An Explication of the Second PLATE.
Figure 1. Is the deceitful Balance; which yet is _in Æquilibrio_ because
the Weights 23 and 24 are reciprocally proportional to their Distances
from the Center of Motion. Now this Cheat is easily discover'd by changing
the Position of the Weights, and putting each of them into the other
Scale, which will then be very unequal, or nearly as 11 to 12.
_Fig. 2._ Is that sort of Balance which is called a Stiliard, and of
frequent Use among us. It is only a Common Balance, with Weights at
Distances from the Center of Motion reciprocally Proportionable to
themselves: Only here the Length of Part of the Beam is compensated by a
large Ball or Weight B, fixed to the shorter Beam; and one Weight as w
removed along equal Divisions is made use of to weigh several others, as
6 w. _&c._
_Fig. 3_. Is design'd to shew how any Force is diminish'd by its
Obliquity; and that a Weight hung obliquely at 3, 2, 1, in the
Circumference of a Circle or Wheel, is of no more Efficacy, as to the
turning of the Wheel round, than if it were hung perpendicularly at the
corresponding Points 3, 2, 1, in the Semidiameter of the same Circle.
_Fig. 4._ Is the Demonstration of the former Case, by shewing that in
those Circumstances the Force P B is resolved into two B F and B G, of
which B F pulls directly from the Center, and is of no Use to the turning
the Wheel round: And so all the remaining Force is represented by the
perpendicular Force B G, which is wholly spent in turning it round. So
that as B P is to B G, so is the whole oblique Force, to the real or
direct Force: Or so, in the similar Triangle B E C, is B C the whole
oblique Radius, to C E the Perpendicular: Or so in the foregoing Figure is
O 1, O 2, O 3, the common Hypotenuse or entire Radius, to O 1, O 2, O 3,
the Bases or shorter Radij, where the String cuts the entire Radius
perpendicularly.
_Fig. 5._ Is the first Sort of Lever, where C the Prop is between the
Resistance to be overcome, or Weight to be moved 5 w, and w 1 the Power or
Weight to move the other by: And is so like the Case of the Balance or
Stiliard, that it needs no particular Explication. A Crow of Iron is of
this Sort.
_Fig. 6._ Is the second Sort of Lever, where the Resistance to be
overcome, or Weight to be moved w 3, is between the Prop C and the Point
A, to which by the means of the Pulley P, the Power or Weight to move the
other by, is applied. Bakers Knives for cutting Bread are commonly of this
Sort.
_Fig. 7._ Is the third Sort of Lever, where the Resistance to be overcome,
or Weight to be moved, w 2 is at one End, the Prop at the other, and the
Power or Weight w 3 between them. A Ladder lifted up by the Middle, in
order to be rear'd, where one End is fixed, is of this Sort. Only the
Force being in this Case nearer the Prop than the Resistance to be
overcome, or Weight to be moved, this Sort of Lever diminishes Force
instead of increasing it, and is therefore of little Use.
_Fig. 8._ Is a common Lever of the first Sort, with its Prop and equal
Divisions, fit to be used as the Stiliard.
_Fig. 9._ Is a compound Lever of the first Sort, as long as the single one
just above it, where a Weight at G, by being doubled three several Times,
will raise eight Times its own Weight at A, as well as the other does it
at once. This last is therefore of the same Force as the former, and no
more; and by being compounded, is less considerable than the other.
_N. B._ Had the Proportion in the Compound Lever, _Fig. 9._ been
otherwise, as suppose the Part B C on one Side of the Prop B three Times
the Length of A B on the other Side, and the same in the other two Levers
C E and E G; then the Weight G being but the 27th Part of the Weight at A,
will be in _Æquilibrio_ with it.
_Fig. 10._ Is a bended Lever of the first Sort, where C the Prop is at an
Angle, and the Force is increas'd with C H, the Distance of the Weight
w 1, which by the means of the Pulley P, is applied to the longer Part of
the Lever; and in this Lever, the Power is to the Resistance reciprocally
as their Distances. An Hammer drawing out a Nail is such a bended Lever.
_Fig. 11, 12._ Shew that Levers or Balances that are even when horizontal,
may be uneven in other Positions; that is, too light when the Center of
Gravity of one Weight is fix'd to the Lever or Balance above, and it is
elevated; or below, and depress'd: Because the Perpendicular cuts the
horizontal Line too near the Center in these Cases.
[[Plate III. ― Sutton Nicholls sculp:]]