# Calendar: 1852-1853 Page 331

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GENERAL LITERATURE AND SCIENCE Ex If χ pass througli the intersection of and a3 f2 find Two bodies Ρ and balance on lever find the alteration of the fulcrum when -th part of and th part of are η removed Draw tangent to an ellipse and show that if it be drawn to the extremity of the latus rectum and any ordinate Ν Ρ to point Ρ in the ellipse be produced to meet it in that Ν Find the law of force by which circle may be described the centre of force being external The sum of the curvatures of any two normal sections at right angles to each other is constant chord Ρ cuts the axis of parabola vertex in Ο ordinates Ρ Ν and Μ being drawn show that Α Μ Ν AO 10 An isosceles roof vertex supports given weight at find the horizontal force at Why must pointed arch carry heavy weight at the vertex 11 Find the centre of gravity of the sector of sphere 12 Integrate the following differentials xA χ adx dx -- -- -- 3י ץ2ן cosAr sin χ tan 13 An imperfectly elastic ball lies on billiard table deter- mine the direction in which an equal ball Β must strike it in order that they may impinge upon side of the table at equal given angles d2u d2u 14 If andtf2 r2j then d2 du י -- r2 15 Eliminate the arbitrary functions when bx ay-bx 16 Find point within triangle from which if lines be drawn to the angular points their sum shall be the least possible

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