290 CALCULATING PRODIGIES [CH. XIII 



mistakes were at once corrected on his being told that his 

 result was wrong. This remarkable performance took place 

 when Bidder was over 50. 



His method of calculating logarithms is set out in a paper* 

 by W. Pole. It was, of course, only necessary for him to deal 

 with prime numbers, and Bidder began by memorizing the 

 logarithms of all primes less than 100. For a prime higher 

 than this he took a composite number as near it as he could, 

 and calculated the approximate addition which would have to 

 be added to the logarithm : his rules for effecting this addition 

 are set out by Pole, and, ingenious though they are, need not 

 detain us here. They rest on the theorems that, to the 

 number of places of decimals quoted, if log n is p, then 

 log (n + n/10 2 ) is p + log 101, i.e. isp + 0-0043214, log (n + w/10 3 ) 

 is p + 0-00043407, log (n+n/10 4 ) is ^+00000434, log (n+n/W) 

 is p + 0-0000043, and so on. 



The last two methods, dealing with compound interest and 

 logarithms, are peculiar to Bidder, and show real mathematical 

 skill. For the other problems mentioned his methods are much 

 the same in principle as those used by other calculators, though 

 details vary. Bidder, however, has set them out so clearly that 

 I need not discuss further the methods generally used. 



A curious question has been raised as to whether a law for 

 the rapidity of the mental work of these prodigies can be found. 

 Personally I do not think we have sufficient data to enable us 

 to draw any conclusion, but I mention briefly the opinions of 

 others. We shall do well to confine ourselves to the simplest 

 case, that of the multiplication of a number of n digits by 

 another number of n digits. Bidder stated that in solving 

 such a problem he believed that the strain on his mind (which 

 he assumed to be proportional to the time taken in answering 

 the question) varied as n*, but in fact it seems in his case 

 according to this time test to have varied approximately as w 5 . 

 In 1855 he worked at least half as quickly again as in 1819, but 

 the law of rapidity for different values of n is said to have been 



* Institution of Civil Engineers, Proceedings, London, 1890 — 1891, vol. our, 

 p. 250. 



