Centre of Gyration, Principles of Rotation. 1. The distance of R the centre of gyration, from c the centre or axis of motion, in some of the most useful cases, is exhibited below. In a circular wheel of uniform thickness c R = rad. ✔✅ §. In the periphery of a circle revolving centre.. } CR = rad. ✔ §. In a cone revolving about its vertex. . c R = 1 √ 12 a2 + } r2 In a cone. its axis.. CR = r√3 In a paraboloid 10° CR = r √ §. In a straight lever whose arms are R and r, c R = √3 (R+r)* 2. If the matter in any gyrating body were actually to be placed as if in the centre of gyration, it ought either to be disposed in the circumference of a circle whose radius is C R, or at two points R, R', diametrically opposite, and at distances from the centre each = c R. 3. By means of the theory of the centre of gyration, and the values of C R = 5, thence deduced, the phenomena of rotation on a fixed axis become connected with those of accelerating forces for then, if a weight or other moving power p act at a radius r to give rotation to a body, weight w, and dist. of centre of gyration from axis of motion = e, we shall have for the accelerating force, the expression and consequently for the space descended by the actuating weight or power P, in a given time t, we shall have the usual formula introducing the above value of f 4. In the more complex cases, the distance of the centre of gyration from the axis of motion may best be computed from an experiment. Let motion be given to the system, turning upon a horizontal axis, by a weight P acting by a cord over a |