This only holds good when the power is a heavy body, as well as the weight; but does not take place, when the power is some immaterial active force, such as that of an elastic medium, the strength of a spring, &c., whose weight is inconsiderable.

18. These principles, also, are very useful, and necessary to be known, where water-works are concerned.

The pressure of the atmosphere upon a square inch is 14.7 lb. avoird. at a medium.

The weight of a column of water, equal to the weight of the atmosphere, is 11 yards.

A cubic foot of water weighs 624 lb. avoird. and contains 6.128 ale gallons.

An ale gallon of water contains 282 inches, and weighs 10.2 lb. avoird.

A tun of water, ale measure, weighs 1.1 tun avoird. at 63 gallons the hogshead.

A cylinder of water a yard high, and d inches in diameter, contains dd ale gallons, and weighs dd pounds avoird.

THE DESCRIPTION OF COMPOUND MACHINES OR ENGINES, AND THE METHOD OF COMPUTING THEIR POWERS OR FORCES; WITH SOME ACCOUNT OF THE ADVANTAGES AND DISADVANTAGES OF THEIR CONSTRUCTION.

PROP. CXX.

THEIR FORCES OR EFFECTS.

There are two things required to make a good mechanic or engineer. The first is, a good invention for contriving all the parts of a machine, to perform its motions and effects in the most simple and easy manner. The next is, to be able to compute the power or force of it, to know whether it can really perform the effect expected from it, or not. The foundation of both these has been already laid down in this book. What seems to be necessary farther is, to give some examples in practice, by shewing the construction of several mechanic engines, and computing their powers. As there is great skill and sagacity in con triving fit and proper ways to perform any motion, so this is principally to be attained by practice, and a thorough acquaintance

with machines of several kinds. I shall, therefore, give the mechanical construction of several sorts of machines, made for seve ral different purposes, which will assist the reader's invention, and give him some idea how he may proceed in contriving a ma chine for any end proposed. Of which I shall only give a short explanation of the principal parts, not troubling the reader with any description of their minuter ones, nor how they are joined together, or strengthened, &c. It is sufficient here to shew the disposition and nature of the principal members; the rest belongs to carpenters, joiners, smiths, &c. and is easily understood by any one.

To compute their powers.

1. As to simple machines; they are easily accounted for, and their forces computed, by the properties of the mechanic powers. 2. For compound machines; suppose any machine divided into all the simple ones that compose it. Then begin at the power and call it 1; and, by the properties of the mechanic powers, find the force with which the first simple machine acts upon the second, in numbers. Then call this force 1, and find the force it acts upon the third, in numbers. And putting this force 1, find the force acting on the fourth, in numbers; and so on to the last. Then multiply all these numbers together, the product will give the force of the machine, supposing the first power 1.

3. When pullies are concerned in the machine, all the parts of the same running rope, that go and return about several pullies, freely and without interruption, must be all numbered alike for the force. And if any rope act against several others, it must be numbered with the sum of all these it acts against.

4. In a combination of wheels; take the product of the number of teeth in all the wheels that act upon and drive others, for the power; and the product of the teeth in all the wheels moved by them, for the weight. Or, instead of the teeth, take the dia

meters.

Or thus,

When a machine is in motion, if you measure the velocity of the weight, and that of the power, in numbers; then the first number to the second, gives the proportion of the power to the weight.

Otherwise thus,

In wheel work, there are always two wheels fixed upon one axis, or else one wheel, and a pinion, trundle, or barrel, which supplies the place of a wheel. Of these two, call that wheel the leader, which is acted on by the power, or by some other wheel; and the other, on the same axis, called the follower, which dr.ve

N

some other forward. Then, having either the number of teeth, or the diameter of each, take the product of all the leaders, for the weight; and the product of all the followers, for the power. Here the leader receives the motion, and the follower gives it.

5. And if the velocity of the power or weight be required: Take the product of all the leaders, for the velocity of the power; and the product of all the followers, for the velocity of the weight. Other things that are more complex and difficult, must be referred to the general laws of motion.

EXAMPLE I.

Scissars, pinchers, &c. may be referred to the lever of the first kind. A hundspike and crow are levers of the first kind. Knives fixed at one end, to cut wood, bread, &c. are levers of the second kind. The bones in animals, also tongs, are levers of the third kind. A hammer to draw a nail is a bended lever.

EXAMPLE II.

A windlass, and a capstan in a ship, and a crane to draw up goods out of a ship or boat, may be referred to the wheel and axle.

EXAMPLE III.

All edge tools and instruments with a sharp point, to cut, cleave, slit, chop, pierce, bore, &c. as knives, hatchets, scissars, swords, bodkins, &c. may be reduced to the wedge.

EXAMPLE IV.

The bar AB (Fig. 7. Pl. XVIII.) bearing a weight C, may be referred to the lever, where the weight upon A to the weight upon B:: is as BC; to AC.

EXAMPLE V

Likewise, if two horses draw the weight W, (Fig. 5. Pl. XVIII.) in the directions A 1, B 2, by help of the swingtree AB, this may be referred to the lever. And the strength or force at A, to that of B is as BC; to AC.

EXAMPLE VI.

ACB (Fig. 6. Pl. XVIII.) is a balance, where the brachia AC, CB being equal, the weights in the two scales D, E will be equal. The properties of a good balance are, 1. That the points of suspension of the scales, and the centre of motion of the beam, be in one right line. 2. That the brachia or arms be exactly of equal length from the centre of motion. 3. That they be as long as possible with conveniency. 4. That there be as little friction as possible in the motion. 5. That the centre of gravity of the beam be in, or but very little below, the centre of motion. 6. That they be in equilibrio, when empt y.

If one brachium AC be longer than the other CB, then the weight in the scale E must be greater than that in D, to make an equilibrium. And then you will have a deceitful balance, which being empty, or loaded with unequal weights, shall remain in equilibrio. For AC: CB:: weight in E: weight in D; by the property of the lever. But changing the weights from one scale to the other will discover the deceit; for the balance will be no longer in equilibrio.

EXAMPLE VII.

The steelyard AB (Fig. 8. Pl. XVIII.) is nothing but a lever, whose fulcrum is C, the centre of motion. If the weight P, placed at D, reduces the beam AB to an equilibrium; and there be taken the equal divisions D 1, 1 2, 2 3, 34, &c. then the weight P, placed successively at 1, 2, 3, 4, &c., will equi-ponderate with weights as W, suspended at B, which are, also, as the numbers 1, 2, 3, 4, &c. respectively. Moreover, if the divisions D1, 1 2, 2 3, &c. be each CB; then, if P be successively placed at 1, 2, 3, &c. the weight W to balance it, will be, respectively, equal to P, 2P, 3P, &c. that is to 1, 2, 3 pounds, &c. if P is a pound. For, by the property of the lever, CP x P+ CD × P=CB x W, that is, PD x P = CB x W. And CB: PD:: P: W, universally. Whence, if DP or D1 CB, then WP. If DP or D2 = 2CB, then W = 2P, &c. But if CB be greater than D1, 1 2, &c., then will the constant weight P be greater than W, 2W, &c.

The properties necessary for a steelyard to have, are these:

1. That the fixed weight P being placed at D, where the divisions begin, shall make the beam in equilibrio.

2. That the divisions D 1, 1 2, 23, &c. be equal to one another.

3. That CB may be of any length, provided the weight P be rightly adjusted to it, viz. so that CB: D1:: P: 1 pound, if W be pounds. Or CB: D1:: P: 1 stone, if W be stones.

4. That the beam be straight, and the upper edge in a line with the centres C, B.

5. That it move easily and freely on its centre C.

Many steelyards are likewise graduated on the under side, which may be used by turning them upside down. Generally, one side is for small weights, and the other for great ones. And each side is adjusted by the foregoing rules; and all the crooks hanging at it (except the moveable one for the weight) must go to the weight of the beam.

EXAMPLE VIII.

Let AB (Fig. 9. Pl. XVIII.) be a cheese press; CE, FG are