Calendar: 1849-1850 Page 293

APPLIED SCIENCES 201 If chord be drawn through the focus of parabola the tangent at one extremity is parallel to the normal to the other Find the equation to the Cissoid and the volume of the solid formed by its revolution round its asymptote Integrate log ך from χ to χ Trace ץ χ find whether the curve is con- cave or convex to the axis prove that the axes are tangents and find the area included by them and the curve 10 In the ellipse find the angle the normal Ρ makes with the axis major when the angle CP is maximum 11 Shew that the equation τ χ 2x2-j5 represents two straight lines Η 12 If log cos find μ in series of cosines 13 Find the area defined by 14 If and be the radii of the ends of parabolic frustum the Parabolic frustum Inscribed Conic frustum a2 a2 ab δ III -iurrljnmut Explain the meaning of the term Work and show that the work accumulated in moving body is half its vis viva Show that the vis viva of rigid body is equal to its vis viva of rotation added to its vis viva of translation Find the moment of inertia of uniform rod turning about one end What is meant by the term Effective Force When an angular velocity is communicated to beam turning about point show that the moment of the effective forces about that point is equal to moment of inertia multiplied by angular velocity Explain the method of finding the motion of free beam after the impact of ball upon it