And it is evident that the same part of W is sustained. Hence the whole pressure on the axis is 4PW P+W 582. Generally the time of an oscillation through an arc, the versed sine of half of which is (h), is (see 571.) I being the radius or length of the pendulum. Now A the are being small compared with the whole circumference, we have A2 h = 21 and if n be the number of degrees in this arc, we get Hence, if the pendulum oscillating through n degrees keeps true time, the error arising from its vibrating through N degrees is 583. The accelerating force down the plane is sin. è, and พ 0 the mass + inertia = w + = w, being the inclination 2 3 2 to counteract which by means P, we must have which gives the ratio of the height of the plane to its length. 584. Let a be the length of the rod, then S being the moment of inertia, M the mass, and k the distance of the centre of gravity from the axis of suspension, the length of the first pendulum (see Venturoli) is 585. Take any zone contained between two sections indefinitely near to each other, made by planes axis of rotation, VOL. II. 2r2 surface of sphere x 3 2r2 3 ..the distance of the centre of gyration from the axis of ro tation, is r ✓2 (Venturoli.) 586. Let x be the weight required, a, k, M; x', k', M' the distances of the centres of oscillation from the axis of rotation, those of the centres of gravity and the masses of the respective parts d, l-d. Also, let x", k", M", x", k"", x be those of [the weights added to the lower and upper extremities of the rod; then the length of the pendulum is = _—_d, x' = —— (1−d), x′′ = 1 — d, x′′" = d. λ= al (l–d) × d 2d Let L, L' be the lengths of the two pendulums. Then |