Calendar: 1887-1888 Page 666

670 GENERAL LITERATURE AND SCIENCE Division -ficfoton £pf crtcat Crtgonomctrp anH Cijcori 01 Squationi What is the test that varying quantity tends to finite limit Prove strictly that to infinity is SI Π Find value of χ so that the value of- shall differ from χ by less than 002 Shew how Newton's method of finding the area included within curvilinear boundary by summing inscribe figures may be adapted to polar coordinates Apply it to find the area of cos Θ Prove that in curves of finite curvature the ultimate ratios of vanishing arcs chords and tangents are ratios of equality Through TPQ TP'Q' are drawn to cut circle in PQP'Q' prove that when TP'Q' moves into coincidence with TPQ the ultimate ratio of the vanishing arcs PP' is equal to TP TQ If the relation between the perpendicular from the origin on the tangent and the radius vector of curve isf prove that the corresponding relation for the pedal curve is Find the equation of circle referred to point on the circumference and deduce that of the cardioid Prove that hypocycloid may be described in two ways by the rolling of circle within another circle and that the sum of the radii of the two rolling circles is equal to the radius of the fixed circle The arc of great circle drawn from the pole of great circle to any point on the circumference is quadrant and is at right angles to the circumference Hence shew that if in