The sequel to the above episode was that, with the aid of my movable star-chart, I made the following notes of the apparent positions of the circumpolar constellations at the times of sunrise, midnight and sunset, choosing the periods of the solstices and equinoxes in order to obtain an exact division of the year (pl. I). Whilst studying these I realized that the midnight position was the only stable one, since the actual visibility of the constellations before dawn and after dusk would be subject to considerable variation, according to seasons, latitudes and atmospherical conditions. Having noted these positions, I next combined them separately, obtaining the remarkable results given in fig. 4. The combined midnight positions of the Ursa Major or Minor, at the four divisions of the year, yielded symmetrical swastikas, the forms of which were identical with the different types of swastika or cross-symbols (the normal, ogee and volute, etc.), which have come down to us from remote antiquity and are reproduced here for comparison (pl. II, _a-f_). Reflection showed me that such composite pictures of the Ursa constellations constituted an exact record of their annual rotation, and afforded a perfect sign for the period of a year. I moreover perceived how the association of rotatory motion with the advance of time, and its division into fixed periods or cycles, would be the natural outcome of the recognition of the annual rotation of the star-groups. The Calendar-Swastika, or cross of ancient Mexico (pl. II, _g_) constitutes an absolute proof of the native association of the cross-symbol with the ideas of rotatory motion and the progress of time, and furnishes an indication that, in an analogous manner, the swastika may have been primarily and generally employed by primitive races, as a sign for a year or cycle. A close scrutiny of the respective forms of the crosses yielded by Ursæ Major and Minor shows that the normal swastika and suavastika may be explained as the separate representations of the two constellations—the angular break in the outline of Ursa Major suggesting the direction of the bend to the right of the arms of the normal swastika, whilst the form of Ursa Minor obviously suggests the bend to the left which is characteristic of the suavastika. [Illustration.] Figure 5