cases it is impossible even to guess their
etymology and original meaning. We see that the names for two and eight
are dual, while those for three and four clearly have plural endings. But
why eight in the primitive Aryan was a dual, and what were the two
tetrads, which, combined in _asht-au_, _oct-o_, {~GREEK SMALL LETTER OMICRON WITH PSILI~}{~GREEK SMALL LETTER KAPPA~}{~GREEK SMALL LETTER TAU~}-{~GREEK SMALL LETTER OMEGA WITH OXIA~}, expressed the
number eight, will probably never be discovered. It is possible that
_asht-i_ was a name for the four phases of the moon, or for the four
fingers of the hand without the thumb. Analogies occur in other families
of language, but certainty is beyond our reach. If we now consider what
mental effort is necessary to work out a decimal system, and to secure
general recognition and value for the name given to each number, we shall
readily realise what remote periods in the development of the human mind
open up before us here, and of how little use it would be to try to
establish chronological limits. Old as the Vedas, old as the Homeric songs
may be, what is their age compared with the periods that were required not
only to work out the numerals but the entire treasury of Aryan words, and
the wonderful network of grammar that surrounds this treasure, which also
was complete before the separation of the Aryan languages began. The
immeasurable cannot be measured, but this much stands immovable in the
mind of every linguist, that there is nothing older in the entire Aryan
world than the complete primitive Aryan language and grammar, in which
nearly all the categories of thought, and consequently the whole scaffold
of our thinking, have found their expression.

Of course it will be said that all this only applies to the Aryan race,
and that they constitute only a small and perhaps the youngest portion of
the human race. Well, it is difficult to prove that the Aryans constitute
the least numerous subdivision. We know too little of their great masses
to attempt a census. That they are the youngest branch of the human race
is really of no consequence; we should then have to assume against all
Darwinian principles, various, not contemporaneous, but successive
monstrosities, slowly ascending to humanity, and this would only be pure
invention. Nothing absolutely compels us to ascribe a shorter earthly life
to those races which speak Chinese, Semitic, Bantu, American, Australian,
or other langua