These three examinations were all conducted more than twenty years ago, before standardized methods of measurement had been developed. It is difficult to glean from them, and from the biographical material compiled by Scripture and by Mitchell, what the truth is, as regards the extent to which this gift for calculation was special in these persons. Many of them, as we have seen, were certainly men of genius, with general capacity for selective thinking. Several others probably were not of superior general intelligence, but in no case can we be certain, on the basis of anecdotal evidence alone. Some of them were peasants or slaves, born to manual toil, in the absence of free schools, and in the presence of rigid class distinctions. It is not inconceivable that a child of IQ over 170, condemned by unavoidable environment to herd sheep or pick cotton through his youth, might find relief from the monotony of his work by calculating. As Mitchell, himself a lightning calculator, says, “Given a knowledge of how to count, and later a few definitions, and any child of average ability can go on, once his interest is accidentally aroused, and construct, unaided, practically the whole science of arithmetic, no matter how much or how little he knows of other things.” This statement is probably true, if we change one word, and substitute for “child of average ability,” “child of great ability.” All who have examined lightning calculators, or searched their biographical records, are agreed that the secret of their power lies in highly developed mechanics. Special _habits_ of combining and recognizing numbers are formed, which differ from ordinary calculation comparatively in somewhat the same way as the method of the child who added 7 + 5 by adding 7 + 2 + 2 + 1, the latter being analogous to the usual method. The lightning calculator memorizes combinations far beyond those ordinarily memorized, so that he is, for instance, able to add 2581 + 1763 as quickly as an ordinary person can add 15 + 8. He learns multiplication tables up to 100 × 100, whereas we learn only through 12 × 12. He devises and uses many “short cuts,” _e.g._ multiplying by two easy numbers and taking the difference, instead of multiplying by an awkward number. Multiplication is probably used as the fundamental operation.