Saddle shaped coils for generating a field perpendicular to the axis of a cylindrical shell to which the coils are confined can be designed in a compact and easily constructed form. The central magnetic field of such a system and its second derivatives with respect to displacements from the center are given as functions of the coil dimensions, and conditions for minimizing these derivatives are discussed. A coil pair with a length‐to‐diameter ratio of 2 and circular arcs of 120° will have no second order central field derivatives in any direction.