Symmetry 169 



counterclockwise and that this holds for each succeeding pair. This rela- 

 tionship is not a random one, for the two types show a regular order as 

 one progresses to successively later pairs so that the symmetry of each 

 flower is predictable. Furthermore, the relative position in each flower 

 of the "odd" sepal also changes with complete regularity. In one member 

 of a given pair of flowers it has rotated 72° in a clockwise direction from 

 the single flower next them, and in the other, 72° counterclockwise. The 

 particular edge of the sepal which is inside also has a definite and pre- 

 dictable position. The whole inflorescence is thus a complex pattern of 

 symmetries, each successive floral meristem fitting precisely into its place 

 in this pattern. The factors that determine the symmetry of each flower 

 are therefore not purely local ones but operate as members of a much 

 larger system. Such a system, with its parts so widely separated and so 

 easy of observation, offers a particularly good opportunity for the ex- 

 perimental study of symmetry. 



BILATERAL SYMMETRY 



This is a relatively rare type in which there are two planes of sym- 

 metry, so that front and back, and right and left sides, are similar. A 

 bilaterally symmetrical organ resembles a radial one that has been com- 

 pressed equally on two opposite sides. 



This type occurs chiefly in vertically oriented structures in which, from 

 one cause or another, one of the dimensions is smaller. Thus the stems 

 of certain cacti such as Opuntia are bilaterally symmetrical, as are the 

 still further flattened phylloclads of Muehlenbeckia and Phyllocladus. 

 These have doubtless arisen from radial types. The leaves of Iris and 

 similar plants are essentially bilateral but have probably come from 

 dorsiventral structures. All plants, such as the grasses and some other 

 monocotyledons, which are truly distichous (the leaves arising only on 

 two opposite sides of the stem) may be regarded as bilaterally sym- 

 metrical. So may the flowers of the mustard family, Cruciferae, since two 

 of the six stamens, directly opposite each other, are short and the other 

 four long. A few of the simpler bryophytes have distichous leaves or 

 leaf-like structures, as in Schizostegia, and are thus bilateral, as is the 

 pinnate plant body of the coenocytic alga Bryopsis. The thallus of some 

 of the larger algae, notably forms like Fucus and Laminaria, is flattened 

 and shows this type of symmetry. 



In a few cases, as in some of the algae, a transition from radial to 

 bilateral symmetry may be seen, and in Schizostegia the apex is radial. 

 Doubtless in many instances one type could be induced from the other 

 experimentally. Certain abnormal structures, such as many fasciated 

 stems, are bilaterally symmetrical. 



