418

HISTORY OK ENGINEERING.

Rook I.

4 s 6 7 s 9 ib

Fig.419-

O, and the other part of the beam cut off, they wouldthen hang in equilibrio, that is, n and r would be equal.

Rut if the other part of the beam was to be added, andthe weight n was carried on the beam as far as thenumber 10, and suppose the weight was but one poundeach, then I say that the weight r must have 9 poundsadded to it to make it balance the weight n, when re-moved so far from the centre. But here it is necessaryto observe, that in making these instruments, the weightthat is occasioned by the length of the beam is alwaysaccounted for before they begin to divide, and it is veryeasy to discover what weight did belong to a pair ofsteelyards, supposing it to be lost, by taking the dis-tance between the centres of the hooks, that is, betweenO and r, and apply it to the proper edge, and the di-vision there will tell you what the weight should be,for it is that distance multiplied into the whole length, as you may sec in the figure. Buthere in this present case the beam is only imaginary, for it is the distance from the centrethat occasions all those different gravitations, for if we suppose the circle a, b, c, tf, to be awheel, and o its centre, and a weight of one pound to be fixed at its periphery at b, and thewheel to be turned round, the weight when it is got to a will be 3 pounds, and at z 5 pounds,and the gravitation of such a weight will increase in the same proportion as if it was carriedalong the beam e, as you may see by the divisions. By this useful instrument may also bediscovered the power of the lever, from a perpendicular to a horizontal position, and mayvery justly be called a scale, to measure all mechanical pow'ers that act from centres, aminotwithstanding our present subject be two levers set up one against another, yet I believethe next figure will make it appear very plain that they also depend on the same theory,and are subject to the same laws of gravitation. For as the two levers a,a, in the figure G,support one another at the top, and prevent their falling or acting like levers, yet I conceivethat gravity w'ill act on the bottoms, when the friction is taken off by wdiccls, in the sameproportion as if they were turned end to end, according to the left hand side of the figure Gwhen turned upside down, that is, to put the confined end downwards, and let the upperends fall one from the other : I say, in the fall of such a lever, the gravitation would beincreased in the same proportion as is there set down, for if the lever a, by falling from theperpendicular line G, should have gained a force of 1 pound, it would at e have gained3 pounds, at z 5 pounds, and so on in proportion, as was gained by the weight at the peri-phery of the wheel in figure E, until it becomes horizontal. In the same proportion Iconceive gravity to act at the bottom of the two levers, a,a, that is, if at a they should wantan abutment of 1 pound at each foot to keep them in their position, at e they would want3, and at z 5, and so on in the same proportion, as they are set down in the righthand side of the figure G, until they become so far extended, as to lie level on the plane theymoved on : from wdiat has been demonstrated from figure G, it is plain that gravity acts onpediments, according as their sides are elevated or depressed ; and if so, it must certainlyact on all arches in the same proportion, as their inscribed pediments are to one another inrespect to their height. And from hence may be discovered how much weight one archwill bear more than another that is the same width, and hath the same abutments to supportit; that is, if the lower arch D will bear500 pounds weight, the arch a will bear600, and the arch b 700, and so on ac-cording to what height you rise maythe weight be increased, which willalways be in proportion, as the sidesof the inscribed pediments are to oneanother, when their chord lines orwidths are the same. NotwithstandingI have given this method to show how , .much one arch will bear more than [Oanother of the same width and abut-ment, yet I do not pretend to know Fig - 42 °*

how much weight any arch will bear, for there is no arch that I know of that can be saidto bear all the weight that is built perpendicularly over it, because that part hath commu-nication with the rest of the building, and cemented to it in such a manner, that takes off aconsiderable part of the weight that would otherwise press upon it if that communicationwas destroyed; and I may venture to say, that it is from this reason that arches some-times become so loose, that their keystones are almost ready to drop for want of sufficientweight to keep their parts together. From this observation it is plain that all arches want