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versing with him; and they have 281,474,976,710,656, he was all been struck with astonishment right in every figure. He was at his extraordinary powers. It is then tried as to other numbers, correctly true, as stated of him, consisting of one figure; all of that—" fle will not only deter, which he raised (by actual multi. mine, with the greatest facility plication and not by memory) as and dispatch, the exact number high as the tenth power, with so of minutes or seconds in any given much facility and dispatch that period of time; but will also solve the person appointed to take down ang other question of a similar the results, was obliged to enjoin kind. He will tell the exact pro- him not to be so rapid ! With re. duct arising from the multiplica. spect to numbers consisting of two tion of any number, consisting of figures, he would raise some of two, three, or four figures, by any them to the sixth, seventh, and other number cunsisting of the eighth power; but not always like mber of figures. Or, any with equal facility: for the larger number, consisting of six or seven the products became, the more places of figures, being proposed, difficult he found it to proceed. he will determine, with equal ex. He was asked the square root of pedition and case, all the factors 106929, and before the number of which it is composed. This could be written down, he imme. singular faculty consequently ex. diately answered 327. He was tends not only to the raising of then required to name the cube powers, but also to the extraction root of 268,336, 125, and with of the square and cube roots of the equal facility and promptness he number proposed; and likewise replied 645. Various other questo the means of determining whe- tions of a similar nature, respecto ther it be a prime number (or a ing the roots and powers of very number incapable of division by high numbers, were proposed by any other number); for which several of the gentlemen present, case there does not exist, at pre. to all of which he answered in a sent, any general rule amongst similar mamer. One of the matbematicians." All these, and party requested him to name the a variety of other questions con- factors which produced the num. nected therewith, are answered ber 247483, which he immediateby this child with such prompt. ly did by mentioning the two ness and accuracy (and in the numbers 941 and 263 ; which inmidst of his juvenile pursuits) as deed are the only two numbers to astonish every person who has that will produce it. Another of visited him.

them proposed 171395, and he At a meeting of his friends named the following factors as the which was held for the purpose only ones that would produce it; of concerting the best method of viz. 5 x 34279, 7 x 24485, 59 promoting the views of the father, 2905, 83 x 2065, 35 4897, this child undertook, and com. 295 x 581, and 413 * 415. He pletely succeeded in, raising the was then asked to give the factors number 8 progressively up to of 36083; but he immediately the sixteenth power !!! and in replied that it had none; which naming the last result, viz, in fact was the case, as 36083 is a prime number. Other numbers the usual mode of proceeding were indiscriminately proposed to with such subjects; and moreover, him, and he always succeeded in he is entirely ignorant of the com. giving the correct factors, ex• mon rules of arithmetic, and can. cept in the case of prime numbers, nut perform, upon paper, a sim. which hç discovered almost as ple sum in multiplication or divi. soon as proposed. One of the sion. But, in the extraction of gentlemen asked him how many roots and in mentioning the facminutes there were in forty-eight tors of high numbers it does not years; and before the question appear that any operation can take could be written down he replied place; since he will give the an25,228,800: and instantly added swer immediately, or in a very that the number of seconds in the few seconds, where it would resame period was 1,513,728,000. quire, according to the ordinary Various questions of the like kind method of solution, a very diffi. were put to bim ; and to all of cult and laborious calculation : them he answered with nearly and moreover, the knowledge of equal facility and promptitude; a prime number cannot be obso as to astonish every one present, tained by any known rule. and to excite a desire that so ex- It has been already observed, traordinary a faculty should (if that it was evident, from some possible) be rendered more exten- singular facts, that the child ope. sive and useful.

rated by certain rules known only It was the wish of the gen. to himself. This discovery was tlemen present tu obtain a know- made in one or two instances, ledge of the method by which when he had been closely pressed the child was enabled to answer, upon that point. In one case he with so much facility and correct. was asked to tell the square of ness, the questions thus put to 4395; he at first hesitated, fear. him ; but to all their inquiries ful that he should not be able to upon this subject (and he was answer it correctly; but when he closely examined upon this point) applied himself to it he said it he was unable to give them any was 19,316,025. On being ques. informatiou. He positively de- tioned as to the cause ct bis besiclared (and every observation that lation, he replied that he did not was made seemed to justify the like to multiply four figures by assertion) that he did not know four figures : but, said be, "I how the answers came into his found out another way ; I multi. mind. In the act of multiplying plied 293 by 293, and then mul. iwo numbers together, and in the tiplied this product twice by the raising of powers, it was evident number 15, which produced the (not only from the motion of his same result.” On another occalips, but also from some singular sion, bis highness the Duke of facts which will be hereafter men• Gloucester asked bim the product tioned) that some operation was of 21,734 multiplied by 543 : be going forward in his mind; yet immediately replied 11,801,562 : ibat operation could not (from ihe but, upon some remark being readiness with wbich the answers made on the subject, the child were furnished) be at all allied to said that he had, in his own mind,

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multiplied 65202 by 181. Now, with Newton himself,) could realthough in the first instance it member the first six powers of must be evident to every mathe- every number under 100, This, . matician that 4395 is equal to probably, must be taken with 293 x 15, and consequently that some restrictions ; but, if true to (4395,2=(293), *(152; and fur. the fullest extent, it is not more ther that in the second case 543 astonishing than the etiorts of this is equal to 181 × 3, and conse, child: with this addicional cir- ' quently that 21734*(181x3 = cumstance in favour of the latter, (21734*3)* 181; yet, it is not that he is capable of verifying, in the less remarkable ihat this com. a very few seconds, every figure bination should be immediately which he may have occasion for. perceived by the child, and we li has been further remarked by cannot the less admire his inge- the biographer of ihat eminent nuity in thus seizing instantly the mathematician, that "he perceived easiest method of solving the ques. almost at a simple glance, the faction proposed to him.

tors of which his formulæ were Il must be evident, from what composed; the particular system has here been stated, that the sin- of factors belonging to the quesgular faculty which this child pos- tion under consideration; the vasesses is not altogether dependent rious artifices by which that sysupon his memory. In the multi- tem may be simplified and replication of numbers and in the duced ; and the relation of the raising of powers, he is donbtless several factors to the conditions of considerably assisted by that re- the hypothesis. His expertness markable quality of the mind: and in this particular probably result. in this respect he might be consi. ed, in a great measure, from the dered as bearing some resemblance ease with which he performed (if the difference of age did not mathematical investigations by prevent the justness of the com. head. He had always accustomed parison) to the celebrated Jede- himself to that exercise; and, diah Buxton, and other persons having practised it with assiduity, of similar note. But, in ihe ex- (even before the loss of sight, traction of the roots of numbers, which afterwards rendered it a and in determining their factors matter of necessity, he is an in. (if any), it is clear, to all those stance to what an astonishing dewho have witnessed the astonish. gree it may be acquired, and how ing quickness and accuracy of this much it improves the intellectual child, that the memory has little powers. No other discipline is or nothing to do with the process. so effectual in strengthening the And in this particular point con- faculty of attention : it gives a sists the remarkable difference be- facility of apprehension, an actween the present and all former curacy and steadiness to the coninstances of an apparently similar ceptions; and (what is a still kind.

more valuable acquisition) it baIt has been recorded as an as- bituates the mind to arrangement tonishing effort of memory that in its reasonings and reflections." the celebrated Euler (who, in the It is not intended to draw a science of analysis, might vie even comparison between the humble, though astonishing, efforts of this ideas more expanded, he will be intant-prodigy and the gigantic able not only to divulge the mode powers of that illustrious charac. by which he at present operates, ter to whom a reference has just but also point out some new sources been made: yet we may be per. of information on this interesting mitted to hope and expect that subject. those wonderful talents, which are The case is certainly one of great so conspicuous at this carly age, novelty and importance : and every may by a suitable education be literary character and every friend considerably improved and ex. to science must be anxious to see tended: and that some new light the experiment fairly tried, as to will eventually be thrown upon the effect which a suitable eductthose subjícts, for the elucidation tion may produce on a mind conof which his mind appears to be stituted as his appears to be. With peculiarly formed by nature, since this view a number of gentlemen he enters into the world with all have taken the child under their those powers and faculties which patronage, and have formed them. are not even attainable by the most selves into a Committee for the eminent at a more advanced prriod pårpose of superintending his edu. of life. Every mathematician cation. Application has been must be aware of the important made to a gentleman of science, advantages which have sometimes well known for his mathematical been derived from the most simple abilities, who has consented to and trifling circumstances; ibe take the child under his immediate full effect of which has not always tuition: the Committee therefore been evident at first sight. To propose to withdraw him, for the mention one singular instance of present, from public exhibition, this kind. The very simple im- in order that he may fully devote provement of expressing the pow. himself to his studies. But whether lers and roots of quantities by they shall be able wholly to ac. means of indices, introduced a complish the object they have in new and general arithmetic of ex. view, will depend upon the as. ponents; and this algorithm of sistance wbich they may receive powers led the way to the inden- from the public: and they take tion of logarithms, by means of this opportunity of inviting the which all arithmetical computa- friends of science to support a plan tions are so much facilitated and which promises to be attended abridged. Perhaps this child with so many advantages, possesses a knowledge of some more important properties connected with this subject ; and al.

Book-Worm.--No. III. though he is incapable at present SIR, September 6, 1812. of giving any satisfactory account I know not how I can better of the state of bis mind, or of com. pursue my design of giving you municating to others the know- occasionally some account of old Jedge which it is so evident he books, than by noticing those does possess, yet there is every writers, especially, who opposed reason to believe that when his popular errors, now generally exmind is more cultivated and his ploded, at a period when they had scarcely any associates in that delusion, insisted on by the Hea, hazardous contention. The fol, then priests of old, ---so far as they lowing title-page of a small volume, comprehend all that notion of a now before me, will discover such wirch, which may be found in a writer,

scripture," were " juggling, in, The Question of Witchcraft chanting, conjecturing, divining. Debated; or, a Discourse against A description of these introduces their Opinion that affirm IVitekes, an explanation of Deuteronomy, London, printed in the year 1669, xviii, 10, 11, pteceded by the fole 18mo, pp. 80.

lowing improved translation, which The preface to this anonymous your readers may easily compare work, which has the signature of with the common version, J. W. begins with a complaint that “ Let there not be found among “the zealous affirmers of witch, you any one tbąt maketh his son craft, tbink it no slander, to charge of his daughter pass through the all those who deny it with Athen fire, or that useth divinations, or ism."

a staragazer, or a conjecturer, or My author retorts that 6 the a mirucle-monger, or an inchanter, affirmers of witchcraft may, more or a seeker of an oracle, or a wize justly, be accounted Heathens ;- ard, or a necromancer." I subjoin in regard their opinion doch ne, the version of Dr, Geddes, as corcessarily infer plurality of Gods, rected in his Critical Remarks by attributing omnipotent effects “ Let not one be found among to more than one.- Effects so ri. you, who maketh his son or his diculously absurd, and some of daughter pass through the fire, or them so impossible for all the who is a fortune-teller, or an au, devils in hell to compass, that 'is gur, or a diviner, or a sorcerer, apparent they are partly founded or an inchanter, or a pythonist, in mistaken interpretations of or a wizard, or a consulter of the scripture, partly in the kpayish dead (or necromancer]" and gainful impostures of some My author complains of three men, partly in the vain foolish notorious mistakes of our English credulity, and frightful fancies of translators. The first, their call. other men." This short preface ing a conjecturer an inchanter, concludes with a determination to the re being not the least hint of oppose "sçripture history and solid such a signification in the Hebrew, reason,” to “ Platonic dreams, far better rendered in the old trans similitudes and fabling whimsies," lation, a regarder of the flying of

The first chapter is designed to fowls, altbough not all the truth, shew “ that the Bible hath been the night of fowls being but one falsely translated, in those places way of many, which cunjecturers which speak of Witchcraft.Pure made use of," suing his purpose, the author re, " The second mistake of our marks how" the craft and tricks translators" is said to be their of superstition,” aided as the force calling a miracle-monger a witch. of arms,” to “ uphold that so, The Hebrew word which the lute and unlimited power, with Septuagint renders by the Greek which the Eastern nations were word Papuaxon, meaning an always governel." The ways of impostor, not a poisoner. In

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