Vhen the wood cleaves at any distance before the wedge (as it generally does) the power impelling the wedge will not be to the resistance of the wood as the length on the back of the wedge is to the length of both its sides, but as half the length of the back is to the length of ei ther side of the cleft, estimated from the top or acting part of the wedge. For, if we suppose the wedge to be lengthened down fl'011Ithe top CE, to the bottom of the cleft at D, the same proportion will hold ; namely, that the power will be to the re sistance as half the length of the back of the wedge is to the length of either of its sides : or, which amounts to the same thing, as the whole length of the back is to the length of both the sides. The wedge is a very great mechanical power, since not only wood, but even rocks, can .
be split by it ; which it would be impossi ble to effect by the lever, wheel, and axle, or pulley ; for the force of the blow, or stroke, shakes the cohering parts, and thereby makes them separate more ea sily.
The sixth and last mechanical power is the screw ; which cannot properly be called a simple machine, because it is ne ver used without the application of a le ver or winch to assist in turning it ; and then it becomes a compound engine of a very great force, either in pressing the parts of bodies closer together, or in rais ing great weights. It may be conceived to be made by cutting a piece of paper, ABC (fig. 23.) into the form of an inclin ed plane or half wedge ; and then wrap ping it round a cylinder (fig. 24.) the edge of the paper AC, will form a spiral line round the cylinder, which will give the thread of the screw. It being evident that the winch must turn the cylinder once round, before the weight of resist. ance can be moved from one spiral wind. ing to another, as from d to c ; therefore, as much as the circumference of a circle described by the handle of the winch is greater than the interval or distance be tween the spirals, so much is the force of the screw. Thus, supposing the distance of the spirals to be half an inch, and the length of the winch twelve inches, the circle described by the handle of the winch where the power acts, will be 76 inches nearly, or about 152 half inches ; and consequently 152 times as great as the distance between the spirals ; and therefore a power at the handle, whose intensity is equal to no more than a single pound, will balance 152 pounds acting against the screw ; and as much additional force as is sufficient to overcome the friction, will raise the 152 pounds ; and the velocity of the power will be to the velocity of the weight as 152 to 1. Hence it appears, that the longer the winch is, and the nearer the spirals are to one ano ther, so much the greater is the force of the screw.
A machine for skewing the force or power. of the screw may be contrived in the following manner : let the wheel C have ar screw (fig. 25.) on its axis, work ing in the teeth of the wheel 1), which suppose to be 48 in number. It is plain, that for every time the wheel C and screw are turned round by the winch A, the wheel D will be moved one tooth by the screw ; and therefore, in 48 revolutions of the winch, the wheel D will be turned once round. Then, if the circumference of a circle, described by the handle of the winch A, be equal to the circumference of a groove round the wheel D, the velo city of the handle will be 48 times as great as the velocity of any given point in the groove. Consequently, if a line G goes
round the groove, and has a weight of 48 pounds hung to it, a power equal to 1 pound at the handle will balance and sup port the weight. To prove this by expe riment, let the circumferences of the grooves of the wheels C and D be equal to one another ; and then if a weight II, of one pound, be suspended by a line go ing round the groove of the wheel C, it will balance a weight of 4.8 pounds hang ing by the line G ; and a small addition to the weight 11 will cause it to descend, and so raise up the other weight.
If a line G, instead of going round the groove of the wheel I), goes round its axle 1, the power of the machine will be As much increased as the circumference of the groove exceeds the circumference of the axle : which. supposing it to be six times, then one pound at ft will balance six times 43, or 288 pounds, hung to the line on the axle : and hence the power or advantage of this machine will be as 283 to 1. That is to say, a man, who by his natural strength could lift an hundred weight, will be able to raise 288 cwts. by this engine. If a system of pales were applied to the cord II, the power would be increased to an amazing degree. When a screw acts in a wheel in this manner, it is called an endless screw. When it is not employed in turning a wheel, it consists of two parts : the first is called the male, or outside screw, being cut in such a manner as to have a prominent part going round the cylinder in a spiral manner ; which prominent part is called the thread of the screw ; the other. part, which is called the female, or inside screw, is a so lid body, containing a hollow cylinder, whose concave surface is cut in the same manner as the convex surface of the male screw, so that the prominent parts of the one may fit the concave parts or the other. A very considerable degree of friction always acts against the power in a screw ; but this is fully compensated by other advantages ; for on this account the screw continues to sustain a weight, even after the power is removed, or ceases to act, and presses upon the body against which it is driven. Hence the screw will sustain very great weights, insomuch, that several screws, properly applied, would Support a large building, whilst the foun dation was mending, or renewed.
The screw is of extensive use in the printing press, and in the press for coin tug money, and in a great variety of other purposes. It has lately been employed in the flour-mills in America, for pushing the flour which comes from the mill stones to the end of a long trough, from which it is conveyed to other parts of the .machinery, in order to undergo the re maining processes. In this case, the spi ral threads are very large in proportion to the cylinder on which they are fixed. As the lever used with the screw moves through a large space, when compared with the velocity of its other extremity, or of any body which it puts in motion ; the screw is of very great use in subdivid ing any space into a great number of minute parts. Hence it is employed in the engines for dividing mathematical in struments, &c. See Oscutaiatuv, Pz:sau LITM, SUSPENSION, &c.