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indeed no other than the lever, or at least may be reduced to it, by considering the center of the wheel as the fulcrum, while two opposite radii, one of the wheel and the other of the axis, constitute the longer and shorter arms of the lever; and as these radii are the respective distances of the power and weight from the common center of motion, or fulcrum, the power and weight are to each other inversely as these radii or distances from the fulcrum; as was shown to be the case in the lever.

It is usual to combine a multiplicity of wheels together in various machines, such as clocks, watches, &c. and the power of the whole combination may be computed from the proportion given above. If, for example, the teeth of a wheel, which are in number sixty round the circumference, drive the wings or pinions of an axis, which are only six in number; it is evident that the wheel must move with one tenth of the velocity of the axis; or that the second axis must move ten times as fast as the first wheel, and therefore will raise ten times the weight of the power, supposing the weight raised to be applied to an axle of the same diameter; but if the cord that raised the weight were wound round an axle of only one fourth of the diameter supposed above; one pound applied to the circumference of the first wheel would raise forty pounds applied to the axis of the second: and so for any number of teeth in any combination of wheels, and any diameters of the wheels and axles.

THE INCLINED PLANE AND WEDGE.

The inclined plane is a machine for raising weights by being rolled up the plane. By this machine a considerable part of the weight is supported, while the

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remainder is drawn or pushed up by the power. To know when there will be an equilibrium between the power and the weight, we must consider the velocities of each, or the spaces, that are passed over by each in the same time. Now, it is plain, that when the weight has been rolled up the whole length of the plane, and the power, connected with it by a cord, has descended the same distance, the weight is only advanced, in perpendicular altitude, the height of the plane, while the power has descended through a space equal to the length of the plane. These spaces therefore passed over in the same time are the measures of their respective velocities. Hence, as there will be an equilibrium between the power and the weight, when they are to one another inversely as their respective velocities; the power sufficient to sustain a weight on any inclined plane, will be to that weight, as the height or perpendicular altitude of the plane is to the length of the plane: e. g. If the length of the plane be ten times its height, then a power of ten pounds is sufficient to sustain one of a hundred on such a plane.

THE WEDGE.

The wedge is no other than two inelined planes joined together; and is used for splitting timber, or raising weights, by being driven under them by a stroke, whose momentum is here called the power, while the resistance of the timber, or the gravity of the body to be raised is called the weight. When it is therefore put under any weight, the force with which the wedge will lift that weight, when driven under it, by a blow on the end, will bear the same proportion to the force, wherewith the blow would act on the weight, if directly applied to it, as the velocity which the wedge receives from the blow, bears to the velo

eity, wherewith the weight is lifted by the wedge. Therefore the power is to the weight, as half the thickness of the wedge is to its length.

THE SCREW.

The screw is also applied for raising weights, by pressing upon them, when fixed in a frame; and while the power which is applied to the handle of the screw passes over the circumference of the circle in which it moves, the weight is raised only the distance between two contiguous threads of the screw, and these distances are proportional to their respective velocities. Therefore the power is to the weight, as the distance between two contiguous threads of the screw is to the circumference of the circle described by the power in one revolution. For they are to one another inversely as their velocities.

These are all the simple mechanic powers, and of these are all the machines in the world composed, by such various combinations, as may best answer the intention of the artist.

Instead of raising weights, the design of the artist is sometimes only to cause some light body, whose gravity is not regarded, to move with a certain determinate velocity, such as in clocks and watches, orreries, &c. which are usually constructed with wheels, whose circumferences are divided into a certain number of teeth playing in the pinions on the axle of another wheel; so that by the proper adjustment of the number of the teeth and pinions the velocity of the wheels, with respect to one another, may be increased or diminished in any proportion.

These may be easily computed by the proportions above laid down.

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What we have said, in our explanation of the effect of these simple mechanic powers, proceeds upon the supposition, that the parts of the machine suffer no retardation in their motions, by friction, or the rubbing of one part upon another. But great allowances must be made on this account, as it generally destroys one third part of the effect of those machines, that are designed for raising weights. This friction is always in proportion to the weight of the parts of the machine that move on others, and to the velocity of their motion. Now it is of great consequence in the construction of machines, that the parts be as well polished and smooth as the nature of the materials will admit of; and that the velocity of the parts that rub on others, be as much diminished as possible. The friction of the end of an axle is much lessened, by inserting a gudgeon in the end, that it may revolve on this; as the velocity of the rubbing parts is diminished in the proportion of the diameter of the axle, to the diameter of the gudgeon. And the velocity may be still farther lessened, by laying the gudgeon on the circumferences of two wheels, which are carried round by the gudgeon, without any friction, but what arises from the slow motion of the axes of these friction wheels.

Hence we see the reason of laying a heavy body on wheels or rollers, that it may be transported from place to place, with little friction, while the wheel or roller sustains the weight. Wheel carriages meet with less resistance than any other kind of carriages, from the inequalities of the road. The larger that the wheels are, so much easier is the draught, until the radius becomes equal to the height of the horse's breast. The larger that a wheel is, at so much the greater

distance from the point of contact between the wheel and the ground will it reach an obstacle, over which the load is to be drawn, and thereby affords the advantage of an inclined plane of a greater length, for raising the weight over the obstacle. Besides this, the larger wheels have less friction on their axes, because their velocity is less, than that of small wheels, in passing over any given distance, in a given time. And small wheels sink deeper in a soft road, than larger wheels, and thereby increase the difficulty of transportation. Hence a carriage of four large wheels is drawn with less force, than one of two large and two small wheels. And a carriage with unequal wheels is drawn with less force, when the load is laid on the axis of the larger wheels, than when laid on the axis of the lesser. But these advantages of larger wheels are in some measure counterbalanced by the difficulty of turning in a small and narrow compass. Hence carriages are generally constructed with unequal wheels. And this construction has this farther advantage, that the line of traction through the axis inclines to the horizon before the horses and below their breasts, so that in drawing they in some measure lift the load over any obstacle, while a contrary inclination would press the load into the earth and increase the difficulty of drawing it along.

OF COMPOUND MACHINES.

In a combination of levers, the power will sustain the weight, when the power is to the weight, as the product of all the distances of the weight from the fulcra is to the product of all the distances of the power from the fulcra; or as the product of all the shorter ends of the levers, is to the product of all the

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