In almost every point, indeed, where comparison is possible, we shall find this computative gift resembling other manifestations of subliminal faculty,--such as the power of seeing hallucinatory figures,--rather than the results of steady supraliminal effort, such as the power of logical analysis. In the first place, this faculty, in spite of its obvious connection with general mathematical grasp and insight, is found almost at random,--among non-mathematical and even quite stupid persons, as well as among mathematicians of mark. In the second place, it shows itself mostly in early childhood, and tends to disappear in later life;--in this resembling visualising power in general, and the power of seeing hallucinatory figures in particular; which powers, as both Mr. Galton's inquiries and our own tend to show, are habitually stronger in childhood and youth than in later years. Again, it is noticeable that when the power disappears early in life it is apt to leave behind it no memory whatever of the processes involved. And even when, by long persistence in a reflective mind, the power has become, so to say, adopted into the supraliminal consciousness, there nevertheless may still be flashes of pure "inspiration," when the answer "comes into the mind" with absolutely no perception of intermediate steps. I subjoin a table, compiled by the help of Dr. Scripture's collection, which will broadly illustrate the main points above mentioned. Some more detailed remarks may then follow. TABLE OF PRINCIPAL ARITHMETICAL PRODIGIES. +-----------------------+---------------+---------------+---------------+ | Name | Age when gift | Duration of | | | (alphabetically). | was observed. | gift. | Intelligence. | +-----------------------+---------------+---------------+---------------+ |Ampère | 4 | ? | eminent | |Bidder | 10 | through life | good | |Buxton | ? | ? | low | |Colburn | 6 | few years | average | |Dase [or Dahse] | boyhood | through life | very low | |Fuller | boyhood | ? | low | |Gauss | 3 | ? | eminent | |Mangiamele | 10 | few years | average? | |Mondeux | 10 | few years | low | |Prolongeau | 6 | few years | low | |Safford | 6 | few years | good | |"Mr. Van R., of Utica" | 6 | few years | average? | |Whately | 3 | few years | good | +-----------------------+---------------+---------------+---------------+