s, "are mostly of symbolic
origin and have been in use among various tribes within the historic
period from the Great Lakes to Mexico." With the kind permission of the
editor of the Journal, I reproduce some of Mr. Willoughby's illustrations
on Plate III.

[Illustration.]

Figure 24. Crosses And Circles Representing Star Symbols, Arizona.

Returning to consider the probable result of the gradual diffusion of
star-cult owing to natural causes and of the consequent divergence from
the idea of the Centre, which had so deeply influenced the minds of
primitive men during many centuries, with earnest, and extended
astronomical observation, keeping pace with the development of the idea of
the Above and Below, it is obvious that the utmost attention would be next
given to the conspicuous star groups and planets which are visible at
certain times and then seem to have departed or descended into the under
world. Any one who has read the interesting communications by Herr Richard
Andree (Globus. bd. LXIV, nr. 22), On the relation of the Pleiades to the
beginning of the year amongst primitive people, followed by a note by Herr
Karl von den Steinen on the same subject, will realize that
widely-separated tribes of men, by dint of simple observation, knew the
exact length of the periodical appearance and disappearance of this star
group and regulated their year accordingly. Herr Andree cites, for
instance, that "in the Society islands, the year was divided into two
portions, the first of which was named Matari-i-inia=the Pleiades above.
It began and lasted during the time when these constellations were visible
close to the horizon after sunset. The second period, named
Matarii-i-raro=the Pleiades below, began and lasted for the time during
which the star-group was invisible after sunset" (W. Ellis, Polynesian
Researches, vol. II, p. 419, London 1829). That the ancient Mexicans had
likewise observed the Pleiades and been deeply impressed by them is proven
by the well-known fact that the ceremony of the kindling of the sacred
fire, which betokened the commencement of a new cycle, was performed "when
the Pleiades attained the zenith at midnight precisely." In my complete
monograph in the ancient Mexican calendar-system it will be my endeavor to
present all the data I have collected concerning the degree of elementary
astronomical knowledge attained by the native astronomers. I shall,
therefore, conten