Calendar: 1858-1859 Page 418

120 GENERAL LITERATURE AND SCIENCE 10 Investigate tbe equation to plane in terms of its intercepts on the axes Determine the equation to the plane which passes through given point and cuts the axes at distances from the origin in the proportion of 11 Define hyperboloid of one and two sheets find the equation to the former and show that it has an interior conical asymptote 12 Show how curve in space may be defined by equations and investigate the equation to the normal plane at any point II- ίΗίφηίαί anil &na1O$tattciS Find the resultant of two parallel forces acting on body weight of 10 lbs is attached to point in the circumference of circle find the weights which must be attached at two points whose angular distance from the above are 90 and 120 in order that the circle may rest in horizontal position when supported at the centre Define the centre of gravity of body or system of bodies and find that of system of particles in one plane At the angular points of regular pentagon are placed in order weights which are in arithmetical progression find the distances of their centre of gravity from the greatest and least Determine the condition of equilibrium on the screw Enunciate the principle of virtual velocities and prove it for the inclined plane Two imperfectly elastic balls impinge directly on one another find their velocities after impact Show that the motion of their centre of gravity is unaltered by the impact Prove the formula J- ft If particle has an initial velocity find the velocity alter describing given space under ttie action of an accelerating forceyin the direction of motion particle is projected from given point in an inclined plane find the range and the time of flight Define fluid Find the pressure at any point of mass of fluid at rest under the action of gravity