82 RELATION OF PHYLLOTAXIS TO MECHANICAL LAWS. 



The special cases of phyllotaxis may now be considered under 

 the headings : — 



(1) Asymmetry of the normal Fibonacci series. 



(2) Symmetrical construction, in which the Fibonacci ratios 

 are lost. 



(3) The special case of " Least concentrated " asymmetry. 



(4) Non-concentrated symmetry. 



While separate sections will be devoted to — 



(5) Multijugate systems. 



(6) Anomalous systems. 



Subsequent sections will include the consideration of secondary 

 disturbances in the primary system, the relations of dorsiventral 

 primordia, deductions from the mathematical investigation of the 

 log. spiral systems, and the relation of all these factors to the 

 interpretation of floral structures in the form of floral diagrams. 



nearly to the volume occupied wlien fresh. By making a careful camera 

 lucida drawing on a large scale, about 12 ins. by 8, the construction lines can 

 be followed with a considerable amount of accuracy. The diagrams are 

 subsequently blocked in with a brush, as the contour is thus more accurately 

 kept than by a pen. The errors of the diagrams are due to — (1) contraction 

 of the spirit-material ; (2) error of the lens and camera lucida ; (3) error of 

 cutting the section strictly transverse. The last mentioned, being judged only 

 by eye and hand, is clearly the greatest source of error, and can only be 

 eliminated by comparison of several sections. On such figures, distances can 

 be measured in millimetres, and angles to half a degree, with a reasonable 

 amount of accuracy. All the figures used as illustrations are much reduced 

 in reproduction. 



