An Explication of the Fourth PLATE.
Figure 1. Is a System of Pulleys connected together, whereby the Force is
increased by Addition in Proportion to the Number of Cords; so that one
Pound, w 1, sustains five Pounds, w 5, as must happen from the Equality of
the stretching of the whole Cord, and the consequent Division of the whole
Weight into five equal Parts, as equally supported by them all.
_Fig. 2._ Is a System of Pulleys not connected together, whereby the Force
is increas'd, for every lower Pulley; according to the Numbers, 2, 4, 8,
in a double Proportion; because every lower Pulley doubles the Force of
the former; as is evident at the first Sight; since the Velocity of Ascent
or Descent of the greater Weight is every Time but half so great as
before.
_Fig. 3._ Is the Axis in Peritrochio; or Wheel, with its Axel; where any
Weight or Force applied round E F, or C D, or A B, has just so much
greater Power to move the Wheel, or entire Machine about the Axis, as the
Velocity or Distance from the Geometrical Axis it self is greater. Nor is
there any farther Difficulty in this plain Engine.
_Fig. 4._ This is only a Train of Wheel-work; which by Composition of
Wheels vastly increases the Force. Thus suppose the Diameter of the Barrel
E F, be ten times the Diameter of the Pinion G: And the Diameter, or
Number of equal Teeth in G, be one tenth of the Diameter, or Number of
equal Teeth in H I: And the Diameter and Velocity of the Teeth in H I, be
ten times the Diameter and Velocity of the Pinion K; and the Diameter or
Number of equal Teeth in K, be one tenth of the Diameter, or Number of
equal Teeth in L M; And that the Barrel N O, be of the same Diameter with
the Wheel L M. Then a Weight on the Barrel E F will balance a Weight one
hundred times as heavy upon the Barrel N O; which is done by its moving an
hundred Times as swift as the other. For the Velocity in the first Barrel
E F, to that of its Pinion G, is as ten to one; and that in the Wheel H I,
to that in its Pinion K, is also as ten to one. While the Velocities at
each Wheel, and its corresponding Pinion in the other Wheel, as well as at
the Wheel L M, and its Barrel N O, are equal.
_Fig. 5._ Is a compound Engine, to prove that in a Wedge, as E M G,
depress'd by a Weight w, or by its own Weight, or by a Stroke, the Force
is diminished in Proportion to the Sine of its Aperture, compar'd with the
Line of its Depth: So that when the former Sine is double or triple, _&c._
the Force is diminished one half, or one third, _&c._ This is here prov'd
by the Wedges separating two Cylinders, which are drawn together by other
Weights, in the Scales R and S beneath, when its Sides are screw'd nearer
or farther off, to adjust their Distance to those Weights perpetually.
_Fig. 6._ Is a Wedge by it self, where the Force is increas'd in the
Proportion of the Sines of the Angles of Aperture, D F and D E, to the
Radius D B; or is resolv'd into two Forces, the one perpendicular, and the
other parallel to the Plain of the Tree or Timber it is to reeve: And this
because the Velocity downward is ever to the Velocity side-ways in the
Proportion of D B to D F and D E, or to 2 D F. _i. e._ by the Similitude
of Triangles, as A B or C B to A C.
_Fig. 7._ Is a Paper Wedge, H F G coil'd round a Cylinder, and so
representing a Screw; and shews that its Force must be increas'd in
Proportion to the Progress along its Cylinder, when it is compar'd with
the Circumferences on the same Cylindrical Surface, or as H F to H G.
_Fig. 8._ Is a compound Engine to explain and measure the Power of the
Screw: from whence it appears, that the Force of Screws is reciprocally
proportional to the Distance of the _Helix_'s or Threads which compose
them.
[[Plate V. ― Sutton Nicholls del. & sculp:]]