The free portion of the chain BDC will hang in a symmetrical curve (CATERNARY, q.v.), and its tension will therefore be the same at B and at C. Hence the other portion BAC of the chain will be free to move, unless the resolved part of the weight of AB, acting down the inclined plane AB, just balance that of the corresponding portion of the chain down AC. If these balance, the parallelogram of forces is proved; if not, one side will preponderate, and we shall evidently obtain the perpetual motion.
We will briefly sketch the history of the simpler part of the problem, where mechanical and hydrostatical arrangements alone are contemplated, and where the impossibility of procuring the perpetual motion had been completely shown by-Newton.
The leading features of the various devices suggested as self-moving engines are three: 1. The machine being a combination of mechanical powers driven by weights, was to be constructed so as constantly to wind up those weights as they fell, and there fore to be constantly in the same circumstances as to power in each successive complete revolution. The ideal of this, in its simplest form, is that of a wheel moving about a horizontal axis, and so adjusting certain heavy sliding pieces on its surface as to have always a preponderance on one particular side. 2. The type.of the second class differs from that of the first only in the substitution of liquids for the weights in the first class, and the consequent introduction (often in most extravagant forins) of hydrostatical laws, which the inventors seem to have less certain and more pliablo-than the stem facts of common mechanics. 3. The machine depends on some natural power, such as rain, change of temperature, wind, fluctuations of the barometer, tides, etc. The con sideration of this third class is very interesting, but we will defer it for a little.
Of the first class, the only machines that seem ever to have succeeded in permanently deceiving any but their inventors are those of the marquis of Worcester and of councilor Ortlyreus. Contemporary with the former was bishop Wilkins, who candidly zind.inge nionsly points out the fallacies of various devices of his own, depending severally on weights,' on magnets, and on Archimedes's screw. His first attempt seems to have been closely allied to that of the marquis of Worcester, of whose engine we haVe no drawing, and only a very vague description. The following figure gives us. however, some notion
of its probable nature. In Wilkins's and Jackson's perpetual notions, levers were used instead of halls.
In all three, the attempt is by the sliding of the balls in their cells, or by the turning of the levers, to give the preponderance to the descending side of the wheel. But even the cut shows that, though the weights on the descending side are on the whole further front the axis of the wheel than those on the ascending side, yet there are snore balls on the latter than on the former side; and a careful examination, like that made by Wilkins, shows that [heir moments in opposite directions about the axis' balance each other. With reference to the invention of the marquis of Worcester—who is otherwise (Nell known as one of the first to foresee, and even in part to realize experimentally, the advantage of steam as a motive-power—we find the following iu his Century if Inven tions : " An Advantageous Mange of prouide and make that all y° weights of yo descending syde of a wheele shat be perpetually further from yo center, then those of ye mounting syde, and yett equall in number and heft of r one syde as ye other. A most incredible thing if not scene, butt tryed before ye late king of happy aud glorious memorye in yo tower by my directions, two extraorduary ambassadors accompanying his Ma" and y° D. of Richmond, D. Hamilton, and most part of y° court attending hint. The wheele was 14 foote otter, and 40 weights of tit) pd apiece; Sr Wm. Belford, then of y° Tower, and yet lining can justify it with seuerall others; They all saw that noe sooner these great weights passed y° Diameter Line of ye vpper syde but they hung a foote further from r center, 110r110 sooner passed the Diameter Line of the lower syde, butt they hung a foote nearer; bee pleased to judge ye consequence." The machine of Orffyreus, by which 'S GravesaMle was completely taken in, so much so that he wrote to Newton expressing his belief that the perpetual motion was really found, consisted of a large wheel or drum covered with canvas, to prevent the interior from being seen, and rotating about a thick horizontal axle. This machine, when set agoing in either direction, moved with accelerated speed till it reached a rate of twenty five turns in a minute: and on one occasion was sealed up by the elector of Cassel for two months, and at the expiration of that time found to be moving as rapidly as ever.