_Fig. 2._ Is a Cycloid with its equal Sides A B, A C, and pendulous Body E, oscillating therein. And, _Note_, That by the Make of the Figure, the Line B C is equal to the Circumference of the Circle D G F, 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 G F; that its included Area B D C F, 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 E F; and that therefore the Time of every Oscillation, in all Angles whatsoever, is always equal. _Fig. 3._ A C B 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._ A B 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 C A K, 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.