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" I express them on the table in the order as more simple than that of Saunderson, the inren. they are dictated to me; the first figure at the left tion of Dr. Moyes. He speaks of it in the fuiof the first number, upon the first square to the lowing terms: left of the first line; the second figure to the left “ The following brief account of a palpable of the first number, upon the second square to notation 1 bave generally used for these 20 years the left of the same line; and so of the rest. to assist my memory in numerical computations.

"I place the second number upon the second When I began to study the principles of arithrow of squares, units beneath units, and tens be- metie, which I did at an early period of life, I soon Death tens, &c.

discovered to my mortification, that a person en"I place the third number upon the third row tirely deprived of light could scarcely proceed in of squares, and so of the rest. Then with my that useful science without the aid of palpable tingers running over each of the rows vertically symbols representing the ten numerical characfrom the botturn to the top, beginning with that ters. Being at that time unacquainted with the which is nearest to my right, I work the addition writings of Saunderson, in which a palpable notaof the numbers which are expressed, and mark the tion is described, I embraced the obvious, though, sur, lus of the tens at the foot of that column. I As I afterwards found, imperfect expedient of cutthen pass to the second column, advancing towards ting into the form of the numerical characters thin the left: upon which I operate in the same man- pieces of wood or metal. By arranging these on ber; from thence to the third ; and thus in suc- the surface of a board, I could readily represent cession I finish my addition.

any given number, not only to the touch, but also “We shall now see bow the same table served to the eye; and by covering the board with a labim for demonstrating the properties of rectilineal mina of wax, my symbols were prevented from figures. Let as suppose this proposition to be de- changing their places, they adhering to the board monstrated, That parallelograms which have the from the slightest pressure. By this contrivance, {ame basis and the same height are equal in their I could solve, though slowly, any problem in the surfaces. He placed his pins as may be seen fig. 4. science of numbers: but it soon occurred to me, He gave names to the angular points, and finished that my notation, consisting of ten species of his demonstration with his fingers.

symbols or characters, was much more com" If we suppose that Saunderson only employed plicated than was absolutely necessary, and that pios with large heads to mark the limits of bis any given number might be distinctly expressed figures, around these he might arrange his pins by three species of pegs alone. To illustrate my with small heads in nine different manners, all of neaning, let A, B, C, D, fig. 5. represent a square which were familiar to him. Thus be scarcely piece of mahogany a foot broad and an inch in found any embarrassment but in those cases where thickness; let the sides A B, BC, CD, D A, be each the great number of angular points which be divided into 24 equal parts; let every two oppowas under a necessity of naming in his demon- site divisions be joined by a groove cut in the stration obliged him to recur to the letters of the board sufficiently deep to be felt with the finger, a pbabet. We are not informed how he employed and let the board be perforated at each intersecthem.

tion with an instrument a tenth of an inch in dia“ We only know, that his fingers ran over the meter. board with astonishing agility; that he undertook “ The surface of the board being thus divided with success the longest calculations; that he into 576 little squares, with a small perforation Could interrupt the series, and discover bis mis- at each of their angles, let three sets of pegs or takes; that he proved them with the greatest ease; pins, resembling those represented in the Plate at and that his labours required infinitely less time the figures 6, 7, 8, be so fitted to the holes in the than one could have imagined, by the exactness board, that when stuck into them they may keep and promp itude with which he prepared bis in- their positions like those of a fiddle, and require struments and disposed bis table.

some force to turu them round. The head of each ." This preparation consisted in placing pins peg belonging to the first set is a right-angled triwith larze heads in the centres of all the squares: angle about one-tenth of an inch in thickness ; haring done this, no more remained to him but to tbe head of each peg belonging to the second set fix their values by pins of smaller heads, except differs only from the former in having a small in cases where it was necessary to mark an unit; notch in its sloping side or hypothenuse; and the then he placed in the centre of a square a pin with head of each peg belonging to the third set is a a small head, in the place of a pin with a large square of which the breadth should be equal to head, with which it had been occupied.

the base of the triangle of the other two. These " Sometimes, instead of forming an entire line pegs should be kept in a case consisting of three with these pins, he contented himself with placing boxes or cells, each cell being allotted to a set, and some of them at all the angular points or points the case must be placed close by the board preof intersection; around which he tied silk threads, vious to the commencement of every operation. vbich finished the formation of the limits of his Each set should consist of 60 or 70 pegs (at least figures." See fig. 4. It may be added by way of when employed in long calculations); and when improvement, that for the division of one series of the work is finished they should be collected from noinbers from another, a thin piece of timber in the the board, and carefully restored to their respecforin of a ruler with which lines are drawn, bav. tive boxes. iog a pin at each end for the holes in the squares, “ Things being thus prepared, let a peg of the might be interposed between the two series to be first set be fixed into the board, and it will acquire distinguished.

four different values according to its positiou reBy the notation here exhibited every modic specting the calculator. When its sloping side is fication of number may be expressed, and of con- turned towards the left, it denotes one, or the first sequence every aritbmetical operation success- digit; when turned upwards, or from the calcufully performed; but we have represented in the lator, it denotes two, or the second digit; when plate, and shall now describe another form of pal. turned to the right, it represents three; and when pable arithmetic, equally comprehensive and much turned downwards, or towards the calculator, it dovo'cs four, on the fourth digit. Five is denoted best and the least troublesome apparatus which a by a peu of the second set, having its sloping side blind man can use. We can see no reason why geor bypotheeuse turnd to the left; six, by the neral ideas of geography or topography might not same tunud upuar's; seven, by the same turn. d be conveyed to him in the same manner, by In the right; and tight, by the same turned direct. spheris composed of or covered with the same ly down, or towards the body of the calculator. impressible matter. Nine is expressed by a peug of the third set when The view he proposed to take of this subject its gts are directed to right and left; and the has led us to notice the different inventions for same per expresses the cyplier when its edges are the improvement of the blind, which have bad direct. d up and down. By three different pegs their origin in our own country, but we should by the relative values of the ten digits may therefore no means omit a plan published at Paris under be distinctly expressed with facility; and by the title of “ An Essay on the Education of the sufficient number of cach set the steps and result Blind,” which supersedes every former attempt to of the longest calculation may be clearly repre- facilitate their improvement. The invention of a sented to the sense of feeling. It seems uune- plau so arduous in its appearance, and so pruitscessary to illustrate this by an example; suffice it cable in its exccution, demand d the highest exto express in our caracters, the present year of ertions of the noblest genius to produce it, and the the Christian æra 1988: Take a peg of the tirst most strenuous etforts of inlctatigable humanity se: and hx it in the board with its sloping side to render it effectual. Its object is to teach thei', tuinka tokards the le:t equal to one; take now a by palpable characters impressed on paper, 1st peg of the second sct and fix it in the next hole only the liberal arts and sciences, but likewise the in the same groure, proceeding as usual from left principles of mechanical operation, in such a ipanto right, with its sloping side torned to the rigtit ner, that those who have no genius for b.terary equal to 7; next take a peg of the same set and improvement may yet become respectable, useful, fix it in the next hule, with its sloping side turled and independent members of society, in the cadownwds, equul to 8; lastly, take another peg pacity of common artisans. By these tangible of the same set and place it in the next hole in signatures, they are taught to read, to write, and the same position, equal to 8; and the whole will to print; they are likewise instructed in geometry, express the number required.

in algebra, geography, and, in short, in every " When it is incessary to express a vulgar branch of vatural philosophy. Nor are their effraction, I place the numerator in the groove im- fonts circunscribed by mire utility; a taste for mediately above, and the denominator in that ime the fine arts has likewise been cultivated among mediately below the groove in which the integers them. They have been taught to read music will! stand ; and in decimal arithimetic an empty hole their fingers as others do with their eyes; and in the integer-groure represents the comma or de- though thry cannot at once feel tbe notes and percimal point. By similar breaks I also denote form thein upori an instrument, yet they are capouls, shillings, pence, &c., and by the sune pable of acquiring any lesson with as much exact. expedient i separate in division the divisor and ness and rapidity as those who enjoy all the adquotient from the dividend.

vantages of sight. We shall now give a more par. “ This notation, which supplies me completely ticular account of the topies contained in this with ccefficients and indices in algebra and fluxo essay. In his first chapter the author discovers jons, seems much superior to any of the kivid the end propiesed by that delineation of culture bitherto made public in the west of Europe. That which he offers to the blind; it is to enlarge their invented and described by Mr. Grenville, having sphere of knowledge, and of consequence to in. no less than ten sets of pers, is by much too crease their capacities and improve their powers complicated for general practice; and that which of action, so that they may become happy and inwe one to the celebrated Saunderson is apt to dependent in themselves, and useful and agree. prizzle and embarrass the calculator, as the pegs able to others. The 2d chapter contains an an. representing the numerical digits can seldom vr swer to the objections urged against the general never be in the same straight line.”

utility of this institution. These objections are In the higher parts of mathematics, such as candidly stated, and answered in the most satisconic sections, the same solid figures which are factory manner; but were we to recapitulate them mediums of perception to those who se, my in detail, it would protract this article to an unperform the same usefui office to the blind. Eui, justitiable length. The zd chapter treats of readfor the structure of superficial ligures, we should ing as adapted to the practice of the blind. The imagine, that a kind of matter might be found, 4th chapter consists of answers to various obiec. soit enough to be easily susceptible of impreso tions against the method of reading proposed for sions, yet hard enough to retain them till etfaced the blind; but these, for reasons formeriy given, by an equal pressure. Suppose, for instance, we cannot with propriety delineate in this article. table were forined, four feet broad and eight in lo the 5th chapter is shown the art of printing as length; for the figures, that they may be the practised by the blind for their peculiar use. In mi re sensible to the touch, onght to be larger ihe oth chapter is described the manner of teachthun ordinary. Suppose this table had brins or a ing the blind the art of printing for those that see. Huiding round it, rising an inch above the sur- In the 7th is represented the manner of teaching face: let the whole expanse, then, be filled with the blind to write. The 8th chapter explains the bres-wax, and the surface above pressed extremely method of tcaching the blind arithmetic; the gib, even with a polisteu buaril, foimed exact'y to fit geography; the soth, music. The irth contains the space within the mouldings. This board will an accouit of the mechanic arts in wbich the blind always be necessary to eflace the figures employed are employed, and of the way by which they are iu former propositions, and prepare the surface formed for such occupations. The 12th shows in bir new ones. We think we have imagined the general the proper manner of instructing the Juinutest inconvenience that can arise irom this biod, and draws a parallel betireen their educaDuthid of delineating and conceiving grometrical tion and that of the draf and dumb. Chapter truths; and, after all, the table appears to us the Izeh treats of the metbod of instructing them in

the languages, mathematics, history, &c. What suffer him by no means to be initiated in it. If remains of the book is taken up with notes which his natural genius favours the attempt, the harpillustrate each particular chapter; a short histo- sichord, barp, or organ, are the most proper inrical account of the rise, the progress, and the struments for him to begin with; because by these prespat state of the Academy for the Formation of instruments he may be made more easily acthe Blind; an ode on the cultivation of the blind, quainted with the extent of musical scales, with by one that laboured under that affliction; an ex- the powers of harmony, with the relations of which tract from the register of the Royal Academy of it is constituted, and of course with the theory of Sciences; opinion of the printers; models of the bis art. It would be not only unnecessary, but various pieces which blind children are capable of impracticable, to carry him deep into the theory, printing; and an account of the exercises per- before he has attained some facility in the pracformed by blind children in presence of the king, tice. Let, therefore, his head and his hands (if quera, and royal family, during the Christmas we may use the expression), be taught to go pari suiemnities in 1786.

passu. Let the one be instructed in the simplest Having thus given a cursory view of the various elements, and the others conducted in the easiest cupies contained in the essay, we proceed to give operations first: contemplation and exercise will bine account of the manner in which the blind produce light in the one, and promptitude in the prut and write. The blind compositor, then, has other. But as his capacity of speculation and a box for every alphabetical character in use; on powers of action become more and more inature, the outside of these boxes are palpably marked discoveries more abstract and retired, tasks more the peculiar character belonging to each; they arduous and difficult, may be assigned bim. He are tilled with types, which he chooses and sets as should be taught the names and gradations of the they are called for, but not in the position in which diatonic scale, the nature and use of time, the ditbey are to be read; on the contrary, they are in- versity of its modes whether simple or mixed. He verted as objects are seen painted on the retina of should be taught the quantity or value of notes, an eye by an optician. Having thus fixed and ar- not only with respect to their pitch, but to their ranged his types, he chooses a page of the strong- duration. Yet, let him be instructed not to conest paper that can be found, which he gently sider these durations as absolutely fixed, but varimoisteas in a degree sufficient to render it more able according to the velocity of the movements eavily susceptible of impressions, without being in which they are placed. Thus we reckon a semidilacerated or worn by the shock which it must breve equal to 4 vibrations of a pendulum; a afterwards undergo. He then lays it upon the minin to 2; a crotchet to 1, &c. But if the types; and by the cautious operation of the press, number of aliquot parts, into which a semibreve is or by the easy strokes of a little bammer, which divided, be great, and consequently the value of are frequently repeated over the whole expanse, each particular part snall, the minim, crotchet, he causes the impression of the type to rise on quaver, &c. will increase in their intrinsic du. the opposite side of the paper, where, when dry, rations, though they must always preserve the it coutinues not only obvious to the sight but the same proportions relatively one to another. He luch, and is far from being easily effaced. On should never be habituated to take a piece of the upper side of the paper the letters appear in music either from the sound of a voice or an intheir proper position, and by their sensible eleva- strument. His companion onglit to read the tion above the common surface render it practic music by the names and values of its characters, table for the blind to read them with their fingers. With the same exactness as the words in any other Their manner of writing is analogous to this ope- language. When he becomes a considerable adept tation: the papil, by repeated experiments, hav- in the art, tangible signs may be invented, by dag familiari.ed himself to the forms of the letters, which he may not only be enabled to read, but even both in their inverted and in their proper position, to set, music for himself. Such exercises will rengradually learns to delineate them upon paper, der hin infinitely more accurate, both in his prinmoistened as before, with the point of an iron pen, ciples and practice, than he would otherwise be. which has no split, and which is just sharp envugh The cushion of Mr. Cheese appears to have to impreis without piercing the paper: thus, on more powers than any other instrument for the the side next to the writer's band, the letters are same purpose that bas bitherto occurred, and formed, sunk, and inverted; but when the paper is though not without objections, we shall here deturned they appear right and in relievo. Thus the scribe it. It may possibly, however, be best for blind are enabled to form and decypher, not only every blind adept in the musical art, after being the characters required in common language, but sufficiently instructed in its theoretical and pracalso mathematical diagrams, arithmetical and geo- tiral principles, to invent for himself a table, by graphical processes, and all the characters used which may be expressed all the various phenoin the written language of music. That these are mena of music, in which, by varying the forms not idle pretences, or intended to impose on the and positions of his pegs, he may habitually ascredulous, many undeniable fucts might be ad- sociate them with sounds, durations, rests, interduced to prove. And in fact, the blind themselves vals, chords, cadences, da capos, repeats, and all are made to exhibit at their own academy every the various graces which give animation and exWednesday and Saturday to crowds of charitable pression to musical sounds: for thus, being the admirers, by whose liberal donations the institu- immediate creatures of his own imagination, they Lion is now chiefly supported.

will inore easily become familiar to his memory, There is little doubt. but that the blind are ca, and be more strongly and readily associated with pable of being taught astronomy, natural and the phenomena which they are intended to signify, moral pbilosophy, theology, grammar, logic, his- than if he had assumed the inventions of any try, and the belles lettres; but above all music, other person. which is pertraps of all other sciences the most at- The following is Mr. Cheese's description of his Lainable, the most practicable, and the most con- machine for teaching music to people deprived of bolatory to the mind. If the pupil, however, be sight, and to enable them to preserve their comwol endowed with natural talents for the latter, positions, in the act of composing, without the

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