280 CALCULATING PRODIGIES [CH. XIII 



where he gave exhibitions: in these he impressed all observers as 

 being modest, frank, and straightforward. He was then ignorant 

 of reading and writing : these arts he subsequently acquired. 



His earlier performances were not specially remarkable as 

 compared with those of similar calculating prodigies, but with 

 continual practice he improved. Thus at Lyons in 1873 he 

 could multiply together almost instantaneously two numbers of 

 three digits. In 1874 he was able to multiply a number of six 

 digits by another number of six digits. Nine years later he 

 could work rapidly with numbers of nine or ten digits. Still 

 later, in Paris, asked by Darboux to cube 27, he gave the 

 answer in 10 seconds. In 13 seconds he calculated how many 

 seconds are contained in 18 years 7 months 21 days 3 hours : 

 and he gave immediately the square root of one-sixth of the 

 difference between the square of 4801 and unity. He also 

 calculated with ease the amount of wheat due according to 

 the traditional story to Sessa who, for inventing chess, was 

 to receive 1 grain on the first cell of a chess-board, 2 on the 

 second, 4 on the third, and so on in geometrical progression. 



He can find the integral roots of equations and integral 

 solutions of problems, but proceeds only by trial and error. 

 His most remarkable feat is the expression of numbers less 

 than 10 5 in the form of a sum of four squares, which he can 

 usually do in a minute or two ; this power is peculiar to him. 

 Such problems have been repeatedly solved at private perform- 

 ances, but the mental strain caused by them is considerable. 



A performance before the general public rarely lasts more 

 than 12 minutes, and is a much simpler affair. A normal 

 programme includes the subtraction of one number of twenty- 

 one digits from another number of twenty-one digits : the 

 addition of five numbers each of six digits : the multiplying 

 of a number of four digits by another number of four digits : 

 the extraction of the cube root of a number of nine digits, and 

 of the fifth root of a number of twelve digits : the determina- 

 tion of the number of seconds in a period of time, and the day 

 of the week on which a given date falls. Of course the 

 questions are put by members of the audience. To a pro- 



