“On being interrogated as to the manner in which he obtained these results, the boy constantly said he did not know _how_ the answers came into his mind. In the act of multiplying two numbers together, and in the raising of powers, it was evident (alike from the facts just stated and from the motion of his lips) that _some_ operation was going forward in his mind; yet that operation could not (from the readiness with which his answers were furnished) have been at all allied to the usual modes of procedure, of which, indeed, he was entirely ignorant, not being able to perform on paper a simple sum in multiplication or division. But in the extraction of roots, and in the discovery of the factors of large numbers, it did not appear that any operation _could_ take place, since he gave answers _immediately_, or in a very few seconds, which, according to the ordinary methods, would have required very difficult and laborious calculations, and prime numbers cannot be recognised as such by any known rule.” I should hope that many of the above figures are wrong. I have verified them carefully with Dr. Carpenter’s quotation, but further than this I cannot and will not go. Also I am happy to find that in the end the boy overcame the mathematics, and turned out a useful but by no means particularly calculating member of society. The case, however, is typical of others in which persons have been found able to do without apparent effort what in the great majority of cases requires a long apprenticeship. It is needless to multiply instances; the point that concerns us is, that knowledge under such circumstances being very intense, and the ease with which the result is produced extreme, it eludes the conscious apprehension of the performer himself, who only becomes conscious when a difficulty arises which taxes even his abnormal power. Such a case, therefore, confirms rather than militates against our opinion that consciousness of knowledge vanishes on the knowledge becoming perfect—the only difference between those possessed of any such remarkable special power and the general run of people being, that the first are born with such an unusual aptitude for their particular specialty that they are able to dispense with all or nearly all the preliminary exercise of their faculty, while the latter must exercise it for a considerable time before they can get it to work smoothly and easily; but in either case when once the knowledge is intense it is unconscious.