124 
MECHANICS. 
the point b, 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 
another in the inverse proportion of their 
distances from it. For it is well known, that 
the nearer either of them is to the burden, 
the greater share he bears of it; and if he 
goes directly under it, he bears the whole, 
bio if one man is at A, and the other at a, 
having pole or stick resting on their 
shoulders ; if the burden or weight B is placed 
five times as near the man at A, as it is to the 
man a, the former will bear live times as 
much weight as the latter. 
This is likewise applicable to the case of 
-two horses of unequal strength to be so yok- 
ed, that each horse may draw a part pro- 
portionable 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 former exceeds that of the 
latter. 
To this kind of lever may be reduced 
•oars, rudders of ships, doors turning upon 
lunges, cutting-knives which are fixed at the 
point, &c. 
If in this lever we suppose the power and 
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 between 
the power and the weight, the intensity 
of the power must exceed the intensity 
of the weight just as much as the distance of 
the weight from the prop exceeds the dis- 
tance of the power. Thus, let E (fig. 4.) be 
the prop of the lever EF, 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 
tiie power must be equal to three pounds, in 
order to 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, the muscle that exerts 
its force to raise that weight is fixed to the 
bone about one-tenth part as far below the 
elbow as the 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 weight that is 
raised. 
As this kind of lever is a disadvantage to 
the moving power, it is used as little as pos- 
sible; but in some cases it cannot be avoided, 
such as that of a ladder, which being fixed at 
one end, is by the 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 ham- 
mer. 
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 pulling backwards the 
end of the shaft, a man will draw a nail with 
one-fifth part of the power that he must use 
tQ pull it out with a pair of pincers, in which 
case the nail would move as fast as his hand ; 
but with the hammer the hand moves five 
times as much as the nail, by the time that 
the nail is drawn out. 
Let ACB (fig. 5.) represent a lever of this 
sort, bent at C, which is its prop, or centre 
of motion. P is a power acting upon the 
longer arm AC, at A, by the means of the 
cord DA going over the pulley D; and W is 
a weight or resistance acting upon the end B 
of the shorter arm CB. If the power is to the 
weight as CB is to CA, they are in equilibrio : 
thus, suppose W to be five pounds, acting at 
the distance of one foot from the centre of 
motion C, and P to be one pound, acting at 
A, five feet from the centre C ; the power 
and weight will just balance each other. 
Thus we see, that in every species of lever 
there will be an equilibrium, when the power 
is to the weight, as the distance of the weight 
from the fulcrum is to the distance of the 
power from the fulcrum. 
In making experiments on the mechanic 
powers, some difficulties arise from the weight 
of the materials; betas it is impossible to 
find any that are without weight, we take 
care that they are perfectly balanced them- 
selves, before the weights and powers are ap- 
plied. The bar, therefore, used in making 
experiments on fevers, has the short end so 
much thicker than the long arm, as will be 
sufficient to balance it on the prop. 
Hitherto we have supposed that the power 
and weight acted perpendicularly upon the 
lever ; but if they do not, they act with less 
force upon it; the power should, therefore, 
if possible, be always made to act at right 
angles to the lever. 
If several levers are combined together in 
such a manner, as that a weight being ap- 
pended to the first lever, may be supported 
by a power applied to the last, as in fig. 6. 
(which consists of three levers of the first kind, 
and is so contrived, that a power applied at 
the point L of the lever C, may sustain a 
weight at the point S of the lever A), the 
power must here be to the weight, in a ratio, 
or proportion, compounded of the several 
ratios, which those powers that can sustain 
the weight by the help of each lever, when 
used singly and apart from the rest, have to 
the weight. For instance: if the power which 
can sustain tire weight P by the help of the 
fever A, is to the weight as 1 to 5 ; and if the 
power which can sustain the tame weight by 
the lever B alone, is to the weight as l to 4 ; 
and if the power which could sustain the same 
weight by the lever C, is to the weight as 1 
to 5 ; then the power which will sustain the 
weight by the help of the three levers joined 
together, will be to the weight in a propor- 
tion consisting of the several proportions 
multiplied together, of 1 to 5, 1 to 4, and 1 
to 5 ; that is, of 1 to 100. 
For since, in the lever A, a power equal to 
one-fifth of the weight P pressing down the 
lever atL, is sufficient to balance the weight; 
and since it is the same thing whether that 
power is applied to the lever A at L, or the 
lever B atS, the point S bearing on the point 
L ; a power equal to one-fifth of the weight 
P, being applied to the point S of the lever B, 
will support the weight; but one-fourth of 
the same power being applied to the point L 
of the lever B, and pushing the same upward, 
will as effectually depress the point S of the 
same lever, as if the whole power was applied 
at S ; consequently a power equal to one- 
fourth, of one-fifth, that is, one-twentieth of 
the weight P, being applied to the point L ofi 
the lever B, and pushing up the same, will 
support the we ght ; in like manner, it mat- 
ters not whether that force is applied to the 
point L of the lever B, or to the point S of the 
lever C, since, if S be raised, L, which rests 
on it, must be raised also; but one-fifth of the 
power applied at the point L of the lever C, ‘ 
and pressing it downwards, will as effectually 
raise the point S of the same lever, as if the 1 
whole power was applied at S, and pushed 
up the same; consequently a power equal to 
one-fifth of one-twentieth, that is, one-hun- 
dredth part of the weight P, being applied to 
the point L of the lever C, will balance the 
weight at the point S of the lever A. 
The balance, an instrument of very exten- 
sive use in comparing the weights of bodies, 
is a lever of the first kind, whose arms are of 
equal length. The points from which the 
weights are suspended being equally distant 
from the centre of motion, will move with i 
equal velocity; consequently, if equal weights' 
are applied, their momenta will be equal, 
and the balance will remain in equilibrio. 
In order to have a balance as perfect as 
possible, it is necessary to attend to the fol- 
lowing circumstances: 1. The arms of the 
beam ought to be exactly equal, both as to 
weight and length. 2. 'Flic points from which 
the scales are suspended should be in aright 
line, passing through the centre of gravity of 
the beam ; for by this the weights will act di- 
rectly against each other, and no part of 
either will be lost on account of any oblique j 
direction. 3. If the fulcrum, or point upon 
which the beam turns, is placed in the centre I 
of gravity of the beam, and if the fulcrum 1 
and the points of suspension are in the same : 
right line, the balance will have no tendency j 
to one position more than another, but will 
rest in any position it may be placed in„ 
whether the scales are on or off, empty or 
loaded. 
if the centre of gravity of the beam, w hen 
level, is immediately above the fulcrum, it j 
will overset by the smallest action ; that is, : 
the end which is lowest will descend; and it- 
will do this witli more swiftness, the higher the j 
centre of gravity is, and the less the points of. 
suspension are loaded. 
But if the centre of gravity of the beam is- 
immediately below the fulcrum, the beam 
will not rest in any position but when level ; 
and if disturbed from that position, and then, 
left at liberty, it will vibrate, and at last come 
to rest on the level. In a balance, therefore, 
the fulcrum ought always to be placed a little 
above the centre of gravity. Its vibrations 
will be quicker, and its horizontal tendency 
stronger, the lower the centre of gravity,,' 
and the less the weight upon the points of 
suspension. 
4. llie friction of the beam upon the axis' 
ought to be as little as possible; because, 
should the friction be great, it will require a 
considerable force to overcome it; upon 
which account, though one weight should a.' 
little exceed the other, it will not preponde- 
rate, the excess not being sufficient to over*-- 1 
come the friction, and bear down the beam! 
The axis of motion should be formed with an' 
edge like a knife, and made very hard ; these 
edges are at first made sharp, and then round- 
ed with a fine hone, or piece of buff leather, 
which causes a sufficient blimtness, or rolling* 
edge. On the regular form and excellence 
