We live in days when more than ordinary care is taken to extract from jam-pots, gardens, dust-bins and ourselves the maximum of productivity; and in such times why should mathematical tables be exempt from the general squeeze? To all of us, I suppose, there come moments when we say “For this calculation I wish I had tables giving more figures”: such cases occur especially when anything is found as the difference of two much larger quantities, in which a small percentage-error may appear greatly magnified in their difference (weighing the ship’s cat by the displacements before and after she fell overboard). I shall outline here and attempt to justify the least laborious that I know of methods by which the inevitable approximation-errors can be cut down to a much smaller mean than is involved in using the crude values as printed.