It is with this unsatisfactory material, then, that we have to deal in searching for the early history of the Hindu-Arabic numerals, and the fact that many unsolved problems exist and will continue to exist is no longer strange when we consider the conditions. It is rather surprising that so much has been discovered within a century, than that we are so uncertain as to origins and dates and the early spread of the system. The probability being that writing was not introduced into India before the close of the fourth century B.C., and literature existing only in spoken form prior to that period,[66] the number work was doubtless that of all primitive peoples, palpable, merely a matter of placing sticks or cowries or pebbles on the ground, of marking a sand-covered board, or of cutting notches or tying cords as is still done in parts of Southern India to-day.[67] {19} The early Hindu numerals[68] may be classified into three great groups, (1) the Kharo[s.][t.]h[=i], (2) the Br[=a]hm[=i], and (3) the word and letter forms; and these will be considered in order. The Kharo[s.][t.]h[=i] numerals are found in inscriptions formerly known as Bactrian, Indo-Bactrian, and Aryan, and appearing in ancient Gandh[=a]ra, now eastern Afghanistan and northern Punjab. The alphabet of the language is found in inscriptions dating from the fourth century B.C. to the third century A.D., and from the fact that the words are written from right to left it is assumed to be of Semitic origin. No numerals, however, have been found in the earliest of these inscriptions, number-names probably having been written out in words as was the custom with many ancient peoples. Not until the time of the powerful King A['s]oka, in the third century B.C., do numerals appear in any inscriptions thus far discovered; and then only in the primitive form of marks, quite as they would be found in Egypt, Greece, Rome, or in {20} various other parts of the world. These A['s]oka[69] inscriptions, some thirty in all, are found in widely separated parts of India, often on columns, and are in the various vernaculars that were familiar to the people. Two are in the Kharo[s.][t.]h[=i] characters, and the rest in some form of Br[=a]hm[=i]. In the Kharo[s.][t.]h[=i] inscriptions only four numerals have been found, and these are merely vertical marks for one, two, four, and five, thus: | || ||| |||| In the so-called ['S]aka inscriptions, possibly of the first century B.C., more numerals are found, and in more highly developed form, the right-to-left system appearing, together with evidences of three different scales of counting,--four, ten, and twenty. The numerals of this period are as follows: [Illustration]