PLATE VI.

A machine for showing the force or power of the screw may be contrived in the following Fig. 14. manner;-Let the wheel C have a screw ab on its axle, working in the teeth of the wheel D, which suppose to be 48 in number. It is plain, that for every time the wheel C and screw ab 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 the groove e 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, Consequently if a line G (above number 48), goes round the groove e, and has a weight of 48 pounds hung to it below the pedestal EF, a power equal to one pound at the handle will balance and support the weight.-To prove this by experiment, let the circumferences of the grooves of the wheels C and D be equal to one another; and then if a weight H of one pound be suspended by a line going round the groove of the wheel C, it will balance a weight of 48 pounds hanging by the line G; and a

screws, one of which moyes in the other, and has a thread fewer in an inch than the male screw of the one in which it moves. If we suppose the one screw A to have 20 threads in an inch, and the other B to have 21; and if the screw B be so fixed that it can move forwards without moving round; then one turn of A will make the screw B advance 1-21th x 1-20th or 1-420th of an inch. Thus the compound screw produces an effect much superior to the common one; for the latter must have 420 threads in an inch before it could produce an effect equal to the former, which would weaken it to such a degree that it would be unable to resist any considerable force. As it is impossible in the short compass of a note to convey an accurate account of this excellent improvement, we must refer the reader to the 71st vol. of the Philosophical Transactions, where it is described by the inventor.-E. ED.

small addition to the weight H' will cause it to descend, and so raise up the other weight.

If the line G, instead of going round the groove e of the wheel D, goes round its axle I, the power of the machine will be increased, in proportion to the circumference of the groove e above the circumference of the axle. Now, supposing this to be six times, then one pound at I will balance six time 48, or 288 pounds hung to the line on the axle: and hence the power or advantage of this machine will be as 288 to 1; that is to say, a man, who, by his natural strength, could lift a hundred weight, will be able to raise 288 hundred, or 14,8 ton weight by this engine.

nation of

But the following engine is still more power- PLATE ful, on account of its having the addition of VII. four pulleys; and in it we may look upon all the mechanical powers as combined together, even if we take in the balance. For, as the Fig. 1. axle D of the bar AB enters its middle at C, it is plain that if equal weights be suspended upon any two pins equi-distant from the axis C, they will counterpoise each other. It be- A combicomes a lever by hanging a small weight P all the me upon the pin n, and a weight as much heavier chanical upon either of the pins b, c, d, e, or f, as is in powers. proportion to the pins being so much nearer the axis. The wheel and axle HG is evident; so is the screw E, which takes in the inclined plane, and with it the half-wedge. Part of a cord goes round the axle, the rest under the lower pulleys K, m, over the upper pulleys L, n, and then it is tied to a hook at m in the lower or moveable block, on which the weight W hangs.

In this machine, if the wheel H have thirty teeth, it will be turned once round in thirty revolutions of the bar AB, which is fixed on the axis D of the screw E; if the length of the bar be equal to twice the diameter of the wheel, the pins a and n at the ends of the bar will move sixty times as fast as the teeth of the wheel do, and consequently, one ounce at P will balance sixty ounces hung upon a tooth at g in the horizontal diameter of the wheel.Then, if the diameter of the wheel H be ten times as great as the diameter of the axle G, the wheel will have ten times the velocity of the axle; and therefore one ounce P at the end of the lever AC, will balance 10 times 60, or 600 ounces hung to the rope H which goes round the axle. Lastly, if four pulleys be added, they will make the velocity of the lower block K, and weight W, four times less than the velocity of the axle: and this being the last power in the machine, which is four times as great as that gained by the axle, it makes the whole power of the machine 4 times 600, or 2400. So that a man who could lift one hundred weight in his arms by his natural strength, would be able to raise 2400 times as much by this engine. But it is here as in all other mechanical cases; that the time lost is always as much as the power gained, because the velocity with which the power moves will ever exceed the velocity with which the weight rises, in proportion as the intensity of the weight exceeds the intensity of the power.

The friction of the screw itself is very considerable; and there are few compound engines but what, upon account of the friction of the

parts against one another, will require a third part more of power to work them when loaded, than what is sufficient to constitute a balance between the weight and the power.*

*The following table of the relative strength of metals, &c. is subjoined for the use of the practical mechanician.

Box, yew, plumbtree, oak,

Elm, ash,

Walnut, thorn,

11

8.5

7.5.

Red fir, holley, elder, plane, crabtree, appletree, 7
Beech, cherrytree, hazle,

Alder, asp, birch, white fir, willow or saugh,

Iron,

Brass,

Bone,

Lead,

Fine free-stone,

6.7

6

107

50

22

6.5

1

For further information on this subject, see Emerson's Mechanics, Lect. 8; and Cavallo's Nat. Phil. vol. 2, p. 145-6.E. ED.

80

PLATE
VII.

A common
mill.
Fig. 2.

LECTURE IV.

Of Mills, Cranes, Wheel-carriages, and the
Engine for driving Piles.

AS these engines are so universally useful, it would be needless to make any apology for describing them.

Of various Kinds of Mills.

In a common breast-mill,* where the fall of water may be about ten feet, AA is the great wheel, which is generally about 17 or 18 feet in diameter, reckoned from the outermost edge of any float-board at a to that of its opposite float at b. To this wheel the water is conveyed through a channel, and, by falling upon the wheel, turns it round.

**Water-mills are divided into breast-mills, undershot-mills, and overshot-mills. In breast-mills, the water falls at right angles upon the float-boards or buckets, placed upon the circumference of the wheel. When float-boards are used, the water acts by its impulse; but, when buckets are employed, both the weight and impulse of the water are concerned in turning the wheel. In undershot-mills, float-boards only are employed; and the motion of the wheel affected merely by the force of the stream, which strikes the boards below the wheel's centre. overshot-mills, buckets only are used, and the wheel is turned chiefly by the weight of the water which is poured over its top into the buckets. An undershot-mill requires the greatest quantity of water; and an overshot-mill the least. It has long been disputed among mechanical philosophers, whether overshot or undershot-mills produce the greatest effect. M. Belidor (Architecture Hydraulique) maintained, that undershot-mills were greatly superior to the other kind; while Dr. Desaguliers held a contrary opinion. It appears, however, from the accurate experiments of Mr. Smeaton, that in undershot-mills the power is to the effect as 3 to 1, and in overshot-mills as 3 to 2, or rather as 5 to 4.-E. ED.