round. Then if the circumference of the circle defcribed by the handle of the winch A be equal to the circumference of a groove round the wheel D, the velocity of the handle will be 48 times as great as the velocity of any given point in the groove; confequently, if a line G goes round the groove D, and has a weight of 48 pounds fufpended from it, below the pedestal E F, a power equal to one pound at the handle will fupport this weight; or, if a groove be made in the wheel C, equal in radius to the circle defcribed by the handle, the weight H of one pound, suspended therefrom by a line in the groove, will balance the 48 pounds, as before. If the line G, instead of going round the groove of the wheel D, go round its axle I, the power of the machine will be as much increased, as the circumference of the groové exceeds that of the axle, as fhewn under the wheel and axle. And if a fyftem of pullies were applied to the cord H, the power could be increased to an amazing excefs.

The ufes to which the screw is applied are various; it is chiefly used for preffing bodies clofe together, as the preffes for bookbinders, packers, hot-preffers, &c.

The friction in the fcrew is very confiderable, as it is alfo in the wedge, which generally requires a third part more of the power to work them when loaded, than what is fufficient to conftitute a balance between the weight and power.

If machines or engines could be made without friction, the leaft degree of power above what is fufficient to balance the weight, would be sufficient to raise it. In the lever the friction is little or nothing: in the wheel and axle it is but fmall in pullies it is confiderable: and in the inclined plane, wedge, and fcrew, it is very great.

Wood greafed, or metal oiled, have nearly the fame friction; and the fmoother they are, the lefs is their friction, provided they be not too highly polished. In polished steel moving upon polished fteel or pewter, the friction is about a

fourth

fourth part of the weight, on copper a fifth part, and on brass a fixth part of the weight: iron or steel running in brass has the least friction of any. And metals of the same fort have more friction than different forts; and in general the friction increases in the fame proportion with the weight, but is greater with a greater velocity.

The friction in pullies is now almost reduced to nothing, by the contrivance of Mr. Garnett, in his patent friction rollers, which produce a great faving of labour and expense, as well as wear of the materials, both when applied to pullies and the axles, of wheel-carriages. By this contrivance, there is a hollow space left between the nave and axle, or centre and pin-box, which is filled up by folid equal rollers, nearly touching each other, and furnished with axles, each of which is inferted into a circular ring at each end, by which their relative distances are preferved; and they are kept parallel by means of wires fastened to the rings between the rollers, and to which the wires are rivetted.

It is a general property in all the mechanic powers, that when the weight and power balance each other, if they be put in motion, the power and weight will be to each other reciprocally as the velocities of their motion; or the power is to the weight as the velocity of the weight is to the velocity of the power; fo that their two momenta are equal: viz.-The product of the power, multiplied by its velocity, is equal to the product of the weight multiplied by its velocity. And hence the general rule: viz. That what is gained in power is loft in time. For the weight moves as much flower as the power is lefs.

VOL. I

SECT.

SECT. II.

OF THE APPLICATION OF THE POWERS TO MILLS AND MACHINES.

In order to discover the properties of any machine confifting of the mechanical powers, it is neceffary to confider the weight that is to be raised, or the refiftance to be overcome; and alfo the power required to raise the weight, or overcome the refiftance. For this purpose, there are two principal problems, the refolution of which is requifite to fhow the powers of any engine.-The first problem is, T determine the proportion that the power and weight ought to have to each other, that they may be in the just equilibrium.— The fecond is, To determine what the proportion Should be between the power and weight, that the machine may produce the greatest effect in a given time.

The first problem is folved by this general rule, viz.— That the power and weight fuftain each other, or are in equilibrium, when the power and weight are reciprocally proportional to the distances of the directions in which they act from the centre of motion; or when the product of the power multiplied by the distance of its direction is equal to the product of the weight multiplied by the distance of its direction. This is the proportion of the weight and power when they are in equilibrium, fo that the one would not prevail over the other if the engine were at reft; and if it be fet in motion, it would continue to proceed uniformly if there were no friction of its parts and other refiftances. And in

general

general the effect of any power or force is as the product of that force multiplied by the diftance of its direction from the centre of motion; or the product of the power, and its velocity when in motion, for the velocity is proportional to the distance from that centre.

The fecond general problem in Mechanics, is of the greatest importance, though it has been little attended to by mechanical writers, viz.-To determine the proportion between the power and weight, fo that when the power prevails, and the machine is in motion, the greatest effect poffible may be produced by it in a given time. When the power is only a little greater than what is fufficient to fuftain the weight, the motion is ufually too flow; and though a greater weight be raifed in this cafe, it is not fufficient to compenfate for the lofs of time. And when the power is much greater than what is fufficient to fuftain the weight, the weight is raifed in lefs time; but it often happens, that this is not fufficient to compenfate for the lofs which arifes from the load being reduced; therefore, the only general rule that can be given is, to find when the product of the weight, multiplied by its velocity, is the greatest; for this product measures the effect of the machine in a given time, which is always greater in proportion as both the weight and velocity are greater.

In the construction of compound machines, where it is neceffary to alter the direction of the motion, recourse must be had to what is called bevel geer, the principle of which is as follows:

Let A and B (fig. 15) be two cones revolving on their centres a c and a b; if their bases be equal, they will each perform their revolution in the fame time; and any two points in each cone equally distant from the centre, as d 1, d 2, 3, &c. will revolve in the fame time as f 1, f 2, f 3, &c. refpectively. But if one cone be twice the diameter of the other, as the cone a d e (fig. 20), which is twice the diameter of the cone fa d, then as they turn upon their centres,

002

centres, when the cone a fd has made one revolution, the cone a de will have made but half a revolution, and every part in each cone, equally distant from the centre a, will have the fame proportion in their revolutions to each other, as f 1, f 2, f 3, &c. will have made two revolutions to the points e 1, e 2, e 3, &c. for one revolution of the other cone refpectively, &c. Now, if the cones are fluted, or have teeth cut in them, diverging from the centre a to the bases de, df (fig. 16), they would then become bevel geer. The teeth at the point of the cone being small, and of little use, may be cut off; or, inftead of the two cones, may be used two fhafts, with bevel wheels fixed to them, as the shaft a b (fig. 18), with the bevel wheel c d, which turns the bevel wheel e f, with its fhaft b g, and the teeth work freely into each other, as in figure 16. The teeth may be made of any dimenfions, according to the strength required, and by this means a motion may be communicated in any direction, or to any part of a building, with very little trouble and friction.

The method of constructing the wheels for any proportion, is as follows:-Draw the line a b (fig. 21) to represent a fhaft of a wheel; draw the line e d to interfect the line a b, in the direction that the motion is to be conveyed, and the line e d will represent the other fhaft of the motion.

Then suppose the shaft e d is to revolve three times in the time that the fhaft a b revolves once; draw the parallel line ii at any distance, from a scale (fuppofe one foot); then draw the other parallel line k k at three feet distance; after which, draw the line w x through the interfections of the two fhafts a b and ed, and likewife through the intersections of the two parallel lines ii and kk, in the points xy, which will be the pitch line of the two bevel wheels, or the lines where the teeth of the two wheels act on each other, as may be feen in figure 19, where there are three wheels.

Where it is required to communicate a continued uniform motion, and where the angle does not exceed 40 degrees,

and