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 star for each cross-arm. But this gave two central stars, each of which would represent two stars. Unless enclosed in a circle and considered as a central group by themselves, the four and the two repetitions of Polaris could not convey the idea of a pivot or fixed centre. The three respective numerical values obtained from these experimental combinations were 4×6+1=25, 4×7=28, and finally 2×13 or 4×6+2=26. In each swastika the central star forcibly stood for and represented two or four (fig. 15). [Illustration.] Figure 14. In the triskelions the same perplexity arose: if Polaris was repeated, the idea of a fixed centre was lost (fig. 15); if figured singly, it nevertheless necessarily and inevitably stood as an embodiment of three stars. Reasoning from my own experience, I could but perceive, in the foregoing facts, a fruitful and constant source of mental suggestions, the natural outcome of which would be the association of the central star with an enhanced numerical value, and a familiarity with the idea of one star being an embodiment of two, three or four. [Illustration.] Figure 15.