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oil: high-grade materials and workmanship, 0.10; average quality materials and workmanship, 0.12; poor workmanship, 0.15. The use of castor oil as a lubricant lowered f from 0.10 to 0.066. The coefficients of static friction (at starting) were 30 percent higher. Table 3.2.8 gives representative values of efficiency. Screws with V Threads (Fig.3.2.12) Let c ϭ half the angle between the faces of a thread. Then, using the same notation as for squarethreaded screws, for a screw in motion (neglecting

1); hence for 1 Ͻ n Ͻ k, cn is negative. This is approximately the case in air compression up to a few hundred pounds pressure. The following are the principal formulas: Fig. 4.1.4 area between the curve and the axis OV is given by the integral v2 3 p dV and therefore represents the external work W12 done by v1 the gas during the change. The area included by a closed cycle represents the work of the cycle (as in the indicator diagram of the steam engine). 2. T and S (Fig. 4.1.5). The absolute

Accelerations* cm/s2 to ft/min2 km/(h и s) to mi/(h и s) km/(h и s) to knots/s ft/s2 to mi/(h и s) ft/s2 to knots/s ft/min2 to cm/s2 mi/(h и s) to km/(h и s) mi/(h и s) to knots/s knots/s to mi/(h и s) knots/s to km/(h и s) 1 2 3 4 5 118.1 236.2 354.3 472.4 590.6 0.6214 1.243 1.864 2.485 3.107 0.5400 1.080 1.620 2.160 2.700 0.6818 1.364 2.045 2.727 3.409 0.4572 0.9144 1.372 1.829 2.286 0.008467 0.01693 0.02540 0.03387 0.04233 1.609 3.219 4.828 6.437 8.046 0.8690 1.738 2.607

Line through (x1, y1) with slope m. y Ϫ y1 ϭ m(x Ϫ x1). ANALYTICAL GEOMETRY y 2 y1 7. Line through (x1, y1) and (x2, y2). y 2 y 5 2 1 x2 2 x1 sx 2 x1d. 8. Line parallel to x axis. y ϭ a; to y axis: x ϭ b. Angles and Distances If u ϭ angle from the line with slope m1 to the line with slope m2, then tan u 5 sin u. For every value of the parameter u, there corresponds a point (x, y) on the circle. The ordinary equation x2 ϩ y2 ϭ a2 can be obtained from the parametric equations by eliminating

and yЉ ϭ f Љ(x) are the first and second derivatives of f (x) at the point P. Note that dx ϭ ds cos u and dy ϭ ds sin u. The curvature, K, at the point P, is K ϭ 1/R ϭ du/ds; i.e., the curvature is the rate at which the angle u is changing with respect to the length of arc s. If the slope of the curve is small, K < f ssxd. is easy. The most common integrable forms are collected in the following brief table; for a more extended list, see Peirce, “Table of Integrals,” Ginn, or Dwight, “Table of