Calendar: 1856-1857 Page 368

GENERAL LITERATURE AND SCIENCE 369 OX OA OB OC &e- the locus of is straight line 10 If chord be parallel to the diameter of an ellipse the supplemental chord is parallel to the conjugate diameter 11 Find the volume of the solid generated by the revolution of the witch round its asymptote 12 CP and CD are semi-conjugates and Ρ Κ and Κ normals at Ρ and show that CK is perpendicular to Ρ II -iHtrijantca Cfjtorg of Equations cone is cut by plane perpendicular to and bisecting the axis find the centre of gravity of the frustum Determine the conditions of equilibrium of the wedge the friction of the points in contact being considered Define the term virtual velocity and apply the principle to find the position of equilibrium of beam resting between two given inclined planes Ρ descending draws over pulley if Ρ be detached determine the motion of λ χ-y Trace the curve find its asymptote and area Show that the curve defined by x- -a -a is parabola find its latus rectum and the position of its vertex and axis Transform the equation x3 7χ into one whose roots are the squares of the differences of its roots and show that all the roots of the original are real Express the sum of the mth powers of the roots of an equa- tion in terms of the coefficients and the sums of the inferior powers Give Descartes' method for the solution of biquadrate- Ex xl- 1x Λ Λ