Calendar: 1881-1882 Page 625

626 general literature and science of radius intending to play see-saw The plank being balanced with boy at either end one of them then moves slowly down the plank towards the wall Show that they will come to grief when he has traversed distance from his end -f 2w to tan-1 μ being the coefficient of friction between wood and brick Find the direction-cosines and length of the perpendicular let fall from fgh on ζ η Show that the foot of this perpendicular is given by -g -f -f Find the equation to the right cone of angle having the point abc for vertex and Imn for direction-cosines of axis Find the angle and axis of the cone 10 Find the equation to the normal to the ellipsoid Μ at the point fgh If be the centre of the ellipsoid and CY the perpendicular on the tangent-plane at Ρ fgh then if the normal at Ρ meet the plane in show that ct pq Sa'w b2 c2 11 Determine the axes of the section of the ellipsoid τ 42 c2 by the-plane my and the centre of the section by the plane Ix f- my nz