[Illustration: Fig. 19. DETAIL OF CYPRIAN AMPHORA IN METROPOLITAN MUSEUM OF ART, NEW YORK CITY. Lotus with curling sepals and different Swastikas. Goodyear, "Grammar of the Lotus," pl. 47, figs. 2, 3.] [Illustration: Fig. 20. THEORY OF THE EVOLUTION OF THE SPIRAL SCROLL FROM LOTUS. One Volute. Goodyear, "Grammar of the Lotus," fig. 21.] According to Professor Goodyear,[64] these bent sepals of the lotus were exaggerated and finally became spirals,[65] which, being projected at a tangent, made volutes, and, continuing one after the other, as shown in fig. 20, formed bands of ornament; or,[66] being connected to right and left, spread the ornament over an extended surface as in fig. 21. One of his paths of evolution closed these volutes and dropped the connecting tangent, when they formed the concentric rings of which we see so much. Several forms of Egyptian scarabæi, showing the evolution of concentric rings, are shown in figs. 22, 23, and 24. [Illustration: Fig. 21. THEORY OF LOTUS RUDIMENTS IN SPIRAL. Tomb 33, Abd-el Kourneh, Thebes. Goodyear, "Grammar of the Lotus," p. 96.] By another path of the evolution of his theory, one has only to square the spiral volutes, and the result is the Greek fret shown in fig. 25.[67] The Greek fret has only to be doubled, when it produces the Swastika shown in fig. 26.[68] Thus we have, according to him, the origin of the Swastika, as shown in figs. 27 and 28.[69] Professor Goodyear is authority for the statement that the earliest dated instances of the isolated scroll is in the fifth dynasty of Egypt, and of the lotus and spiral is in the eleventh dynasty. The spiral of fig. 19 (above) belongs to the twelfth dynasty.[70] [Illustration: EGYPTIAN SCARABÆI SHOWING EVOLUTION OF CONCENTRIC RINGS. Fig. 22. CONCENTRIC RINGS CONNECTED BY TANGENTS. From a figure in Petrie's "History of Scarabs." Fig. 23. CONCENTRIC RINGS WITH DISCONNECTED TANGENTS. Barringer collection, Metropolitan Museum of Art, New York City. Goodyear, "Grammar of the Lotus," pl. 8, fig. 93. Fig. 24. CONCENTRIC RINGS WITHOUT CONNECTION. Farman collection, Metropolitan Museum of Art, New York City. Goodyear, "Grammar of the Lotus," pl. 8, fig. 95.] [Illustration: Fig. 25. SPECIAL EGYPTIAN MEANDER. An illustration of the theory of derivation from the spiral. Goodyear, "Grammar of the Lotus," pl. 10, fig. 9.] Professor Goodyear devotes an entire chapter to the Swastika. On pages 352, 353 he says: