f a hand, but
the half of the whole person, which you get by counting his hands only.
The syllable _ma_, which means "hand," makes its appearance in the
words five and ten, and no where else; just as it should do. When we
come to twenty, we have _cempoalli_, "one counting;" that is, one whole
man, fingers and toes--corresponding to the Vei word for twenty, "a
person is finished."

I think we need no more examples to show that people--in almost all
countries--reckon by fives, tens, or twenties, merely because they
began to count upon their fingers and toes. If the strong man who had
six fingers on each hand, and six toes on each foot, had invented a
system of numeration, it would have gone in twelves, nearly like the
duodecimals which our carpenters use; unless, indeed, he had been
stupid after the manner of very strong men, and not gone beyond sixes.
We see how the Romans, though they inherited from their Eastern
ancestors a numeration by tens up to _decem_, and then beginning again
_undecim_, &c., yet when they began to write a notation could get no
farther than five--I., II., III., IV., V.; and then on again, VI.,
VII., up to ten, from ten to fifteen, and so on.

There is a very curious vulgar error which prevails, even among people
who have a good practical acquaintance with arithmetic. It is that the
number _ten_ has some special virtue which fits it for counting up to.
The fact is that ten is not the best number for the purpose; you can
halve it, it is true, but that is about all you can do with it, for its
being divisible by five is of hardly any use for practical purposes.
_Eight_ would be a much better number, for you can halve it three times
in succession; and _twelve_ is perhaps the most convenient number
possible, as it will divide by two, three, and four. It is this
convenient property that leads tradesmen to sell by dozens, and
grosses, rather than by tens and hundreds. If we used eights or twelves
instead of tens for numeration, we might of course preserve all the
advantages of the Indian or Arabic numerals; in the first case, we
should discard the ciphers 8 and 9, and reckon 5, 6, 7, 10; and in the
second case, we should want two new ciphers for ten and eleven; and 10
would stand for twelve, and 11 for thirteen. Our happening to have ten
fingers has really led us into a rather inconvenient numerical system.

[Illustration: AZTEC HEAD, IN TERRA COTTA. (PROBABLY EITHER A
HOUSEHOLD-GOD OR A VOTIVE OFFERIN