478 Journal of the Asiatic Society of Bengal. [July, 1907, 



custom of the language which expressed the smaller elements 

 first and in contradiction to other systems of notation -which, 

 later on, were in common use among the Hindus ; and we 

 find many examples of dates expressed in words only or in words 

 and figures, and, in such cases, the words are often formulated 

 somewhat as follows: "nava-sata panchashashty-adhikeshu,'* that 

 is, with the hundreds first, then the units hefore the tens — a mixed 

 order it may he termed. But in the very early instances, accord- 

 ing to Don Martino de Zilva Wickremasinghe (Joum. Roy. Asiatic 

 Soc. 1901, p. 301), these *' ancient Brahmi numerals are in- 

 Tariahly read either from right to left or from hottom to top. 

 Thus, in writing 128, the symbols would he written either 



horizontally as /^ Q ^ (*'.c„ 100, 20, 8), or vertically 



In Sanskrit this would be read ashta-vimsati-satam, i.e., eight- 

 twenty-hundred," 



This old Indian notation has never been completely super- 

 seded. Ephigraphical instances of the thirteenth century A.D. 

 have been found, and, according to Biihler, ''The Malaylam 

 MSS. have preserved it to the present day. " (Biihler, Indian 

 Paleography^ 77). 



Aryabhata introduced, it is said, an alphabetical notation, 

 as there was no convenient system in use in his time.^ This 

 notation of Aryabhata's appears to be a somewhat crude adapta- 

 tion from the Greek (or Arabic) plan. Its merit (?) is that it 

 can be used in verse and, probably, it was not used for actual 

 calculations. Aryabhata did not employ the idea of ' place value * 

 and used twenty-five letters for the first twenty-five numbers. 

 For this pui'pose were allotted the classified consonants. The 

 unclassed consonants he used for the tens (above twenty) and the 

 vowels as multipliers. Thus the consonants ^, iff, ;«',.-. - 



W stood for 1, 2, 3 25. For 30, 40 ... . 90 he used 



'^, ^, . . . ^ ; while X* -^ indicated multiplication 



by 100 ..... 10,000, etc. Strangely enough this notation is 

 not used In the mathematical part of Aryabhata's work. It occurs 

 only in the astronomical part. * 



I have found no epigraphical examples of Aryabhata's 

 system in its original form, and the earliest case of an alphabetic 

 notation known to me is of the tw^elfth century A.D. At this time 

 the idea j)t place value had been well established and, conse- 

 quently, Ai*yabhata's notation had become modified. The note- 

 worthy point about all the examples of this alphabetic notation is 

 that it was always employed with the smaller elements first (e.e., 

 on the left). For example : — 



r>^ . - 



^ It is also said that Tanini denoted nambera by tlie letters of the 

 alphabet in their order precisely in the same manner as the Greeks and 

 Arabs (Weber, Ind. Lit., 222). 4 See Kern's edition, p. 17. 



