The daily dispatch. [volume] (Richmond [Va.]) 1850-1884, 1874-09-12
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M da for ss,a RicAa5ond Dispatch.J
[s,IsicAL IETUITI0k.


Remarkable Instances Dire presented by the
occasionsa disI,iay OF extraor dinEsy ar1thmet
icaI bilitp ON thu part. of indlYi duals, no,
IhaYtDg received very little instruction, nave
not onIyanicipated, hat have gone Ifar be.
lyond any power deriYable from instruction
| in almost. Immediate arriving at the an
swers to questions which, according TO 0rdl.
nary arithrneticaI methods, would involve
long computations of very eiab orate c 9ha
acter. The case of3Zerah Coiburn. the son 30
iof an American peasant, Is especially remark.
able among these not only for the immedll;.
Iateness and correctness with which ne gave
/ the answers to questions receivable by simple
hut prolonged computation - such as the pro-
| duct OF two mum bers, each consisting OF Two,
Three. or four figures; the exact number o.
minutes and seconds in a given period OF
time the raising of numbers up TO ID hlghef
mowers, or the extraction Of the square ana lll
| e,1be roots-hut, still more, for his power OF
at once answering, questions to which no RUE
known to ;mathematic ians as would apply. II
was when the lad was under six years OF
noe. and before he had received any insfruc.
tion either in writing or arithmetic, tbat ne
| surprised his father by repeating the pro-
ducts Of several numbers, and then, on 1,l va,
rious arithmetical questions being proposed,
to him. by solving them all with facility and
correctness. at the age Of eight years hs
MOWERS were tested, from which the following
examples are selected: he raised any number
consisting of one figure progressively to the
fenth power; giving the results 10y actual
MULTIPLICATION and not by memory faster
than they could be set down in figures BY
the person appointed to record them! He
raised the number s progressively to the
Sixteenth power, and in naming the last re-
salt which consisted Of fifteen figures, he
was right in every one. Some numbers con-
sisting of tho figures he raised as high as the
eiohth power, though he found difficulty in
proceeding when the products became very
large. COCOON
On being asked the square root OF lO6929,
he answered 1927 before the original number
could be written down.- He was then re-
CURED to find the cube root of 2GS, 1896, 125;
and with equal facility and promptness ne
replied Gao.
He was asked how many minutes there are
in IS wears, and before the question could be
written down he replied 25,22S 800, and i'm
medmteIy afterwards he gave the correct
number of seconds.
On being requested to give the factors
which would produce the number 2474s3.
he Immediately named Oil and 2633, which
are the o,aiy t1oo numbers from the multiple
cation of which IL would result. On 1889
bein proposed, he named 5x342T9, 7x2AS5,
59y2905, S3x2065, 3jX4S97, 295x5SI, and
413y415. He was then asked to give the
factors of 36OS3, but be Immediately replied
that it bad none, which IS really the case,
this being prime number. Other numbers
being proposed TO him indscriminateiy, be
ALWAYS succeeded in giving the correct fac
tors, except in the case Of prime numbers,
which he generally discovered as soon as
proposed. The number o4,967. 297, winch
is 2.32x1, having been given to him, he dis
covered las Euler had previously done) that
it is not the prime number which t'ermat
had supposed It to be, but that it is the pro-
duct of the factors 6,T00,417z5u. The So.
luton of this problem was only given after
the lapse OF some weeks but the method
he took to obtain it clearly showed that he
had not derived his information from any
extraneous source.
When he vas asked to multiply together
numbers both consisting of more tnan three
figures, he seemed to decOmnose one or both
of them into its factors, and to york With
these separately. Thus, on being asked TO
give the square Of 1895, he multiplied 293
by itself, aud then twice multiplied the pro-
duct by Is. And on being asked to tell the
square of 999,999, he obtained the correct
result 1899 .99S, 900. 00l) by twice multiplying
the square of 37037, by 81. He then, Of his
own accord, multiplied that product by 40,
and said that the result as, 999, 1902, 000, 049)
was equal to the square of 6,999,993. He
multiplied this product by 40;
and observe that the result q, 400, 995, 1885,
O02, 4O1) was equal to the square As, 999, 951.
He was again asked to multiply this product
BY 25, and ia naming the result (6O,O24,SI9.-
0,06O, 025) he said it was equal to the square
1899, 755.
On being Intercepted as to the method
by which he obtained these results, the boy
constantly declared that he did not know
ho1c the answers came 10 his mind. In the
act of multiplying two numbers together,
and in the raising of powers, it was evident
(alke from the facts just stated and from the
motion of his lips) that some operation was
going on in his mind yet that operation
could not from the readiness with which the
answers were furnished) have been at all
allied to the usual modes of procedure, OF
which, indeed, he was entirely ignorant, not
being able to perform on paper simple SUM
in multiplication or division. But in the
extraction of roots and in the discovery OF
factors OF large numbers, it did not appear
that any operation could luke place; since he
gave answers Immediately, or INA few sec
onds, which, according to the ordinary
methods, would have required difhcult and
laboriols calculations; and prime numbers
cannot be recognized as such by any known
rule.
It has been remarked that the same faculty,
improved by cultivation, was possessed by
the illustrious Euler, who had not only
most extraordinary memory for numbers
to the extent, it is said, of being able to re-
call the first six powers of any number I'm.
der IOO-but also kind of diuining po,Der,
by which he perceived, almost at a glance,
the factors of which his formula were com.
posed the particular system of factors be-
longing to the question under consideration
the various articles by which the system
might be simpliied and reduced; and the
relation of the several factors to the condi-
tions of. the hypothesis. This power of
divininq truths in advance of existing,
knowledge is the special attribute OF those
mathematicians who have done most for the
development of their science. A notable 10.
stance of it is furnished by the celebrated
formula devised by Newton for the solution
of equations; for, although its correctness
was proved experientially by the results,
of its application in every conceivable va.
riety of case, its rationale seems to have been
unknown to Newton himself, and remained
a puzzle to succeeding mathematician until
discovered by Professor Sylvester. That
such a power as Zerah Colburn's should
exist in child who had never been taught
even the rudiments Of arithmetic, seems to
point to the existence of properties Of num-
6ers as yet undlscovered-somewhat analo-
gous to those on which the system of loga-
rithms is based. And If, as he grew older,