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



l^': 



^he ufse of thi^^i^qt^tion has also been attributed to Arya- 

 bhata and Dr, Kern (Joum. Roy, Asiatic Soc. xx., 371) even 

 concluded from a supposed example of it tliat he quotes that 

 Aryabbata bad made use of the idea of place values ; biit Dr. 

 Bhau Daji sbowed that the passage on which Dr. Kern's cou- 

 eliisiorr was * based is spurious. Woepcke quotes a similar 

 example from the Surya Siddhanta, but concludes only that 

 " L'idee de la valeu^; de position et du zero est done dans Tlnde 

 aussi ancienne, au moinsj que cetfe methoded'ex primer des nombres 

 au'm'oyen"de*mots symboliques " (Journal Asfatique, 1863, p, 447). 

 - - •;; Of- epigraphical instances ■ of these ■ syrabolic lyords" • I have 

 comie across two only of the ninth century, three of the tenth, a 

 few of the eleventh and numbers" of later date. In every in- 

 fitance^ except perhaps very modern ones, the smaller elements are 

 written first as the following examples ghow': 



i.e., reckoned by the hands (2), the arrow 

 ^50); and the p5ra5 (1,300) or 1,352 (Epigr.Ind.v.^ ., ; 



i.e., vedas (4), vasus (80)> fires (.300), moon 

 (1,000); or 1384 (Epigr. lud. i., 94) ; 



^ ^.e., yugas (4), the sky (0), the moon (100), sttid 



the rupa (1,000), or 1104 (Epigr. Ind. vi^ 155) ; etq., etc. 



( ( 



it fpj^g practice does not seem to be one of very great anti- 

 equity, and many of the supposed older dates are doubtful," says 

 'Mr, Damant (Ind. Antiq. vi., 13) 



Albiruni gave a list of words in use in this system. Other 

 lists are giv^n in* Brown's Carnatic Chronology (p. 20f.), Rice's 

 Mysore Inscription^ Biihler's Indian Palseography^ Bumell's South 

 Indian Palaeography ^ etc. The system has been in use in Java, Cia-m- 

 bodia, Burma, etc., and possibly came from the east to India, , . 



In the lists just mentioned 'symboh'cal words are given for 



numbers as far as 48, and as many as forty words are given for 



one particular number. This leads one to suppose that either tlie 



numerical word system was actually in use before the idea of 



place value was known, or that those wlio used it in early times 



were either ignorant of the modem system or ignored it. But as 



the earliest known examples of this word notation being used in 



"^India do npt occur until after the modern notation with its principle 



'of place value 'was introduced this aspect of the question is not of 



great importance. However, from the thousands of examples that 



occur in Ipdiau manuscripts and inscriptions, the fact that the 



order of writing numbers with the smaller element first ^vas a 



"recognised principle throughout India is strongly emphasized. 



The occasional and peculiar use of vertical . writing of 

 numbers has already been noticed. In the Weber MSS. (Joum. 

 Asiatic Soc. Bengal, 1893) examples are found and Dr. Kielhorn 

 discovered some old manuscripts in.which the pages . wei^ 

 numbered vertically as well as in the usual manner. 



From our present point of view it is important to notice that 



