-spread sacred number. Ancient traditions record that
the race inhabiting Mexico consisted of seven tribes who traced their
separate origins to seven caves, situated in the north. In memory of
these, at the time of the Conquest, there were seven places of sacrifice
in the city of Mexico. I shall recur to the number seven further on, in
discussing the native social organization, and now direct attention to the
five stars of Cassiopeia and to the fact that the combination of the stars
in this constellation with Polaris and Ursa Major yields the number
thirteen. This result is specially interesting since the entire
Calendar-system of Mexico and Yucatan is based on the combination of the
numerals 13+7=20, the latter again being 4x5.

[Illustration.]

Figure 13.

On the other hand the same number, 13, is also obtained by the combination
of the Ursae star-groups with Polaris. The number 5 is constantly yielded
by Cassiopeia and the four-fold repetitions of the groups supply the
suggestion of the number 4. The combination of Ursa Minor and Cassiopeia
yields 12. The accompanying figure exhibits swastikas composed of Ursa
Minor accompanied by Ursa Major and Cassiopeia separated and combined
(fig. 14). I next direct attention to the peculiar difference in the
numerical values of the Ursae swastikas.

In the first, the central star, surrounded by four repetitions of the
seven-star constellation, yielded a total of twenty-nine stars--4x5+9.
Further combinations will be seen by a glance at the Ursa Major swastika
(fig. 4). The analysis of the Ursa Minor swastika is not so simple and
occasions a certain perplexity.

When I had first combined the four positions of this constellation, I had,
naturally, and without further thought, figured Polaris but once, as the
fixed centre, whereas I had repeated the other stars of the compact group
four times. It was not until I began to count the stars in the swastika
that I realized how I had, unconsciously, made one central star stand for
four, and thus deprived the composite group of the numerical value of
three stars. On the other hand, if I repeated the entire constellation
four times, I obtained a swastika with four repetitions of Polaris in the
middle. In this way, however, Polaris became displaced, and the idea of a
fixed centre was entirely lost. A third possible method of composing the
swastika was to allow one central st