Calendar: 1851-1852 Page 364

3C8 THE SCHOOL 16 Give short accounts with dates of the following battles Trebia Cannae Philippi Actiutn Drepanum Saguntum 17 Give the geographical position and modern names of Tusculum Ariminum Ligusticus Sinus Latium Cajeta Iapy- gium Brundusium Epitus Eubcea Cythera Pylos SENIOR MATHEMATICAL SCHOLARSHIP -£tattc$ If forces keep point at rest each is as the sine of the angle contained by the directions of the other two In the lever show that if and β be the displacement of the extremities of the lever in the directions of the forces that Ρ β Two forces act in the same plane upon rigid body find the magnitude and point of application of their resultant and deduce from the result the pressure on the fulcrum of lever What mechanical principle is deducible from this proposition There is equilibrium between Ρ and in the inclined plane compare them the friction of the plane being considered beam hinged at rests against rough vertical wall find the pressure against the wall and the reaction of the hinge weight of 100 lbs suspended by string from fixed point is drawn from the vertical through an angle of 60 by horizontal force find this force and the pressure at The top of an isosceles triangle is cut off by section parallel to the base find the centre of gravity of the remainder and are the parallel sides the distance between them II -Cittjouonutn Find the arithmetical values of the sine cosine tangent and secant of 288 a2- -b" lab cos Prove this and adapt it tu logarithmic computation