Calendar: 1871-1872 Page 522

522 GENERAL LITERATURE AND SCIENCE ז- as ρ ar 12 In any plane curve show that dj dP Ρ where ρ is the radius of curvature and ρ the perpendicular on the tangent at the point whose polar coordinates are and Θ 13 Integrate ניW a1 -f- i£ dx cosar 14 Show that the envelope of the circles described on the radii vectores of the curve r2 a3 cos θ is given by the equation ρ cos 119dj יי nieA 311 15 Find the area included between the curve ן a2 ar2 a4 and its asymptotes χ 16 In spherical triangle sin sin 'B sin sin sin sin sin j5 Two angles of opherical triangle and the adjacent side being given find the length of the arc drawn perpendicular to that side from the opposite angle III -aigtbra Find the value of χ χ 8y 8y when χ and Multiply a2 A2 -a ae be by Find the continued product of χ χ χ2 xy χ1 xy y1 Divide 4' by a3 2a2 2aA2