Calendar: 1859-1860 Page 441

442 GENERAL LITERATURE AND SCIENCE Investigate method of determining the asymptotes of an algebraical curve Ex y- 2x y2 r2 4a2 ift Integrate -τ-1- and -- Find the bx cx2 x5 Ja2 x2 area of loop of the curve cos θ State and prove Newton Lemma II Apply it to find the area of parabola Define the circle of curvature at any point of plane curve and prove that the diameter of curvature perpendicular subtense Give figures showing the position of the circle of curvature at the vertex and at any other point of parabola If body move in any orbit about fixed centre of force the areas described by lines drawn from the centre to the body lie in one plane and are proportional to the times of describing them Show that the areas described will not be affected by an im- pulse given to the body in the direction of the force body describes an ellipse under the action of force always tending to the centre find the law of force body is projected with given velocity in given direc- tion about centre of force which varies inversely as the square of the distance find the nature and elements of the orbit described and determine its equation When will it be circle 10 Investigate the equation to plane in terms of the perpen- dicular from the origin and its inclinations to the axes of co- ordinates 11 Find the equation to an oblique cone whose base is circular Determine the equation to the cone whose vertex is at the origin and whose generating line "always touches the sphere a2 12 Find the equation to the surface of the elliptic paraboloid