# Calendar: 1858-1859 Page 420

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422 GENERAL LITERATURE AND SCIENCE water and mercury specific gravity 13 57 are connected by syphon tube filled with mercury the extremities of which are in horizontal line foot below the surfaces of the fluids Explain the effect and find the ultimate difference of height of the fluids Perpendiculars are drawn from given point in the axis of ζ to tangent planes to the surface s1 y2 find the locus of their extremities Planes are drawn touching the surfaces of an ellipsoid and concentric sphere show that the curves which are the loci of the points of contact lie on two concentric ellipsoids MIDDLE SCHOLARSHIP -Conic Sections antJ algebraic eomttrn Find the angle between two lines whose equations are given Ex Between two lines which meet in the point one of which passes through the origin and the other cuts the axis of at distance 25 from the origin Determine the length of the perpendicular from given point on the line χ Ex From the point on the line χ by -ab Show how to transform the equation to curve referred to rectangular axes when the new system is rectangular and in- dined to the former at given angle Apply it to the curve xy -y a3 when the axes are turned through an angle of 45 Investigate the equation to the tangent at any point of circle Show that the tangent is perpendicular to the radius drawn to the point of contact Find the general polar equation to the circle Show that the necessary condition that the two circles r2 21 cos θ 42 and r2 -2 re sin β cP should touch one another is that 42 cPf a2 42 c2 rf2

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