Remarks on Some Attempts Made towards a Perpetual Motion, by the Reverend Dr. Desaguliers. F. R. S.

Cum postea Mala sive Pyra Cydonia permutu- ruisset, quaedam etiam Mali Cydonij particulas ad Microscopium applicavi; & Lanuginem, quae ex Malo Cydonio exhalatur, neque Lanugini Mali Persici Copiâ cedit, delineandam curavi; quae omnia in Icone 4 de- signata vides per H I K L M N O. Ubi H I N O perparva est portio Mali Corticisque Cydonij, per I K L M N Lanugo ex Malis Cydoniis exsudans in- dicatur. Quae Lanugo, licet in Cydoniis longior quam in Persicis, non tamen in illis erigitur, sicut in istis; sed crispando sibi invicem implectitur. X. Remarks on some Attempts made towards a perpetual Motion, by the Reverend Dr. Desagu- liers. F. R. S. The Wheel at Hesse-Cassel, made by Monsieur Or- fèvre and by him called a perpetual Motion, has of late been so much talk'd of, on Account of its wonder- ful Phenomena, that a great many People have believed it to be actually a self-moving Engine; and according- ly have attempted to imitate it as such. Now as a great deal of Time and Money is spent in those Endeavours, I was willing (for the Sake of those that try Experi- ments with that View) to shew that the Principle, which most of them go upon is false, and can by no- Means produce a perpetual Motion. They take it for granted, that if a Weight descend- ing in a Wheel, at a determinate Distance from the Centre, does in its Ascent approach nearer to it; such a Weight a Weight in its Descent will always preponderate, and cause a Weight equal to it to rise, provided it comes nearer the Centre in its Rise; and accordingly as it self rises, will be overbalanced by another Weight equal to it; and therefore they endeavour by various Contrivances to produce that Effect, as if the Consequence of it would be a perpetual Motion. But I shall shew, that they mistake one particular Case of a general Theorem, or rather a Corollary of it, for the Theorem it self. The Theorem is as follows: Theor. If one Weight in its Descent, does by Means of any Contrivance, cause another Weight to ascend with a less Momentum or Quantity of Motion than it self, it will preponderate and raise the other Weight. Cor. 1. Therefore if the Weights be equal, the descending Weight must have more Velocity than the ascending Weight, because the Momentum is made up of the Weight multiplied into the Quantity of Matter. Cor. 2. Therefore if a Leaver or Balance, have equal Weights fasten'd or hanging at its Ends, and the Brachia be ever so little unequal, that Weight will preponderate, which is farthest from the Centre. SCHOLIUM. This Second Corollary causes the Mistake; because those, who think the Velocity of the Weight is the Line it describes, expect that that Weight shall be overpois'd, which describes the shortest Line, and therefore contrive Machines, to cause the ascending Weight to describe a shorter Line than the descending Weight. As for Example, in the Circle A D B a (Fig. 5.) the Weights A and B being supposed equal, they imagine, that if (by any Contrivance whatever) whilst the Weight A describes the Arc A a, the Weight B is carried in any Arc, as B b, so as to come nearer the Centre in its rising, than if it went up the Arc BD; the said Weight shall be overpois'd, and consequently, by a Number of such Weights, a perpetual Motion will be produced. This is attempted by several Contrivances, which all depend upon this false Principle; but I shall only mention one, which is represented by Fig. 6. where a Wheel having two parallel Circumferences, has the Space between them divided into Cells, which being carv'd, will, (when the Wheel goes round) cause Weights plac'd loose in the said Cells, to descend on the Side A A A, at the outer Circumference of the Wheel; and on the Side D to ascend in the Line B b b b, which comes nearer the Centre, and touches the inner Circumference of the Wheel. In a Machine of this Kind, the Weights will indeed move in such a Manner, if the Wheel be turn'd round, but will never be the Cause of the Wheels going round. Such a Machine is mentioned by the Marquis of Worcester, in his Century of Inventions in the following Words, N°. 56. "To provide and make that all the Weights of the descending Side of a Wheel, shall be perpetually farther from the Centre, than those of the mounting Side, and yet equal in Number, and heft to the one Side as the other. A most incredible thing, if not seen; but tried before the late King (of blessed Memory) in the Tower by my Directions, two extraordinary Ambassadors accompanying his Majesty," jesty, and the Duke of Richmond, and Duke of Hamilton, with most of the Court attending him. The Wheel was fourteen Foot over, and had fourty Weights of fifty Pounds a Piece. Sir William Balfour, then Lieutenant of the Tower, can justify it, with several others. They all saw, that no sooner these great Weights passed the Diameter Line of the lower Side, but they hung a Foot farther from the Centre; nor no sooner passed the Diameter Line of the upper Side, but they hung a Foot nearer Be pleased to judge the Consequence. Now the Consequence of this, and such like Machines, is nothing less, than a perpetual Motion; and the Fallacy is this. The Velocity of any Weight is not the Line, which it describes in General, but the Height that it rises up to, or falls from, with respect to its Distance from the Centre of the Earth. So that when the Weight (Fig. 5.) describes the Arc A a, its Velocity is the Line A C, which shews the perpendicular Descent (or measures how much it is come nearer to the Centre of the Earth) and likewise the Line B C denotes the Velocity of the Weight B, or the Height that it rises to, when it ascends in any of the Arcs B b, instead of the Arc B D: So that in this Case, whether the Weight B in its Ascent be brought nearer the Centre or not, it loses no Velocity, which it ought to do, in order to be rais'd up by the Weight A. Nay, the Weight in rising nearer the Centre of a Wheel, may not only not lose of its Velocity, but be made to gain Velocity, in Proportion to the Velocity of its counterpoising Weights, that descend in the Circumference of the opposite Side of the Wheel; for if we consider two Radii of the Wheel, one of which is Horizontal, and the other (fasten'd to and moving with it) inclin'd under the Horizon in an Angle of 60 degr. (Fig. 7.) and by the Descent of the End B of the Radius B C, the Radius C D by its Motion causes the Weight at D, to rise up the Line p P, which is in a Plane that stops the said Weight from rising in the Curve D A, that Weight will gain Velocity, and in the Beginning of its Rise, it will have twice the Velocity of the Weight at B; and consequently, instead of being rais'd, will overpoise, if it be equal to the last mentioned Weight. And this Velocity will be so much the greater, in Proportion as the Angle A C D is greater, or as the Plane P p (along which the Weight D must rise) is nearer to the Centre. Indeed if the Weight at B, Fig. 5. could by any Means be lifted up to β, and move in the Arc β b, the End would be answer'd; because then the Velocity would be diminished, and become β C. Experiment (Fig. 7.) Take the Leaver B C D, whose Brachia are equal in Length, bent in an Angle of 120 degr. at C, and moveable about that Point as its Centre: In this Case, a Weight of two Pounds hanging at the End B of the horizontal Part of the Leaver, will keep in Æquilibrio a Weight of Four Pounds hanging at the End D. But if a Weight of one Pound be laid upon the End D of the Leaver, so that in the Motion of D along the Arc p A, this Weight is made to rise up against the Plane P p (which divides in half the Line A C equal to C B) the said Weight will keep in Æquilibrio two Pounds at B, as having twice the Velocity of it, when the the Leaver begins to move. This will be evident, if you let the Weight 4 hang at D, whilst the Weight 1 lies above it: For if then you move the Leaver, the Weight 1 will rise four times as fast as the Weight 4. XI. A Method for rowing Men of War in a Calm. Communicated by Monsieur Du Quet. To perfect the Art of Navigation, Two Things seem principally wanting; viz. An easy Method for finding the Longitude at Sea; and a Way to give a Vessel its Course, when there's no Wind stirring. I flatter myself to have found the last; and hope to make it appear, by Reason and Experiment, That a Man of War may make a League an Hour in a Calm, by Means of revolving Oars, which are easily apply'd to the Sides of the Ship, without occasioning any Incumbrance: As I shall make appear by the following Account, after having deliver'd my Notion of the Motion of Bodies in Fluids. A Body swims upon Water, when it weighs less than the Volume of Water, whose Place it takes up; and it sinks more or less in the Water, only in proportion as its Volume is more or less increas'd. A Body lying in still Water, is as it were in Equilibrio; the least Effort gives it Motion, and makes it lose that Equilibrium. If the Effort be continued, tho' ever so little, the Motion it communicates will be ve-