"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 common 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 x 15, and consequently that (4395)2=(293)2 x (15); and, further, that in the second case, 543 is equal to 181x3, and consequently that 21734x(181x3)=(21734x3)xl81; 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 lesemblance (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 las 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 Culer (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 single glance, the factors of which his formulae 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. 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 the world with all those powers and faculties which are not even attainable 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 circumstance ; 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, 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 arithmetrcal computations are so much facilitated and abridged. Perhaps this child possesses a knowledge of some more important properties connected with this subject: 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 his education. Application has been made to 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 whether they shall be able to accomplish the object they have in view, will depend upon the assistance which they may receive from the public. What further progress this child made under the patronage and tuition of his kind and benevolent friends, the editor is not, at present, able to ascertain."