The surfaces still retaining a little unctuousness. proportion can be reduced to 0·05. Ioid. § When the grease is constantly renewed and uniformly distributed, this TABLE III. Friction of Gudgeons or Axle-ends, in Motion, upon their Bearings. (From the experiments of Morin.) THE RIGIDITY OF CORDS. 142. It is evident that, by reason of that resistance to deflexion which constitutes the rigidity of a cord, a certain force or pressure must be called into action whenever it is made to change its rectilineal direction, so as to adapt itself to the form of any curved surface over which it is made to pass; as, for instance, over the circumference of a pulley or wheel. Suppose such a cord to sustain tensions represented by P, and P1, of which P, is on the point of preponderating, and let the friction of the axis of the pulley be, for the present, neglected. It is manifest that, in order to supply the force necessary to overcome the rigidity of the cord and to produce its deflection at B, the tension P, must exceed P,; whereas, if there were no rigidity, P, would equal P.; so that the effect of the rigidity in increasing the tension P, is the same as though it had, by a certain quantity, increased the tension P2. Now, from a very numerous series of experiments made by Coulomb upon this subject, it appears that the quantity by which the tension P, may thus be considered to be increased by the rigidity, is partly constant and partly dependent on the amount of P; so as to be represented by an algebraical formula of two terms, one of which is a constant quantity, and the other the product of a constant quantity by P. Thus if D represent the constant part of this formula, and E the constant factor of P2, then is the effect of the rigidity of the cord the same as though the tension P, were increased by the quantity D+E. P. When the cord, instead of being bent, under different pressures, upon circular arcs of equal radii, was bent upon circular arcs of different radii, then this quantity D+E.P,; by which the tension P, may be considered to be increased by the rigidity, was found to vary inversely as the radii of the arcs; so that, on the whole, it may be represented by the formula |
