The ordinal numbers are formed by using the points 2, 3, 5, and 6. Fractions are expressed by writing the numerator as a cardinal, and the denominator as an ordinal number. But Braille's numerals are not well adapted to mathematical calculations, for they make the operations too long and difficult. An adaptation of them to music is more convenient, and is strikingly different from the blind-man's notation described by Guillié. It represents the measures by button-molds, the values of the notes by pieces of cork of various thicknesses, a round note by a ring, a black note by a piece of money, rests by thongs of leather, etc., the whole being strung on a long cord.
The characters, printed or written in relief, are read by the inner side of the end of the forefinger of either the right or the left hand, the hands being held open over the page.
The Braille or anaglyptographic writing was done on a paper which was fixed upon a tablet of wood or metal with an undulating surface presenting parallel, horizontal, and equidistant grooves, of a uniform depth, and about as large as a school-slate. The wooden frame of this tablet is bored on the sides with holes at equal distances apart, into which are fastened with pins the ends of a guide. The guide is furnished with two rows of rectangular openings of the size of the generator sign of the Braille alphabet, while the width of the grooves in the plaque is so calculated that the height of the openings in the guide shall correspond with that of the grooves. The blind writer, holding vertically in his hand a stylus with a rounded point, forms in each of the openings one of the signs he desires to write; in consequence of the slight depth of the grooves, the stylus gives to the paper, which should be of suitable thickness, enough relief to make the writing legible without piercing holes in it. After each word the operator should "jump" an opening so as to give the needed space between that and the next word. The two lines finished, he lifts the guide lightly, and slides it along the frame till the pins drop into the next holes, when he is ready to begin two new lines. It should be remarked that the characters are written in hollows, and have to be read in relief. The writer is therefore obliged to write on the reverse of the paper and form the characters from right to left, in order that they may be read from left to right, as is the usual way. Some blind persons have written the equivalent of one hundred Alexandrine lines an hour on the Braille machine. Various forms have been given to instruments on the Braille principle, some of which are represented in the engraving (Fig. 2). In one kind the upper edge of the paper is held in a board which is hinged to the upper end of the frame. In another kind the paper is fixed between two frames which are boxed into one another, so that when one side has been written upon (recto) it can be turned and written
