834 Dynamic Theory. 



couragements to other classes. If the external impulses become con- . 

 stant the}* modify the habits, and when these are well settled they mod- 

 ify the congenital tendencies of the succeeding generation. It is said 

 of Mozart that the influence of his wife was a potent force in the guid- 

 ance of his actions. 



Zerah Colburn, when a boy eight years old, was taken to England to 

 be exhibited. He had never studied arithmetic and could do nothing on 

 paper, but his mental grasp of the relations of numbers' was something 

 wonderful. He could multiply or divide numbers in his head as fast as 

 an ordinary person could write them down. He raised the number 8 to 

 the 16th power, the result consisting of fifteen figures. Numbers con- 

 sisting of two figures he raised to the eighth power. Being required to 

 find the square root of 106,929, he immediately gave it 327. With 

 equal facility he gave the cube root of 268,336,125 as being 645. Upon 

 request he gave the factors of 247,483, viz., 941 and 263, which are the 

 only ones the number has; of 36,083, he at once said it has no factors, 

 which is true. ^Vhen asked to multiply together numbers consisting of 

 more than three figures, he usually resolved them into factors and 

 worked with these separately. He found the square of 4,395, by using 

 its factors 293 and 15, first squaring 293, then multiplying by 15 twice. 

 The square of 999,999, he got by taking its factors, 37,037 and 27, 

 squaring the first and multiplying that twice by the last, getting 999,- 

 998,000,001. Some of his operations required some time. Thus, it 

 had once been supposed, that 2 raised to the 32d power, plus one 

 ( 2 32 -f 1 ), = 4, 294,967,297, was a prime number. Colburn, after 

 some weeks, discovered its factors to be 6,700,417 X 641. ( This dis- 

 covery had also been made by Euler. ) Colburn could not tell how he 

 performed his work. His answers generally came too quickly to seem to 

 admit of being the result of ordinary methods. Yet the motion of 

 his lips and such hesitation as there was, indicated that some sort of 

 cerebral action was going on, of the nature of which he was unconscious. 

 But if we analyze the ordinary prgcess by which arithmetical " sums" 

 are worked out, we shall see that it contains the potentiality of Colburn's 

 phenomenal genius. Any person can ascertain that 8 times 9 are 72 by 

 counting nine sticks continuously from one to nine, then counting them 

 over again, calling the first one ten, and so on till they have been 

 counted eight times. A native of Australia who cannot count above six, 

 could not possibly learn to multiply 9 by 8. Our children learn the 

 multiplication table by rote, so that a knowledge that 8x9 = 72, be 

 comes secondarily a matter of memory with them, and they remember 

 that 72 is resolvable into the factors 8 and 9. In dealing with these 

 numbers and their multiples, it is no longer necessary to go below them 

 to their factors 3x3x2x2x2. They thus begin their processes 



