On the Systems of Numerical Signs used by different Nations, and on the Origin of the Expression of Value by Position in the Indian Numbers.

By Alexander von Humboldt.

—Quarterly Journ.

of Science, June 1830.

In this learned and interesting essay, which was read in a class session of the Royal Academy of Sciences in Berlin, we find the following additional information on the numerical signs of the Muyscas, to which we have alluded in a notice on the Asiatic origin of the tribes inhabiting the uplands of Bogota:—

“In the Chibcha language of the Muyscas, (who, like the inhabitants of Japan and of Thibet, had an ecclesiastical and a laical chief; and whose method of intercalating the 37th month, like the inhabitants of North India, has been published and explained by me,) 11, 12, 13, are called foot one (quihieha ata,) foot two (quihieha bosa,) foot three (quihieha mica,) from quihieha or quhieha (foot,) and the first three unities, ata, bozha or bosa, and mica.

The arithmetical signification of foot is ten, because the foot begins to be taken into account, when both hands are passed through.

To express twenty, the Muyscas use in their arithmetical lauguage the expression foot ten, or the small house (gueta,) perhaps because they used, in counting, grains of maize, and such a heap of maize reminded them of the barn, where maize was laid up.

By means of the expression small house (or barn,) and twenty (both feet and hands) they formed the expressions for 30, 40, 80, by joining them together, as, twenty plus ten; twice twenty; four times twenty.

Quite similar are the Celtic expressions which have passed into the languages of Roman origin, as, quatre vingt, and quinze vingt, or those more rarely met with, as six vingt, sept vingt, huit vingt.

Deux vingt and trois vingt are not used in French; but in the Gaelic or Celtic dialect of West Britany, through which I passed a few years ago, twenty is called ugent, forty daou-ugent, or two twenty; sixty tri-ugent, or three twenty.

It is even said deh ha nao ugent, or ten over nine twenty = 190.”