1, it would be fuftained by one ounce, hanging freely, as in the former inftance.

Hence, in drawing a cart or waggon up hill, if the power of the horses be proportioned to the weight of the waggon, as the height of the hill is to it's fide, the waggon will not run back, and a little additional power will draw it up hill.

OF THE WEDGE.

The wedge is the next mechanical power. Thofe among you who have feen men cleave wood, cannot be at a lofs to know that the wedge is a piece of wood or iron, thin at one end, and thick at the back. The thin end is applied to the timber to be cleft, and the thick end ftruck upon by an hammer.

Mathematicians have long debated concerning the true theory of the wedge. Hamilton, s'Gravefand, Defaguliers, &c. affert that the power is to the refiftance, as half the back to the height. Keil, Whifton, Nicholfon, &c. fay, that it is as the whole of the back to the height.

There are many natural obftructions to a complete theory of the wedge: among thefe arc to be reckoned the friction, the elafticity, and tenacity of the materials. Indeed the theory thereof will probably remain for a long time a matter of ufelefs fpeculation, fince it is connected with a part of physical knowledge of which we are at prefent wholly ignorant; I mean the nature and force of adhefion in bodies, their tenacity, and the flexibility of the fibres. All thefe circumftances, with many others, fhew, that the experiments where preffure is ufed as a power, cannot be adduced as illuftrating the theory of this machine: for a wedge, when laden with a vaft weight, will have fcarce

any

any effect in cleaving wood; whereas a blow upon the head of the wedge,will drive it easily into a hard body, Percuffion puts all the parts of the wood into a tremulous motion; which, by difuniting them, leffens the stickage, and thereby facilitates the motion of the wedge. It has been alfo thought, that the motion communicated to the materials may, in fome degree, contribute to the force of the wedge.

I fhould therefore fay no more on the fubject of the wedge, if it were not neceffary to explain to you that part of your mechanical apparatus which is conftructed to prove the effects of the wedge. You must however perceive, from what I have juft now mentioned, that this part of the apparatus cannot be adequate to the establishing any theory. Experiments made therewith will fhew the power of the wedge, according to the hypothefis of the maker, but bear very little femblance to the na

tural action thereof.

The two pieces of brafs EH and GH, fig. 4, pl. 5, are joined at H, H by a hinge, and are drawn together by the threads h i, fg, going over the pullies i and g, having weights at the lower end of the cords. If a light wedge be drawn into this frame, by means of the weight 1, hanging at the cord de D, fastened to the wedge, and going over the pulley e; if the weight L be in the fame proportion to the weights R, I, as the half back of the wedge is to either of it's fides, the weight which acts as a power for making the wedge go into the frame, will ballance the weight which pulls the fide of the cleft, as a refiftance against the fides of the wedge.

Thus fixteen ounces on each fide will balJance, or be equal to eight ounces of power at the back of the wedge, when the back is equal to the fides.

But when the back is only half the length of

one

one of the fides, four ounces of power will be equal to fixteen ounces of refiftance on each fide.

Fig. 5, pl. 4, is another apparatus for illuftrating the nature of the wedge. IK LM, and LMNO, are two flat picces of brafs joined together by a hinge at LM; P is a graduated arch of brafs, on which the faid pieces of wood may be opened to any angle not exceeding fixty degrees, and then fixed at the given angle by means of the two fcrews a b; IK NŎ reprefents the back of the wedge, and IKLM, LMNO the two fides of the wedge against which the wood acts in cleaving. By means of the arch P, the wedge may be fo opened, as to adjust the thicknefs of the back in any proportion to the length of either of it's fides, but not to exceed that length; and any weight, as , may be hung to the wedge from the hook at the bottom thereof, which weight, together with that of the wedge, is the impelling power. A B, and CD, are two cylinders, to the edges whereof two flat plates are fitted, to prevent the wedge from flipping off edgeways from between them. A fmall cord goes over the pivot at the end of each cylinder; the cords S, T, belonging to the cylinder A B, go over the fixed pullies W and X, and are faftened at the other end to the bar w x, on which any weight, z, may be hung. In like manner the cords R,Q, from the cylinder DC, go over the fixed pullies uv to the bar vn, from which a weight Y, equal to Z, may be hung. These weights, by drawing the cylinder towards one another, are to be confidered as the refiftance of the wood acting equally against the oppofite fides of the wedge. The cylinders move on two bars, which are fupported by the pillars E, F, G, H, when the back of the wedge is of the fame length as either of the fides. The wedge with a weight p, fufficient to make it equal to forty ounces, will be in equilibrio against

forty

forty ounces hanging at the lines belonging to each cylinder. If the back of the wedge be only half the length of the fides, it will be in equilibrio with eighty ounces at each cylinder.

To the wedge are referred the axe or hatchet, the fpade, chiffels, needles, &c. in a word, all kinds. of inftruments which, beginning from edges or points, grow gradually thicker. A faw is a number of chiffels fixed in a line; a knife may be confidered as a chiffel, when employed in fplitting; but if attention be paid to the edge, it is found to be a fine faw, as is clear from it's producing a much greater effect by a drawing stroke, than would have followed from a direct action of the edge.

One confiderable ufe of the wedge, is the raifing up the beam of a houfe, to underprop it, when a floor begins to give way, by reafon of too great a burden laid upon it; and fo much force may be applied in this way, that fome thoufand tons may be raised together with the floor, and all fecured by means of this fmall machine, which for this purpofe is more convenient than either the fcrew or the lever.

OF THE SCREW.

The mechanic power that next prefents itself for our confideration, is the fcrew; a machine of great efficacy in raifing weights, or preffing bodies clofe together.

The fcrew confifts of two parts; the firft is called the male, or outfide fcrew, being cut in fuch. manner as to have a prominent part going round the cylinder in a spiral manner, which prominent part is called the thread of the fcrew; the other part, which is called the female, or infide fcrew, is a folid body, containing an hollow cylinder, whofe

concave surface is cut in the fame manner as the convex furface of the male fcrew, fo that the prominent parts of the one may fit the concave parts

of the other.

One part is commonly fixed, whilft the other is turned round; and in each revolution the moveable part is carried, in the direction of the cylinder, through a space equal in length to the interval between two contiguous threads; whereby the body to be moved is carried through a fpace equal to that interval, which therefore expreffes the vclocity of the weight or refiftance, while the circumference, which is defcribed by the power whereby the moveable part of the screw is turned round, expreffes the velocity of the power.

You may conceive how the fcrew is made, by cutting a piece of paper into the form of an inclined plane, and then wrapping it round a cylinder. The inclined plane, rifing round the cylinder in a spiral manner, forms what is called the threads of the fcrew. Now it is evident, that the fcrew must be turned once round, before the resistance can be moved from one spiral winding ta another.

A ferew is feldom ufed without the applicacation of a lever to affift in turning it; confequently, as much as the circumference of a circle defcribed by this handle or winch, is greater than the intervals or distance between the fpirals, fo much is the force of the screw.

Thus, fuppofing the diftance between the fpirals to be half an inch, and the length of the winch to be twelve inches, the circle defcribed by the handle of the winch, where the power acts, is nearly 76 inches, or 152 half inches, and confequently 152 times as great as the distances between the fpirals; and therefore a power at the handles, where the power acts, of no inore than one pound,