Calendar: 1855-1856 Page 368

304 GENERAL LITERATURE AND SCIENCE 11 body is projected in vacuo with given velocity at an angle of elevation θ find the length of the path described and show that when the length is greatest θ may be found from the equation- λ cosec cosec sec θ 12 Find the equation to the surface every point of which is equidistant from two given points 13 If be the volume of solid and yf be the coordinates of point in it then-- V-zdxdy 14 Apply the preceding expression to find the volume of the solid xy ζ a3 included by three coordinate planes 15 Draw tangent plane to the ellipsoid find the length of the perpendicular from the centre upon it and the locus of its extremity 16 body describes circle round point within it deter- mine the force and find the periodic time Explain the circumstances of the motion when the point is without the circle 17 perfectly elastic ball falling from the top of tower strikes half-way down ledge inclined at an Ζ θ to the height of the tower find Θ that the ball may reach the ground at distance from the tower's foot equal to half the tower's height II -Conic Sections Differential antJ ihitcgral Calculus IfSQ be drawn bisecting the angle Ρ in an ellipse and equal to the mean proportional between and SJP show that will describe an ellipse of which is the centre and find its eccentricity Find the value of log when η η is zero Trace the curve defined by 7r Θ 12 cos Θ show that the distances at which it cuts the axis are inversely and the tangent of the angles directly as the odd numbers commencing with unity