Calendar: 1886-1887 Page 677

GENERAL LITERATURE AND SCIENCE 679 finite angle prove that the ultimate value of the ratios of PT9 the arc PQ and the chord PQ when moves up to are ratios of equality Deduce that lte lt$ θ θ Determine so that the straight lines χ 1-4 5- 4- may intersect and find the point of intersection 10 Examine the nature of the surface represented by xy az 11 Circles are described on the chords of given circle that pass through given point in its circumference as diameters in planes perpendicular to the plane of the original circle find the equation of the surface generated 12 Determine the position of the centre of gravity of an arc of the cycloid χ α θ -f sin Θ cos0 and prove that if the arc be of length 2c the difference of the ordinate of the middle point of the arc and of the centre of gravity is c2 2£a 13 heavy particle falls from rest subject to resistance which varie as the square of the velocity prove that the velocity will continually increase but not surpass certain limit If projected downwards with this limiting velocity what will be the character of the motion 14 State and prove the conditions of equilibrium of body floating in fluid If right circular cone float with generating line vertical the specific gravity of the cone must be to that of the fluid as cos 2a 00$2α where 2a is the vertical angle of the cone II algebra an Siffmnttal Calculus Land has been sold in London at the rate of million pounds an acre find the value of square inch to the nearest ha eni