Calendar: 1861-1862 Page 492

GENERAL LITERATURE AND SCIENCE 493 MATHEMATICS -SENIOR SCHOLARSHIP -fHrcijamcS anlf $pttro£tattr0 Fisd the resultant of two forces whose directions are parallel Two forces act along opposite sides of quadrilateral in circle towards the same parts and are respectively proportional to these sides prove that the resultant will pass through the intersection of the diagonals stick is placed between two horizontal bars with its end resting on the ground find the pressure on the ground and on each bar Prove the principle of virtual velocity in the case of the lever in the case of the pully where each string is attached to the weight the weight of the moveable pullies being considered heavy hemisphere just rests with its convex surface on rough inclined plane Find the plane's inclination Prove the equations ftim ג 2ע body is projected up an inclined plane find how far it will ascend Find the equation to the path of projectile and thence deduce the greatest altitude and range second-pendulum is taken to the bottom of mine depth find the alteration in the number of beats Ex let mile 10 When two fluids that do not mix meet in bent tube the altitudes of their surfaces above the horizontal plane in which they meet are inversely as their densities II siphon is used for decanting fluid whose specific gravity is find the limit to the height of the highest point of the siphon above the surface of the fluid when the barometer stands at 29 inches 12 Find the pressure of fluid on any surface cube and sphere of equal surfaces are just immersed in fluid Show that the pressure on sphere that on cube Ν π