The thrust magnitude programme of a rocket missile being supposed specified, the problem is solved of programming the thrust direction to achieve maximum range on the Earth's surface. Earth curvature and rotation, and variation of gravity with height are taken into account, but air resistance is neglected. Motion is assumed to take place in the Equatorial plane. Tables are included from which the optimal trajectories of missiles may be computed when two design parameters are known and these tables are used to assess the advantage to be gained at extreme ranges by firing in the sense of the Earth's rotation rather than against it.