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was then tried as toother numbers, confining of one figure ; 
all of which he raifed (by affual multiplication, and not 
by memory) as high as the tenth power, with. fo much 
facility and difpatch, that the perfon appointed to take 
down the refults was obliged to enjoin him not to he fo ra¬ 
pid ! With refpecl to numbers confifting of two figures, he 
would raife fome of them to the fixth, feventh, and eighth, 
power: but not always with equal facility; for the larger 
the products became, the more difficult he found it to 
proceed. He was afked the fquare root of 106,919; and, 
before the number could be written down, he immediately 
anfwered 327. He was then required to name the cube 
root of 268,336,125; and with equal facility and prompt- 
nefs he replied, 645. Various other queftions of a fimilar 
nature, refpe&ing the roots and powers of very high num¬ 
bers, were propofed by fevernl of the gentlemen prefent; 
to all of which he anfwered in a fimilar manner. One of 
the party requefted him to name the fadfors which pro¬ 
duced the number 247,483, which he immediately did by 
mentioning the two numbers 941 and 263 ; which indeed 
are the only two numbers that will produce it. Another 
of them propofed 171,395 ; and he named the following 
fadfors as the only ones that would produce it, viz. 5 X 34279, 
7X24485, 59X2905, 83X2065, 35X4397? 295X5^1? and 
413X4-15- He was then afked to give the fadfors of 36,083 ; 
but he immediately replied that it had none; which, in 
fadt, was the cafe, as 36,083 is a prime number. Other 
numbers were indifcriminately propofed to him ; and he 
always fucceeded in giving the correct fadfors, except in 
-the cafe of prime numbers, which he difcovered almoft as 
foon as propofed. One of the gentlemen afked him how 
many minutes there were in forty-eight years ; and, before 
the queftion could be written down, he replied, 25,228,800 ; 
and inffantly added, that the number of feconds in the 
fame period was 1,513,728,000. Various queftions of the 
like kind were put to him ; and to all of them he anfwered 
with nearly equal facility and promptitude, fo as to afto- 
nifli every one prefent, and to excite a defire that fo ex¬ 
traordinary a faculty fhould (if poflible) be rendered more 
ex ten five and ufeful. 
It was the wifh of the gentlemen prefent to obtain a 
knowledge of the method by which the child was enabled 
to anfwer, with fo much facility and correffnefs, the quef¬ 
tions thus put to him; but to all their inquiries upon this 
fubjedl (and he was clofely examined upon this point) he 
was unable to give them any information. He pofitively 
declared (and every obfervation that was made feemed to 
juftify the affertion), that he did not know how the an- 
fwers came into his mind. In theadl of multiplying two 
numbers together, and in the railing of powers, it was 
evident (not only from the motion of his lips, but alfo 
from fome fingular facls which will be hereafter mention¬ 
ed), that fome operation was going forward in his mind; 
yet that operation could not (from the readinefs with 
which the anfwers were furnifhed) be at all allied to the 
tifual mode of proceeding with l'uch fubjedts ; and, more¬ 
over, he is entirely ignorant of the common rules of arith¬ 
metic, and cannot perform, upon paper, a fnnple fum in 
multiplication or divifipn. But, in the extraction of roots, 
and in mentioning the fadfors of high numbers, it does not 
appear that any operation can take place, fince he will give 
the anfwer immediately, or in a very few feconds, where 
it would require, according to the ordinary method of 
folution, a very difficult and laborious calculation ; and, 
moreover, the knowledge of a prime number cannot be 
obtained by any known rule. It has been already ob- 
ferved, that it was evident, from fome fingular fadts, that 
the child operated by certain rules known only to hinifelf. 
This dil'covery was made in one or two inftances, when 
he had been clofely preffed upon that point. In one cafe 
he was afked to tell the fquare of 4395 ; heat firft hefitated, 
fearful that he fhould not be able to anfwer it corredfly : 
but, when he applied hirnfelf to it, he faid it was 19,316,025. 
On being queftioned as to the caufe of his liefitation, he 
DON. 
renlie'd that he did not like to multiply four figures by 
four figures; but, faid he, “I found out another way; I ' 
multiplied 293 by 293, and then multiplied this product 
twice by the number 15, which produced the fame re- 
fult.” On another occafion, his highnefs the duke of 
Gloucefier afked him the produdf of 21,734 multiplied 
by 543 ; he immediately replied, 11,801,562; but, upon 
fome remark being made on the fubjedf, the child laid 
that he had, in hisown mind, multiplied 65,202 by 181. 
Now, although, in the firft inftance, it mult be evident to 
every mathematician that 4395 is equal to 293X15, and 
consequently that (4395) 2 “(293)2 X (15) 2 ; and fur¬ 
ther, that, in the fecond cafe, 543 is equal to iSiX3» 
and confequently that 21734X (181 X 3) = (21 734X 3). 
X >8i ; yet, it is not the lefs remarkable, that this com¬ 
bination fliould be immediately perceived by the child; 
and we cannot the lefs admire his Ingenuity in thus feiz- 
ing inffantly the eafieft method of folving the queltion 
propofed to him. 
It muff be evident, from what has here been ftated,that 
the fingular faculty which this child po'ffefl'es is not alto¬ 
gether dependent upon his memory. In the multiplica¬ 
tion of numbers, and in the raifingof powers, he is doubt- 
lefs confiderably afiilted by that remarkable quality of the 
mind ; and in this refpedt he might be confidered as bear¬ 
ing fome refemblance (if the difference of age did not 
prevent the juftnefs of the comparifon) to the celebrated 
jedediah Buxton, and other perfons of fimilar note. But, 
in the extraction of the roots of numbers, and in deter¬ 
mining $beir fadfors (if any), it is clear, to all thofe who 
have vvitneffed the altoniffiing quicknefs and accuracy, of 
this child, that the memory has little or nothing to do 
with the procefs. And in this particular point confifls 
the remarkable difference between the prefent and all for¬ 
mer inftances of an apparently fimilar kind. It has been ■ 
recorded as an affonifhing effort of memory, that the ce¬ 
lebrated Euler could remember the firft fix powers of every 
number under 100. This, probably, muff be taken with 
fome reftridfions; but, if true to the fulleft extent, it is 
not more affonifhing than the efforts of this child; with 
this additional circumftance in favour of the latter, that 
he is capable of verifying, in a very few feconds, every 
figure which he may have occafion for. It is not intend¬ 
ed to draw a comparifon between the humble, though afto- 
nifhing, efforts of this infant prodigy and the gigantic 
powers of that illuftrious character to whom a reference 
has juft been made; yet we may be permitted to hope 
and expedf that thofe wonderful talents, which are fo con- 
fpicuous at this early age, may, by a fuitable education, 
be confiderably improved and extended; and that fome 
new light will eventually be thrown upon thofe fubjedfs, 
for the elucidation of which his mind appears to be pecu¬ 
liarly formed by nature; fince he enters into the world 
with all thofe powers and faculties which are not even at¬ 
tainable by the moll eminent at a more advanced period 
of life. Every mathematician muft be aware of the im¬ 
portant advantages which have fometimes been derived 
from the mod fimple and trifling circumftances; the full 
effedt of which has not always been evident at firft fight. 
To mention one fingular inftance of this kind: the very 
fimple improvement of exprelfing the powers and roots 
of quantities by means of indices, introduced a new and 
general arithmetic of exponents; and this algorithm of 
powers led the way to the invention of logarithms, by 
means of which, all arithmetical computations are fo much 
facilitated and abridged. Perhaps this child poffeffes a 
knowledge of fome more important properties connedfed 
with this lubjedf; and, although he is incapable at pre¬ 
fent of giving any fatisfadfory account of the ftate of his 
mind, or of communicating to others the knowledge 
which it is fo evident he does poffels, yet there is every 
reafon to believe that, when his mind-is more cultivated, 
and his ideas more expanded, he will be able not only to 
divulge the mode by which he at prefent operates, but 
i alfo- 
