CH. XIII] CALCULATING PRODIGIES 283 



it : he immediately repeated it correctly. The number was : — 

 2,563,721,987,653,461,598,746,231,905,607,541,128,975,231. 



Of the four fundamental processes, addition and subtraction 

 present no difficulty and are of little interest. The only point 

 to which it seems worth calling attention is that Bidder, in 

 adding three or more numbers together, always added them one 

 at a time, as is illustrated in the examples given below. Rapid 

 mental arithmetic depended, in his opinion, on the arrangement 

 of the work whenever possible, in such a way that only one fact 

 had to be dealt with at a time. This is also noticeable in 

 Inaudi's work. 



The multiplication of one number by another was, naturally 

 enough, the earliest problem Bidder came across, and by the time 

 he was six years old he had taught himself the multiplication 

 table up to 10 times 10. He soon had practice in harder sums, 

 for, being a favourite of the village blacksmith, and constantly 

 in the smithy, it became customary for the men sitting round 

 the forge-fire to ask him multiplication sums. From products 

 of numbers of two digits, which he would give without any 

 appreciable pause for thought, he rose to numbers of three 

 and then of four digits. Halfpence rewarded his efforts, and 

 by the time he was eight years old, he could multiply together 

 two numbers each of six digits. In one case he even multiplied 

 together, two numbers each of twelve digits, but, he says, 

 "it required much time," and "was a great and distressing 

 effort." 



The method that he used is, in principle, the same as that 

 explained in the usual text-books, except that he added his 

 results as he went on. Thus to multiply 397 by 173 he pro- 

 ceeded as follows : — 



We have 100 x 397 = 39700, 



to this must be added 70 x 300 = 21000 making 60,700, 



70 x 90 = 6300 „ 67,000, 



"„ 70 x 7 = 490 „ 67,490, 



"„ 3 x 300 = 900 „ 68,390, 



3 x 90 = 270 „ 68,660, 



3x 7= 21 „ 68,681. 



