Extending work by F. K. Harris, we show how to produce a highly uniform magnetic field in a rectangular box long compared with its cross section, by using a pair of rectangular coils placed on opposite sides of the box. If the width of each coil is 3½times the distance between them, the region in which the field deviates less than one percent from the value at the center is about nine times larger than that obtained with previous coils having other width‐distance ratios. The use of square wire‐bundlles causes the main correction terms depending on finite cross section to vanish. The homogeneity achieved compares favorably with that obtainable by Helmholtz coils.