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 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 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 past 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.

"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 x 34279, 7 x 24485, 59 x 2905, 83x2065, 35x4897, 295x581, and 413x415. 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.