Calendar: 1848-1849 Page 253

GENERAL LITERATURE AND SCIENCE 251 If from the angles of Δ Λ Β through any point lines Bb Cc be drawn to the opposite sides then Β Cb aC If and be the radii of the circumscribed and inscribed circles of triangle ABC η It sin sin sin 21 21 Find the equation to the epicycloid in terms of ρ and and show that its evolute is also an epicycloid 10 Find the law of force tending to the focus of an ellipse and deduce the periodic time 11 chain slides off fixed pulley find the time 12 The difference in length between an hyperbola and its asymptote is finite 13 Find the equation to straight line in terms of the per- pendicular from the origin and the part intercepted by the axes Ρ 14 If when χ its value may in general be found by the diff calculus Ex log -x when χ 15 The chord arc and tangent are ultimately equal Lemma 16 Find the locus of the vertices of the parabolas which have given focus and which touch given line 17 weight Ρ is attached to the extremity of the string CP which'passes through ring at the end of string BC find position of equilibrium and tension of BC and Β being in horizontal line 18 Find the equation to the uniform catenary and the co-ordinates of the centre of gravity of the semi-arc 19 uniform rod rests with one end against vertical line and the other on curve find the equation to the curve that the rod may rest in any position 20 Integrate x-Vir2- es1n -0