The symbolic representation of Yin and Yang is a circle divided by two arcs with opposite centres, while the symbol of Ta Ki adds a third arc from above uniting these two. [Illustration: FIG. 4. ] [Illustration: FIG. 5. ] It is possible that these symbols are of late origin, devised to express the ideas above named. One Chinese scholar (Mr. S. Culin) tells me that it is doubtful if they occur earlier than the twelfth century, A. D., and that they were probably introduced for purposes of divination. In this case, I believe that they were introduced from the South, and that they originally had another and concrete significance, as I shall explain later. Others consider these symbols as essentially Mongolian. The Ta Ki or Triskeles is to them the Mongolian, while the Svastika is the ethnic Aryan symbol. Such writers suspect Indo-European immigration where they discover the latter, Chinese immigration were they find the former emblem. The Svastika, I need hardly say, is the hooked cross or gammated cross, usually represented as follows: [Illustration: FIG. 6. ] the four arms of equal length, the hook usually pointing from left to right. In this form it occurs in India and on very early (neolithic) Greco-Italic and Iberian remains. So much has been written upon the Svastika, however, that I need not enter upon its archæological distribution. Its primary significance has been variously explained. Some have regarded it as a graphic representation of the lightning, others as of the two fire-sticks used in obtaining fire by friction, and so on. Whatever its significance, we are safe in considering it a form of the Cross, and in its special form obtaining its symbolic or sacred association from this origin. The widely-spread mystic purport of the Cross symbol has long been matter of comment. Undoubtedly in many parts of America the natives regarded it with reverence anterior to the arrival of Europeans; as in the Old World it was long a sacred symbol before it became the distinctive emblem of Christianity. As in previous writings I have brought together the evidence of the veneration in which it was held in America, I shall not repeat the references here. I believe we may go a step further and regard all three of these symbols, the Ta Ki or Triskeles, the Svastika, and the Cross as originally the same in signification, or, at least, closely allied in meaning. I believe, further, that this can be shown from the relics of ancient American art so clearly that no one, free from prejudice, and whose mind is open to conviction, will deny its correctness. My theory is that all of the symbols are graphic representations of the movements of the sun with reference to the figure of the earth, as understood by primitive man everywhere, and hence that these symbols are found in various parts of the globe without necessarily implying any historic connections of the peoples using them.