Part 82

_Compound_ MACHINES, are formed by various combinations, and serve for different purposes; in all which the same general law takes place, viz. that the power and weight sustain each other, when they are in the inverse proportion of the velocities they would have in the directions wherein they act, if they were put in motion. Now, to apply this law to any compound _machine_, there are four things to be considered: 1. The moving power, or the force that puts the _machine_ in motion; which may be either men or other animals, weights, springs, the wind, a stream of water, &c. 2. The velocity of this power, or the space it moves over in a given time. 3. The resistance, or quantity of weight to be removed. 4. The velocity of this weight, or the space it moves over in the same given time.

The two first of these quantities are always in the reciprocal proportion of the two last; that is, the product of the first two must always be equal to that of the last; hence, three of these quantities being given, it is easy to find the fourth; for example, if the quantity of the power be 4, its velocity 15, and the velocity of the weight 2, then the resistance, or quantity of the weight, will be equal to

4 × 15 60 ------ = -- = 30. 2 2

The following rules will direct the mechanic how he may contrive his _machine_, that it may answer the intended purpose, to the best advantage.

1. Having assigned the proportion of your power, and the weight to be raised, the next thing is to consider how to combine levers, wheels, pullies, &c. so that working together they may be able to give a velocity to the power, which shall be to that of the weight something greater than in the proportion of the weight to the power. This done, you must estimate your quantity of friction; and if the velocity of the power be to that of the weight still in a greater proportion than the weight and friction taken together are to the power; then your _machine_ will be able to raise the weight. And note, this proportion must be so much greater, as you would have your engine work faster.

2. But the proportion of the velocity of the power and weight must not be made too great: for it is a fault to give a _machine_ too much power, as well as too little; for if the power can raise the weight and overcome the resistance, and the engine perform its proper effect in a convenient time and work well, it is sufficient for the end proposed; and it is in vain to make additions to the engine to increase the power any farther; for that would not only be a needless expence, but the engine would lose time in working.

3. As to the power applied to work the engine, it may either be a living power, as men, horses, &c. or an artificial power, as a spring, &c. or a natural power, as wind, water, fire, weights, &c.

When the quantity of the power is known, it matters not, as to the effect, what kind of power it is; for the same quantity of any sort will produce the same effect; and different sorts of powers may be applied in an equal quantity a great variety of ways.

The most easy power applied to a _machine_ is weight, if it be capable of effecting the thing designed. If not, then wind, water, &c. if that can be conveniently had, and without much expence.

A spring is also a convenient moving power for several _machines_: but it never acts equally as the weight does; but is stronger when much bent, than when but a little bent, and that in proportion to the bending, or the distance it is forced to; but springs grow weaker by often bending or remaining long bent: yet they recover part of their strength by lying unbent.

The natural powers, wind and water, may be applied to vast advantage in working great engines, when managed with skill and judgment.--The due application of these has much abridged the labors of men; for there is scarce any labor to be performed, but an ingenious artificer can tell how to apply these powers to execute his design, and answer his purpose; for any constant motion being given, it may, by due application, be made to produce any other motions we desire. Therefore these powers are the most easy and useful, and of the greatest benefit to mankind. Besides, they cost nothing, and do not require any repetition nor renewing, like a weight or a spring, which require to be wound up. When these cannot be had, or cannot serve our end, we have recourse to some living power, as men, horses, &c.

4. Men may apply their strength several ways in working a _machine_. A man of ordinary strength, turning a roller by the handle, can act for a whole day against a resistance equal to 30 pounds weight; and if he works ten hours in a day, he will raise a weight 30lb. 3¹⁄₂ feet in a second; or if the weight be greater, he will raise it so much less in proportion.

But a man may act, for a small time, against a resistance of 50lb. or more.

If two men work at a windlass or roller, they can more easily draw up 70lb. than one man 30lb. provided the elbow of one of the handles be at right angles to that of the other: and with a fly or heavy wheel applied to it, a man may do ¹⁄₃d part more work; and for a little while act with a force, or overcome a continual resistance of 80lb. and work a whole day when the resistance is but 40lb.

Men used to carrying weighty burdens, such as porters, will carry some 150lb. others 200lb. or 250lb. according to their strength.

A man can draw but about 70 or 80lb. horizontally; for he can but apply half his weight.

If the weight of a man be 140lb. he can act with no greater force in thrusting horizontally, at the height of his shoulders, than 27lb.

A horse draws to greatest advantage, when the line of direction is a little elevated above the horizon, and the power acts against his breast: and can draw 200lb. for eight hours in a day, at two miles and an half an hour. If he draws 240lb. he can work but six hours, and not quite so fast; and, in both cases, if he carries some weight he will draw better than if he carried none. And this is the weight a horse is supposed to be able to draw over a pully out of a well. In a cart a horse may draw 1000lb. The most force a horse can exert is when he draws something above a horizontal direction.

The worst way of applying the strength of a horse, is to make him draw or carry up a hill: and three men with 100lb. on their backs, will climb up a steep hill faster than a horse with 300lb.

A round walk for a horse to draw in at a mill, &c. should not be less than 40 feet diameter.

5. Every machine should be made of as few parts, and those as simple as possible, to answer its purpose; not only because the expence of making and repairing will be less, but it will also be less liable to be put out of order.

6. If a weight is to be raised but a very little way, the lever is the most simple, easy, and ready machine; or, if the weight be very great, the common screw is most proper; but if the weight is to be raised a great way, the wheel and axle is a proper power, but blocks and pullies render the labor still more easy: the same may be done by the perpetual screw.

Great wheels, to be wrought by men or cattle, are of most use and convenience when their axles are perpendicular to the horizon; but if by water, &c. then it is best to have their axles horizontal.

7. As to the combination of simple _machines_ to make a compound one, though the lever when simple cannot raise a weight to any great height, and in this case is but of little service; yet it is of great use when compounded with others. Thus the spokes of a great wheel are all levers perpetually acting; and a beam fixed to the axis to draw the wheel about by men or horses, is a lever. The lever also may be combined with the screw, but not conveniently with pullies or with the wedge. The wheel and axle is combined to great advantage with pullies: but the perpetual screw, with the wheel is very serviceable. The wedge cannot be combined with any other mechanical power; and it only performs its effect by percussion; but this force of percussion may be increased by engines.

Pullies may be combined with pullies, and wheels with wheels. Therefore if any single wheel would be too large, and take up too much room, it may be divided into two or three more wheels and trundles, or wheels and pinions, as in clock work, so as to have the same power, and perform the same effect.

In wheels with teeth, the number of teeth that play together in two wheels, should be prime to each other, that the same teeth may not meet at every revolution: for when different teeth meet, they by degrees wear themselves into a proper figure: therefore they should so be contrived that the same teeth meet as seldom as possible.

8. The strength of every part of the _machine_ should be made proportional to the stress it is to bear: and therefore let every lever be made so much stronger, as its length and the weight it is to support are greater; and let its strength diminish proportionally from the fulcrum, or point where the greatest stress is to each end. The axles of wheels and pullies must be so much stronger as they are to bear greater weight. The teeth of wheels, and the wheels themselves, which act with greater force, must be proportionally stronger; and in any combination of wheels and axles, make their strength diminish gradually from the weight to the power, so that the strength of every part be reciprocally as its velocity. The strength of ropes must be according to their tension; that is, as the squares of their diameters: and, in general, whatever parts a _machine_ is composed of, the strength of every particular part of it must be adjusted to the stress upon the whole; therefore in square beams the cubes of the diameters must be made proportional to the stress they bear: and let no part be stronger or bigger than is necessary for the stress upon it; not only for the ease and well going of the _machine_, but for diminishing the friction; for all superfluous matter in any part of it, is a dead weight upon the machine, and serves only to impede its motion: hence he is the most perfect mechanic, who not only adjusts the strength to the stress, but who also contrives all the parts to last equally well, so that the whole _machine_ may fall together.

9. To have the friction as little as possible, the _machine_ should be made of the fewest and simplest parts. The diameters of the wheels and pullies should be large, and the diameters of the arbors or spindles they run on, as small as can be consistent with their strength. All ropes and cords must be as pliable as possible, and for that end rubbed with tar or grease: the teeth of wheels must be made to fit and fill up the openings, and cut into the form of epicycloids. All the axles, where the motion is, and all teeth where they work, and all parts that in working rub upon one another, must be made smooth: and when the machine goes, must be oiled or greased.

10. When any motion is to be long continued, contrive the power to move or act always one way, if it can be done, for this is better and easier performed than when the motion is interrupted, and the power is forced to move first one way, and then another; because every change of motion requires a new additional force to effect it. Besides, a body in motion cannot suddenly receive a contrary motion, without great violence: and the moving any part of the _machine_ contrary ways by turns, with sudden jerks, tends only to shake the _machine_ to pieces.

11. In a _machine_ that moves always one way, endeavor to have the motion uniform.

12. But when the nature of the thing requires that a motion is to be suddenly communicated to a body, or suddenly stopped: to prevent any damage or violence to the engine by a sudden jolt, let the force act against some spring, or beam of wood, which may supply the place of a spring.

13. In regard to the size of the _machine_, let it be made as large as it can conveniently; the greater the machine, the more exact it will work, and perform all its motions the better; for there will always be some errors in the making, as well as in the materials, and consequently in the working of the _machine_. The resistance of the medium in some _machines_ has a sensible effect; but all these mechanical errors bear a less proportion in the motion of great machines, than in that of little ones; being nearly reciprocally as their diameters, supposing they are made of the same matter, and with the same accuracy, and are equally well finished.

14. For engines that go by water, it is necessary to measure the velocity, drop in pieces of sticks, &c. and observe how far they are carried in a second, or any given time.

But if it flows through a hole in a reservoir, or standing receptacle of water, the velocity will be found from the depth of the whole below the surface.

Thus let _s_ = 16¹⁄₁₂; _v_ = velocity of the fluid per second; _B_ = the area of the hole; _H_ = the height of the water; all in feet. Then the velocity of _v_ = √(2 _s H_); and its force = the weight of the quantity

_v v_ -----_B_ 2 _s_

or _H B_ of water, or =

62¹⁄₂ -----_H B_ 112

hundred weight: because a cubic foot = 62¹⁄₂ lb. avoirdup. Also a hogshead is about 8¹⁄₂ feet, or 531lb. and a tun is 4 hogsheads.

When you have but a small quantity of water, you must contrive it to fall as high as you can, to have the greater velocity, and consequently more force upon the engine.

15. If water is to be conveyed through pipes to a great distance, and the descent be but small, much larger pipes must be used because the water will come slow.

Water should not be driven through pipes faster than four feet per second, by reason of the friction of the tubes; nor should it be too much wire-drawn, that is, squeezed through smaller pipes, for that creates a resistance, as water-way is less in narrow pipes.

16. When any thing is to be performed by a water-wheel, moved by the water running under it and striking the paddles or ladle-boards, the channel it moves in ought to be something wider than the hole of the adjutage, and so close to the floats on every side as to let little or no water pass; and when past the wheel, to open a little, that the water may spread. It is of no advantage to have a great number of floats or paddles; for those past the perpendicular are resisted by the back water, and those before it are struck obliquely. The greatest effect that such a wheel can perform, in communicating any motion, is when the paddles of the wheel move with one-third the velocity of the water; in which case, the force upon the paddle is four-ninths only; supposing the absolute force of the water against the paddle, when the wheel stands still, to be 1: so that the utmost motion which the wheel can generate, is but ⁴⁄₂₇ths of that which the force of the water against the paddles at rest would produce.

MADRAS. Fort St. George. A town and fort on the Coromandel coast, in the East Indies, belonging to the English. The town is called Madras by the inhabitants, but by the natives, Chilipatam. It is divided into two towns, the one called the White, and the other the Black town; the former being inhabited by Europeans, and the latter by Gentoos. The diamond mines of Golconda are a week’s journey from this place. The town is governed by a mayor and aldermen, with other officers. It is 63 miles north of Pondicherry, lat. 13, 5, N. long. 80, 34, E. It may not be irrelevant to state, that the establishments belonging to Great Britain, on the coast of Coromandel, is divided into several governments, independent of each other. Bombay commands the factories on the western side of the peninsula, commonly called the Malabar coast; together with those in Guzzerat: the establishments and possessions on the eastern or Coromandel coast, are under the government of Madras; and those in Bengal depend on Calcutta.

MADRIERS, are long planks of broad wood, used for supporting the earth in mining, carrying on a sap, making coffers, caponiers, galleries, and various other purposes at a siege; also to cover the mouth of petards after they are loaded, and are fixed with the petards to the gates or other places designed to be forced open. When the planks are not strong enough, they are doubled with plates of iron.

MAGAZIN, _Fr._ magazine.

_Petit_-MAGAZIN. _Fr._ This was a sort of intermediate building, called entrepot, where stores, provisions, &c. to answer daily consumptions were deposited.

MAGAZIN _d’approvisionnement_, _Fr._ magazine of stores.

MAGAZIN _d’artillerie_, _Fr._ gunpowder magazines.

MAGAZINE, a place in which stores are kept, or arms, ammunition, provisions, &c. Every fortified town ought to be furnished with a large magazine, which should contain stores of all kinds, sufficient to enable the garrison and inhabitants to hold out a long siege, and in which smiths, carpenters, wheel-wrights, bakers, &c. may be employed in making every thing belonging to the artillery, as carriages, waggons, &c.

_Powder_-MAGAZINE, is that place where the powder is kept in very large quantities. Authors differ greatly both in regard to situation and construction; but all agree, that they ought to be arched, and bomb-proof. In fortifications they are frequently placed in the rampart; but of late they have been built in different parts of the town. The first powder magazines were made with gothic arches; but M. Vauban, finding them too weak, constructed them in a semicircular form, whose dimensions are, 60 feet long, within; 25 broad; the foundations are eight or nine feet thick, and eight feet high from the foundation to the spring of the arch; the floor is 2 feet from the ground, which keeps it from dampness.

An engineer of great experience some time since, had observed, that after the centres of semicircular arches are struck, they settle at the crown and rise up at the hances, even with a straight horizontal extrados, and still much more so in powder magazines, whose outside at top is formed like the roof of a house, by two inclined planes joining in an angle over the top of the arch, to give a proper descent to the rain; which effects are exactly what might be expected agreeable to the true theory of arches. Now, as this shrinking of the arches must be attended with very ill consequences, by breaking the texture of the cement, after it has been in some degree dried, and also by opening the joints of the voussoirs, at one end, so a remedy is provided for this inconvenience, with regard to bridges, by the _arch of equilibration_ in Mr. Hutton’s book on bridges; but as the ill effect is much greater in powder magazines, the same ingenious gentleman proposed to find an arch of equilibration for them also, and to construct it when the span is 20 feet the pich or height 10, (which are the same dimensions as the semicircle) the inclined exterior walls at top forming an angle of 113 degrees, and the height of their angular point above the top of the arch, equal to seven feet: this very curious question was answered in 1775 by the Rev. Mr. Wildbore, to be found in Mr. Hutton’s _Miscellanea Mathematica_.

_Artillery_-MAGAZINE, in a _siege_, the magazine is made about 25 or 30 yards behind the battery, towards the parallels, and at least 3 feet under ground, to hold the powder, loaded shells, port-fires, &c. Its sides and roof must be well secured with boards to prevent the earth from falling in: a door is made to it, and a double trench or passage is sunk from the magazine to the battery, one to go in and the other to come out at, to prevent confusion. Sometimes traverses are made in the passages to prevent ricochet shot from plunging into them.

MAGAZINES. The present practice is not to make large powder magazines for batteries, but to disperse the barrels of powder, or cartridges _here_ and _there_ in small magazines, about 6 or 7 fathoms, in the rear of the battery; as it appears better to lose a small quantity from time to time, than to run the risk of the whole being destroyed, by a single shell falling into the magazine. These small magazines or entrenchments, will hold about one or two tons of powder; and are about eight or 9 feet square. They ought to be well covered from the fire of the place, and always in the rear of one of the merlons. When they cannot be sunk in the ground, they should be secured by sand bags or gabions. They should be made with attention, as should the communication from them to the battery. Two magazines of this kind will be required for a battery of six pieces.

_Permanent powder magazines._ According to Vauban’s plan, powder magazines are commonly made 10 fathoms long, and 25 feet wide, in the clear. The foundation of the longest sides, is 9 or 10 feet thick, and 6 feet or more deep, according to the nature of the ground. The side walls raised upon these are 8 or 9 feet thick; and if there is not to be an upper story, 8 feet will be sufficient height above the foundation. By this means the flooring may be raised above the ground, free from damp, and there will remain 6 feet from the floor to the spring of the arch. The arch is formed of layers of bricks, arched one over the other, and ought to be 3 feet thick at the top. The exterior surface of the arch terminates with an angle at top, like a roof; which angle must be of such magnitude as to make a thickness of 8 feet over the key stone of the arch. The foundation at the gable ends is 5 feet thick, and the same depth as the sides; these ends are built up 4 feet thick, from the foundation to the top of the roof. The long sides are supported by counterforts, 6 feet thick and 4 feet long; and placed 12 feet asunder. The ventilators are placed, one in the centre of each space between the counterforts, and are made with a die across them of 1¹⁄₂ feet. These ventilators are also closed with plates of iron. The magazine is lighted by a window in each end, high up, which are opened and shut by means of a ladder. These windows are secured, each by two shutters, made of plank 2 or 3 inches thick; and the outer one covered with sheet iron, and both fastened with strong bolts. The entrance to the magazine is closed by two doors, one of which opens inwards, and the other outwards; the outward one is covered with sheet iron. The entrance of the magazine should, if possible, be placed towards the south. A wall of 1¹⁄₂ feet thick, and 10 feet high, is built round the magazine at 12 feet distance. A magazine of the above dimensions will contain about 94,800 lbs. of powder, in piles of 3 barrels each; for a greater number piled above each other destroys the barrels, damages the powder, and occasions accidents.

MAGNITUDE, or quantity, any thing locally continued, or that has several dimensions. Its origin is a point, which though void of parts, yet its flux forms a line, the flux of that a surface, and of that a body, &c.

MAGNA CHARTA, the great charter of liberties granted to the people of England in the 9th year of Henry III. and confirmed by Edward I. It is so called on account of the supposed excellence of the laws therein contained; or according to some writers, because another lesser charter, called Charter de Foresta, was established with it; or because it contained more than any other charter, &c. or in regard of the remarkable solemnity in the denouncing excommunications against the infringers of it. It is nevertheless a code of barbarity characteristic of the age; and to which imposture has given it all the consequence which ignorance ascribes to it.

MAHONNE, _Fr._ a species of galeas or double galley which the Turks use. The Venetian galeasses are larger and stronger built.