Calendar: 1858-1859 Page 429

APPLIED SCIENCES 431 β Find the locus of point from which the circular disks of the sun and moon will appear of the same magnitude Integrate the differentials f- τ Vru Sin C03 de and χ a2-from χ to χ If AP and AQ be drawn from the vertex of parabola to points Ρ and in the curve and PAQ be right angle AP AQ 16 α2 ΛΡ If chord and diameter of an ellipse be parallel the supplemental chord is parallel to the conjugate diameter 10 Find the radius of curvature of the parabola and the coordinates of its centre 11 Trace the curve defined by the equation 3- axy -f- x3 and find the area of the part within the positive axes of and 12 Prove Leibnitz's Theorejn for the differential co- efficient of the product of two functions Ex Find the 5th coefficient when x6 Cos II -$racttral anil Sesmptt'be Seonutrp The solutions to be strictly geometrical The semi-axes of an ellipse are and inches Draw tangent to the curve inclined to the axis at 37 Determine the centre of curvature at the point of contact Draw circle of 175 inches radius from any point 35 inches from the centre draw line to make an angle of 60 with the diameter through take two points Α Β PA 75 Ρ Β inches in this line draw circle to pass through and Β and to touch the given circle Draw the plan of regular pentagon of 15 inches side when two sides not adjacent are inclined at 35 55 to the plane of projection The plane of one face of regular tetrahedron of 25 inches edge is inclined at 28 and one edge in that plane is inclined at