hands together with the feet”—­or in the shorter “ended both feet” of the Zamucos, in which case we may presume that he is conscious that his count has been completed by means of the four sets of fives which are furnished by his hands and feet.  But it is at least equally probable that he instinctively divides his total into 2 tens, and thus passes unconsciously from the quinary into the decimal scale.  Again, the summing up of the 10 fingers and 10 toes often results in the concept of a single whole, a lump sum, so to speak, and the savage then says “one man,” or something that gives utterance to this thought of a new unit.  This leads the quinary into the vigesimal scale, and produces the combination so often found in certain parts of the world.  Thus the 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: