Some Particulars respecting the arithmetical Powers of Zerah Colburn, a Child under Eight Years of Age.

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London, Aug. 20, 1812. "HE attention of the philosophical world has been lately attracted by the most singular phænomenon in the history of the human mind that perhaps ever existed. It is the case of a child, under eight years of age, who, without any previous knowledge of the common rules of arithmetic, or even of the use and power of the Arabic numerals, and without having given any particular attention to the subject, possesses (as if by intuition) the singular faculty of solving a great variety of arithmetical questions by the mere operation of the mind, and without the usual assistance of any visible symbol or contrivance.

The name of the child is Zerah Colburn, who was born at Cabut (a town lying at the head of Onion river, in Vermont, in the United States of America), on the 1st of September, 1804. About two years ago (August, 1810), although at that time not six years of age, he first began to show those wonderful powers of calculation which have since so much attract

ed the attention and excited the astonishment of every person who has witnessed his extraordinary abilities. The discovery was made by accident. His father, who had not given him any other instruction than such as was to be obtained at a small school established in that unfrequented and remote part of the country, (and which did not include either writing or cyphering,) was much surprised one day to hear him repeating the products of several numbers Struck with amazeinent at the circumstance, he proposed a variety of arithmetical questions to him, all of which the child solved with remarkable facility and correctness. The news of this infant prodigy soon circulated through the neighbourhood; and many persons came from distant parts to witness so singular a circumstance. The father, encouraged by the unanimous opinion of all who came to see him, was induced to undertake, with this child, the tour of the United States. They were every where received with the most flattering expressions; and in the several towns which they visited, various plans were suggested to educate and bring up the child, free from all expense to his family. Yielding, however, to the pressing soli

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citations of his friends, and urged by the most respectable and powerful recommendations, as well as by a view to his son's more complete education, the father has brought the child to this country, where they arrived on the 12th of May last: and the inhabitants of this metropolis have for these last three months had an opportunity of seeing and examining this wonderful phænomenon, and of verifying the reports that have been circulated respecting him.

Many persons of the first eminence for their knowledge in mathematics, and well known for their philosophical inquiries, have made a point of seeing and conversing with him; and they have all been struck with astonishment at his extraordinary powers. It is correctly true, as stated of him, that He will not only determine, with the greatest facility and dispatch, the exact number of minutes or seconds in any given period of time; but will also solve any other question of a similar kind. He will tell the exact product arising from the multiplication of any number, consisting of two, three, or four figures, by any other number consisting of the like number of figures. Or, any number, consisting of six or

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number); for which case there does not exist, at present, any general rule amongst mathemati cians." All these, and a variety of other questions connected therewith, are answered by this child with such promptness and accuracy (and in the midst of his juvenile pursuits) as to astonish every person who has visited him.

At a meeting of his friends which was held for the purpose of concerting the best methods of promoting the views of the fatber, this child undertook, and completely succeeded in, raising the number 8 progressively up to the sixteenth power!!! and in naming the last result, viz. 281,474,976,710,056, he was right in every figure. He was then tried as to others numbers, consisting of one figure; all of which he raised (by actual multiplication and not by memory, as high as the tenth power, with so much facility and dispatch that the prson appointed to take down the results, was obliged enjoin him not to be so rapid' With respect to numbers consisting of two fi gures, he would raise some of them to the sixth, seventh, and eighth power; but not always with equal fcility: for the larger the products became, the more difficult he found it to proceed. He was asked the square root of 106929; and before the number could be written down, he immediately answered 327. He was then required to name the cube root of 268,336,125, and with equal facility and promptness he replied, 645. Various other questions of a similar nature, respecting the roots and powers of very high numbers, were proposed by several of the gentle men present, to all of which he

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answered in a similar manner. One of the party requested him to name the factors which produced the number 247483, 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 proposed 171395, and he named the following factors as the only ones that would produce it, viz. 5×34279, 7×24485, 9 × 2905, 83 x 2005, 35 x 4897, 295×581, and 413 × 415. He was then asked to give the factors of 36083; but he immediately replied that it had none; which, in fact, was the case, as 30083 is a prime number. Other numbers were indiscriminately proposed to him, and he always succeeded in giving the correct factors, except in the case of prime Lumbers, which he discovered almost as soon as proposed. One of the gentlemen asked him how many minutes there were in forty-eight years; and before the question could be written down, he replied, 25,228,800; and instantly added, that the number of seconds in the same period was 1,513,728,000. Various questions of the like kind were put to him; and to all of them he answered with nearly equal facility and promptitude, so as to astonish every one present, and to excite a desire that so extraordinary a faculty should (if possible) be rendered more extensive and useful.

It was the wish of the gentlemen present to obtain a knowledge of the method by which the child was enabled to answer, with so much facility and correctness, the questions thus put to him: but to all their inquiries upon this sub

ject (and he was closely examined upon this point) he was unable to give them any information. He positively declared (and every observation that was made seemed to justify the assertion) that he did not know how the answers came into his mind. In the act of multiplying two numbers together, and in the raising of powers, it was evident (not only from the motion of his lips, but also from some singular facts which will be hereafter mentioned), that some operation was going forward in his mind; yef that operation could not (from the readiness with which the answers were furnished) be at all allied to the usual mode of proceeding with such subjects: and, moreover, he is entirely ignorant of the common rules of arithmetic, and cannot perform, upon paper, a simple sum in multiplication or division. But in the extraction of roots, and in mentioning the fac tors of high numbers, it does not appear that any operation can take place, since he will give the answer immediately, or in a very few seconds, where it would require, according to the ordinary method of solution, a very difficult and labo rious calculation; and moreover, the knowledge of a prime number cannot be obtained by any knowa rule.

It has been already observed, that it was evident, from some singular facts, that the child operated by certain rules known only to himself. This discovery was made in one or two instances, when he had been closely pressed upon that point. In one case he was asked to tell the square of 4395; he at first hesitated, fearful that he should not be able to answer it correctly:

correctly but when he applied himself to it, he said it was 19,316.025. On being questioned as to the cause of his hesitation, he replied that he did not like to multiply four figures by four figures: but, said he, I found out another way; I multiplied 293 by 293, and then multiplied this product twice by the number 15, which produced the same result." On another occasion, his highness the Duke of Gloucester asked him the product of 21,734 multiplied by 543; he immediately replied, 11,801,562 but, upon some remark being made on the subject, the child said that he had, in his own mind, multiplied 65202 by 181. Now, although, in the first instance it must be evident to every mathematician that 4395 is equal to 293 x 15, and consequently that (4395)2 = (293)2 × (15); and, further, that in the second case, 543 is equal to 181 x 3, and consequently that 21734 × (181 × 3) = (21734 × 3) × 181; yet, it is not the less remarkable, that this combination should be immediately perceived by the child, and we cannot the less admire his ingenuity in thus seizing instantly the easiest method of solving the question proposed to him.

It must be evident, from what has here been stated, that the sin gular faculty which this child pos sesses is not altogether dependant upon his memory. In the multiplication of numbers, and in the raising of powers, he is doubtless considerably assisted by that remarkable quality of the mind: and in this respect he might be considered as bearing some resemblance (if the difference of age

did not prevent the justness of the comparison) to the celebrated Jedediah Buxton, and other persons of similar note. But, in the extraction of the roots of numbers, and in determining their factors (if any), it is clear, to all those who have witnessed the astonishing quickness and accuracy of this child, that the memory has little or nothing to do with the process. And in this particular point consists the remarkable difference between the present and all former instances of an apparently similar kind.

It has been recorded as an astonishing effort of memory, that the celebrated Euler (who, in the science of analysis, might vie even with Newton himself,) could remember the first six powers of every number under 100. This, probably, must be taken with some restrictions: but, if true to the fullest extent, it is not more astonishing than the efforts of this child; with this additional circumstance in favour of the latter, that he is capable of verifying, in a very few seconds, every figure which he may have occasion for. It has been further remarked by the biographer of that eminent mathematician, that," he perceived, almost at a simple glance, the factors of which his formulæ were composed; the particular system of factors belonging to the question under consideration; the various artifices by which that system may be simplified and reduced; and the relation of the several factors to the conditions of the hypothesis. His expertness in this particular probably resulted, in a great measure, from the ease with which he performed mathematical investigations by head.

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He had always accustomed himself to that exercise; and, having practised it with assiduity (even before the loss of sight, which afterwards rendered it a matter of necessity), he is an instance to what an astonishing degree it may be acquired, and how much it improves the intellectual powers. No other discipline is so effectual in strengthening the faculty of attention: it gives a facility of apprehension, an accuracy and steadiness to the conceptions; and (what is a still more valuable acquisition) it habituates the mind to arrangement in its reasonings and reflections."

.. It is not intended to draw a comparison between the humble, though astonishing, efforts of this infant prodigy and the gigantic powers of that illustrious character to whom a reference has just been made: yet we may be permitted to hope and expect that those wonderful talents, which are so conspicuous at this early age, may, by a suitable education, be considerably improved and extended; and that some new light will eventually be thrown upon those subjects, for the elucidation of which his mind appears to be peculiarly formed by nature, since he enters into the world with all those powers and faculties which are not even at tainable by the most eminent at a more advanced period of life. Every mathematician must be aware of the important advantages which have sometimes been derived from the most simple and trifling circumstances; the full effect of which has not always been evident at first sight. To mention one singular instance of this kind. The very simple improvement of expressing the powers and roots of

quantities by means of indices, în-' troduced a new and general arithmetic of exponents: and this al gorithm of powers led the way to the invention of logarithms, by means of which, all arithmetical computations are so much facilitated and abridged. Perhaps this child possesses a knowledge of some more important properties connected with this subject; and although he is incapable at present of giving any satisfactory account of the state of his mind, or of communicating to others the knowledge which it is so evident he does possess, yet there is every reason 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 present operates, but also point out some new sources of information on this interesting subject.

The case is certainly one of great novelty and importance: and every literary character, and every friend to science, must be anxious to see the experiment fairly tried, as to the effect which a suitable education may produce on a mind constituted as his appears to be. With this view a number of gentlemen have taken the child under their patronage, and have formed themselves into a committee for the purpose of superintending bis education. Application has been made to a gentleman of science, well known for his mathematical abilities, who has consented to take the child under his immediate tuition: the committee, therefore, propose to withdraw him, for the present, from public exhibition, in order that he may fully devote himself to his studies. But whe

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