18 
COMPUTATIONS OP Z. COLBURN. 
On numerical 
computations ; 
particularly 
those perform- 
ed by Z. Col- 
ls iwn. 
The root 7654 is,already found, as the fourth root is known 
by inspection 3 but, to prove correctness. 
Deduct 3 rrfiq 
588 
6 m nq 
100*8 
3 n % p 
- 540 
3 mp z 
- 52*5 
6 m p q 
- - 8*4 
3 iPq 
4*32 
3 mq* 
- -336 
3 up* 
- 4*500 
6 n p q 
- 720 
P 3 
- - 125 
3p*1 
- - 30 
3 n q* 
28*8 
3 p<? 
2 4 
q 3 
064 
813/62-264 
It will be perceived that, in multiplying four figures by four, 
and in extracting roots, the rules are derived from the same 
property of numbers 3 and any person, who can accomplish 
the first operation, may be qualified in a day to effect the other 
two. 
I am inclined to believe, that the preceding methods are 
employed by the calculating boy 3 and that he has attained 
them exclusively from the laborious and instructive attentions 
of a preceptor. To learn, and to apply them, does not require 
faculties more intelligent than those which are exhibited by 
other children in the kingdom. The combination of words, in 
the most simple language, is fifty times more complex 3 and .so 
is the modulation of varied tones, which express the several 
feelings 3 yet these things are mechanical 3 and every child 
attains them by observa 0 and practice, without knowing the 
scientific rules by which his expressions are regulated. If the 
proper instruction is early communicated to the infant mind, 
the use of figures may be gradually rendered as familiar as the 
letters of the alphabet, or the words of a vocabulary. 
I conclude, agreeably to my preceding sentiments, that the 
capabilities of the calculating boy are not the indigenous shoots 
of uninnoculated genius, but the slowly matured fruits of 
instruction 
