

The Indians of North America. 85 
Indians count their time by nights. They take special note of 
the North Star, of the circumpolar stars, and of conspicuous con- 
stellations, to which they give names and attribute certain supersti- 
tious influences. 
They all note the motions of the shadow of a plumb line, as the 
sun traverses his course from rising to setting. 
They note north and south points on the meridian, the east and 
west points on the prime vertical, as well as the sun’s change in 
azimuth—as it passes between the extreme limits of its rising and 
setting on the 21st of March and the 21st of December. This 
enables them to determine the length of the solar year, and those 
nations that had fixed abodes and lived in houses, like the Mexi- 
cans, attained a most wonderful knowledge of astronomy (see de 
Gama). 
In arithmetic they used the decimal system, counting on their 
fingers. Their games and tradings made them familiar with numbers, 
as in the game of straws, which was played with two hundred and 
one, or with fifty-two twigs or straws. 
The Aztecs of the City of Mexico kept the neighboring nations 
in subjection, and compelled them to pay tribute to Montezuma. 
Among the articles supplied were four million nine hundred thou- 
sand three hundred fanigas of maize. Dots were used to designate 
the first nineteen numbers. Twenty is designated by a flag; four 
hundred by a feather; and eight thousand by a mirror. It must 
have required much arithmetical skill to keep the necessary 
accounts connected with this business of collecting tribute, and 
in the calculations of solar and lunar calendars. 
All social compacts required the surrender of individual or party 
rights to the good of the whole nation. 
The nationality was determined by blood; they were divided 
into gintes, fratres and tribes. 
A tribe was an association of kindred, a nation an association of 
tribes. Certain badges or tokens distinguished different families 
and different nations. 
The government in theory was monarchical, in war it was des- 
potic, in general practice 1t was democratic. Public affairs were 
decided upon in council. 
We find that the tribal organizations of all aborigines are divided 
into gens, fratres and tribes. 
1st, The GENS are bound together by ties of blood, having a 
common gentile name. 
