If the slab CD were tilted up, so as to form an inclined plane, until AB were on the point of sliding, the angle of inclination would be found to be equal to the limiting angle of resistance RQP.
Knowing the coefficient of F. of any two substances, their limiting angle of resistance is easily found. Example.—The coefficient of brick upon hard limestone is .60; required the limiting angle. Take a line QR' of any convenient length, raise a per pendicular RP' equal to A of QR', and join QP'; R'QP' is the angle required: if measured, it would be found to be about 31°. In any structure, then, the obliquity of the thrust between two surfaces of these materlals must always he considerably within this limit, in order to be safe.
The friction of quiescence, that is, the resistance to the commencement of motion, is greater than the resistance to its continuance; and the more so if the surfaces have been a considerable time in contact. But the slightest shock or jar is sufficient to destroy this cohesion, or whatever it is that constitutes the peculiar initial resistance; so that it is only the constant and regular F. of motion that is of much consequence in practice.
F. is very much diminished by the use of grease or ungnents. The coefficient of wrought-iron upon oak, which, in the dry state, is .49, is reduced by the application. of water to .26, and by dry soap to .21. The result of experiments on this subject is stated to be, " that with the unguents, hog's-lard and olive-oil, interposed in a continuous stratum between them, surfaces of wood on metal, wood on wood, metal on wood, and metal on metal (when in motion), have all of them very nearly the same coefficient of F., the value of that coefficient being in all cases included between .07 and .08." Tal low gives the same coefficient as the other unguents, except in the case of metals upon metals, in which the coefficient rises to .10. In the case of wood on wood, black-lead is frequently employed for the same purpose.
The most important fact, perhaps, and one that could hardly have been anticipated before experiment, is that the le. of motion is wholly independent of the velocity of the motion.
The resistance to the motion of a wheeled carriage proceeds from two sources; the F. of the axle, and the inequalities of the road. The resistance of F. to the turn ing of a shaft in its bearings, or of an axle in its box, has evidently the greater lever age, the thicker, the journal or the axle is; the axles of wheels are accordingly made as small as is consistent with the required strength. The resistance that occurs between the circumference of the wheel and the road, constitutes what is called rolling friction. There are on all roads, to a greater or less extent, visible rigid prominences, such as small stones, in passing over which the wheel and the load resting on it have to be lifted up against gravity. But even were these wanting, the hardest road yields, and allows the wheel to sink to a certain depth below its surface; so that in front of the wheel there is always an eminence or obstacle, which it is at every instant surmounting and"crushing down. This is the case even on iron rails, though of course to a much •less extent than on any other road. Now, for overcoming this resistance, it can he shown, on the principle of the lever, that a large wheel has the advantage over a small one; and by numerous experiments, the fact has been fully established, that on hori zontal roads of uniform quality and material, the traction varies directly as the load, and inversely as the radius of the wheel.
The best direction of traction in a two-wheeled carriage is not parallel to the road, but at a slight inclination upward, in proportion to the depth to which the wheel sinks in the road.
.On a perfectly good and level macadamized road, the traction of a cart is found to be -4 of the load; that is to draw a ton, the horse requires to pull with a force equal to 75 lbs. On a railway, the traction is reduced to of the load, or to 8 lbs. per ton.
While F. thus acts as an obstruction to motion, and wastes a portion of the motive Power, it has also important uses. It is, in fact, an indispensable condition, no less than gravity, in the stability of every structure, and in every mechanical motion on the eartlVs:surface. How essential it is to our own movements, we experience when we try to walk. on ice. Even on ice there is still considerable F., so that one foot can be slightly.advanced before the other; were it altogether annihilated, we could not stir a fraction of an inch, even supposing we could stand upright. Without F., a ]adder could not be planted against a wall, unless there were a hole in the ground to retain the foot. In short, no oblique pressure of any-kind could be sustained. The advan tage of railways consists chiefly in the diminution of F.; but were this diminution car ried much further, there could be no motion whatever, at least by means of locomotives. Without considerable F., the driving-wheels of the locomotives would slide round on the rails without advancing; and this sometimes happens, when particular states of the weather render the rails as if they were greased.
The force of F. is often directly employed in mechanics. It is used, for instance, to communicate motion by means of belts, chains, etc. It is the force that holds a knot. It is specially-tiseful when a machine, with great Momentum, has to be checked or arrested in its motion. The best example of this is the break used on railways. By means of a system of levers, blocks of wood are made to press against the circumfer ences of a number of the carriage-wheels; and thus the momentum of a train weighing hundreds of tons, and moving with a velocity of perhaps 50 m. an hour, is gradually destroyed in a wonderfully short space of time.
Friction:ft heels are employed to diminish the F. of axles on their supports. Two wheels, of large circumference in proportion to their weight, are placed close together, parallel to each other, and so that the one seems to overlap the half of the other; in the notch thus formed by the upper circumferences of the wheels one end of the axle rests; a similar arrangement being made for the other end. The F., which formerly acted directly on the axle, is by this arrangement referred to the axleS of the friction-wheels, and is, by the laws of mechanics, reduced in the ratio of the circumference of the friction wheel to the circumfefence of its axle. In order to render the F. of the friction wkeels themselves the least possible, they are made as light and as large as is practicable.