THE SYMMETRICAL CONCENTRATED TYPE. 151 



a diagram in the transverse plane, in the form of a floral-diagram, 

 by placing the observed number of apparently perfectly similar 

 members on a series of concentric circles to represent the whorls, a 

 scheme will be plotted out which is therefore identically that of the 

 telescoped axis (fig. 56). In such an irregular system the paras- 

 tichies present a hopeless medley, straight in places, curved in others, 

 but still roughly equal in nuniber when counted in either direction, 

 at a given level, so far as they can be counted. When the con- 

 struction circles are rubbed out, no interpretation of such a condensed 

 system is possible to the eye ; in Uquiseium, the symmetrical 

 condition is rendered obvious by precocious gamophylly and second- 

 ary elongation of the system ; but in the absence of such a second 

 zone of growth, it is evident that it could only be included under 

 the loose term " indefinite," and that no such system can be verified' 

 nor can the construction be described. When such constructions 

 occur in flowers, as very noticeably for example in Clematis, it is 

 possible to regard it as a degenerate symmetrical one, when as in 

 this ease the whole of the other phyllotaxis relations of the plant are 

 symmetrical ; but it is clear that all reduction systems must closely 

 resemble one another in their capacity for becoming undeterminable. 

 In the presence of a primary phyllotaxis system, therefore, whether 

 wt the case of asymmetry or symmetry, it is only possible to give an 



ptiylly of the lateral members that it is evident that leaf-production is no longer ' 

 normal, while the interpretation of "primary and secondary teeth" (Reess) is 

 also doubtful. Thus Hofmeister, when he first investigated the apex, called the 

 whole sheath one leaf which produced more teeth as it became older (which is 

 certainly one way of interpreting the termination of the shoot as expressed in 

 fig. 56), and that 4 was the primary number (Higher Gryptogamia, 1862, p. 270). 

 Eeess futher admitted the possibility of the formation of a number of primary 

 teeth (7-8), of which 3 was not a factor, so that the sextant segments must have 

 been unequally affected. It is remarkable that these views should have been 

 accepted without any drawings or accurate evidence in favour of them ; the 

 fact that the annular ridge is formed quite independently of the apical segmenta- 

 tion being sufficiently clear to the unprejudiced eye. (Gf. Cramer's drawings, 

 Pflanzenphys. Unters., Nageli imd Cramer, iii. plate xxxiii. figs. 19, 20 ; xxxiv. 

 1-3 ; also in text-books.) The same fact has been pointed out by Schwendener 

 (Botanishche Mittheilungen, vol. i. p. 153), who examined the critical case of E. 

 scirpoides, with the cycle of three members. There is thus no doubt that the 

 symmetrical formation of the impulses which produce the lateral members is 

 wholly independent of the asymmetrical segmentation into cell-units. 



