The Principles of Phyllotaxis. 
by 
ARTHUR H. CHURCH, M.A., D.Sc., 
Lecturer in Natural Science, Jesus College , Oxford. 
With seven Figures in the Text. 
I N a preliminary note published some time ago \ exception was taken 
to the conventional methods adopted for the description and even 
interpretation of phyllotaxis phenomena, and a suggestion was made 
that appeared to be not only more in accord with modern conceptions 
of the phenomena of energy distribution, but it was further indicated that 
such a theory when carried to its mathematical limits threw a strong light 
both on the mechanism of shoot production and the inherent mathematical 
properties of the lateral appendage usually described as a ‘leaf-member,’ 
as opposed to any secondary and subsidiary biological adaptations. 
As publication of the entire paper has been delayed, and the new 
standpoint has not received any special support from botanists to whom 
the mathematical setting proved possibly a deterrent, the object of the 
present note is to place the entire argument of the original paper in as 
concise a form as possible 2 . The preliminary discussion is sufficiently 
familiar 3 . 
The conventional account of phyllotaxis phenomena involves a system 
of ‘ fractional expressions ’ which become interpreted into angular diver- 
gences ; and in practice the appearance of ‘ orthostichies ’ has been taken 
as a guide to the determination of the proper ‘ fractional expression.’ 
This method, elaborated by Schimper (1830-5), has more or less held 
the field to the present time ; and, for want of something better, has 
received the assent, though often unwilling, of such great investigators 
as Hofmeister and Sachs, to say nothing of lesser lights. Although 
elaborated into a system by Schimper and Braun, who added the peculiar 
mathematical properties of the Fibonacci series to the academical account 
1 Note on Phyllotaxis, Annals of Botany, xv, p. 481, 1901. 
2 On the Relation of Phyllotaxis to Mechanical Laws. Part I, Construction by Orthogonal 
Trajectories, 1901. Part II, Asymmetry and Symmetry, 1902. 
3 Descriptive Morphology-Phyllotaxis. New Phytologist, i, p. 49. 
[Annals of Botany, Vol. XVIII. No. LXX. April, 1904.] 
