Calendar: 1851-1852 Page 314

GENERAL LITERATURE AND SCIENCE Trace the curve defined by the equation- a3 And find the area between the curve and asymptote Find the range of projectile upon an inclined plane passing through the point of projection its greatest height above the plane and the force with which the plane is struck 10 If be the resultant of any number of forces acting upon point in the same plane and be perpendicular from any point upon its direction and ρ be also perpendicular on force show that- Rr Σ Pp 11 When heavy body descending draws up very light one by means of string passing over fixed pulley the pressure on the pulley is four times the weight of the smaller body 12 The spaces described from rest by body acted on by any finite force are in the beginning of the motion as the time "' 13 body moving in parabola has its velocity suddenly doubled what is th orbit now described 14 CP CQ are drawn at right angles to each other from the centre of an ellipse find when their rectangle is greatest 15 If be positive for all values of χ between and a- -h then -j is also positive 16 Draw tangent plane to any surface find the content of the pyramid cut oil'by it from the three axes and show that this pyramid is less for the surface xy ζ a3 than for any other 17 If two chords of circle drawn from the same point present two forces and if one subtend an arc of 90 find the other when the resultant is maximum 18 Apply the Integral Calculus to sum the series-