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 6w. &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 PB is resolved into two BF and BG, of which BF 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 BG, which is wholly spent in turning it round. So that as BP is to BG, so is the whole oblique Force, to the real or direct Force: Or so, in the similar Triangle BEC, is BC the whole oblique Radius, to CE the Perpendicular: Or so in the foregoing Figure is O1, O2, O3, the common Hypotenuse or entire Radius, to O1, O2, O3, 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 5w, and w1 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 w3, 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, w2 is at one End, the Prop at the other, and the Power or Weight w3 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 BC on one Side of the Prop B three Times the Length of AB on the other Side, and the same in the other two Levers CE and EG; 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 CH, the Distance of the Weight w1, 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.