FRICTION

, the act of rubbing or grating the furfaces of bodies against or over each other, called also Attrition.

The phenomena arising from the Friction of divers bodies, under different circumstances, are very numerous and considerable. Mr. Hawksbee gives a number of experiments of this kind; particularly of the attrition or Friction of glass, under various circumstances; the result of which was, that it yielded light, and became electrical. Indeed all bodies by Friction are brought to conceive heat; many of them to emit light; particularly a cat's back, sugar, beaten sulphur, mercury, sea water, gold, copper, &c, but above all diamonds, which when briskly rubbed against glass, gold, or the like, yield a light equal to that of a live coal when blowed by the bellows.

, in Mechanics, denotes the resistance a moving body meets with from the surface on which it moves.

Friction arises from the roughness or asperity of the surface of the body moved on, and that of the body moving: for such surfaces consisting alternately of eminences and cavities, either the eminences of the one must be raised over those of the other, or they must be both broken and worn off: but neither can happen without motion, nor can motion be produced without a force impressed. Hence the force applied to move the body is either wholly or partly spent on this effect; and consequently there arises a resistance, or Friction, which will be greater as the eminences are greater, and the substance the harder; and as the body, by continual Friction, becomes more and more polished, the Friction diminishes.

As the Friction is less in a body that rolls, than when it slides, hence in machines, lest the Friction should employ a great part of the power, care is to be taken that no part of the machine slide along another, if it can be avoided; but rather that they roll, or turn upon each other. With this view it may be proper to lay the axes of cylinders, not in a groove or concave matrix, as usual, but between little wheels, called Friction wheels, moveable on their respective axes: for by this contrivance, the Friction is transferred from the circumference of those wheels to their pivots. And in like manner the Friction may be still farther diminished, by making the axis of those wheels rest upon other Friction wheels that turn round with them. This was long since recommended by P. Casabus; and experience confirms the truth of it. Hence also it is, that a pulley moveable on its axis resists less than if it were fixed, and the cord sliding over the circumference. And the same may be observed of the wheels of coaches, and other carriages. Indeed about 20 years ago Friction balls or rollers were placed within the naves of carriage wheels by some persons, particularly a Mr. Varlo; and lately Mr. Garnett had a patent for an improved manner of applying Friction wheels to any axis, as of carriages, blocks or pulleys, scale beams, &c, in which the inclosed wheels or rollers are kept always at the same distance by connecting rods or bars.

From these principles, with the assistance of the higher geometry, Olaus Roemer determined the figure of the teeth of wheels, that should make the least resistance possible, which he found should be epicycloids. And the same was afterwards demonstrated by De la Hire, and Camus.

M. Amontons, by experiment, attempted to settle a foundation for the precise calculation of the quantity of Friction; which M. Parent endeavoured to confirm from reasoning and geometry. M. Amontons' principle is, that the Friction of two bodies depends only on the weight or force with which they press each other, being always more or less in proportion to that pressure; esteeming it a vulgar error, that the quantity of Friction has any dependence on the extent of the surface that is rubbed, or that the Friction increases with the surface: arguing that it will require the same weight to draw along a plane, a piece of wood on its narrow edge, as on its broad and flat side; because, though on the broad side there be 4 times the number of touching particles, yet each particle is pressed with but 1/4 of the weight bearing on those of the narrow side; and since 4 times the number multiplied by 1/4 of the weight is equal to 1/4 of the number multiplied by 4 times the weight, it is plain that the effect, that is, the resistance, is equal in both cases, and therefore requires the same force to overcome it.

On the first proposal of this paradox, M. De la Hire| very properly had recourse to experiments, as the best test, had they been judiciously performed: such as they were however, they succeeded in favour of this system. He laid several pieces of rough wood on a rough table; their sizes were unequal; but he laid weights on them, so as to render them all equally heavy: and he found that the same precise sorce, or weight, applied to them by a little pulley, was required to put each in motion, notwithstanding all the inequality of the surfaces. The experiment succeeded in the same manner with pieces of marble, laid on a marble table. After this, by reasoning, M. de la Hire gave a physical solution of the effect. And M. Amontons settled a calculus of the value of Friction, with the loss sustained by it in machines, on the foundation of this new principle. In wood, iron, lead, and brass, which are the chief materials used in machines, he makes the resistance caused by Friction to be nearly the same in all, when those materials are anointed with oil or fat: and the quantity of this resistance, independent of the magnitude of the surface, he makes nearly equal to a third part of the weight of the body moved, or of the force with which the two bodies are pressed together. Others have observed, that if the surfaces be hard and well polished, the Friction will be less than a third part of the weight; but if the parts be soft or rugged, it will be much greater. It was farther observed, that in a cylinder moved on two small gudgeons, or on a small axis, the Friction would be diminished in the same proportion as the diameter of these gudgeons is less than the diameter of the cylinder; because in this case, the parts on which the cylinder moves and rubs, will have less velocity than the power which moves it in the same proportion, which is in effect making the Friction to be proportional to the velocity. So that, from the whole of their observations, this general proposition is deduced, viz, That the resistances arising from Friction, are to one another in a ratio compounded of the pressures of the rubbing parts, and the velocities of their motions. Principles which, it is now known from better experiments, are both erroneous; notwithstanding the hypothesis of M. Amontons has been adopted, and attempted to be consirmed by Camus, Desaguliers, and others.

M. Muschenbroek and the abbé Nollet, however, on the other hand, have concluded from experiments, that the Friction of bodies depends on the magnitude of their surface, as well as on their weight. Though the former says, that in small velocities the Friction varies very nearly as the velocity, but that in great velocities the proportion increases faster: he has also attempted to prove, that by increasing the weight of a body, the Friction does not always increase exactly in the same ratio. Introd. ad Phil. Nat. vol. 1, c. 9, and Lect. Phys. Exp. tom. 1, p. 241. Helsham and Ferguson, from the same kind of experiments, have endeavoured to prove, that the Friction does not vary by changing the quantity of surface on which the body moves; and the latter of these asserts, that the Friction increases very nearly as the velocity; and that by increasing the weight, the Friction is increased in the same ratio. Indeed there is scarce any subject of experiment, with regard to which, different persons have formed such various conclusions. Of those who have written on the theory, no one has established it altogether on true principles, till the experiments lately made by Mr. Vince of Cambridge: Euler, whose theory is extremely elegant, and would have been quite satisfactory had his principles been founded on good experiments, supposes the Friction to vary in proportion to the velocity of the body, and its pressure upon the plane; neither of which is true: and others, though they have justly imagined that Friction is a uniformly retarding force, have yet retained the other supposition, and so rendered their solutions not at all applicable to the cases for which they were intended.

For these reasons a new and ingenious set of experiments was successfully instituted by the rev. Samuel Vince, A. M. of Cambridge, which are published in the 75th vol. of the Philos. Trans. p. 165. The object of these experiments was to determine,

1st, Whether Friction be a uniformly retarding sorce.

2d, The quantity of Friction.

3d, Whether Friction varies in proportion to the pressure or weight.

4th, Whether the Friction be the same on whichever of its surfaces a body moves.

Mr. Vince says, “the experiments were made with the utmost care and attention, and the several results agreed so very exactly with each other, that I do not scruple to pronounce them to be conclusive.”—“ A plane was 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 or horizon. 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. But let me first observe, that if Friction be a uniform force, the difference between it and the given force of the moving power must be also uniform, and therefore the moving body must descend with a uniformly accelerated velocity, and consequently the spaces described from the beginning of the motion must be as the squares of the times, just as when there was no Friction, only they will be diminished on account of the Friction.” Accordingly the experiments are then related, which are performed agreeably to these ingenious and philosophical ideas, and from them are deduced these general conclusions, which may be considered as established and certain facts or maxims. viz,

1st, That Friction is a uniformly retarding force in hard bodies, not subject to alteration by the velocity; except when the body is covered with cloth, woollen, &c, and in this case the Friction increases a little with the velocity.

2dly, Friction increases in a less ratio than the quantity of matter, or weight of the body. This increase however is different for the different bodies, more or less; nor is it yet sufficiently known, for any one| body, what proportion the increase of Friction bears to the increase of weight.

3dly, The smallest surface has the least Friction; the weight being the same. But the ratio of the Friction to the surface is not yet accurately known.

Mr. Vince's experiments consisted in determining how far the sliding bodies would be drawn, in given times, by a weight hanging freely over a pulley. This method would both shew him if the Friction were a constant retarding force, and the other conclusions above stated. For as the spaces described by any constant force, in given times, are as the squares of the times; and as the weight drawing the body is a constant force, if the Friction, which acts in opposition to the weight, should also be a constant force, then their difference, or the force by which the body is urged, will also be constant, in which case the spaces described ought to be as the squares of the times; which happened accordingly in the experiments.

Mr. Vince adds some remarks on the nature of the experiments which have been made by others. These, he observes, the authors “have instituted, To find what moving force would just put a body at rest in motion: and they concluded from thence, that the accelerative force was then equal to the Friction; but it is manifest, that any force which will put a body in motion must be greater than the force which opposes its motion, otherwise it could not overcome it; and hence, if there were no other objection than this, it is evident, that the Friction could not be very accurately obtained; but there is another objection, which totally destroys the experiment, so far as it tends to shew the quantity of Friction, which is the strong cohesion of the body to the plane when it lies at rest.” This he confirms by several experiments, and then adds, “From these experiments therefore it appears, how very considerable the cohesion was in proportion to the Friction when the body was in motion; it being, in one case almost <*>/3, and in another it was found to be very nearly equal to the whole Friction. All the conclusions therefore deduced from the experiments, which have been instituted to determine the Friction from the force necefsary to put a body in motion (and I have never seen any described but upon such a principle) have manifestly been totally false; as such experiments only shew the resistance which arises from the cohesion and Friction conjointly.” Philos. Trans. vol. 75, pa. 165.

Mr. Emerson, in his Principles of Mechanics, deduces from experiments the following remarks relating to the quantity of Friction: When a cubic piece of soft wood of 8 pounds weight, moves upon a smooth plane of soft wood, at the rate of 3 feet per second, its Friction is about 1/3 of the weight; but if it be rough, the Friction is little less than half the weight: on the same supposition, when both the pieces of wood are very smooth, the Friction is about 1/4 of the weight: the Friction of soft wood on hard, or of hard wood upon soft, is 1/5 or 1/6 of the weight; of hard wood upon hard wood, 1/7 or 1/<*>; of polished steel moving on steel or pewter, 1/4; moving on copper or lead, 1/<*> of the weight. He observes in general, that metals of the same sort have more Friction than those of different sorts; that lead makes much resistance; that iron or steel running in brass makes the least Friction of any; and that metals oiled make the Friction less than when polished, and twice as little as when unpolished. Desaguliers observes that, in M. Camus's experiments on small models of sledges in actual motion, there are more cases in which the Friction is less than where it is more than 1/3 of the weight. See a table, exhibiting the Friction between various substances, formed from his experiments in Desag. Exp. Philos. vol. 1, p. 193 &c. also p. 133 to 138, and p. 182 to 254, and p. 458 to 460. On the subject of Friction, see several vols. of the Philos. Trans. as vol. 1, p. 206; vol. 34, p. 77; vol. 37, p. 394; vol. 53, p. 139, &c.