into either the decimal or the vigesimal.  The result is, of course, a compound of two, and sometimes of three, systems in one scale.  A pure quinary or vigesimal number system is exceedingly rare; but quinary scales certainly do exist in which, as far as we possess the numerals, no trace of any other influence appears.  It is also to be noticed that some tribes, like the Eskimos of Point Barrow, though their systems may properly be classed as mixed systems, exhibit a decided preference for 5 as a base, and in counting objects, divided into groups of 5, obtaining the sum in this way.[235]

But the savage, after counting up to 10, often finds himself unconsciously impelled to depart from his strict reckoning by fives, and to assume a new basis of reference.  Take, for example, the Zuni system, in which the first 2 fives are: 

   5. oepte = the notched off.
  10. astem’thla = all the fingers.

It will be noticed that the Zuni does not say “two hands,” or “the fingers of both hands,” but simply “all the fingers.”  The 5 is no longer prominent, but instead the mere notion of one entire count of the fingers has taken its place.  The division of the fingers into two sets of five each is still in his mind, but it is no longer the leading idea.  As the count proceeds further, the quinary base may be retained, or it may be supplanted by a decimal or a vigesimal base.  How readily the one or the other may predominate is seen by a glance at the following numerals: 

  GALIBI.[236]

   5. atoneigne oietonai = 1 hand.
  10. oia batoue = the other hand.
  20. poupoupatoret oupoume = feet and hands.
  40. opoupoume = twice the feet and hands.

  GUARANI.[237]

   5. ace popetei = 1 hand.
  10. ace pomocoi = 2 hands.
  20. acepo acepiabe = hands and feet.

  FATE.[238]

   5. lima = hand.
  10. relima = 2 hands.
  20. relima rua = (2 x 5) x 2.

  KIRIRI

   5. mibika misa = 1 hand.
  10. mikriba misa sai = both hands.
  20. mikriba nusa ideko ibi sai = both hands together with the feet.

  ZAMUCO

   5. tsuena yimana-ite = ended 1 hand.
  10. tsuena yimana-die = ended both hands.
  20. tsuena yiri-die = ended both feet.

  PIKUMBUL

   5. mulanbu.
  10. bularin murra = belonging to the two hands.
  15. mulanba dinna = 5 toes added on (to the 10 fingers).
  20. bularin dinna = belonging to the 2 feet.

  YARUROS.[239]

5.  kani-iktsi-mo = 1 hand alone.
10.  yowa-iktsi-bo = all the hands.
15.  kani-tao-mo   = 1 foot alone.
20.  kani-pume     = 1 man.

By the time 20 is reached the savage has probably allowed his conception of any aggregate to be so far modified that this number does not present itself to his mind as 4 fives.  It may find expression in some phraseology such as the Kiriris employ—­“both