A Treatise of Mechanics Author:Olinthus Gregory Purchase of this book includes free trial access to www.million-books.com where you can read more than a million books for free. This is an OCR edition with typos. Excerpt from book: velocity, whatever the tension may be: in such sort that it ceases to be perceptible under great tensions, and that theiv, are but very few circumstances in whic... more »h it may not be neglected in practice: this augmentation with regard to the velocity appears, besides, much greater in new than in old cords, and in tarred cords than in those which are white or untarred." 42. M. Coulomb deduces from these experiments the following general conclusions: (1.) That with respect to practice, in all rotatory machines the ratio of the pressure to the friction may always be supposed constant, and that the influence of the velocity is too small to need our regard. (2.) That the resistance which must be overcome to bend a cord over a roller or pulley is represented by a formula composed of two terms; the first is a constant quantity independent of the tension, and of the form (art. 31.) where a is a constant quantity determined by experience, d" is a power of the diameter d of the cord, and r the radius of the roller; the second ftdft 17- 11 term is a, where 0 is a constant quantity, a, n, and r, as before, and a the tension of the cord. Thus the complete formula expressing the stiffness of the cord is (a + 6a). The power n varies according to the flexibility of the cord, but is usually about 1-7 or 1-8, or the resistance is nearly proportional to the square of the diameter of the cord: when the cord is much used n decreases to 1-5 or even 1-4. The following is a summary of results. Its. White V"'" Cord, J-15imettua in u yarn . o.iv u y-u r r . 12= 5-1, j ( of 30 Tarred ) , C 6threads in a yarn . . -0-2 . .= 2-2 . =6-6 . .=11-6Cord, £ g ...... = 5-6 . =0-4 . .= 2-443. Our knowledge of the nature of the friction of axes, and stiffness of cords, though ...« less