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.
In the first, the central star, surrounded by four repetitions of the seven-star constellation, yielded a total of twenty-nine stars—4x5+9. [pg 030] 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]).
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 [pg 031] value, and a familiarity with the idea of one star being an embodiment of two, three or four.
