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femblance to the case wherein two moving bodies ftop each other, when they meet together with equal quantities of motion, that Dr. Wallis, and after him moft of the late Writers, have thought the cause of an æquilibrium in the several machines, might be immediately affigned: by saying, That, since one body cannot produce in another a quantity of motion equal to its own, without losing its own at the same time; two heavy bodies, counteracting each other by means of a machine, must continue at rest, when they are so circumstanced that one cannot descend, without causing the other to ascend at the same time, and with the fame quantity of motion; and therefore two heavy bodies in such cases, must always counterbalance each other. Now, this argument would be a juft one, if it could properly be faid, that the motion of the ascending body was produced by that of the descending one : but, since the bodies are so connected, that one cannot possibly begin to move before the other, I apprehend, that if the bodies are supposed to move, it cannot be said that the motion of one is produced by that of the other : since, whatever force is supposed to move one, it must be the immediate cause of motion in the other also; that is, both their motions must be simultaneous effects of the same cause, just as if the two bodies were really but one. And therefore, if I was to suppose, in this case, that the fuperior weight of the heavier body (which may be in itself much more than able to sustain the lighter) should overcome the weight of the lighter, and produce equal motions in both bodies; I do not think, that from thence I could be reduced to the absurdity of fuppofing, that one body, by its motion, might produce in another, a motion equal to its own, and yet not lose its own at the fame time. But those who argue from the equality of motions on this occafion say further, that, since the two bodies must have equal motions when they do move, they must have equal endeavours to move, even whilst they are at rest, and therefore these endeavours to move, being equal and contrary, muft destroy each other, and the bodies must continue at rest, and confequently ballance each other. In answer to this I must observe, that the absolute force with which a heavy body endeavours to descend from a ftate of reft, can only be proportionable to its weight; and therefore I think it is neceflary that some cause should be alligned why (for instance) the endeavour of one pound to descend, shall be equal to that of four pounds; and especially as the fulcrum on which both weights act, requires no greater force to support it than that of five pounds.

« From these confiderations I infer, that the reason why very unequal weights may ballance each other, should be assigned not from their having equal momenta when made to move together,

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but by proving a priori, without considering their motions, that eicher the reaction of the fixed parts of the machine, or some other cause, so far takes off from the weight of the heavier body, as to leave it only just able to support the lighter.'

The Doctor proceeds next to the examination of the methods which Archimedes, Huygens, Sir Isaac Newton, and Mac Laurin, have taken to demonstrate an equilibrium from the fimple properties of the lever: concerning all which methods, he obferves, that they either take that for granted, which they are intended to prove, or are in other respects defective.

The postulatum on which he founds his own proof, is the following ; which he conceives will be readily granted him.

• If a force, says he, be uniformly diffused over a right line ; that is, if an equal part of the force acts upon every point of the line, and if the whole foree acts accordingly to one and the same plane; this force will be fustained, and the line kept in equilibrio; by a single force applied to the middle point of the line, equal to the diffused force, and acting in a contrary dijection.'

To this postulatum the Doctor adds, by way of lemma, that • If a right line be divided into two segments, the distances bes tween the middle of the whole line, and the middle points of the fegments, will be inversely as the segments. This is self-evident when the segments are equal; and, when they are unequal, then, since half of the whole line is equal to half of the greater and half of the lefser segment, it is plain that the diftance between the middle of the whole line and the middle of one segment, must be equal to half of the other segment, fo that there distances must be to each other inversely as the segments.'

Hence the Doctor goes on to prove, that of three weights or forces, any two of which are (by the construction) to each other inversely as their distances from the third, will sustain each oiher, and keep the line on which they act in equilibrio.

This is the first and most simple case of the property of the Jever; the Doctor proceeds, however, to explain some others deducible from it; as also to mention some well-known truths in Mechanics; which, he thinks, cannot be proved otherwise, than by deducing them from what he here demonstrates, Art. 29. A Method

of lessening the quantity of Friction in Engines,

By Keane Fitzgerald, Elq; The method here described, is the common one of Friction Wheels; by means of which, with another additional improvement, we are cold, the fire-engine at York-building Water. works, is now made to perform the same service better in five hours, than ever it did before in fix. As to the method of applying these wheels, and their use, they are generally known to Mechanics: the additional improvement above-mentioned, however, is not quite so well known, and may be of use in other cases as well as in that to which it is here applied.

works,

It is a common errour in Millwrights, and other Mechanics, to place the axis on which a beam is hung or ballanced, underneath the beam: by which means the center of motion is below the center of gravity of such beam ; so that, tho' it will remain in an horizontal position when fo placed and equally balanced, yet when it is made to incline to either side, it will continue to move on that side till it becomes parallel to the horizon, with the center of motion above the beain: 6 for when either end is depressed in the least degree, it becomes more distant from the center of gravity*; and the opposite end, which is raised in proportion, is brought nearer to it, although both ends still continue equidistant from the center of motion.'

Hence it is, that when the beam is of great weight, this method of construction is a great hindrance to the working of the machine; as was the case in the engine above-mentioned; whose lever, with its arch-heads, weighed about ten tons; the upper edge of it being about two feet nine inches above the cen. ter of the axis upon which it turned. Thus, when it was placed in a horizontal pofition, it required but ninety three pounds and a half to overcome the resistance from friction in the pivots ; yet, when either end was depressed four feet below the level, it required 534 pounds to be applied to the opposite end to lift it up again: fo that a power equal to four hundred and forty pounds and a half was required, on account of the center of gravity being so much changed by the position of the axis underneath the beam.

After having placed the axis, therefore, on the top of the beam, and applied the friction wheels to the pivots, Mr. Fitzgerald observes, that the lever, which before required a power of ninety-five pounds to overcome the least resistance from friction, was as easily effected by the application of three quarters of a pound; and the resistance from friction occasioned by a weight of fix tons, is of so little consequence, that the lever may be fwung with a flight thread, and will continue in a state of vibration for several minutes after.'

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• These are Mr. Fitzgerald's words; but it is plain he meant, the point where the center of gravity refted, when the beam was in its horizontal position.

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The visible effect, continues this Writer, with regard to the working of the engine, according to the most exaćt obfervations by different persons, both before and after these several alterations were made, is, that it now makes eighteen strokes, at eight feet per stroke, for fifteen that it ever made before, with the same, or rather a smaller, quantity of fuel ; and must therefore discharge one-sixth more water in equal time; which consequently saves one-fixth of the fuel. But the effect is found ftill greater, as to supplying the tenants with water : the engine performing a greater service in this respect in the proportion first mentioned. Some part of this effe&, however, is imputed to an improvement of the boiler ; of the nature of which we are not informed. On the whole, this is a very sensible and useful article, well worthy the careful perusal of all such as are concerned in the erection of fixed mechanical engines of any kind whatever.

ANTIQUITIES. Art. 26. An account of some subterraneous apartments with Etruf

can inscriptions and paintings, discovered at Civita Turchino, in Italy. By J. Wilcox Esquire.

• Civita Turchino, about three miles to the north of Corneto, is an hill of an oblong form, the summit of which is almost one continued plain. From the quantities of medals, intaglios, fragments of inscriptions, &c. that are occasionally found here, this is believed to be the very spot, where the powerful and most ancient city of Tarquinii once stood : though at present it is only one continued field of corn. On the south-east side of it runs the ridge of an hill, which unites it to Corneto. This ridge is at least three or four miles in length, and almost entirely covered by several hundreds of artificial hillocks, which are called, by the inhabitants, Monti Rosli. About twelve af these hillocks have at different times been opened ; and in every one of them have been found several subterranean apartments cut out of the solid rock. These apartments are of various formas and dimensions : some consist of a large outer room, and a small one within ; others of a small room at the first entrance, and a larger one within: others are supported by a column of the folid rock, left in the centre, with openings on every part, from twenty to thirty feet. The entrance to them all is by a door about five feet in height, by two feet and an half in breadth. Some of these have no other light but from the door, while others seem to have had a small light from above, through an hole of a pyramidical form. Many of these apartments have an elevated part that runs all round the wall, being a part of the rock left for that purpofe. The moveables found in these apart"ments confift chiedy in Etruscan vases of various forms; in several 1

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indeed have been found fome plain sarcophagi of stone with bones in them. The whole of these apartments are stucco'd, and or. namented in various manners : some indeed are plain ;. but others, particularly three, are richly adorned; having a double Jow of Etruscan inscriptions running round the upper parts of the walls, and under it a kind of frieze of figures in painting : some have an ornament under the figures, that seem to fupply the place of an architrave. There have been no relievos in Itucco hitherto discovered. The paintings seem to be in fresco, and are in general in the same stile as those which are usually feen on the Etruscan vases : though some of them are much superior perhaps to any thing as yet seen of the Etruscan art in painting. The paintings, though in general flight, are well conceived, and prove that the artist was capable of producing things more studied and more finished: though in such a subterranean fituation, almost void of light, where the delicacy of a finished work would have been in a great measure thrown away; these artists (as the Romans did in their best ages, when employed in such sepulchral works) have in general contented themselves with slightly expressing their thoughts. But among the immense number of thofe fubterranean apartments which are yet unopened, it is to all appearance very probable that many and valuable paintings and inscriptions may be discovered, fufficient to form a very entertaining, and perhaps a very useful, work: a work which would doubtless intereft all the learned and curious world, not only as it may bring to light (if fuccefs attends this undertaking) many works of art, in times of such early and remote antiquity, but as perhaps it may also be the occasion of making some considerable discoveries in the history of a nation, in itself very great, though, to the regret of all the learned world, at present almost unknown. This great scene of antiquities is almost entirely unknown even in Italy. Mr. Jenkins, now resident at Rome, is the first and only Englishman who ever visited it. Art., 28. Observations on two ancient Roman Inferiptions discovered

at Netherby in Cumberland. By the Rev. Dr. Taylor. The first of the inscriptions here specified, was discovered in the beginning of the present century; the other in the year 1762. They both make mention of Marcus Aurelius Salvius, Tribune of the Cohors prima Ælia Hispanorum Milliaria Equitata. Art. 34. Roman Inscriptions at Tunis in Africa, copied about the

year 1730. By Dr. Carilos, a native of Madrid, then Physician to the Dey of Tunis. Of these inscriptions it is impoffible to give any abstract.

Art. 45.

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