Calendar: 1850-1851 Page 327

APPLIED SCIENCES 323 If tan φ cos tan Θ then shall φ Θ tan 2- sin tan 4- sin &c semicycloid revolves round its axis find the surface of the solid generated Γ X- odd from χ to χ and a2 ג cos θ θ e2cos 20 10 Describe the greatest isosceles triangle about given ellipse 11 Trace the curve χ 10 χ χ2 and find its area 12 If Sand Η be the foci and Ρ point in an ellipse find the locus of the centre of the circle touching the sides of Η JUNIOR SCHOLARSHIP Prove the parallelogram of forces If three forces keep rigid body at rest show that if they meet at all they must meet at the same point Determine the conditions of equilibrium of three parallel forces acting on rigid rod What is the centre of gravity of body and how may it be found experimentally Determine the centre of gravity of triangle When set of forces act upon lever show how to find the pressure on the fulcrum Determine the relation between the power and the weight in the case of the inclined plane the power acting along the plane