Calendar: 1863-1864 Page 522

522 GENERAL LITERATURE AND SCIENCE that the defeat of Hannibal ensured the empire of the ancient world to Rome 13 Describe the town of Carthage "and give some account of the last siege 14 Draw map of ancient Sicily with towns mountains rivers &c 15 AVrite in Latin short account of Hamilcar SENIOR MATHEMATICAL SCHOLARSHIP 1863 -iHfrrti iHafljemattrsi body weighing cwt rests between two planes whose gradients are and find the pressure on each of the planes ball falls from the top of an inclined plane find where it will meet another ball projected from the bottom with velocity acquired in falling down an equally inclined plane times as long botli balls starting at the same instant particle rests upon the arc of parabola and is acted upon by gravity parallel to the axis and force perpendicular to it which is proportional to the distance of the particle from the axis find the position of equilibrium Two equal cylinders containing equal quantities of different fluids which do not mix are connected by an exhausted siphon find how much fluid will run from one vessel into the other Prove Lemma II and apply it to find the area of the curve in which the ordinate varies as the cube of the abscissa Find the law of force tending to the focus of an ellipse If r2 be the velocities at two points of the ellipse equally distant from the axis on the same side the velocity at the ex- tremity of the minor axis V1 In the equiangular spiral find the force to the pole the velocity at any point and the time to the centre body revolving in parabola has its direction suddenly changed at the extremity of the latus rectum from which it is