It is possible, therefore, in the last resort, to explain the Elberfeld mystery by the no less obscure mystery that surrounds numbers. This really only means moving to another spot in the gloom; but it is often just by that moving to another spot that we end by discovering the little gleam of light which shows us a thoroughfare. In any case, and to return to more precise ideas, more than one instance has been cited to prove that the gift of handling great groups of figures is almost independent of the intelligence proper. One of the most curious is that of an Italian shepherd boy, Vito Mangiamele, who was brought before the Paris Academy of Science in 1837 and who, at the age of ten, though devoid of the most rudimentary education, was able in half a minute to extract the cubic root of a number of seven figures. Another, more striking still, also mentioned by Dr. Clarapede in his paper on the learned horses, is that of a man blind from birth, an inmate of the lunatic-asylum, at Armentieres. This blind man, whose name is Fleury, a degenerate and nearly an idiot, can calculate in one minute and fifteen seconds the number of seconds in thirty-nine years, three months and twelve days, not forgetting the leap-years. They explain to him what a square root is, without telling him the conventional method of finding it; and soon he extracts almost as rapidly as Inaudi himself, without a blunder, the square roots of numbers of four figures, giving the remainder. On the other hand, we know that a mathematical genius like Henri Pomcare confessed himself incapable of adding up a column of figures without a mistake. 29 >From the maybe enchanted atmosphere that surrounds numbers we shall pass more easily to the even more magic mists of the final theory, the only one remaining to us for the moment: the mediumistic or subliminal theory. This, we must remember, is not the telepathic theory proper which decisive experiments have made us reject. Let us have the courage to venture upon it. When one can no longer interpret a phenomenon by the known, we must needs try to do so by the unknown. We, therefore, now enter a new province of a great unexplored kingdom, in which we shall find ourselves without a guide.