An Explication of the Sixth Plate.

Figure 1. Is an Instrument to shew the various Parabola's that are made by Projectils, and particularly the Truth of the several Rules in the Art of Gunnery. Wherein AB is a Tunnel full of Quicksilver, DK is a Glass Tube, let into a Groove or Frame of Wood for its Support, and at K is a fine Stem, accommodated to the Arch of a Quadrant LM, and turning upon its Center, to direct the projected Quicksilver to any Angle; while the Tube's perpendicular Altitude, or the Force that produces the Projection, is either the same, or altered by a different Inclination at Pleasure, according to the Nature of the several Experiments.

Fig.2. Is a Cycloid with its equal Sides AB, AC, and pendulous Body E, oscillating therein. And, Note, That by the Make of the Figure, the Line BC is equal to the Circumference of the Circle DGF, by which it was describ'd; that the Length of the Cycloid it self is four times that Circle's Diameter; that every Part of it from F the Vertex is still double to the Chord of the Correspondent circular Arch GF; that its included Area BDCF, is Three times the Area of the former Circle; that the Force upon the Pendulum at any Point E, is exactly proportional to the Distance along the Cycloid of the Point from the Vertex, as EF; and that therefore the Time of every Oscillation, in all Angles whatsoever, is always equal.

Fig.3. ACB is a Syphon with Quicksilver from A to C, and a Pendulum of half that Length; to shew here also that the Force is as the Line to be describ'd, and that by Consequence the Vibrations in the Syphon are all equal: as also to shew that they are equal to those of a Pendulum, of half the same Length: As is plain from the former Case of the Cycloid, where the Length of the Pendulum is half that of the Cycloid in which the Body moves.

Fig.4. AB are two Spheres, to denote the several Laws of Motion in the Collision of Bodies, whether Elastical or not Elastical, to be tried in the Cycloid, or in a Circle, with proper Corrections: Which Experiments yet are most of them too difficult for such a Course as this is.

Fig.5. Is an Instrument to explain muscular Motion; supposing the Muscles to be some way like a String of Bladders; by shewing that a smaller Quantity of an elastical Fluid may equally raise equal Weights with a larger; and to shew exactly what Quantity is necessary for any particular Effect. For thus will the lesser Quantity of Air, (measured in both Cases by the Gage CAK, as condens'd by the Syringe H A) equally raise an equal Weight to the same Height by the lesser three Bladders, that the greater Quantity raises the same by the one larger Bladder.

Fig.6. Are several Pendulums of several Sorts of Matter, heavy and light; where the Centers of Suspension and Oscillation are equally distant, and the Times of those Oscillations are all equal. This also hints the other remarkable PhÆnomena of Pendulums; viz. that the Semicircular and Cycloidal Times of Oscillation are to each other as 34 to 29: That in both the Length of the Strings of Pendulums are in a duplicate Proportion to their Times of Oscillation; and that the Heights of Roofs, &c. may be found from the Times of the Oscillations of Pendulous Bodies fixed to them, on the known Hypothesis that a Pendulum of 39.2 Inches vibrates in one Second of Time.

Fig.7. Is a Fountain running on Wheels, and made by Air condens'd on the Surface of Quicksilver, and so forcing the Quicksilver to ascend through the Pipe G: And is to shew that the Lines of Projectils, or other Bodies, are not alter'd by the common Motion of the whole Instrument or Floor on which they are plac'd; and that all Motions on the Earth, if it move, will be the same as if it stand still.

Fig.8. Is a Parabola with the several Lines belonging to it, in order to demonstrate the Doctrine of Projectils; and particularly the Art of Gunnery.

Fig.9. Is an Engine moving on Wheels, that lets a Ball fall down from a Groove through a Hole, as it is in Motion; to shew that it will then fall on the same Point of the Frame that it falls upon when it is at rest; as does a Stone let fall from the Top of the Mast of a Ship under Sail: and that all respective Motions on the Earth must be the very same, while it self moves as if it were at rest.

Fig.10. Is a Cylindrical Iron AB, swinging on a Pin EF, in the very same time that a pendulous Body D of two thirds of its Length CD does; to shew that two thirds is the Center of Oscillation or Percussion in all such prismatick or cylindrical Bodies.