Calendar: 1857-1858 Page 397

GENERAL LITERATURE AKD SCIENCE 399 Eliminate and from the equation ax1 by" bx y-x Integrate the differentials zdx sin Oa ο ά and --- i-t-enn σ 10 and HZ are perpendiculars from the foci on the tangent of any point Ρ of an ellipse find the intersection of SΖ and HY and its locus 11 Find an expression for the radius of curvature when the arc is the independent variable and apply it to the curve in which Iβ log 12 Find the area of the evolute of an ellipse where -6 ab 13 Prove that χ άη 2θ χϊύη ΖΘ יי χ sin θ -j--- -----f- &c c08 β sin cos ο 14 The equation -f- ry χ expressed by polar co-ordinates the origin being the pole is r2 a2 tan θ trace the curve and find its area IL-fHttijantcS Cljrorp of Equations Find the resultant of two parallel forces acting upon rigid line Find the relation between the coefficients and roots of an equation Form the equation of which the roots are Find the centre of gravity of the quadrant of circle AB is given horizontal fine BC uniform beam of given