This being premised, let the elevation of the plane A B be gradually increased until the tendency of the weight to descend just overcomes the friction, but not so much as to allow the box to descend with accelerated speed. The proportion of the whole weight, which then acts down the plane, will be found by measuring the height A E, and the pressure will be determined by measuring the base B E. Now let the weight in the box be increased, and it will be found that the same elevation is necessary to overcome the friction; nor will this elevation suffer any change, however the pressure or the magnitude of the surfaces which move in contact may be varied. Since, therefore, in all these cases, the height A E and the base B E remain the same, it follows that the proportion between the friction and pressure is undisturbed. (324.) The law that friction is proportional to the pressure, has been questioned by the late professor Vince of Cambridge, who deduced from a series of experiments, that although the friction increases with the pressure, yet that it increases in a somewhat less ratio; and from this it would follow, that the variation of the surface of contact must produce some effect upon the amount of friction. The law, as we have explained it, however, is sufficiently near the truth for most practical purposes. (325.) There are several circumstances regarding the quality of the surfaces which produce important effects on the quantity of friction, and which ought to be noticed here. This resistance is different in the surfaces of different substances. When the surfaces are those of wood newly planed, it amounts to about half the pressure, but is different in different kinds of wood. The friction of metallic surfaces is about one fourth of the pressure. In general the friction between the surfaces of bodies of different kinds is less than between those of the same kind. Thus, between wood and metal the friction is about one fifth of the pressure. It is evident that the smoother the surfaces are the less will be the friction. On this account, the friction of surfaces, when first brought into contact, is often greater than after their attrition has been continued for a certain time, because that process has a tendency to remove and rub off those minute asperities and projections on which the friction depends. But this has a limit, and after a certain quantity of attrition the friction ceases to decrease. Newly planed surfaces of wood have at first a degree of friction which is equal to half the entire pressure, but after they are worn by attrition it is reduced to a third. If the surfaces in contact be placed with their grains in the same direction, the friction will be greater than if the grains cross each other. Smearing the surfaces with unctuous matter diminishes the friction, probably by filling the cavities between the minute projections which produce the friction.