Calendar: 1849-1850 Page 284

282 GENERAL LITERATURE AND SCIENCE If and χ be considered functions of the length of curve and be the radius of curvature Ex χ log αί Draw tangent to an ellipse which shall cut the circle on the axis major at 45 and show that this is nut possible fur every degree of eccentricity If -f sin expand in terms of Find the roots of the equation r3 -f ρ χ by the inter- section of straight line with circle 10 Find the pressure on the fulcrum of bent lever 11 If ζ -f ax Χ φ eliminate the arbitrary function 12 The homologous sides of similar curvilinear figures are proportionals and the areas are in the duplicate ratio of the homologous sides 13 Let straight line have its extremities always in the circumferences of two equal circles Find the locus of the middle point of 14 If Ρ Τ be tangent to parabola at given point and Τ be any other tangent the angle Τ is constant 15 Prove that- tan χ χ r3-4 25 י "יr 4י" ג" 16 Integrate- dx Cos χ cos η χ cos ρ χ χ χ χϊ χ3 tan -Κ dx 17 Given the base and altitude of pyramid construct it so as to have the least surface 18 right angled triangle rests between two given props the right angle downwards determine its position of equilibrium