Calendar: 1868-1869 Page 501

APPLIED SCIENCES 503 13 If PG be normal to an ellipse show that the tan CPG e2 j2 CP 14 In the ellipse the length of the focal chord 15 Find the angle through which the axes must be turned in order that 5yx y2 may be reduced to Ax1 Bf 16 If β2 5xy χ 2y be reduced to χ2 y2 a2 V2" show that -זד --- Also find a2 a2 L2 6' V2 17 The straight lines drawn from any point in an equilateral hyperbola to the extremities of any diameter are equally inclined to the asymptotes VII Department of tfte &ppliefc Sciences -PlatijematicS The Mathematical Papers are the same in each case as those given for the Department of General Literature and Science II -flatural $Ι ίΙο ορϊ £ SECOND AND THIRD YEARS If the coefficient of friction of rough screw be the length of the cylinder feet and the circumference inches find the least number of turns that may be given to the thread in order that weight may be supported on the screw without the action of any power From board in the form of square an equilateral triangle having one of the sides of the square for its base is cut out find the position of the centre of gravity of the remainder pressure is applied in direction inclined at 60 to the