~30. The Cause of Sliding Friction~ is the interlocking of the asperities of one surface with those of another; and only by the riding of one set over the other, or by a rubbing down or tearing off of projecting parts, can motion take place. It follows, then, that roughness is conducive to friction; and that the smoother the surface the less the friction will be. ~31. The Cause of Rolling Friction~ is the irregularity and lack of symmetry of the surfaces between which it occurs. It acts as a resisting, or retarding, force when a smoothly curved surface rolls upon another surface, plane or curved. Motion is prevented, or retarded, by the irregular variation of the distance between the center of gravity and the line of motion in the common tangent of the two bodies at the point of contact, caused by the irregularity of form, or of surface, in the one or the other body. Rolling friction is small where hard, smooth, symmetrical surfaces are in contact, and increases as the surfaces are soft, rough or irregular. In a knife edge support, seen in some forms of pendulums, is exhibited a form of rolling friction. ~32. Solid Friction~, either sliding or rolling, could be overcome if it were possible to produce _absolutely_ smooth surfaces. It is evident, then, that the character of the material, as well as the form of their surfaces, determines the amount of friction. In all time-keeping mechanism both sliding and rolling friction manifest themselves; the former principally between the surfaces of pivots and bearings and in the escapements, the latter mainly between the surfaces of the teeth of wheels, and to some extent in some of the pivots, and sometimes in parts of escapements. It is not the intention of the author to treat of the proper shape of the teeth of wheels, leaves of pinions, or the proportions of the escapements, the nature and scope of this work not permitting of it; but he will confine his remarks principally to the parts that involve lubrication. ~33. The Laws of Sliding Friction~, as given by Thurston,[7] with solid, unlubricated surfaces, are, up to the point of abrasion, as follows: 1. The direction of frictional resisting forces is in the common tangent plane of the two surfaces, and directly opposed to their relative motion. 2. The point, or surface, of application of this resistance is the point, or the surface, on which contact occurs. 3. The greatest magnitude of this resisting force is dependent on the character of the surfaces, and is directly proportional to the force with which two surfaces are pressed together. 4. The maximum frictional resistance is independent of the area of contact, the velocity of rubbing, or any other conditions than intensity of pressure and condition of surfaces. 5. The friction of rest or quiescence, "statical friction," is greater than that of motion, or "kinetic friction."