resemblances noted above are hardly more significant than those occurring in two Polynesian languages, the Fatuhivan and the Nakuhivan,[222] where “new” is associated with the number 7.  In the former case 7 is fitu, and “new” is fou; in the latter 7 is hitu, and “new” is hou.  But no one has, because of this likeness, ever suggested that these tribes ever counted by the senary method.  Another equally trivial resemblance occurs in the Tawgy and the Kamassin languages,[223] thus: 

  TAWGY.  KAMASSIN.

8.   siti-data   = 2 x 4.            8.   sin-the’de = 2 x 4.
9.   nameaitjuma = another.          9.   amithun    = another.

But it would be childish to argue, from this fact alone, that either 4 or 8 was the number base used.

In a recent antiquarian work of considerable interest, the author examines into the question of a former octonary system of counting among the various races of the world, particularly those of Asia, and brings to light much curious and entertaining material respecting the use of this number.  Its use and importance in China, India, and central Asia, as well as among some of the islands of the Pacific, and in Central America, leads him to the conclusion that there was a time, long before the beginning of recorded history, when 8 was the common number base of the world.  But his conclusion has no basis in his own material even.  The argument cannot be examined here, but any one who cares to investigate it can find there an excellent illustration of the fact that a pet theory may take complete possession of its originator, and reduce him finally to a state of infantile subjugation.[224]

Of all numbers upon which a system could be based, 12 seems to combine in itself the greatest number of advantages.  It is capable of division by 2, 3, 4, and 6, and hence admits of the taking of halves, thirds, quarters, and sixths of itself without the introduction of fractions in the result.  From a commercial stand-point this advantage is very great; so great that many have seriously advocated the entire abolition of the decimal scale, and the substitution of the duodecimal in its stead.  It is said that Charles XII. of Sweden was actually contemplating such a change in his dominions at the time of his death.  In pursuance of this idea, some writers have gone so far as to suggest symbols for 10 and 11, and to recast our entire numeral nomenclature to conform to the duodecimal base.[225] Were such a change made, we should express the first nine numbers as at present, 10 and 11 by new, single symbols, and 12 by 10.  From this point the progression would be regular, as in the decimal scale—­only the same combination of figures in the different scales would mean very different things.  Thus, 17 in the decimal scale would become 15 in the duodecimal; 144 in the decimal would become 100 in the duodecimal; and 1728, the cube of the new base, would of course be represented by the figures 1000.