MECHANICS, 
asd that in every motion uniformly accele- 
rated from rest, the spaces described are 
in tiie duplicate ratio of the times of de- 
scription: after this he applied the doctrine 
to the ascent and descent of bodies on in- 
clined planes. For a more particnlar ac- 
count we may refer to Dr. Keil’s “ Phy- 
sics.” Under the articles Centre of g-ra- 
isihj, Dynamics, Elasticity, Force, 
Or wiTATioN, Motion, &c. will be 
found much relating to the doctrine of 
mechanics ; we shall therefore in this place 
chiefly treat of the mechanical powers, 
which are usually reckoned six in number : 
viz. the lever ; the wheel and axis, or, as it 
is frequently called, “ the axis in peritro- 
cliio the pulley ; the inclined pique ; the 
wedge ; and the screw. Some writers on 
tins subject reduce the six to two, viz. the 
lever, and the inclined plane; the pulley, 
and wheel and axis being, in tl.eir estima- 
tion, assemblages of the lever; and the 
wedge and the screw being modifications 
of the inclined plane. 
When two forces act against each other, 
by the intervention of a machine, the one 
is denominated the power, and the other 
the weight. The weight is the resistance 
to be overcome, or the effect to be pro- 
duced. The power is the force, whether 
animate or inanimate, which is employed 
to overcome that resistance, or to produce 
the required effect. 
The power and weight are said to ba- 
lance each other, or to be in equilibrio, 
when tlie effort of the one to produce mo- 
tion in one direction, is equal to tlie effort 
of the other to produce it in the opposite 
direction ; or when the weight opposes that 
degree of resistance which is precisely re- 
quired to destroy the action of the power. 
The power of a machine is calculated when 
it is in a state of equilibrium. Having dis- 
covered what quantity of power will be re- 
quisite for this purpose, it will then be ne- 
cessary to add so much more, viz. one- 
fourth, or, perhaps, one-tliird, to overcome 
the friction of the machine, and give it mo- 
tion. 
The lever is the simplest of all machines, 
and is a straight bar of iron, wood, or other 
material, supported on, and moveable about 
a prop called the fulcrum. In tlie lever, 
there are three circumstances to be prin- 
cipally attended to : 1. The fulcrum, or 
prop, by which it is supported, or on which 
it turns as a centre of motion : 2. The 
power to raise and support the weight : 3. 
'I'he resistance or weight to be raised or 
sustained. The points of suspension are 
those points where tiie weights really are, 
or from which they hang freely. The 
power and the weight are always supposed 
to act at right angles to the lever, except 
it be otherwise expressed. The lever is 
distinguished into three sorts, according to 
the different situations of the fulcrum, or 
prop, and the power, witli respect to each 
other. 1. When the prop is placed be- 
tween the power and the weight, as in steel- 
yards, Scissars, pincers, &c. 2. When the 
prop is at one end of the lever, the power 
at Uie other, and the weight between them, 
as in cutting knives fastened at, or near 
the point of the blade; also in oars moving 
a boat, the water being the fulcrum. 3. 
When the prop is at one end, the weight 
at the other, and the power applied be- 
tween them, as in tongs, sheers, &c. 
The lever of the first kind is principally 
used for loosening large stones ; or to raise 
great weights to small heights, in order to 
get ropes under them, or other means of 
raising them to still greater heights : it is 
the most common species of lever. A B G 
(Plate I, Mechanics, fig. 1.) is a lever of this 
kind, in which F is the fulcrum, A the end 
at which the power is applied, and C the 
end where the weight acts. To find when 
an equilibrium will take place between the 
power and the weight, in this as well as in 
every other species of lever, we must ob- 
serve that when the momenta, or quantities 
of force, in two bodies are equal, they will 
l)alance each other. Now, let us consider 
when this will take place in the lever. 
Suppose the lever AB, fig. 2, to be turned 
on its axis, or fulcrum, so as to come into 
the situation DC; as the end D is farthest 
from the centre of motion, and as it has 
moved through tlie arch AD in the same 
time as tlie end B moved through the arch 
BC, it is evident that the velocity of AB 
must have been greater than that of B. 
But the momenta being the products of the 
quantities of matter multiplied into tlie velo- 
cities, the greater the velocity, the less the 
quantity of matter to obtain the same pro- 
duct. Therefore, as the velocity of A is 
the greatest, it will require less' matter to 
produce an eqiiilibriura than B. 
I^et us now examine how much more 
weight B will require than A, to balance. 
As the radii of circles are in proportion to 
their circumferences, they are also propor- 
tionate to similar parts of tiiem; therefore, 
as the arches, AD, CB, are similar, the 
radius, or arm, DE, bears the same propor- 
