Calendar: 1854-1855 Page 354

35G GENERAL LITERATURE AND SCIENCE Find the equation to cylindrical surfaces when the directrix is curve of which the equations are x2 -f- r2 cx Given the time of comet's passage from one extremity of the latus rectum to the other find the length of the latus rectum 10 The sum of the curvatures of any two normal sections at right angles to each other is constant 11 Of all the straight lines which touch surface in give point find that whose inclination to the plane of χy is greatest 12 sphere is pierced by cone the diameter of whose has is equal to and coincident with the radius of the sphere draw tangent to the curve of their intersection and find the locus the point where the tangent meets the plane of χy 13 The earth being supposed to be an oblate spheroid fin the actual gravity in given latitude 11 Prove Newton Prop and from the expression for the force deduce the equations and apply them to find the force to the pole of the Lemniscate and the velocity at any point 15 If be continuous between χ and χ and if and its η-1 derivatives vanish when χ α Λ 7ך 16 Sis the focus and Β the semi-minor axis of an ellipse body falls from Β along Β till it acquires the velocity in the curve at it is then projected perpendicularly to SB with the acquired velocity find the eccentricity of the curve that will be described III -Cl ricj of ium1 eitvibctlj The questions upon this subject were the same as those set for the Senior Classical Scholarship See ante 346