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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