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femblance to the cafe wherein two moving bodies stop 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 faying, That, fince one body cannot produce in another a quantity of motion equal to its own, without lofing its own at the fame time; two heavy bodies, counteracting each other by means of a machine, muft continue at reft, when they are fo circumstanced that one cannot defcend, without caufing the other to afcend at the fame time, and with the fame quantity of motion; and therefore two heavy bodies in fuch cafes, muft always counterbalance each other. Now, this argument would be a just one, if it could properly be faid, that the motion of the afcending body was produced by that of the defcending one: but, fince the bodies are fo connected, that one cannot poffibly begin to move before the other, I apprehend, that if the bodies are fuppofed to move, it cannot be faid that the motion of one is produced by that of the other: fince, whatever force is fuppofed to move one, it must be the immediate caufe of motion in the other also ; that is, both their motions must be fimultaneous effects of the fame cause, just as if the two bodies were really but one. And therefore, if I was to fuppofe, in this cafe, that the fuperior weight of the heavier body (which may be in itself much more than able to sustain the lighter) fhould 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 abfurdity 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 thofe who argue from the equality of motions on this occafion fay further, that, fince the two bodies must have equal motions when they do move, they must have equal endeavours to move, even whilft they are at reft, and therefore thefe endeavours to move, being equal and contrary, muft deftroy each other, and the bodies must continue at reft, and confequently ballance each other. In anfwer to this I muft obferve, that the abfolute force with which a heavy body endeavours to defcend from a ftate of reft, can only be proportionable to its weight; and therefore I think it is neceflary that fome caufe fhould be affigned why (for inftance) the endeavour of one pound to descend, fhall be equal to that of four pounds; and efpecially as the fulcrum on which both weights act, requires no greater force to fupport it than that of five pounds.

From thefe confiderations I infer, that the reafon why very unequal weights may ballance each other, fhould be affigned not from their having equal momenta when made to move together,

· but

but by proving a priori, without confidering their motions, that either the reaction of the fixed parts of the machine, or fome other cause, so far takes off from the weight of the heavier body, as to leave it only juft able to fupport the lighter.'

The Doctor proceeds next to the examination of the methods which Archimedes, Huygens, Sir Ifaac Newton, and Mac Laurin, have taken to demonftrate 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 refpects defective.

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

If a force, fays he, be uniformly diffufed over a right line; that is, if an equal part of the force acts upon every point of the line, and if the whole force acts accordingly to one and the fame plane; this force will be fuftained, and the line kept in equilibrio, by a fingle force applied to the middle point of the line, equal to the diffufed force, and acting in a contrary direction.'

To this poftulatum the Doctor adds, by way of lemma, that If a right line be divided into two fegments, the distances between the middle of the whole line, and the middle points of the fegments, will be inverfely as the fegments. This is felf-evident when the fegments are equal; and, when they are unequal, then, fince half of the whole line is equal to half of the greater and half of the leffer fegment, it is plain that the distance between the middle of the whole line and the middle of one fegment, must be equal to half of the other fegment, fo that thele diftances must be to each other inverfely as the fegments.'

Hence the Doctor goes on to prove, that of three weights or forces, any two of which are (by the conftruction) to each other inverfely as their diftances from the third, will fuftain each other, and keep the line on which they act in equilibrio,

This is the first and most fimple cafe of the property of the lever; the Doctor proceeds, however, to explain fome others deducible from it; as alfo to mention fome well-known truths in Mechanics; which, he thinks, cannot be proved otherwife, than by deducing them from what he here demonfirates.

Art. 29. A Method of !ffening the Quantity of Frittion in Engines, By Keane Fitzgerald, Efq;

The method here defcribed, is the common one of Friction Wheels; by means of which, with another additional improvement, we are told, the fire-engine at York-building Water

works,

works, is now made to perform the fame fervice 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 fo well known, and may be of use in other cafes as well as in that to which it is here applied.

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 fuch beam; fo that, tho' it will remain in an horizontal pofition when fo placed and equally balanced, yet when it is made to incline to either fide, it will continue to move on that fide till it becomes parallel to the horizon, with the center of motion above the beam: for when either end is depreffed in the leaft degree, it becomes more diftant from the center of gravity*; and the oppofite end, which is raised in proportion, is brought nearer to it, although both ends ftill continue equidiftant 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 cafe in the engine above-mentioned; whofe lever, with its arch-heads, weighed about ten tons; the upper edge of it being about two feet nine inches above the center 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 refiftance from friction in the pivots; yet, when either end was depreffed four feet below the level, it required 534 pounds to be applied to the oppofite 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 fo much changed by the pofition 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 obferves, that the lever, which before required a power of ninety-five pounds to overcome the leaft refiftance from friction, was as eafily effected by the application of three quarters of a pound; and the refiftance from friction occafioned by a weight of fix tons, is of fo little confequence, that the lever may be fwung with a flight thread, and will continue in a state of vibration for feveral minutes after.'

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

The

The visible effect, continues this Writer, with regard to the working of the engine, according to the most exact obfervations by different perfons, both before and after thefe feveral alterations were made, is, that it now makes eighteen strokes, at eight feet per stroke, for fifteen that it ever made before, with the fame, or rather a fmaller, quantity of fuel; and must therefore discharge one-fixth more water in equal time; which confequently faves one-fixth of the fuel. But the effect is found ftill greater, as to fupplying the tenants with water: the engine performing a greater service in this refpect in the proportion first mentioned. Some part of this effect, 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 fenfible and useful article, well worthy the careful perufal of all fuch as are concerned in the erection of fixed mechanical engines of any kind whatever.

ANTIQUITIES.

Art. 26. An account of fome fubterraneous apartments with Etrufcan infcriptions and paintings, difcovered at Civita Turchino, "in Italy. By J. Wilcox Efquire.

• Civita Turchino, about three miles to the north of Corneto, is an hill of an oblong form, the fummit of which is almoft one continued plain. From the quantities of medals, intaglios, fragments of infcriptions, &c. that are occafionally found here, this is believed to be the very spot, where the powerful and moft ancient city of Tarquinii once ftood: though at prefent it is only one continued field of corn. On the fouth-eaft fide 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 feveral hundreds of artificial hillocks, which are called, by the inhabitants, Monti Roffi. About twelve of thefe hillocks have at different times been opened; and in every one of them have been found feveral fubterranean apartments cut out of the folid rock. These apartments are of various forms and dimenfions: fome confift of a large outer room, and a fmall one within; others of a small room at the first entrance, and a larger one within; others are fupported 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 feem to have had a fmall light from above, through an hole of a pyramidical form. Many of thefe 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 thefe apartments confift chiefly in Etrufcan vafes of various forms; in several

I

indeed

indeed have been found some plain sarcophagi of stone with bones in them. The whole of thefe apartments are stucco'd, and ornamented in various manners: fome indeed are plain; but others, particularly three, are richly adorned; having a double Iow of Etrufcan infcriptions running round the upper parts of the walls, and under it a kind of frieze of figures in painting: fome have an ornament under the figures, that feem to supply the place of an architrave. There have been no relievos in ftucco hitherto difcovered. The paintings feem to be in frefco, and are in general in the fame ftile as thofe which are usually seen on the Etrufcan vafes: though fome of them are much fuperior perhaps to any thing as yet feen of the Etrufcan art in painting. The paintings, though in general flight, are well conceived, and prove that the artift was capable of producing things more ftudied and more finifhed: though in fuch a fubterranean 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 beft ages, when employed in fuch fepulchral works) have in general contented themselves with flightly expreffing their thoughts. But among the immenfe number of thofe fubterranean apartments which are yet unopened, it is to all appearance very probable that many and valuable paintings and infcriptions may be difcovered, 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 fuch early and remote antiquity, but as perhaps, it may also be the occafion of making fome confiderable difcoveries in the hiftory of a nation, in itfelf very great, though, to the regret of all the learned world, at prefent almost unknown. This great fcene of antiquities is almost entirely unknown even in Italy. Mr. Jenkins, now refident at Rome, is the first and only Englishman who ever vifited it.

Art. 28. Obfervations on two ancient Roman Inferiptions discovered at Netherby in Cumberland. By the Rev. Dr. Taylor.

The first of the infcriptions here specified, was discovered in the beginning of the prefent century; the other in the year 1762. They both make mention of Marcus Aurelius Salvius, Tribune of the Cohors prima Ælia Hifpanorum Milliaria Equitata.

Art. 34. Roman Inferiptions at Tunis in Africa, copied about the year 1730. By Dr. Carilos, a native of Madrid, then Phyfician to the Dey of Tunis.

Of these inscriptions it is impoffible to give any abstract.

Art. 45.

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