176 RELATION OF PHY LLOT AXIS TO MECHANICAL LAWS. 



being obtained by using a transitional curve-tracing wbich expresses 

 progressive dorsiventrality. The system would be theoretically 

 mapped out by taking 16 long and 26 short curves in the ratio 

 8 : 13 ; the ordinary (3 + 5) curve being approximately accurate. 



From the (16 + 26) curves, the (6 + 10) set are readily selected 

 by taking paths in tte system from No. 1 in the manner described 

 for Helianthus; complexity coming in with the presence of two 

 points of origin 1 and 1' (fig. 65). 



The construction may now be compared with the section; 

 segments 1, 3, 5 and 1', 3', 5' are clearly determined by these 

 primary curves alone, and the transition commences with the pair 

 7 and 7'. Thus 7 and 7' each add a long curve, and 9 and 9' follow 

 the same rule, with the result that at this moment the system is 

 (10 + 10) ; as in Helianfhus, however, such transitional symmetry is 

 ignored and the new curves go on being added. A difference, how- 

 ever, is now noticed, evidently due to the clashing of two Fibonacci 

 series: 11 is bounded by two new curves, that is to say, adds one long 

 and one short. The system is now (12 + 12) ; similarly 13 adds two 

 curves, and so does 15, the system thus maintaining symmetry at 

 (14+14) and (16 + 16). Beyond this point, 17 adds one short 

 curve only, and is followed by 19, 21, 23, and 25 ; the system again 

 becoming asymmetrical and ending as (16 + 26). The transition 

 from (6 + 10) to (16 + 26) is thus effected on the diagram at the 

 26th member; but the first six did not enter this expanding series, 

 but represent the members of transition from the previous (2+4) 

 foliage shoot. 



The number of transitional members is thus apparently lower 

 than in the normal series, cf. Helianthus, but agreement is shown in 

 the fact that the outer 16 members which establish contact around 

 the axis, constitute a species of protective involucre to the base of 

 the inflorescence, and it is remarkable that their relative bulk is 

 very approximately indicated by the area of the rhombs correspond- 

 ing to them, a curious confirmation of the uniform character of 

 growth in unspecialised members. 



There can be little doubt but that this construction represents 

 the actual distribution of growth in originating the inflorescence 

 of Dvpsacus, and any deviations from it must be regarded as 



