fingers may or may not have been used—­probably not; and that when the next start is made, and 3, 4, 5, and so on are counted, the fingers first come into requisition.  If the grammatical structure of the earlier languages of the world’s history is examined, the student is struck with the prevalence of the dual number in them—­something which tends to disappear as language undergoes extended development.  The dual number points unequivocally to the time when 1 and 2 were the numbers at mankind’s disposal; to the time when his three numeral concepts, 1, 2, many, each demanded distinct expression.  With increasing knowledge the necessity for this differentiatuin would pass away, and but two numbers, singular and plural, would remain.  Incidentally it is to be noticed that the Indo-European words for 3—­three, trois, drei, tres, tri, etc., have the same root as the Latin trans, beyond, and give us a hint of the time when our Aryan ancestors counted in the manner I have just described.

The first real difficulty which the savage experiences in counting, the difficulty which comes when he attempts to pass beyond 2, and to count 3, 4, and 5, is of course but slight; and these numbers are commonly used and readily understood by almost all tribes, no matter how deeply sunk in barbarism we find them.  But the instances that have already been cited must not be forgotten.  The Chiquitos do not, in their primitive state, properly count at all; the Andamans, the Veddas, and many of the Australian tribes have no numerals higher than 2; others of the Australians and many of the South Americans stop with 3 or 4; and tribes which make 5 their limit are still more numerous.  Hence it is safe to assert that even this insignificant number is not always reached with perfect ease.  Beyond 5 primitive man often proceeds with the greatest difficulty.  Most savages, even those of the tribes just mentioned, can really count above here, even though they have no words with which to express their thought.  But they do it with reluctance, and as they go on they quickly lose all sense of accuracy.  This has already been commented on, but to emphasize it afresh the well-known example given by Mr. Oldfield from his own experience among the Watchandies may be quoted.[109] “I once wished to ascertain the exact number of natives who had been slain on a certain occasion.  The individual of whom I made the inquiry began to think over the names ... assigning one of his fingers to each, and it was not until after many failures, and consequent fresh starts, that he was able to express so high a number, which he at length did by holding up his hand three times, thus giving me to understand that fifteen was the answer to this most difficult arithmetical question.”  This meagreness of knowledge in all things pertaining to numbers is often found to be sharply emphasized in the names adopted by savages for their numeral words.  While discussing in a previous chapter