MECHANICS. 
tion to E C that the arch A D bears to C B. 
But the arches AD and C B represent the 
velocities of the ends of the lever, because 
they are the spaces which they moved over 
ill t!ie same time ; therefore the arms D E 
and E C may also represent these velocities. 
Hence, an equilibrium will take place, when 
the length of the arm AE, multiplied into 
the power A, shall equal EB, multiplied 
into the weight B ; and consequently, that 
the shorter E B is, the greater must be the 
weight B ; that is, the power and the 
weight must be to each other inversely, as 
their distances from the fuicruin. Thus, 
suppose AE, the distance of the power 
from the prop, to be twenty inches, and 
E B, the distance of the weight from the 
prop, to be eight inches, also the weight 
lo be raised at B to be five pounds ; then 
the power to be applied at A, must be two 
pounds; because the distance of the weight 
from the fulcrum eight, multiplied into the 
weight five, makes forty ; therefore twenty, 
the distance of the power from the prop, 
must be multiplied by two, to get an equal 
product; which will produce an equilh 
biium. 
The second kind of lever, when tlie 
weight is between the fidcnim and the power, 
is represented by fig. 3, in wliich A is the 
fulcrum, B the weight, and C tlte power. 
The advantage gained by this lever, as in 
the first, is as great as the distance of the 
power from the prop exceeds the distance 
of the weigtit from it. Thus, if the point 
a, on which the power acts, be seven times 
as far from A as the point h, on which the 
weight acts, then one pound applied at C 
will raise seven pounds at B. This lever 
shews the reason why two men carrying a 
burden upon a stick between them, bear 
shares of the burden which are to one ano- 
ther in the inverse proportion of their dis- 
tances from it. 
It is likewise applicable to the case of 
two horses of unequal strength to be so 
yoked, as that each horse may draw a part 
proportionable to his strength; which is 
done by so dividing the beam they pull, 
that the point of traction may be as much 
nearer to the stronger horse than to the 
weaker, as the strength of the formes- ex- 
ceeds that of the latter. To this kind of 
lever may be reduced rudders of ships, 
doors turning upon hinges, &c. Tlie hinges 
being the centre of motion, the hand ap- 
plied to the lock is the power, while thg 
door is the weight to be moved. 
If in tliis lever we suppose the power gnd 
weight to change places, so that the power- 
may be between the weight and the prop, 
it will become a lever of the third kind ; 
in which, that there may be a balance be- 
tween the power and the weight, the in- 
tensity of the power must exceed tlie in- 
tensity of the weight just as inacli as the 
distance of the weight from tlie prop e.x- 
ceeds the distance of the power. Thus, 
let E, fig. 4, be the prop of the lever E F, 
and W, a weight of one pound, placed three 
times as far from the prop as the power P 
acts at F, by the cord going over the fixed 
pulley D : in this case, the power must be 
equal to three pounds, in order lo support 
the weight of one pound. To this sort of 
lever are generally referred the bones of a 
man's arm; for when he lifts a weight by 
the hand, tlie muscle that exerts its force 
to raise that weight, is fixed to the bone 
about one tenth part as far below the 
elbow as tlie hand is. And the elbow being 
the centre round which the lower part of 
the arm turns, the muscle must therefore 
exert a force ten times as great as the 
weiglit that is raised. As this kind of lever 
is a disadvantage to the moving power, it 
is used as little as possible; but in some 
cases it cannot be avoided ; such as that 
of a ladder, which being fixed at one end, 
is by tiie strength of a man’s arms reared 
against a wall. -- 
What is called the hammer-lever, differs 
in nothing but its form from a lever of the 
first kind. Its name is derived from its use, 
that of drawing a nail out of wood by a 
hammer. Suppose the shaft of a hammer 
to be five times as long as the iron part 
which draws the nail, the lower part resting 
on the board, as a fulcrum ; then, by pull- 
ing backwards the end of the shaft, a man 
will draw a nail with one-fifth part of the 
power that he must use to pull it out with 
a pair of pincers ; in which case, the nail 
would move as fast as Iiis hand ; but with 
the h-ammer, tlie hand moves five times as 
much as the irail, by the time that the nail | 
is drawn out. Hence it is evident, that 
in every species of lever tliere will be an 
equilibrium, when the power is to the weight 
as the distance of the weight from the ful- 
crum is to the distance of the power fmjn 
the fulcrum. In experiments with tlie 
lever we take care that the parts are per- 
fectly balanced before the weights and 
powers are applied. The bar, therefore, 
has the short end so much thicker than the 
long arm, as will be sufficient t |0 balance 
it on the prop. 
