MECHANICS. 
If several levers be combined together 
in such a manner, as liiat a weiglrt being 
appended to the first lever, may be stt{)- 
ported by a power applied to the last, as 
in fig. 5, wl.'ich 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, compound- 
ed 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. Fcu' instance, 
if the power which can sustain the weight 
W by the help of the lever A, be to the 
w'eight as 1 to a ; and if the power which 
can sustain the same weight, by the lever 
B alone, be to the weight as 1 to 4 ; and 
if the power which could sustain the same 
weight by the lever C, be to the weight as 
1 to .9 ; then the power which will sustain 
the weight by help of the three levers 
joined together, will be to the weight in a 
proportion consisting of the several propor- 
tions multiplied together, of 1 to .9, 1 to 4, 
nd 1 to 9 ; that is as 1 ; 9 X 4 X 9, or 
of 1 : 100. For since, in the lever A, a 
power equal to one-fifth of the w^eight W 
pressing down the lever at L, is sufficient 
to balance the weight, and since it is the 
same thing whether that power be applied 
to the lever A at L, or the lever B at S, 
the point S bearing on the point L, a power 
equal to one-fifth of the weight P, being 
applied to the point fe 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 up- 
ward, will as effectually depress the point 
S of the same lever, as if the whole power 
were applie'd 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 of the lever B, aird pushing up 
the same, will support the weight : in like 
manner, it matters not w'hether that force 
be -applied to the poitit L of the lever B, or 
to the point S of the lever C, since, if 
iS be raised, L, whicb rests on rt, must be 
raised -also; but one-fifth of the power ap- 
plied 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 
whole povrer were applied at S, and pusnerl 
np the same ; consequently a power equal 
to one-fiftli of one-twentieth, that is, one- 
hundredth part of the weight P, being ap- 
plied to the point L of the fever C, wd! 
balance the weight at the point S of the 
lever A. This method of combining levers 
is frequently used in machines and instru- 
ments, and is of great service, either in 
obtaining a greater power, or in -applying 
it with more convenience. 
The balance, an instrument of very ex- 
tensive use in comparing th/e weights of 
bodies, is a lever of the first kind, whose 
arms are of e<jual length. The points from 
which the weigl.ts are suspended being 
equaliy distant from the centre of motion, 
will move with equal velocity ; consequently 
if equal weights be applied, their momenta 
will be equal, and the balance will remain 
in equiiibrio. In order to have a balance 
as perfect as possible, it is necessary ta 
attend to the following circumstances: 1. 
The arms of the beam ought to be exactly 
equal, both as to weight -and length. 2, 
The points from which the scales are sus- 
pended, should be in a right line, passing 
through the centre of gravity of the beam ; 
for by this, the weights wail act directly 
against each other, and no part of either 
will be lost, on -account of any oblique 
direction. 3. If the fulcrum be placed in 
tlie centre of gravity of the beam, and if 
tl)e fulcrum and the points of suspension 
be in the same right line, the balance will 
have no tendency to one position more 
than another, but will rest in any position 
it may be placed in, whetlier the scales be 
on or off, empty or loaded. If the centre 
of gravity of the beam, when level, be 
immediately above the fulcrum, it will 
overset by the smallest action ; that is, the 
end whicii is lowest will descend ; and it 
will do this with more swiftness, the higher 
the centre of gravity be, and the less the 
points of suspension be loaded. But if 
the centre of gravity of the beam be im- 
mediately ’ 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 ba- 
lance, therefore, the fulcrtim ought alw-ays 
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. The friction of the beam upon the axis 
ought to he as little as possible ; because, 
shotdd the friction be great, it will require 
a considerable force to overcome it; upon 
which account, tliough one weight should a 
little exceed the other, it will not prepon- 
