VAEYIKG GROWTH IN LATERAL MEMBERS. 323 



edged ones instead of the " 5 " series, and the angle subtended by 

 the members diminishes from 37° in 'No. 66 to 33° in the member 

 numbered 1. 



A still clearer example of this eifect of the diminution of the 

 angle subtended by older members is afforded by the previously 

 cited seedling of Finns Pinea, on which the angles were carefully 

 measured. The fall ranged from 53°, the maximum angle sub- 

 tended by young sliding dorsiventral members, to 35° and even 30° 

 at the extreme periphery: from the measurement of theoretical 

 construction diagrams, the angle subtended by a member of a 

 (5 + 8) system is 51 '5°, that by a member of an (8 + 13) system 

 32°. When the small amount of sliding-growth is regarded as in 

 this example compensated by a rounding off of the angles of the 

 leaves, the completeness of the transition is remarkable, and the 

 corresponding apparent alteration in the system is obvious, the 

 " 8 " long smooth-edged curves being the most prominent feature 

 of the section.* 



A similar simple case of great interest is afforded by the 

 comparison of the appearances observed on a closed (wet) and 

 open (dry) cone of Finns. Thus, in P. austriaca the scales on 

 the closed cone present facets averaging 12 mm. in diameter, 

 while the cone itself is about 30 mm. in diameter at the widest 

 part ; the angle subtended by a scale varies between 45° and 50°, 

 and the apparent phyllotaxis system is therefore (5 -|- 8), as seen 

 in the contact-parastichies. When the cone is fully expanded 

 (fig. 5), the diameter of the structure is increased to 60 mm. or 



* Note that the angles subtended by rhombs of the theoretical log. spiral 

 construction, as also any divergence angles measured from the centre of the 

 system, will continue to hold good for the plane projection of the transverse 

 section, whatever subsequent changes may take place in the rate of radial 

 expansion. While, that is to say, all allowance for the radial retardation of the 

 actual specimen is omitted from the theoretical quasi-square construction, all 

 angular measurements continue to hold for members in the same transverse 

 plane, and thus the calculated divergence angles of the different systems 

 {Mathematical Note V.) are the true divergence angles of plant phyllotaxis, 

 however much the radial rate of growth may be aflfeoted, since a reduction in 

 the tangential rate, by producing a dome-shaped apex, pulls the members 

 involved down out of the transverse plane. 



