It was found by Coulomb that, when cue solid slides over another, the resistance to the motion is proportional to the pressure normal to the surfaces of contact, and is independent of the area of the surfaces and of the velocity with which the moving body slides over the other. It depends upon the nature of the bodies and the character of the surfaces of contact. The ratio of the force required to keep the moving body in uniform motion to the force acting upon it normal to the surfaces of contact is called the coefficient of friction.
It was shown experimentally by Poiseuille that the rate of outflow of a liquid from a vessel through a long straight tube of very small diameter is proportional directly to the diiierence in pressure in the liquid at the two ends of the tube, to the fourth power of the radius of the tube, and inversely to the length of the tube. The flow of liquid under such conditions can be determined by mathematical analysis, and it is found that the results obtained by Poiseuille can only occur if the coefficient of friction between the liquid and the wall of the tube be very great. In other words, we may think of the liquid particles nearest the wall as adhering to it and forming a tube of molecules of the same sort as those of the liquid. The outflow then depends only upon the coefficient of viscosity of the liquid.
The frictional resistance experienced by a solid moving through a liquid or a gas is a function of its velocity. When the motion is slow, approximate results are reached by setting it proportional to the velocity. For higher velocities it is more nearly proportional to their squares, and for very high velocities to still higher powers.
It results from this that the motion of a body falling toward the earth will be resisted by a force that increases as its velocity increases, so that after it has attained a certain velocity the frictional resistance and its weight may become equal, and the body, from that time on, will move with a constant velocity. This explains why rain-drops or falling shot reach the earth with much lower velocities than they would have if there were no friction. Further, since the friction depends on the surface, while the weight is pro-
