by which x and y can be computed for any point of the sphere. If from these equations we eliminate [omega], we get the equation to the parallel whose latitude is [phi]; it is an ellipse whose centre is in the central meridian, and its greater axis perpendicular to the same. The radius of curvature of this ellipse at its intersection with the centre meridian is k cos [phi] / (h sin [gamma] + sin [phi]). The elimination of [phi] between x and y gives the equation of the meridian whose longitude is [omega], which also is an ellipse whose centre and axes may be determined. The following table contains the computed co-ordinates for a map of Africa, which is included between latitudes 40° north and 40° south and 40° of longitude east and west of a central meridian. +-----+------------------------------------------------------------------------------+ | | Values of x and y. | |[phi]+--------------+---------------+---------------+---------------+---------------+ | | [omega] = 0° | [omega] = 10° | [omega] = 20° | [omega] = 30° | [omega] = 40° | +-----+--------------+---------------+---------------+---------------+---------------+ | 0° | x = 0.00 | 9.69 | 19.43 | 29.25 | 39.17 | | | y = 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | | | | | | | | | 10° | x = 0.00 | 9.60 | 19.24 | 28.95 | 38.76 | | | y = 9.69 | 9.75 | 9.92 | 10.21 | 10.63 | | | | | | | | | 20° | x = 0.00 | 9.32 | 18.67 | 28.07 | 37.53 | | | y = 19.43 | 19.54 | 19.87 | 20.43 | 21.25 | | | | | | | | | 30° | x = 0.00 | 8.84 | 17.70 | 26.56 | 35.44 | | | y = 29.25 | 29.40 | 29.87 | 30.67 | 31.83 | | | | | | | | | 40° | x = 0.00 | 8.15 | 16.28 | 24.39 | 32.44 | | | y = 39.17 | 39.36 | 39.94 | 40.93 | 42.34 | +-----+--------------+---------------+---------------+---------------+---------------+ [Illustration: FIG. 13.]