Page:Encyclopædia Britannica, Ninth Edition, v. 9.djvu/814

778 F R I _ F 11 I is required. Tlio analogy with stress appears complete ; the motion of the " driving link " of a machine is communicated to all the other parts, modified or unchanged as the case may be, by the stresses in those parts ; but the actual setting in motion of the driving link itself cannot come about by stress, but must have for its production force ob tained directly from the expenditure of some form of energy. It is important, however, that the use of the term " resist ance " should not be allowed to mislead. Friction resists the motion of one surface upon another, but it may and fre quently does confer the motion of the one upon the other, and in this way causes, instead of resists, the motion of the latter. This maybe made more clear, perhaps, by an illus- stration. Suppose we have a leather strap A passing over a fixed cylindrical drum B, and let a pulling force or effort be applied to the strap. The force applied to A can act on B only at the surfaces of contact between them. There it becomes an effort tending either to move A upon B, or to move the body B itself, according to the frictional condi tions. In the absence of friction it would simply cause A to slide on B, so that we may call it an effort tending to make A slide on B. The friction is the resistance offered by the surface of B to any such motion. But the value of this resistance is not in any way a function of the effort itself, it depends chiefly upon the pressure normal to the surfaces and the nature of the surfaces. It may therefore be either less or greater than the effort. If less, A slides over B, the rate of motion being determined by the excess of the effort over the resistance (friction). But if the latter be greater, no sliding can occur, i.e., A cannot, under the action of the supposed force, move upon B. The effort between the surfaces exists, however, exactly as before, and it must now tend to cause the motion of B. But the body B is fixed, or, in other words, we suppose its resist ance to motion greater than any effort which can tend to move it, hence no motion takes place. It must be specially noticed, however, that it is not the friction between A and B that has prevented motion, this only prevented A moving on B, it is the force which keeps B stationary, whatever that may be, which has finally prevented any motion taking place. This can be easily seen. Suppose B not to be fixed, but to be capable of moving against some third body C (which might, e.g., contain cylindrical bear ings, if B were a drum with its shaft), itself fixed, and further, suppose the frictional resistance between B and C to be the only resistance to B s motion. Then if this be less than the effort of A upon B, as it of course may be, this effort will cause the motion of B. Thus friction causes motion, for had there been no frictional resistance between the surfaces of A and of B, the latter body would have remained stationary, and A only would have moved. In the case supposed, therefore, the friction between A and B is a necessary condition of B receiving any motion from the external force applied to A. Without entering here on the mathematical treatment of the subject of friction, some general conclusions may be pointed out which have been arrived at as the results of ex periment. The "laws" first enunciated by Coulomb (1781), and afterwards confirmed by Morin (1830-34), have been found to hold good within very wide limits. These are (1) that the friction is proportional to the normal pressure between the surfaces of contact, and therefore independent of the area of those surfaces (i.e., of the intensity of the pressure), and (2) that it is independent of the velocity with which the surfaces slide one on the other. For many practical purposes these statements are sufficiently accurate, and they do in fact sensibly represent the results of experi ment for the pressures and at the velocities most commonly occurring. Assuming the correctness of these, friction is generally measured iu terms simply of the total pressure between the surfaces, by multiplying it by a " coefficient of friction" depending on the material of the surfaces and their state as to smoothness and lubrication. But beyond certain limits the "laws" stated are certainly incorrect, and are to be regarded as mere practical rules, of extensive application certainly, but without any pretension to be looked at as really general laws. Coulomb pointed out long ago that the resistance of a body to be S3t in motion was in many cases much greater than the resistance which it offered to continued motion ; and since his time writers have always distinguished the " friction of rest," or static friction, from the " friction of motion," or kinetic friction. He showed also that the value of the former depended often both upon the intensity of the pres sure and upon the length of time during which contact had lasted, both which facts quite agree with what we should expect from our knowledge of the physical nature, already mentioned, of the causes cf friction. It seems not unrea sonable to expect that the influence of time upon friction should show itself in a comparison of very slow with very rapid motion, as well as in a comparison of starting (i.e., motion after a long time of rest) with continued motion. That the friction at the higher velocities occurring in en gineering practice is much less than at common velocities has been shown by several modern experiments, most re cently by those of Captain Douglas Galton (Brit. Assoc., Dublin Meeting, 1878, and Inst. Mech. Eng., Paris and Manchester Meetings, 1878) on the friction between brake- blocks and wheels, and between wheels and rails. Until quite lately, however, no increase in the coefficient of friction had ever been detected at slow speeds, but the recent expe riments of Prof. Fleeming Jenkin (Phil. Trans., 1877, pt. 2) have shown conclusively that at extremely low veloci ties (the lowest measured was about 0002 feet per second) there is a sensible increase of frictional resistance in many cases, most notably in those in which there is the most marked difference between the friction of rest and that of motion. These experiments distinctly point to the conclu sion, although without absolutely proving it, that in such cases the coefficient of kinetic friction gradually increases as the velocity becomes extremely small, and passes without discontinuity into that of static friction. We know that both at very high and very low pressures the coefficient of friction is affected by the intensity of pressure, and that, just as with velocity, it can only be regarded as independent of the intensity and proportional simply to the total load within more or less definite limits. Recent experiments have not, however, been directed so much to this point as to the influence of velocity, which we have already men tioned. (A. B. w. K.) FRIEDLAND, a town of Bohemia, the chief town of a circle, is situated in the valley of the Wittich at the con fluence of that river with the Rasnitz, 14 miles E. of Zittau. Besides the old town, which is still surrounded by walls, it contains three suburbs. The principal industry is the manufacture of woollen and linen cloth. Friedland is chiefly remarkable for its old castle, which occupies an imposing situation on a small hill commanding the town. The tower of this building was erected in 1014, and the whole structure was completed in 1551. It was several times besieged in the Thirty Years and Seven Years Wars. In 1G22 it was purchased by Wallenstein, and his likeness, painted in 1626, is included in the list of portraits of former possessors of the castle which adorn its walls. The popu lation in 1875 was 4482. FRIEDLAND, a town of Germany, in the grand-duchy of Mecklenburg-Strelitz, circle of Stargard, is situated on the Miihlenteich, 35 miles N.E. of Strelitz. It is surrounded by walls, and possesses a fine Gothic church and a gym nasium. It has manufactures of woollen and linen cloths,