350 Journal of the Asiatic Society of Bengal. (September, 1912. 
mixture of what we should now call Sanskrit and Prakrit 
oe eee eee t appears to have been in general use, in north- 
western India, for literary purposes, till about the end of the 
third century 4.D.’’ 
c e two words dinara and dramma occur. ‘This 
circumstance,’’ he says, ‘‘ again points to some time within the 
first three centuries of the Christian era.’’ 
(d) The peculiar sign of the cross (+) as the sign of negative 
quantity is also ‘‘ indicative of antiquity.’ 
(e) In one of the problems the year is reckoned as 360 
days. 
2 (f) ‘‘ Indian arithmetic and algebra, at least,’’ he assumes, 
** are of entirely native origin.’’ 
) ‘* It is certain,’’ he says, ‘‘ that this principle (notation 
with place value) was known in India as early as 500 A.D. 
There is no good reason why it should not have been dis- 
covered there considerably earlier.’’ 
‘* Regarding the age of the manuscript I am unable,’’ says 
Dr. Hoernle, ‘‘ to offer a very definite opinion...... In any 
case it cannot be well placed later than the tenth century a.D. 
It is quite possible that it is somewhat older.’? His reasons for 
coming to this conclusion are— 
(kh) The composition of a Hindu work on arithmetic seems 
to presuppose a country and a period in which Hindu civiliza- 
tion and Brahmanical learning flourished. 
(t) The country in which Bakhshiii lies ‘‘ was lost to Hindu 
Civilization ..... towards the end of the tenth and the begin- 
ning of the eleventh centuries a.p.”’ 
j) ‘‘In those troublous times it was a common practice 
for the learned Hindus to bury their manuscript treasures.’’ 
Il. 
__ _ (a) The workis written in the Sloka measure and, therefore, 
it is argued must have been composed before a.D. 500. We 
can, however, point to a number of Sarada inscriptions of the 
period from the tenth century onwards in which the Sloka 
measure occurs, e.g. the Brahmor inscription of Yugakara 
Varman'; the Sungal copper-plate grant; the inscription of 

een tani ee 
1 Vogel’s Antiquities of Chamba State, p. 161. ® ib., p. 166, 
