We find in early work discovered in the ancient mounds of North America decorative circles (Fig. 58) in which two S-like lines at right angles to one another are inscribed as shown in Fig. 56, and we find also that these curved rays may be prolonged as a marvellous enveloping spiral coil or helix–especially in the painting of pottery. When the curved rays are many in number, as in Fig. 57, the design has been interpreted by some archæologists as symbolizing the sun, and it is important to remember that the Swastika itself was used in China as the pictograph of the sun. A single curved S-like line has been found cut on a great circular slab, an ancient altar-stone (Fig. 59) in Honduras (Copan)–so as to divide the circle as is done in the Japanese Tomoye. It is obvious that the exact geometric character of the S-like division is of great significance in these designs and requires careful study and explanation. I have briefly discussed this matter at the end of the chapter. In the common "ogee Swastika," Fig. 56, B, the more or less elaborately helicoid arms are merely careless flourishes of the painter's brush. The simple four-rayed figure, shown in Fig. 56, A, is often spoken of as a "tetraskelion," or four-legged scroll, and is associated with the three-legged figure or triskelion which I wrote of in the last chapter. If the curvilinear "tetraskelion" be angularized–that is to say, rectangles substituted for semicircles, we get the correct fully developed Swastika, Fig. 56, C. And if, abandoning the circle, the draughtsman rapidly drew with a brush or on soft clay lines like an S crossing one another at right angles, he produced what is common enough wherever the more formal rectangular Swastika is found, namely, the curvilinear or "ogee Swastika," Fig. 56, B. It is not possible with our present knowledge to penetrate into the remote past and really ascertain the origin of the shape or device called a Swastika. But it is, I think, quite likely that in manipulating the "tomoye" symbol (whether copied from a section of shell or originating by more independent invention and "trying" of lines and curves and circles), very early man duplicated the symmetrical S by which he had divided a circle and produced the tetraskelion seen in Fig. 56, A. The conversion of this into the rectangular Swastika and into varieties of the ogee and menander (which I have not found space to describe) would be an easy and natural sequence. [Illustration: FIG. 59.–An altar-stone of prehistoric age. The circular surface is cut into by a trough of S-shape, which divides it so as to resemble the Japanese "Tomoye." From Copan, Honduras.]