The following is a table of the diameters of shafts, being the first movers, or having 400 for their multipliers: TABLE, Exhibiting the velocity of motion, for boring cast iron Cylinders, Pumps, &c., and heavy turning, with fixed cutters. It will be observed that the surface bored is constantly the same, 78.54 in. per minute; this velocity is found to be the most advantageous a velocity greater than this, not only takes the temper out of the cutters, but also causing more heat, expands the metal; and if the machine stops but for a few seconds, a mark is left from the contraction of the metal. NOTE, Turning has a velocity double to that of boring. N. B. The progression of the cutters may be th of an inch for the first cut, and for the last, th. If hand-tools are employed in turning, the velocity may be consid erably increased. CENTER OF PERCUSSION AND OSCILLATION. The center of percussion and oscillation, is the point in a body revolving around a fixed axis, so taken, that when it is stopped by any force, the whole motion, and tendency to motion, of the revolving body, is stopped at the same time. It is also that point of a revolving body which would strike any obstacle with the greatest effect; and, from this property, it has received the name of percussion. The centers of oscillation and percussion are generally treated separately; but the two centers are in the same point, and therefore their properties are the same. As in bodies at rest, the whole weight may be considered as collected in the center of gravity, so in bodies in motion, the whole force may be considered as concentrated in the center of percussion; therefore, the weight of the rod multiplied by the distance of the center of gravity from the point of suspension, will be equal to the force of the rod divided by the distance of the center of percussion from the same point. Example.-The length of a rod being 20 feet, and the weight of a foot in length equal to. 100 oz.; also, a weight or ball, fixed at under end, weighing 1000 oz. at what point of the rod, from the point of suspension, will be the center of percussion ?* The weight of the rod is 20 × 100=2000 oz., which, multiplied by half its length, 2000 × 10=20000, gives the momentum of the rod. The weight of the ball = 1000 oz., multiplied by the length of rod, =1000 × 20, gives the momentum of the ball. Now, the weight of the rod, multiplied by the square of the length, and divided by 2000 × 202 3= =266666, the force of the rod, and the weight of the ball, multiplied by the square of the length of the rod, 1000× 202-400000, is the force of the ball: therefore, the center of per266666 +-400000 3 666666 =16.66 feet. Example.-Suppose a rod 12 feet long, and 2 lbs. each foot in length, with 2 balls of 3 lbs. each, one fixed 6 feet from the point of suspension, and the other at the end of the rod, what is the distance between the points of suspension and percussion? 12× 2×6=144, momentum of rod. do. of 1st ball. As the center of percussion is the same with the center of oscillation, in the non-application to practical purposes, the following is the easiest and simplest mode of finding it in any beam, bar, &c.: Suspend the body very freely by a fixed point, and make it vibrate in small arcs, counting the number of vibrations it makes in any time, as a minute, and let the number of vibrations made in a minute be called n; then shall the distance of the center of oscillation from 140850 n2 inches. For the length of the the point of suspension be pendulum, vibrating seconds, or 60 times in a minute, being 39 inches; and the lengths of the pendulums being reciprocally as the square of the number of vibrations made in the same time: therefore, n2 602: 391: 602 × 391 140850 being the length of the pendulum, which vibrates n times in a minute, or the distance of the center of oscillation below the axis of motion. There are many situations in which bodies are placed, that prevent the application of the above rules; and, for this reason, the following data are given, which will be found useful when the bodies and forms here given correspond : 1. If the body is a heavy straight line, of uniform density, and is suspended by one extremity, the distance of its center of percussion is of its length. 2. In a slender rod, of a cylindrical or prismatic shape, the breadth of which is very small, compared with its length, the distance of its center of percussion is nearly of its length from the axis of suspension. If these rods were formed so that all the points of their transverse sections were equi-distant from the axis of suspension, the distance of the center of percussion would be exactly of their length. 3. In an isosceles triangle, suspended by its apex, and vibrating in a plane perpendicular to itself, the distance of the center of percussion is of its altitude. A line, or rod, whose density varies as the distance from its extremity, or the point of suspension; also, fly-wheels, or wheels in general, have the same relation as the isosceles triangle, i. e. the center of percussion is distant from the center of suspension of its length. 4. In a very slender cone, or pyramid, vibrating about its apex, the distance of its center of percussion is nearly of its length. |