Calendar: 1857-1858 Page 396

398 GENERAL LITERATURE AND SCIENCE 15 Give instances of Homeric words used in totally wrong sense by the pedantic poets of Alexandria ΠΙ -CtanSlationi The same three pieces as for the Senior Scholarship IV £ptra ageS The same two passages as for the Senior Scholarship SENIOR MATHEMATICAL SCHOLARSHIP -Conic Sections Uiffcrenttal anU integral Calculus The cube is the greatest rectangular solid that can be cut out of sphere Find the equation to the normal at any point in the ellipse and prove that it bisects the angle between the focal distances at the point If Ρ he normal to any point Ρ of an ellipse and CQ perpendicular on it from the centre find the equation to the curve which is the locus of The surface of solid of revolution being denoted by and being the co-ordinates of point the extremity of curve dS ds then -ך π υ ד- dx dx Apply this expression to find the surface of the solid gene- rated by the revolution of semi-cycloid round its axis What is the locus defined by the equation- xy ay 3axi Show that its asymptotes include between the axes of χ and an area a1 Find that point in an ellipse at which line from the vertex makes the greatest angle with the curve