In the production of nuclear magnetic resonance images, it is necessary to provide various magnetic fields with specified orientations and configurations in particular relationships with respect to a cylindrical coil form on which the RF and gradient coils are generally disposed. In particular, it is necessary to produce so-called transverse gradient fields which are oriented transversely with respect to the cylindrical form. It is necessary to produce a component parallel to the axis of the cylinder, but which component varies linearly in intensity in the direction transverse to the axis. That is to say, it is desirable to produce a magnetic field component within the cylinder such that surfaces on which this component is constant are parallel and are generally oriented parallel to the axis of the cylinder. Furthermore, for the purpose of providing proper spatial definition and resolution, it is necessary that this transverse field exhibit a highly linear variation in intensity inside the cylinder. In a nuclear magnetic resonance imaging system, two such coil sets are required and are oriented at right angles to one another so as to generate x-axis and y-axis positioning information. The present invention describes coil winding patterns which are capable of producing such transverse gradient magnetic fields with an exceedingly high degree of linearity.