16 LIFE AND HABIT. 



multiplied this product by 49, and observed that the 

 result (viz., 2,400,995,198,002,401) was equal to the 

 square of 48,999,95 1. He was again asked to multi- 

 ply the product by 25, and in naming the result (viz., 

 60,024,879,950,060,025), he said it was equal to the 

 square of 244,999,75 5. 



" 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, in- 

 deed, he was entirely ignorant, not being able to per- 

 form 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. Car- 

 penter'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 



