A set of three formulae for the longitude λ, latitude φ and back azimuth A of the normal section (to P_o) at a point P on a rotational ellipsoid, given the longitude λ_o and latitude φ_o of an initial point P_o and the distance s and forward azimuth A_o (of the normal section) of P from P_o, as derived by A. R. Clarke (1880). The formulae are correct to about 1 part in 106 at 150 kilometres if 7 significant figures are used in the computations. The useful distance can be increased to about 750 km by using one of several modifications of Clarke's formula by, e.g., Rainsford (the Clarke Rainsford formula).