Note on Phyllotaxis. 



BY 



ARTHUR H. CHURCH, M.A., D.Sc, 



Lecturer in Natural Science, Jestis College, Oxford. 

 With two Figures in the Text. 



WRITERS on Phyllotaxis are generally agreed in 

 accepting the series of formulae known as the 

 Schimper-Braun series of divergences, |, |, j%, &c., as 

 fundamental expressions of the primary phenomena of the 

 arrangement of lateral members. This series of fractional 

 expressions, which involves the utilization of the Fibonacci 

 ratio series a, 3, 5, 8, 13, &c., has thus proved for over sixty 

 years the ground-work of all theories of phyllotaxis, and is 

 usually described in the early pages of textbooks. Taking 

 the ' f ' as a type of these values, this expression implies that 

 in placing five members on a spiral which makes two complete 

 revolutions of an axis, the sixth member is mathematically 

 superposed to the first, and that successive members differ by 

 a divergence-angle of 144°. So simple are these relations and 

 so thoroughly well known that it is not necessary to dwell 

 further on the vast superstructure of morphological theory 

 which has been built up on this foundation. However, as 

 a matter of fact, taking the | divergence again as an example, 

 it is beyond doubt that observation of the actual plant shows 

 that these relations do not strictly hold, and various theories 



CAnnals of Botany, Vol. XV. No. LIX. September, 1901.] 



