e inevitable tendency of
any number system of quinary origin is toward the establishment of another
and larger base, and the formation of a number system in which both are
used. Wherever this is done, the greater of the two bases is always to be
regarded as the principal number base of the language, and the 5 as
entirely subordinate to it. It is hardly correct to say that, as a number
system is extended, the quinary element disappears and gives place to the
decimal or vigesimal, but rather that it becomes a factor of quite
secondary importance in the development of the scale. If, for example, 8 is
expressed by 5-3 in a quinary decimal system, 98 will be 9 x 10 + 5-3. The
quinary element does not disappear, but merely sinks into a relatively
unimportant position.

One of the purest examples of quinary numeration is that furnished by the
Betoya scale, already given in full in Chapter III., and briefly mentioned
at the beginning of this chapter. In the simplicity and regularity of its
construction it is so noteworthy that it is worth repeating, as the first
of the long list of quinary systems given in the following pages. No
further comment is needed on it than that already made in connection with
its digital significance. As far as given by Dr. Brinton the scale is:

1. tey.
2. cayapa.
3. toazumba.
4. cajezea = 2 with plural termination.
5. teente = hand.
6. teyente tey = hand 1.
7. teyente cayapa = hand 2.
8. teyente toazumba = hand 3.
9. teyente caesea = hand 4.
10. caya ente, or caya huena = 2 hands.
11. caya ente-tey = 2 hands 1.
15. toazumba-ente = 3 hands.
16. toazumba-ente-tey = 3 hands 1.
20. caesea ente = 4 hands.

A far more common method of progression is furnished by languages which
interrupt the quinary formation at 10, and express that number by a single
word. Any scale in which this takes place can, from this point onward, be
quinary only in the subordinate sense to which allusion has just been made.
Examples of this are furnished in a more or less perfect manner by nearly
all so-called quinary-vigesimal and quinary-decimal scales. As fairly
representing this phase of number-system structure, I have selected the
first 20 numerals from the following languages:

WELSH.[240]

1. un.
2. dau.
3. tri.
4. pedwar.
5. pump.
6. chwech.
7. saith.
8. wyth.
9. naw.
10. deg.
11