NOTES. 595
of the treatment of friction which is customary in text-books of elementary Mechanics, and which, in my opinion, is very unfavourable to its proper comprehension.
There is first the notion that friction prevents motion, but that it does not produce it. This is the view commonly taken in theoretical text-books. Weisbach, for example (Tkeor. Mech. i, 4th Edition, 167) uses the heading, " the resistances of friction and rigidity," and says in the text, " In relation to the motion of bodies friction isapassiveforce or resist- ance, for it only prevents or retards motion, and never produces or aids it." Kayser (StatiJc 161) says, " Friction may be regarded as a passive force, merely hindering motion, and never causing or aiding it." All writers do not express themselves so frankly, but the prevailing idea is certainly that friction is a " resistance," and substantially this is said by all. Riihlmann is an instance, and Wernicke, Mosele, too, and Poncelet, and even Duhamel. Among modern writers even the clear-headed Bitter has adopted the common mode of expres- sion, indeed, I have found in text-books no exception whatever to the rule. And yet the idea is not founded upon any investigation as to its accuracy, and it stands in manifest contradiction to the known laws of motion, or more generally to the law of the conservation of energy. For friction is a force and must itself be treated as one, no matter whether or how it be derived from other forces. A multitude of other forces are derived in the same sense as it is. There is no real reason why this force (and the stiffness of cords, which is generally treated in the same way as friction) should be suddenly thrown out from all systematic connection with others, why it should be absolutely asserted that this force does not possess the essential characteristic of other forces, the capacity, namely, of producing or aiding motion, why it should always appear with the negative sign. We have here a survival from the ancient Mechanics, from which the modern scientific treatment of the subject has in some places shaken itself entirely free, and against which, in others, it is still struggling.
It is necessary, of course, to prove my position, and it is at the same time exceedingly easy. Both in nature and in machinery there are numerous illus- trations of the falsity of the statement that friction does not produce motion. The wind sets the surface of water in motion by friction ; the wind itself is retarded by its friction upon the water, the latter being at the same time accelerated. The violin-bow sets the string in vibration by friction, in a way which Helmholtz describes as follows : (Sensations of Tone, trans, by Ellis, p. 133) " During the greater part of each vibration the string clings to the bow, and is carried on by it ; then it suddenly detaches itself and rebounds, whereupon it is seized by other points in the bow and again carried for- ward." If a fast-running belt or cord be slid on to a stationary pulley, it slides upon it at first and then, by a more or less gradual operation, sets it in motion. The force which acts as a driving force from a velocity = to a velocity equal to that of the band is friction. It resists the motion of the band, but accelerates that of the pulley. If we look into the matter more closely we shall find that in every single case friction both causes and hinders motion, although the former may occur only as small alterations of form in the body acted upon. It is not even necessary to fall back upon
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