MECHANICS. 
derate, the excess not being sufficient to 
overcome the friction, and bear down 
tlie beam. 6. The pivots, which form the 
axis or fulcrum, should be in a straight line, 
and at right angles to the beam. 6. The 
arms should be as long as possible, relative- 
ly to their thickness, and the purposes for 
which they are intended, as the longer they 
are the more sensible is the balance. They 
slibuld also be made as stiff and inflexible 
as possible ; for if the beam be too weak, 
it will benil, and become untrue. 7 . The 
rings, or the piece on which the axis bears, 
should be hard and well polished, parallel 
to each other, apd of an oval form, that the 
axis may always keep its proper bearing, 
or remain always at the lowest point. 8. 
If the arms of a balance be unequal, the 
weights in equipoise will be tmequal in the 
same proportion. The equality of the arras 
is of use, in scientific pursuits, chiefly in 
the making of weights by bisection. A 
balance with unequal arms will weigh as 
accurately as another of the same work- 
manship with equal arms, provided the 
standard weight itself be first counter- 
poised, then taken out of the scale, and the 
thing to be w’eighed be put into the scale, 
and adjusted against the counterpoise. Or, 
when proportional quantities only are con- 
sidered, the bodies under examination may 
be weighed against the weights, taking care 
always to put the weights in the same 
scale; for then, though the bodies may not 
be really equal to the weights, yet their 
proportions amongst each other will be the 
same as if they had been accurately so. 9. 
Very delicate balances are not only useful 
in nice experiments, but are likewise much 
more expeditious than others in common 
weighing. If a pair of scales, with a cer- 
tain load, be barely sensible to. one-tenth 
of a grain, it will require a considerable 
time to ascertain the weight to that degree 
of accuracy, because the turn must be ob- 
served several times over, and is very small. 
But if no greater accuracy were required, 
and scales were used, which would turn 
with one-hundredth of a grain, a tenth of a 
grain more or less would make so great a 
difference in the turn, that it would be seen 
immediately. 
The statera, or Roman steel-yard, is a 
lever of the first kind, and is used for find- 
ing the weights of different bodies, by one 
single weight placed at different distances 
from the prop or centre of motion D, fig. 6. 
For, the shorter arm D G is of such a weight 
as' exactly to coiinteipoise the longer aim 
D X. If this arm be divided into as many 
equal parts as it will contain, each equal 
to G D, the single weight P (which we may 
suppose to be one pound) will serve for 
weighing any thing as heavy as itself, or as 
many times heavier as there are divisions in 
the arm D X, or any quantity between fts 
own weight and that quantity. As for 
example, if P be one pound, and placed 
at the first division 1 in the arm D X, it 
will balance one pound in the scale \at W ; 
if it be removed to the second division at 
2, it will balance two pounds in the scale ; 
if to the third, three pounds ; and so on to 
the end of the arm D X. If any of these 
integral divisions be subdivided into as 
many equal parts as a pound contains 
ounces, and the weight P be placed at any 
of these subdivisions, so as to counterpoise 
what is in the scale, the pounds and odd 
ounces therein will by that means be as- 
certained. In the Danish and Swedish 
steel-yard, the body to be weighed, and the 
constant weight, are fixed at the extremities 
of the steel-yard, but the point of suspen- 
sion or centre of motion moves along the 
lever till the equilibrium takes place. The 
centre of motion therefore shews the weight 
of the body. 
The wheel and axle, or axis in peritro- 
chio, is a machine much used, and is made 
in a variety of forms. It consists of a w'heel 
with an axle fixed to it, so as to turn round 
with it ; tlie power being applied at the cif- 
cumference of the wheel, the weight to be 
raised is fastened to a rope which coils 
round the axle. 
A B (fig. 7.) is a wheel, and C D an axle 
fixed to it, and which moves round with it. 
If the rope which goes round the wheel be 
pulled, and the wheel turned once round, it 
is evident that as much rope will be drawn 
off as the circumference of the wheel ; but 
while the wheel turns once round, the axle 
turns once round ; and consequently the 
rope by which the weight is suspended will 
wind once round the axis, and the weight 
will be raised through a space equal to the 
circumference of the axis. The velocity of 
the power, therefore, will be to that of the 
weight, as the circumference of the wheel 
to that of the axis. In order, therefore 
that the pow'er and the weight may be in 
equilihrio, the powermust he to the weight 
as tlie circumference of the wheel to that 
of the axis. Circles being to each otlier as 
their respective diameters, the pow'er is to 
the weight, as the diameter also of the axis 
to that of tlie wheel. , Thus, suppose the 
