00 RELATION OF PHYLLOTAXIS TO MECHANICAL LAWS. 



Examination of similar diagrams, constructed with the same 

 approximately correct curve, shows that these ratios follow the 

 same ascending series. 



Thus actual measurements gave: — 



As the error of measurement increases with the rise of the series, 

 it may be assumed that (55+ 89) corresponds to 1 : 34 

 (89 + 144) „ 1:55 



(144 + 233) „ 1 : 89 



With the lower ratios (2 + 3), (1 + 2), (1 + 1), the error of 

 construction becomes obvious, since circles cannot be inscribed 

 in the " squares " to represent the ovoid curves with siifficient 

 accuracy.* 



, Lateral primordia are thus to be regarded as bodies presenting 

 a definite bulk ; and since the last given ratios are the highest 

 known in the plant, it follows that, in dealing with bulky prim- 

 ordia, in contradistinction to the mathematical points and series 

 tending to approach an "ideal angle" of the Schimper-Braun 

 theory, such a limitation of the series while the bulk of the 

 lateral member is stUl relatively considerable, must admit of the 

 possibility of a certain degree of structural error in the systems. 

 This becomes more obvious when the bulk-ratio is expressed in 

 terms of the angle subtended by a primordium. 



Since the ratio of the radii of the primordium and parent axis is 



* A comparison of these values on a carefully constructed diagram three 

 feet in diameter, in which the error of drawing became apparent, showed that 

 these general results hold within a very trifling error ; and that this error is 

 not much more than the diflference between these results and calculated mathe- 

 matical ratios. {Gf. Note IV.) 



