place the 3d number upon the 3d row of fquares, and fo of the reft. Then with my fingers running over each of the rows vertically from the bottom to the top, beginning with that which is nearest to my right, I work the addition of the numbers which are expreffed, and mark the furplus of the tens at the foot of that column. I then pafs to the 2d column, advancing towards the left; upon which I operate in the fame manner; from thence to the 3d; and thus in fucceffion, till I finish my addition. We fhall now fee how the same table served him for demonArating the properties of rectilineal figures. Let us fuppofe this propofition to be demonftrated, That parallelograms, which have the fame bafis and the fame height, are equal in their furfaces. He placed his pins as may be feen in fig. 4. He gave names to the angular points, and finished his demonftration with his fingers. If we fuppofe that Sanderson only employed pins with large heads to mark the limits of his figures, around these he might arrange his pins with fmall heads in 9 different manners, all of which were familiar to him. Thus he fcarcely found an embarraf, ment, but in thofe cafes where the great number of angular points, which he was under a neceffity of naming in his demonftration, obliged him to recur to the letters of the alphabet. We are not informed how he employed them. We only know, that his fingers ran over the board with tonishing agility; that he undertook with fuccefs the longeft calculations; that he cond interrupt the feries, and discover his mistakes; that he proved them with the greateft eafe; and that his labours required infinitely lefs time than one could have imagined, by the exactness and promptitude with which he prepared his inftruments and difpofed his table. This preparation confifted in placing pins with large heads in the centres of all the fquares: having done this, no more remained to him but to fix their values by pins of fmaller heads, except in cafes where it was neceflary to mark an unit; then he placed in the centre of a fquare, a pin with a fmall head, with which it has been occupied. Sometimes, inftead of forming an entire line with thefe pins, he contented Limfelf with placing fome of them at all the angular points, or points of interfection; around which he tied filk threads, which finished the formation of the limits of his figures." See fig. 4. It may be added by way of improvement, that for the divifion of one feries of numbers from another, a thin piece of timber in the form of a ruler with which lines are drawn, having a pin at each end for the holes in the fquares, might be interpofed between the two feries to be diftinguished. By the notation above described every modification of number may be expreffed, and confequently every arithmetical operation fuccefs. fully performed; but there is another form of palpable arithmetic, equally comprehenfive, and inuch more fimple than that of Sanderson, originally invented, and still used in calculation, by Dr Henry Moyes; a gentleman, whofe uncommon attainments we have already endeavoured to illuftrate. See 7. In a letter addrelled to the Editor of Encyclopedia Britannica, the Dr gives the following brief account of a palpable netation, which he has used for thefe 29 years, to affift his memory in numerical computations. "When I began to fludy the principles of arithmetic, which I did at an early period of life, being unacquainted with the writings of Sanderfon, in which a palpable notation is described, I embraced the obvious, though imperfect expedient of cutting in-" to the form of numerical characters thin pieces of wood or metal. By arranging thefe on the furface of a board, I could readily represent any given number, not only to the touch, but also to the eye; and by covering the board with a lamina of wax, my fymbols were prevented from changing their places, they adhering to the board from the flighteit preffure. By this contrivance, I could folve, though flowly, any problem in the fcience of numbers: but it foon occurred to me,. that my notation, consisting of 10 species of fymbols or characters, was much more complicated than was abfolutely neceffary, and that any given number might be diftinctly expreffed by 3 fpecies of pegs alone. To illuftrate my meaning, let A, B, C, D, (fig. 5.) reprefent a fquare piece of mahogany a foot broad and an inch in thicknefs; let the fides A B, B C, C D, D A, be each divided into 24 equal parts; let every two oppofite divifions be joined by a groove cut in the board fufficiently deep to be felt with the finger, and let the board be perforated at each interfection, with an inftrument a tenth of an inch in diameter. The furface of the beam being thus divided into 576 little fquares, with a fmall perforation at each of their angles, let 3 fets of pegs or pins, refembling thofe reprefented in the plate at the figures 6, 7, 8, be fo fitted to the holes in the board, that when ftuck into them they may keep their politions like thofe of a fiddle, and require fome force to turn them round. The head of each peg belonging to the first set is a right-angled triangle, about one tenth of an inch in thicknefs; the head of each peg belonging to the 2d fet differs only from the former, in having a small notch in its floping fide, or hypothenufe; and the head of each peg belonging to the 3d fet is a fquare, of which the breadth fhould be equal to the bafe of the triangle of the other two. These pegs fhould be kept in a cafe confifting of 3 boxes or cells, each cell being allotted to a set, and the cafe must be placed close by the board previous to the commencement of every operation. Each fet fhould confift of 60 or 70 pegs (at least when employed in long calculations); and when the work is finished, they fhould be collected from the board and carefully restored to their refpective boxes. Things being thus prepared, let a peg of the firft fet be fixed into the board, and it will acquire 4 different values according to its pofition refpecting the calculator. When its floping fide is turned towards the left, it denotes 1, or the first digit; when turned upwards, or from the cal culator, it denotes 2, or the 2d digit; when turned to the right, it reprefents 3; and when turned downwards, or towards the calculator, it denotes 4, or the 4th digit. Five is denoted by a peg of the fecond fet, having its floping tide or hypotaemufe turned to the left; 6, by the fame turned upwards; 7, by the fame turned to the right sud 8, by the fame tumed directly down, or to ward, wards the body of the calculator. Nine is expreffed by a peg of the 3d fet, when its edges are directed to right and left; and the fame peg expreffes the cypher, when its edge are directed up and down. By three different pegs the relative value of the ten digits may therefore be diftinctly expreffed with facility; and by a fufficient number of each fet, the steps and result of the longest calculation may be clearly reprefented to the fenfe of feeling. It seems unneceffary to illuftrate this by an example; fuffice it to exprefs in our characters the prefent year of the Chriftian æra 1788: Take a peg of the first fet, and fix it in the board with its floping fide turned towards the left equal to one; take a new peg of the ad fet and fix it in the next hole in the fame groove, proceeding as ufual from left to right, with its Пloping fide turned to the right equal to 7; next take a peg of the fame fet and fix it in the next hole, with its floping fide turned downwards, equal to 8; laftly, take another peg of the fame fet, and place it in the next hole in the fame pofition, equal to 8; and the whole will exprefs the number required. When it is necessary to express a vulgar fraction, I place the numerator in the groove immediately above, and the denominator in that immediately below the groove in which the integers stand; and in decimal arithmetic an empty hole in the integer groove reprefents the comma or decimal point. By fimilar breaks I alfo denote pounds, fhillings, pence, &c. and by the fame expedient I separate in divifion the divifor and quotient from the dividend. This notation, which fupplies me completely with coefficients and indices in algebra and fluxions, feems much fuperior to any of the kind hitherto made public in the weft of Europe. That invented and defcribed by Mr Grenville, having no less than ten fets of pegs, is by much too complicated for general practice; and that which we owe to the celebrated Sanderson is apt to puzzle and embarrafs the calculator, as the pegs representing the numerical digits can feldom or never be in the Lame ftraight line." (16.) BLIND, METHODS OF INSTRUCTING THE, IN MUSIC. There is a hint of tangible figns for teaching mufic, in Tanfure's Mufical Grammar, p. 93, which, though (like the reft of the book) obfcure and indigefted, may be improved and applied with advantage. We have therefore inferted his MUSIC TABLE, in Plate XL. Fig. 11. and fhall here quote his explanation. "Let A-B be a finooth board 3 or 4 feet long, 1 inch thick, and 9 inches wide, with 5 fquare ledges glued thereon, each being half an inch asunder, half an inch wide, and half an inch high; which rifing ledges reprefent our 5 lines of mufic, and their fpaces; and the two outward lines being made a little lower, may ferve as leger lines, on occafion. The cyphers represent so many holes bored into every line and space, half an inch afunder; wherein pegs of different shapes are to be fet, to reprefent the feveral forts of notes and characters of the tune; which pegs the blind perfon may know by feeling, as well as he does his keys of the organ er harpfichord: fo that, by keeping his fingers on the 5 lines, he feels the feveral pegs as they come en, and are fet to reprefent the feveral forts of notes, on both line and space; whilft his right hand ftrikes the refpective key, &c. he first know. ing the names of all his keys, his lines, spaces, and the mark of every peg. Let each peg be about half an inch high, when fet in very faft. [N. B. The blind perfon must first be taught the names of the above lines and spaces in both the treble and bass cliffs; and that he must feel his treble with his right hand, and his bafs with the left hand; each being contrary, as you may fee by the letters of the above table A and B; and must learn each part separate.] Of pegs, he must have a great number of every fort, to fet his tune with, which he may mark as follows: For a Semibreve, 4 top-notches.-Minim, 2 top-notches. -Crotchet, 1 top-notch.-Quaver, 1 corner cut off. Semiquaver, 2 corners cut off.- Demifemiquaver, all 4 corners cut off.-Refts, a notch in the corner. —A Flat, 1 notch on the fide.—Sharp, 2 notches on the fide.-Point, 3 notches on the fide.-Bar, a flat thin top.-Repeat, a fharp-pointed top, &c. &c. &c. But it is beft for every performer to make and mark his own pegs; and deliver them one by one as they are called for by the perfon that fets his tune." Such is Mr Tanfure's plan of Mufical Notation. It is, however, imperfect, and perhaps every table of the kind may be liable to the fame cenfure, as not being comprehenfive of all the characters in the written language of mufic, fo that the blind rather may find no deficiency in acquiring any leffon. Mr CHEESE's Cushion appears to ve more powers than any other inftrument hitherto invented for the fame purpofe; and therefore though it is alfo attended with formi dable objections, we here infert his defcription of it. It may poffibly, however, be beft for every blind adept in the mufical art, after being fuffici ently inftructed in its theoretical and practical principles, to invent for himself a table, by which may be expreffed all the various phenomena of mufic; in which, by varying the forms and pofitions of his pegs, he may habitually affociate them with founds, durations, refts, intervals, chords, cadences, de capos, repeats, and all the various graces which give animation and expreffion to mufical founds: for thus, being the immediate creatures of his own imagination, they will eafily become familiar to his memory, and be more ftrongly and readily affociated with the phenomena which they are intended to exprefs, than the inventions of any other. Mr Cheefe's machine, (fee Plate XL. Fig. 9.) is intended, in "te-ching mufic to people deprived of fight, to enable them to preferve their compofitions, in the act of compofing, without the atlistance of a copyist.”— "That part of the machine, which reprefents the book, or paper, is a fmall cushion fluffed, on a little frame; along which is fewed a number of pack-thread ftrings, at equal diftances from each other; thefe reprefent the lines in a mufic book: the five which compofe the ftave are made of large twine; and thofe which represent the leger or occafional lines drawn through the heads of the notes, where the mufic exceeds the compaís of the established ftave, are made of fmall twine, and are on this machine of the fame length as the others. If the practitioner only wishes to write harpsichord Liufic, the cullion may be what length length he pleases, and about five or fix inches letters which diftinguish them, left confufion may arq are few pieces in mufic which will be found either too intricate to be acquired, or too long to be remembered, by a perfon deprived of fight. Mr Stanley performs what is ftill more aftonishing: He accompanies any leffon with a thorough bafs, though he never has heard it before. We have never yet heard of any perfon, though bleffed with the full ufe of fight, who could thus anticipate harmony before the chords were founded, and accompany it in a manner fuitable to its nature. When the pupil becomes a more profound theorift, he may be farther inftructed by Rameau, in his principles of compofition; by D'Alembert, and by Rouffeau's Mufical Dictionary: (fee Music) Or, if he be perfuaded of the neceflity of geometry in mufic, (which fome think frivolous,) he may perufe Dr Smith's Philosophical Principles of Harmony, Malcolm's Effay, Treydell's Theory and Practice of Mufic; or The Principles and Powerf Harmony; an illuftration of Tartini's theory. the blind arithmetic; the 9th geography; the 10th, mufic. The 11th, contains an account of the mechanic arts in which the blind are employ ed, and of the way by which they are formed for fuch occupations. The 12th fhows in general the proper manner of inftructing the blind, and draws a parallel between their education and that of the deaf and dumb. The 13th treats of the method of inftructing them in the languages, mathematics, hiftory, &c. The book next contains notes illuftrating each chapter; an account of the rife, progrefs, and present state, of the academy for the formation of the blind; an ode on the cultivation of the blind, by one labouring under that affiction; an extract from the regifter of the royal academy of fciences; opinion of the printers; models of the various pieces which blind children are capable of printing; and an account of the exercifes performed by blind children, in the prefence of the late unfortunate king, queen, and royal family, du(17.) BLIND, NEW FRENCH PLAN FOR IMPRO- ring the Christmas folemnities in 1786. The manVING THE. A work has been lately publifhed at ner in which the blind print is thus defcribed; Paris which fuperfedes every former attempt to The blind compofitor has a box for every niphapromote or facilitate the improvement of the betical character in ufe; on the outfide of thefe blind. The invention of a plan fo arduous in its boxes are palpably marked the peculiar character appearance and fo practicable in its execution, de- belonging to each; they are filled with types, manded the higheft exertions of the nobleft genius which he chocfes and fets as they are called for, to produce it, and the most strenuous efforts of inverted. He then takes a piece of the itrongeft indefatigable humanity to render it effectual. It paper that can be found, which he gently moifens is entitled, "An Eflay on the Education of the in a degree fufficient to render it more eafiy fufBlind." Its object is to teach them, by palpabie ceptible of impreffions, without being delacerated characters impressed on paper, not only the libe- or worn by the fhock which it must undergo. He ral arts and sciences, but likewife the principles then lays it upon the types; and by the cautious of mechanical operation, in fuch a manner, that operation of the prefs, or by the eafy ftrokes of a those who have no genius for literary improve- little hammer, which are frequently repeated over ment may yet become refpectable, ufeful, and in- the whole expanfe, he caufes the impreffion of the dependent members of fociety, in the capacity of type to rife on the oppofite fice of the paper, common artifans. By thefe tangible fignatures where, when dry, it continues not only obvious they are taught to read, to write, and to print; to the fight but the touch, and is far from being they are likewife inftructed in geometry, in alge- easily effaced. On the upper fide of the paper bra, geography, and, in fhort, in every branch of the letters appear in their proper pofition, and, by natural philofophy. Nor are their efforts circum- their fenfible elevation above the common furface, fcribed by mere utility; a tafte for the fine arts render it practicable for the bind to read them has likewife been cultivated among them. They with their fingers. Their manner of writing is have been taught to read mafic with their fingers, analogous to this operation: the pupil, by repeatas others do with their eyes; and though they ed experiments, having familiarifed himself to the cannot at once feel the notes and perform them forms of the letters, both in their inverted and upon an inftrument, yet they are capable of ac- proper pofitions, gradually learns to delineate quiring any leffon, with as much exactnefs and ra- them upon paper, moiftened as before, with the pidity, as thofe who enjoy all the advantages of point of an iron pen, which has no fplit, and fight. In the firft chapter of this work, the author which is juft fharp enough to imprefs without points out the end propofed by that culture which piercing the paper: thus, on the fide next to the he offers to the blind; it is to enlarge their fphere writer's hand, the letters are formed funk and inof knowledge, to increase their capacities and im- verted; but when the paper is turned they approve their powers of action, fo that they may pear right and in relievo. Thus the blind are enbecome happy and independent in themfelves, abled to form and decypher, not only the characand uf-ful and agreeable to others. The ad chapters required in common language, but also mater contains an answer to the objections against the general utility of this inflitution. The 3d treats of reading as adapted to the practice of the blind. The 4th confifts of anfwers to various objections against the method of reading propofed. In the 5th is shown the art of printing, as practifed by the blind, for their peculiar ufe. In the 6th is defcribed the manner of teaching the blind the art of printing for thofe that fee. In the 7th is reprefented the manner of teaching the blind to write. The 8th explains the method of teaching thematical diagrams, arithmetical and geographical proceffes, and all the characters used in writing mufic. All thefe wonders they have performed with fuccefs, to the univerfal fatisfaction of numberlefs fpectators whom curiofity and compaion impelled to visit the academy, to behold a fpectacle fo interefting to humanity. The above quoted work is printed and bound by the blind themfelves. They exhibit at their own academy every Wednefday and Saturday between one and two o'clock, P. M. to crowds of charitable admirers, by |