596 NOTES.
pure mathematics, as might easily be done, and show that the retardation is itself a production of motion, motion, that is, with a changed sign. Neither upon practical nor upon scientific grounds, therefore, is there any justi- fication for the popular view, the correction of which is much to be wished, although a number of connected errors may make such correction difficult.
" Every friction causes the disappearance of actual energy," says Helmholtz, in one of his excellent Vortrdge (Hft. ii. p. 129). From this undeniable proposition it is only too easy to infer the other, and false one, " in every case friction causes only the disappearance of actual energy." That friction always causes energy to disappear, in no way contradicts the fact that it also produces energy. It is therefore not unnecessary to warn students that the proposition quoted, although in itself true, may lead to some very erroneous conclusions if it be blindly followed. Let us take the piston of the steam-engine for an example. The piston fits the cylinder closely, and loses not inconsiderably in actual energy by friction against its sides. Even the keen experimenter Him, however, did not succeed in detecting the slightest loss of energy from this cause. He himself gives the reason for this quite rightly in saying that the energy lost by friction appears again in the correspondingly raised temperature of the steam. Here friction causes the simultaneous disappear- ance and re-appearance of energy in such a way that at the end we can perceive nothing of the process. The proposition, " Every friction causes actual energy to disappear," by itself, would not be apparently substantiated by mere measurement ; if it be given in an explanation of the nature of friction (for which purpose Helmholtz did not use it), it must be completed by the addition of the clause, " and also to reappear in another form."
I wish that writers upon Mechanics could be persuaded to give this matter a proper logical treatment, or at least to say something about it in elementary text-books. The further down the defect in logic be mended, the fewer corrections have to be made in the higher part of the work.
Another point to be mentioned is the statement of the laws of friction. Taking up almost any text-book of Mechanics whatever, we find the three following important propositions given : (1) Friction is proportional to the normal pressure between the rubbing surfaces ; (2) it is independent of their extent ; (3) it is independent of the velocity with which sliding takes place between them. These are, as a whole, the propositions of Coulomb and Morin. Later, although now by no means recent, experiments have shown that they express the real phenomena of the case only within very narrow limits ; that for those surfaces and velocities which are commonly to be found in machinery they do not apply ; that in the latter, in fact, we must really read : not proportional and not independent. Indeed we know that machine-design has fallen into a hundred errors through its adhesion to the propositions of Coulomb and Morin, and in fact that in recent practice they have been entirely disregarded, and dimensions adopted which are altogether at variance with them. Is it not time that the experiments of Rennie, Him, Sella, Bochet, and others, were transferred from the notes to the text ? It is to be desired equally for the sake of mechanical science itself and for its many practical applications.
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