To these supplicants the winter solstice betokened little or nothing and it is not surprising to find no proofs of the employment of the triskelion as a sacred symbol in ancient Mexico. On the other hand, it has been traced by Mr. Willoughby on pottery from Arkansas, and in Scandinavia, where the circumpolar constellations have doubtlessly been observed from remote times, and the winter solstice has ever been hailed as the herald of coming spring, the triskelion is often found associated with the swastika. [Illustration.] Figure 12. I am indebted to Prof. Thomas Wilson’s work already cited for the two following illustrations of objects exhibiting this association. The first is a spearhead found in Brandenburg, Germany (fig. 12). The second is a bronze brooch from Scandinavia, to which I shall presently revert (fig. 13). It exhibits, besides the triskelion, swastika and circle, the S-shaped figure which was, as I shall show further on, the sign actually employed by the ancient Mexicans and Mayas as the image of the constellation Ursa Minor, whose outline it indeed effectually reproduces. Before referring to the Mexican and Maya representations of the star-group, I would next demonstrate that the sacred numbers of Mexico, and of other countries situated in the northern hemisphere, coincide exactly with the number of stars in the circumpolar constellations themselves and in simple combinations of the same. Ursa Major and Ursa Minor each contains seven stars, and the number seven is the most widely-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 4×5. [Illustration.] Figure 13. On the other hand the same number, 13, is also obtained by the combination of the Ursæ 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 Ursæ swastikas.