Calendar: 1849-1850 Page 285

GENERAL LITERATURE AND SCIENCE 283 II If Ρ be the chord of an arc of the logarithmic spiral Ρ Τ Τ two tangents and the pole then Τ Ρ Ρ Ρ Τ QT In the parabola if Ρ be the abscissa of any diameter and be the ordinate SP PV V2 Given the base of triangle find the locus of the vertex when the exterior angle is three times the interior and opposite angle trace the curve draw its asymptote and find the area In the hyperbola the focal distances make equal angles with the tangent The nth part of triangle is cut off by line parallel to the base find the centre of gravity of the remainder Find the law of force tending to the centre of an ellipse to the focus of parabola and in case determine the velocity and periodic time row of inelastic balls the magnitudes increasing in geo- metrical proportion are placed at equal distances in straight line given velocity is communicated to the first required the time before the wth is put in motion If chord be drawn through the focus of parabola the tangent at one extremity is parallel to the normal to the other Two perfectly elastic balls impinge vertically on the centres of two planes AC CB inclined to the horizon respectively at angles of 30" and 00 determine the second points of contact of the balls with the planes and the point of intersection of the curves du י 10 Integrate J0 from χ to χ 00 11 Force a- and body is projected with velocity which is to the velocity in circle at the same distance ϋ -y jT Find the major axis eccentricity and periodic time of the ellipse that will be described