' used hy different Nations. 301 



Parisian manuscript ; the peculiar nature of this system in- 

 duced ,me to compare it with the numerical figures of the 

 Mexicans and Chinese ; by the publication of a great number 

 of Indian grammars we have lately obtained the certainty, 

 that in India within the Ganges, as well as without that river, 

 not only different figures and alphabetical signs are used in 

 expressing numbers, but also that the systems themselves of 

 computation differ from one another, — in some of them value 

 being expressed by position, in others not ; lastly, a peculiar 

 Indian method, till now quite unknown, has been preserved 

 and discovered in a scholion of the Greek monk Neophytus. 

 In an Essay composed by me, and read in the Session of the 

 Academic des Inscriptions et Belles Lettres, in 1819, I have 

 already tried to shew, that some nations shorten the unartificial 

 method of juxtaposition by writing exponents, or indicators 

 over thefigui'es, (as it is used by the Mexicans, in the ligatures 

 of four times 13, or 52 years, by the Chinese, the Japanese, 

 and the Hindoos, speaking the Tamul language,) and also the 

 manner in which, by means of these indicators, and the sup- 

 pression of the group-signs written horizontally or vertically, 

 the excellent Indian system, expressing value by position, 

 might have been arrived at. The spreading of this system 

 niust considerably have been favoured by the very ancient use 

 of a particular contrivance, the strings of reminiscence and caU 

 culation. These are either loose cords, as the quippos of the 

 Tartars, Chinese, Egyptians, Peruvians*, and Mexicans, 

 which have been transformed into Christian beads, or ritual 

 calculation-machines -[- ; or they are extended and fixed in a 

 firattie. Jn the last form they are found in the Suanpan, used 

 Jh '^11 'ihe internal countries of Asia, in the abacus of the 

 Ilomans and ancient Tuscans J, and in the instruments of 

 the palpable arithmetic used by the Slavonian tribes §. . f;,s. ^ 

 l^he files o| 9prjjs .gr ^if;es in tli^ y^ry simple Asiatic 



, r ;■> ):l^,r ..^- ■-... ■■ V* *•'-.■- \ ^■" 



*''0n the quippos used for counting the sins in the confessional, see Aoosta, 

 Hist. Natur&l de las ludias, lib. vi., cap. 8. El luca GarcilasO; lib. vi., cap. 9. 

 Freret, Mem. de I'Acad. t. vi., p. 109. 



f Klaproth's Asiat Magaz., t, ii., p»7^» ,.,^ii»Pf ^^rf* W* tm/niqo srfl liO ♦ 



* Otfried Midler's £trusker,t.ii., p. 318. ■ -' ....... 



\ In the llu.ssiau language ch^^ki signifies the beads, and choiif the calculation* 

 board^ vyit^i, its fixed cords.. ,,.^ .irmwiiuiii i«« ^^c*^ , *. 



APRIL.— JUNE, 1830. x^v^J^'. ! '■■i \ , ;k:-»>«^ l -* X 



