disengaged immediately after it, the horses would instantly tumble down, because the load, against which they had been straining hard, is at once taken off; but the gin is connected with a very large fly, which checks any remarkable acceleration, allowing the horses to lean on it during the descent of the load; after which their draught recommences immediately. The spindles, cards, and bobbins, of a cotton mill, are also a sort of flies. Indeed all bulky machines of the rotative kind tend to preserve their motion with some degree of steadiness, and their great momentum of inertia is as useful in this respect as it is prejudicial to the acceleration or any reciprocation when wanted.

21. There is another kind of regulating fly, consisting of wings whirled briskly round till the resistance of the air prevents any great acceleration. This is a very bad one for a working machine, for it produces its effect by really wasting a part of the moving power. Frequently it employs a very great and unknown part of it, and robs the proprietor of much work. It should never be introduced into any machine employed in manufactures.

22. Some rare cases occur where a very different regulator is required: where a certain determined velocity is found necessary. In this case the machine is furnished, at its extreme mover, with a conical pendulum, consisting of two heavy balls hanging by rods, which move in very nice and steady joints at the top of a vertical axis. It is well known, that when this axis turns round, with an angular velocity suited to the length of those pendulums, the time of a revolution is determined. Thus, if the length of each pendulum be 39 inches, the axis will make a revolution in two seconds very nearly. If we attempt to force it more swiftly round, the balls will recede a little from the axis, but it employs as long time for a revolution as before; and we cannot make it turn swifter, unless the impelling power be increased beyond all probability in which case the pendulum will fly out from the centre till the rods are horizontal, after which every increase of power will accelerate the machine very sensibly. Watt and Boulton have applied this contrivance with great ingenuity to their steam engines, when they are employed for driving machinery for manufactures which have a very changeable resistance, and where a certain speed cannot be much departed from without great inconvenience. They have connected this recess of the balls from the axis (which gives immediate indication of an increase of power or a diminution of resistance) with the cock which admits the steam to the working cylinder. The balls flying out cause the cock to close a little, and diminish the supply of steam. The impelling power diminishes the next

moment, and the balls again approach the axis, and the rotation goes on as before, although there may have occurred a very great excess or deficiency of power. See GovERNOR.

23. A fly is sometimes employed for a very different purpose from that of a regulator of motion-it is employed as a collector of power. Suppose all resistance moved from the working point of a machine furnished with a very large or heavy fly immediately connected with the working point. When a small force is applied to the impelled point of this machine, motion will begin in the machine, and the fly begin to turn. Continue to

press uniformly, and the machine will accelerate. This may be continued till the fly has acquired a very rapid motion. If at this moment a resisting body be applied to the working point, it will be acted on with very great force; for the fly has now accumulated in its circumference a very great momentum. If a body were exposed immediately to the action of this circumference, it would be violently struck. Much more will it be so, if the body be exposed to the action of the working point, which perhaps makes one turn while the fly makes a hundred. It will exert a hundred times more force there (very nearly) than at its own circumference. All the motion which has been accumulated on the fly during the whole progress of its acceleration is exerted in an instant at the working point, multiplied by the momentum depending on the proportion of the parts of the machine. It is thus that the coining press performs its office; nay, it is thus that the blacksmith forges a bar of iron. Swinging the great sledge hammer round his head, and urging it with force the whole way, this accumulated motion is at once extinguished by impact on the iron. It is thus also we drive a nail, &c. This accumulating power of a fly has occasioned many to imagine that a fly really adds power or mechanical force to an engine; and, not understanding on what its efficacy depends, they often place the fly in a situation where it only adds a useless burden to the machine. It should always be made to move with rapidity. If intended for a mere regulator, it should be near the first mover: and if it be intended to accumulate force in the working point, it should not be far separated from it. In a certain sense, a fly may be said to add power to a machine, because by accumulating into the exertion of one moment the exertions of many, we can sometimes overcome an obstacle that we never could have balanced by the same machine unaided by the fly. And it is this accumulation of force which gives such an appearance of power to some of our first movers." (See Supplement, Encyclopædia Britan. art. Machinery.)

24. From these observations it is easy to pass to the con

struction of elementary machines: and it will be advantageous to the young mechanist to see several of them collected into one point of view. For this purpose we have exhibited in plates XXXVIII. and XXXIX. (extracted from M. Hachette's ingenious Traité Elémentaire des Machines,) ten distinct series of simple machines, contrived for the purpose of changing or modifying motion. Thus the 1st series exhibits different methods of changing the direction of continued rectilinear motion. The 2d relates to the conversion of continued rectilinear, to alternating rectilinear motion, and so on; the whole being readily classed thus.

The construction of most of these machines will be evident from the respective diagrams. Others will be explained in the course of the present volume. We apprehend it would be highly useful for such persons as are beginning to exercise themselves in the construction of complex machines, to have the substance of these ten series drawn upon a large sheet of pasteboard, with spare compartiments to be occupied by new contrivances in any one class, as they occur. Casting the eye over the whole would frequently suggest an ingenious and beneficial combination.

On Friction, and the Stiffness of Ropes.

25. Most of the propositions laid down in the first volume of this work have been conducted upon the supposition that all bodies are perfectly smooth, that they slide over one another without any friction, and that cords and ropes are perfectly flexible. But since there is no such thing as perfect smoothness in bodies, no machine can move without a mutual rubbing of its parts, at all points of communication; and when we consider the mode of operation of the teeth of wheel work, the

wipers and lifts, the gudgeons of the different axes, &c. we shall see that friction, by which we mean the resistance a body meets with from the surface on which it moves, has considerable effect in retarding the motion of machines, or gives occasion for the exertion of much more power in order that the machine may move with the requisite velocity. Indeed in many machines, as polishing mills, grinding mills, boring and sawing mills, the ultimate task performed is either friction or very much resembles it. So that some knowledge of the nature of friction seems absolutely necessary, to enable us to apply the principles of the simple theory to any useful practical purpose.

Much attention has, therefore, been paid to this subject by many ingenious men; but as yet their labours have not greatly added to the stock of knowledge as to the real nature of friction and although some ingenious theories have been deduced from the experiments which have already been made, they rest upon very limited hypotheses, and are of little, if any, actual utility. This being our opinion, the reader will not expect a minute exposition of the theory in this place. We shall merely present a single proposition, which tends to an obvious practical purpose, and does not require the admission of more than one new principle, viz. that the friction varies nearly as the pressure.

PROP. A power which moves a body along a horizontal plane, acts with the greatest advantage when the line of direction makes an angle of about 18° with the plane. Let B (fig. 2. pl. I.) be the body which is to be moved along the horizontal plane BC, by a given power estimated in quantity and direction by BA. Demit the perpendicular AC: and let the given line AB=1= radius, AC sin ABC=x, BC=✔ (1−x2) = the force moving the body horizontally. The power by its oblique action diminishes the pressure of the weight on the horizontal plane in the ratio of 1:2, therefore Br that part of the pressure which is taken off, and the actual pressure = B― BX. Let friction be =th part of the weight or pressure: that is, let it be ==—- B

m

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B.T. Then the force requisite to move в horizontally must be equal to the horizontal force diminished by friction, or = B ( 1 − x3)* — —=—-B+ Br. This is to be a mininum, or its fluxion

m

'(m2+n2 ) {

sine of the

angle ABC. And if, as has been concluded from many experi

10

then will r=sine of 18° 26′ nearly.

If the plane along which the body is to be moved be inclined to the horizon, the sine of the angle which the line of direction or traction of the power makes with the plane, when it acts with the greatest advantage, will be nearly, being the cosine of the angle of elevation to radius = unity.

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26. The principle assumed in the investigation above is, however, by no means general in its application; as there are many circumstances which modify the operation of friction, and cause deviations from this law. These circumstances will be best learnt by reflecting upon some of the experiments which have been made relative to the friction of bodies in motion. Of such experiments we shall first describe those of Mr. Professor Vince, which were conducted with great care and ingenuity, and led to some important results. The object of this philosopher was to determine the following questions:

1. Whether friction be a uniformly retarding force?

2. What is the quantity of friction?

3. Whether the friction varies in proportion to the pressure or weight?

4. Whether the friction be the same on whichever of its surfaces a body moves?

(1.) With respect to the first of these questions, the author truly observes, that if friction be a uniform force, the difference between it and the given force of the moving power employed to overcome it must also be uniform; and that therefore the moving power, if it be a body descending by its own weight, must descend with a uniformly accelerated velocity, just as when there was no friction. The spaces described from the beginning of the motion will indeed be diminished in any given time on account of the friction; but still they must be to each other as the squares of the times employed.

(2.) A plane was therefore adjusted parallel to the horizon, at the extremity of which was placed a pulley, which could be elevated or depressed, in order to render the string which connected the body and the moving force parallel to the plane. A scale accurately divided was placed by the side of the pulley perpendicular to the horizon, by the side of which the moving force descended; upon the scale was placed a moveable stage, which could be adjusted to the space through which the moving force descended in any given time; which time was measured by a well-regulated pendulum clock vibrating seconds. Every thing being thus prepared, the following experiments were made to ascertain the law of friction.

(3.) Exp. 1. A body was placed upon the horizontal plane, and a moving force applied, which, from repeated trials, was