VoL III, No. 7.] Notes an Indian Mathematics; 483 



[N.S.'} 



In tlie above list I have given, as far as I know, every 

 inscription before the tenth century that has been supposed to 

 be dated in figures of the modern (place-value) notation. Let 

 us now examine these examples and see how they bear on the 

 question of the introduction of the new system of notation. To 

 those who are not familiar witli Indian inscriptions it is necessary, 



in the first place, to explain that *' the task of the student of 

 Indian antiquity isnow-a-days complicated by tLe existence of the 

 most ingenious forgeries in every branches of research." Indeed, 

 about fifty per cent, of the discovered South Indian copper-plate 

 grants are now known to be forgeries, and the chief period of 

 fabrication appears to have been about the end of the eleventh 

 century when " there occurred a specially great opportunity to 

 regain confiscated endowments and to acquire fresh ones. " 

 (Fleet, Ind. Antiq. xxx., 205.) 



It is therefore neeessaiy not to place implicit faith in every 

 inscription one conies across. However, for the present, we must 

 be satisfied with the exclusion of those examples that we can 

 show with sufficient reason to be untrustworthy as evidence ; 



and we must accept those that do not bear obvious marks of 

 unreliability. 



The epigraphists in interpreting these dates have rightly 

 looked principally to historical accui'acy, and when the dates have 

 been given in words the figures have been interpreted so as to fit 

 in with the words. This is natural enough from the epigraphists* 

 point of view, when direct interpretation is impossible ; but it is 

 in just such cases that the figures themselves cannot, except 

 with the greatest circumspection, be adduced as evidence. Again 

 it has generally been assumed (without pix)per authority) that 

 the knowledge of the new notation was common in India much 

 eai'lier than the ninth century A.D., and on this assump- 

 tion some of the Intei^n-etations of the dates are based. The 

 figuiea of these dates, if they are to serve as evidence of the use 

 of the modem notation, must at least be capable of interpreta- 

 tion in themselves; they must, of course, belong to reliable 

 inscriptions and they must contain elements of consistency* 

 Bearing these points in mind let us proceed to the examination 

 of the examples cited, 



(1) The Kalbhavi inscription of S. 261 is ** spurious, so far at 

 any rate, as regards the date ; the writing is of about the eleventh 

 century A D." (Epigr. Ind. vii., p. 22, App., Ind. Antiq., xxiv., 11). 



(2) Dr. Biihler quotes this Gurjara inscription of the Chedi 

 year 346 or A,D. 695 as '*the earliest epigraphic instance of the 

 use of the decimal (/.e. the modem 'place-value') notation" in 

 India. An examination of the plate (Epigr. Ind. ii,, p. 20) suggests 

 the possibility that the figures were added some time after the plate 

 was engraved. The date is given in words as well as figures. It 

 is ' three hundred years exceeded by forty-six , 346/ The symbols 

 are right at the end of the inscription from which they are mai'ked 

 off bj* the double bar in a most unusual manner. The figures 

 (Table I (a)) are of the type of the period, as Biihler remarks, but 



