
of a regular polygon ol seven sides. 
The proportional parts of lines are ascer- 
tained in the same manner, by setting the 
index to that table, the long points measur- 
ing the whole line, and the short ones giving 
the part required, according to the figure 
against which the index on the bridge is set. 
The line of plans, 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 Idttej’ 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 man- 
ner, the difference between the solid con- 
tents of bodies of a regular figure : in this 
case, however-, the bodies must be similarly 
quadrangular, such as cubes j or spherical, 
as balls, globes, &c. ; then, by taking their 
diameter, the table will indicate the dif- 
ference of their solid contents ; the small 
points being considered as implying unity. 
