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, w1, sustains five Pounds, w5, 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 EF, or CD, or AB, 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 EF, 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 HI: And the Diameter and Velocity of the Teeth in HI, 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 LM; And that the Barrel NO, be of the same Diameter with the Wheel LM. Then a Weight on the Barrel EF will balance a Weight one hundred times as heavy upon the Barrel NO; which is done by its moving an hundred Times as swift as the other. For the Velocity in the first Barrel EF, to that of its Pinion G, is as ten to one; and that in the Wheel HI, 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 LM, and its Barrel NO, are equal.

Fig.5. Is a compound Engine, to prove that in a Wedge, as EMG, 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, DF and DE, to the Radius DB; 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 DB to DF and DE, or to 2 DF. i.e. by the Similitude of Triangles, as AB or CB to AC.

Fig.7. Is a Paper Wedge, HFG 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 HF to HG.

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.