Calendar: 1851-1852 Page 315

general literature and SCIEX1 319 II Find the equation to the surface of the hyperboloid of one sheet show that it has an interior conical asymptote and that it can have an infinite number of straight lines entirely coinciding with its surface r2 a2 Deduce the equation ϊτ ------ to the י by or epicycloid and show that the arc corresponding to one revolu- tion of the generating circle ך -f Find the solidity of paraboloid by Newton Lemma Find the law of force tending to the pole of the equi- angular spiral to the focus of an ellipse APQ is rectangular hyperbola the centre Β tangent at the vertex and area η area then l-AD AD Α Β If the origin of the coordinates be the centre of force varying as the distance and particles be projected at the same moment with equal velocities from various points in the axis of they will all arrive at the same point in the axis of χ and at the same moment Find the length and coordinates of the extremity of per- pendicular from given point upon given line Hence to find the locus of point which is equidistant from two lines given in space Two parabolas have common focus and axis tangent to the one intersects tangent to the other at right angles find the locus of their intersection 10 The square of the area of any plane section is equal to the