Symmetry 167 



that where there is eccentricity in the woody axis the position of maxi- 

 mum thickness in any eccentric ring follows a spiral course along the 

 length of the axis. There is also a relation between this eccentricity and 

 spiral grain, for the degree of both decreases upward in the trunk, 

 and the direction of the spiral eccentricity (left or right) is the same as 

 that of the spiral grain in any given axis. 



Priestley (1945) distinguishes between true spiral grain, characteristic 

 of hardwoods and resulting from a twist in the primary cambium cylin- 

 der, and tilted grain, characteristic of softwoods where the grain is al- 

 ways straight in the wood of the first year. 



In Flowers and Inflorescences. Angiosperm flowers are apparently to 

 be regarded, in an evolutionary sense, as shortened axes; and their parts, 

 particularly the calyx and corolla, often show evidence of the same sort 

 of spiral symmetry that exists between leaves. This can rarely be shown 

 by the actual insertion of the parts, since they are at essentially the same 

 level and might be regarded as a whorl, but is evident in the relation of 

 their expanded portions to one another, particularly as visible in the bud. 

 In flowers of dicotyledons there are usually in each circle five parts or a 

 multiple of five. A very common relationship here (in the calyx, for ex- 

 ample) is that two of the sepals have both edges outside the others, two 

 have both edges inside, and one has one edge outside and one inside. 

 This quincuncial arrangement can be interpreted through developmental 

 evidence as a % spiral, since the parts appear in the same order as 

 leaves in % phyllotaxy. Various modifications of this are found, but the 

 typical dicotyledonous flower may be regarded in its symmetry as rep- 

 resenting a % spiral. The flower of monocotyledons, on the other hand, 

 has its parts typically in threes and may be regarded as a % spiral in 

 symmetry. The problem of flower symmetry, particularly as expressed 

 in transverse diagrams, has been the object of long study by floral 

 morphologists and forms the basis of an extensive early literature (Eich- 

 ler, 1875). 



For students of morphogenesis the symmetry displayed by inflo- 

 rescences provides a notable example of the orderly control of growth 

 relationships. Matzke (1929) has described a particularly fine example 

 of such symmetry in Stelloria aquatica (Fig. 7-9). Here the inflorescence 

 is a cyme, and the first flower terminates the main axis. Just below this 

 flower arise two buds in the axils of opposite bracts, and from these buds 

 shoots arise, each of which is likewise terminated by a flower. Below 

 each of these flowers, in turn, two shoots again arise, and so on. The 

 flower in this species shows quincuncial arrangement of the sepals. These 

 sepals may show a clockwise spiral or a counterclockwise one. As an 

 observer looks down on a diagram of such an inflorescence, it is evident 

 that, of the two flowers below the first, one is clockwise and the other 



