Calendar: 1881-1882 Page 624

GENERAL LITERATURE AND SCIENCE 626 then Solve the cubics 2x 30 6U2 26x If be primitive root of the equatic til the roots of the equation are given by a2 a3 an Prove that the sum of the th powers of these roots unless κ is multiple of when it Deduce method for summing the nth terms of known series for example every third term of cos χ or Transform the equation xA -f- px3 2י to one in which the roots are Hence deduce an expression for aA μ 03 £3 The vanishing subtenses of the angle of contac curves ultimately in the duplicate ratio of the chords of the con- terminous arcs Show that if the tangent and normal at any point of curve be taken as axes of χ and then if denote point on the curve near the origin and ρ the radius of curvature at the origin the limit of 2x as the point xy moves up to the origin Find from this or by any other means the radius of curva- ture of an ellipse the top of high wall surmounted by semi-circular coping