In certain esoteric mathematical and computing circles there is, or used to be before the advent of the electronic computer, an interest in near-integral solutions of incommensurable problems. Apart from aesthetic considerations such solutions can have valuable applications in the checking of methods of computation; this is the excuse for the following note.

The investigation from which it arises was itself a by-product. As part of the British contribution to the new Sight Reduction Tables for Marine Navigation (H.O. 229 in U.S.A.; H.D. 605, in the United Kingdom) it was necessary to examine carefully each of the approximately 20 million figures in the six volumes; although the setting was computer-controlled and numerically checked, only visual examination could detect indistinct or broken figures. Such examination is extremely arduous and calls for great powers of concentration if its purpose is not to be wasted.