This section is from the book "A Practical Treatise On Friction, Lubrication, Fats And Oils", by Emil F. Dieterichs. Also available from Amazon: A practical treatise on friction, lubrication, fats and oils.
The force which is felt to resist the motion when one body rubs against another while in motion is called friction. Of all mechanical power used, a large amount is spent or lost to overcome the obstructive force of friction, and means are looked for to reduce this as much as possible. Friction is either sliding or rolling. The laws regarding friction are explained as follows:
When placing a block of wood or iron on a smooth surface of wood or metal, it requires a force of some two-fifths of the weight of the block to make it move along the surface, thereby indicating the friction between the surface, as has been established by carefully conducted experiments. It has been established that two such blocks placed on the plate side by side, so as to form one of double size, require double the force to move them, and when the blocks are placed on top of each other, there is no difference in the amount of force necessary to move them. The friction between any two surfaces increases in proportion to the force with which they are pressed together, regardless of the extent of the surface in contact. A difference, however, exists when wood on iron, iron on iron or, iron on brass press on each other. For oakwood on iron, the moving force required is about two-fifths, or exactly thirty-eight per cent; for iron on iron forty-four per cent, and for cast-iron upon brass about twenty-two per cent, in a dry state and without lubrication. The proportion expressed between the pressure of two surfaces and their friction is called their co-efficient, and is found by dividing the power by the weight moved. The friction of quiescence, or the resistance to the commencement of motion, is greater than the resistance to its continuance, and more so if the surfaces have for a considerable time rested in contact with each other. The friction of motion is entirely independent of the velocity of the motion. The resistance of friction to a shaft turning in its bearings, or of an axle in its box, has evidently a greater leverage the thicker the journal or the axle is, and axles of wheels are accordingly made as small as is consistent with their required strength. The resistance that takes place between the circumference of the wheel on the road is called "rolling friction." In front of the wheel there is always an eminence or obstacle which it is at every instant surmounting and crushing; so also on iron rails, but to a much lesser extent than on other roads. On the principle of the lever, it shows that a larger wheel has the advantage over a smaller one, and it has been fully established that on a horizontal road the traction varies directly as to the load, and inversely as to the radius of the wheel. On a perfectly good and level macadamized road, the traction of a cart is found to be one-thirtieth of the load, so that a horse to draw a ton must pull with a force equal to seventy-five pounds. On a railway the traction is reduced to one two-hun-dred-and-eightieth of the load, or to eight pounds per ton. Friction is akin to and as important as is gravitation in every motion in the universe.
While friction on railways is diminished, further dimunition would stop motion entirely, as the driving wheels of the locomotive would slide around on the rails without advancing.
Friction is most valuable when machinery with great momentum has to be checked or suddenly arrested in its motion, as by a brake against the wheels on railways. It is useful in communicating motion by means of belts, ropes or chains ; it is the force that holds the knot in the rope, and it is the power that stops the momentum of cars in rapid motion. Friction is the constant opponent of motion, which creates heat, which is known as "Frictional Heat."