WEIGHTS AND MEASURES.
The extent of a nation's conquest over the forces of nature is accurately indicated by its system of weights and measures. On these depend the perfection of its tools and the range of its industrial activities. Art in all its branches is inseparably connected with the ideas of equality and pro portion.
Conceptions of Number.—At the base of these ideas are the conceptions of number. Nations, like individuals, vary remarkably in their arithmet ical powers. It would seem impossible that there should be a language without any numerals, yet such is the Chiquito of Eastern Bolivia. Count ing is quite unknown to the members of the tribe. The word which is the nearest to one means " itself" or " the same;" two or more is indicated by " much " or " many." . The tribes on the grassy plains of Northern Buenos Ayres, called El Gran Chaco, are scarcely better provided in this respect. A recent traveller (Pelleschi) relates that an influential chief was unable to count the number of his own fingers. It would be impossible for tribes thus deficient to make any important advances in the con structive arts.
Yet there was a time when none of the human race surpassed them in this respect. This is proved by the systems of numeration and the names of the units in many languages. They are usually of the quinary cha racter; that is, they count by fives, the second and later series of fives being modifications of the first. This indicates that they were first rep resented to the mind by counting the fingers of the hand. Sometimes the word for five means also " hand," or was derived from it. The two hands furnished ten digits, and from this arose the decimal system—not at all a necessary one, and according to sonic arithmeticians not so convenient as either that by eights or that by twelves (oetals or duodecimals). Adding the number of the fingers and toes together gives us twenty, and the sig nificant name of this number in the Maya dialects of Central America is hurt vinak, " one man." The Mayas and many other tribes chose this number as the unit for their higher calculations, relics of which custom are preserved in our own habit of reckoning by scores or twenties, and in the French numeration between sixty and a hundred—soixante-dix ncuf; etc.
The Hfultipication in Aztec and Maya writing the -higher units, multiples of twenty, were indicated by special signs, and both these nations had invented a* multiplication table not more cumbrous apparently than that of the ancient Romans with their alphabetic letters in place of numerals. The convenient notation of the Arabic numerals, so called (though probably an East Indian invention), was rendered possi ble by the introduction of the zero or naught sign, " 0;" an invention which, as Dr. Tylor forcibly remarks, "was practically one of the great est moves ever made in science." Simple as the multiplication table appears to us, it was brought about only by the intense application of the brightest minds of many nations through a long series of centuries. So inapt is the human intellect to frame clear ideas of number that there is perhaps not a single dialect of the widespread Malayan family which has a word for one. The expression for it signifies "the same," or something of that kind, and must be qualified with another word to convey the idea of mathematical unity (F. Muller).
these numerical conceptions are founded all those comparisons for practical purposes which we call denominations of weights and measures. We may classify as follows those which have the greatest ethnologic importance : Measures of Time; Measures of Space; Measures of Direction; Measures of Gravity.
.Measures of alternations of light and darkness resulting from the revolutions of the earth bring about the division of time which most strongly impresses the human mind. Nations, however, reckon it differently. After the manner of the ancient Semites, the book of Genesis speaks of " the evening and the morning" as making up the day. The Indians of the Eastern United States were wont to count by nights, not by days; those of Central America, by "dawns;" the astronomer begins his day at midnight, the sailor at high noon; the New Englander at sunset ; elsewhere the people in the United States at sunrise.