and substituting in equation (b) we get v2 in terms of X, which gives the velocity of the body moving along the straight line or inclined plane. The velocity along the curve is As a particular case, let CA be the common parabola, its vertex being C and axis parallel to DB. Then the equation to the curve being which together with x, x' would still give a very complex expression for v2. Let us farther particularize by making mb, or by supposing the pulley fixed in the curve, and consequently b not <b. In which will also produce a very complicated result. These several computations being rather laborious than difficult, we leave to the student, to whom such exercises may be useful. The question may be still farther simplified by supposing one of the paths a straight line perpendicular to the horizon, and the other any curve whatever. which give the velocities of P and P' when P is at that point of the curve whose abscissa is X. Let the curve which P describes be the common parabola whose equation is P - X P + (a - X)2 2X = d.fX {X.pm {X. pm — X' + p2 (a−X)*}* which gives the velocity of P' in terms of X. If the curve and pulley coincide, we have m=b, pm = pb = a2 and .. Again, let X= a; then λ = 0, and we have P(a2 - a2)+P'l v=2gp. x(p2 + 4a2) p3P' + P. (4a2 + 1) (p3+2a2) 2 which gives the velocity of P' when P arrives at the pulley. 592. Let ADx, AP=z, BC AC a; then resolv ing the vertical tendency of P, viz. a+ P α into directions tangential and normal to the curve, and then again the normal part into vertical and horizontal components, we get the pressure sustained by the curve in a vertical direction expressed by Hence that part of P which remains unsupported by the re that is P' is supported by W. Hence the weight P is supported in all positions. 593. Let a be the height of the given cone, r the radius of its base; then since the moving force is P, and the momentum of inertia is (see Venturoli) M being its whole mass; therefore the accelerating force is 594. 3M + 10P Let R, r, be the radii of the wheel and axle respec tively; then the moving force is |