the number of hair-breadths, without any question being asked, or any calculation expected by the company. When he once understood a question, he began to work with amasing facility, after his own method, without the use of a pen, pencil, or chalk, or even understanding the common rules of arithmetic, as taught in the schools. He would stride over a piece of land, or a field, and tell the contents of it almost as exactly as if one had measured it by the chain. In this manner he measured the whole lordship of Elmton, belonging to Sir John Rhodes, and brought him the contents, not only of some thousands in acres, roods, and perches, but even in square inches. After this, for his own amusement, he reduced them into square hair-breadths, computing 48 to each side of the inch. His memory was so great, that while resolving a question, he could leave off, and resume the operation again, where he left off, the next morning, or at a week, a month, or several months, and proceed regularly till it was completed. His memory would doubtless have been equally retentive with respect to other objects, if he had attended to them with equal diligence; but his perpetual application to figures prevented the smallest acquisition of any other knowledge. He was sometimes asked, on his return from church, whether he remembered the text, or any part of the sermon: but it never appeared that he brought away one sentence; his mind, upon a closer examination, being found to have been busied, even during divine service, in his favourite operation, either dividing some time, or some space, into the smallest known parts, or resolving some question that had been given him as a test of his abilities. As this extraordinary person lived in laborious poverty, his life was uniform and obscure. Time, with respect to him, changed nothing but his age; nor did the seasons vary his employment, except that in winter he used a flail, and in summer a ling-hook. In 1754, he came to London, where he was introduced to the Royal Society, who, in order to prove his abilities, asked him several questions in arithmetic; and he gave them such satisfaction, that they dismissed him with a handsome gratuity. In this visit to the metropolis, the only object of his curiosity, except figures, was to see the king and royal family; but they being at Kensington, Jedidiah was disappointed. During his stay in London, he was taken to see King Richard III. performed at Drury-Lane playhouse; and it was expected, either that the novelty and the splendour of the show would have fixed him in astonishment, or kept his imagination in a continual hurry, or that his passions would, in some degree, have been touched by the power of action, though he did not perfectly understand the dialoge. But Jedidiah's mind was employed in the playhouse just as it was employed in every other place. During

the dance, he fixed his attention upon the number of steps; he declared, after a fine piece of music, that the innumerable sounds produced by the instruments had perplexed him beyond measure; and he attended even to Mr. Garrick, only to count the words that he uttered, in which, he said, he perfectly succeeded. Jedidiah returned to the place of his birth, where, if his enjoyments were few, his wishes did not seem to be greater. He applied to his labour with cheerfulness; he regretted nothing that he left behind him in London; and it continued to be his opinion, that a slice of rusty bacon afforded the most delicious repast.

The following account of the Extraordinary Arithmetical Powers of a Child, is extracted from the Annual Register of 1812. It is entitled, SOME PARTICULARS RESPECTING THE ARITHMETICAL POWERS OF ZERAH COLBURN, A CHILD UNDER EIGHT YEARS OF AGE.

"The attention of the philosophical world, (says the writer,) has been lately attracted by the most singular phenomenon 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 cperation 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 shew those wonderful powers of calculation, which have since so much attracted 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 ciphering,) was much surprised one day to hear him repeating the products of several numbers. Struck with amazement 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 solicitations 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 metroprolis have for these last three months had an opportunity of seeing and examining this wonderful phenomenon, and 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 despatch, 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 seven places of figures, being proposed, he will determine, with equal expedition and ease, all the factors of which it is composed. This singular faculty consequently extends not only to the raising of powers, but also to the extraction of the square and cube roots of the number proposed; and likewise to the means of determining whether it be a prime number (or a number incapable of division by any other number;) for which case there does not exist, at present, any genera! rule amongst mathematicians.' 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.

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'At a meeting of his friends, which was held for the purpose of concerting the best methods of promoting the views of the father, this child undertook, and completely succeeded in raising the number 8 progressively up to the sixteenth power!!! and, in naming the last result, viz. 281,474,976,710,656, he was right in every figure. He was then tried as to other 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 despatch, that the person appointed to take down the results, was obliged to enjoin him

not to be so rapid! With respect to numbers consisting of two figures, he would raise some of them to the sixth, seventh, 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 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 gentlemen present; to all of which he answered in a similar manner. One of the party requested him to name the factors which produced the number 247,483 this he immediately did, by mentioning the two numbers 941 and 263; which indeed are the only two numbers that will produce it, viz. 5×34279, 7× 24485, 59 × 2905, 83 × 2065, 35 × 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 36083 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 numbers, 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 subject (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; yet 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 com

mon rules of arithmetic, and cannot perform, upon paper, a simple sum in multiplication or division. But in the ex traction of roots, and in mentioning the factors of high num bers, 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 laborious calculation; and moreover, the knowledge of a prime number cannot be obtained by any known 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; 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 × 15, and consequently that (4395)=(293) x (15); and, further, that in the second case, 543 is equal to 181x3, 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 singular faculty which this child possesses is not altogether dependent 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 esemblance (if the difference of age did not prevent the justness of the comparison) to the celebrated Jedidiah 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 as little or nothing to do with the process.

And