Now among these thirteen names we have two men of transcendent, and three of high ability. What accounts have they given us of their methods? Of the gift of Gauss and Ampère we know nothing except a few striking anecdotes. After manifesting itself at an age when there is usually no continuous supraliminal mental effort worth speaking of, it appears to have been soon merged in the general blaze of their genius. With Bidder the gift persisted through life, but grew weaker as he grew older. His paper in Vol. XV. of the _Proceedings of the Institute of Civil Engineers_, while furnishing a number of practical hints to the calculator, indicates also a singular readiness of communication between different mental strata. "Whenever," he says (p. 255) "I feel called upon to make use of the stores of my mind, they seem to rise with the rapidity of lightning." And in Vol. CIII. of the same _Proceedings_, Mr. W. Pole, F.R.S., in describing how Mr. Bidder could determine mentally the logarithm of any number to 7 or 8 places, says (p. 252): "He had an almost miraculous power of seeing, as it were, intuitively what factors would divide any large number, not a prime. Thus, if he were given the number 17,861, he would instantly remark it was 337×53.... He could not, he said, explain how he did this; it seemed a natural instinct to him." Passing on to the two other men of high ability known to have possessed this gift, Professor Safford and Archbishop Whately, we are struck with the evanescence of the power after early youth,--or even before the end of childhood. I quote from Dr. Scripture Archbishop Whately's account of his powers. There was certainly something peculiar in my calculating faculty. It began to show itself at between five and six, and lasted about three years.... I soon got to do the most difficult sums, always in my head, for I knew nothing of figures beyond numeration. I did these sums much quicker than any one could upon paper, and I never remember committing the smallest error. _When I went to school, at which time the passion wore off, I was a perfect dunce at ciphering, and have continued so ever since._ Still more remarkable, perhaps, was Professor Safford's loss of power. Professor Safford's whole bent was mathematical; his boyish gift of calculation raised him into notice; and he is now a Professor of Astronomy. He had therefore every motive and every opportunity to retain the gift, if thought and practice could have retained it. But whereas at ten years old he worked correctly in his head, in one minute, a multiplication sum whose answer consisted of 36 figures, he is now, I believe, neither more nor less capable of such calculation than his neighbours. Similar was the fate of a personage who never rises above initials, and of whose general capacity we know nothing.