COMPUTATIONS OF Z. COLBURN. 
11 
of a theorem has more the appearance of intricacy than die On numerical 
rule resulting from it will be found to possess in practice. computations* 
0 r r particularly 
The modes of multiplying four figures by four, and of ex- those pcrfoi in- 
fracting the square and cube roots, are all of them founded 
upon the principles of involution and evolution; and by these 
shall my proceedings be governed. In what way the factors 
are discovered, which enter into the composition of a large 
numerical quantity, and by what rule prime numbers are as- 
certained, l shall not pretend to examine. Upon this subject, 
and indeed upon all others connected with the more important 
properties of numbers, much valuable instruction may be ob- 
tained from the elaborate elements of the ingenious Mr. Bar- 
low. 
To square Jt}54 by the common rule, without recording the 
several operations, would require a memory more perfect than 
the human faculties are generally thought capable of attaining ; 
although, by a peculiar discipline from infancy, the memory is 
capable of being improved to a degree of extraordinary reten- 
tion. The calculating boy is a surprising evidence of this 
fact ; and it becomes a reasonable purpose to seaich for tbose 
expedients which can lead his efforts with most ease to the 
accomplishment of his daily exhibitions. Even with the as- 
sistance of all artificial aids, his occupations demand a very 
cultivated and retentive memory ; but, as some fixed rules are 
positively used by every calculator, whose results are uniformly 
correct, we have only to discover tbose which have the fairest 
character of simplicity, and consider them as his guides. 
To establish the probability, that the subsequent methods of 
calculation resemble those which have been prescribed to the 
computing boy, I shall mention a lew peculiarities that cha- 
racterize; the operations. The young calculator can evolve the 
cube root of twelve figures, where only four of them are 
made known ; he can detect an imperfect cube, and tell the 
nearest root to the quantity given. These three singularities 
belong to the following rules. The multiplication of four 
numbers into each oth r, and the extraction of the square 
and cube roots are conducted upon principles exactly similar, 
which similarity diminishes the application requisite to under- 
stand them, and imposes upon the memory less efforts of reten- 
tiveness. 
