Descriptive Morphology . 51 
developmental stages represented immaturities whose form was 
unessential. 
The whole question is after all one of standpoints, and once 
this ‘adult’ standpoint of older observers is clear, the exact 
significance of their further observations and deductions is rendered 
obvious, Similarly the adult plant remains to the present time that 
of the systematist and descriptive writer. 
In considering, for example, the arrangement of foliar members 
on the shoots of adult plants, the first and most obvious arrange¬ 
ments were described by such terms as opposite, whorled, alternate 
(Sauvages, 1743), while the descriptive work of Linnaeus showed 
little advance; the great majority of leaf arrangements, now classed 
as spiral, being still included under the term Dispositio sparsa, or 
sine online (1751). 
The founder of what has long been known as the Spiral Theory 
was Bonnet (1754), who first defined a spiral arrangement; Bonnet’s 
observations form the basis of all theories of Phyllotaxis, and in 
justice to him, the exact significance of his views requires to be 
clearly stated. Bonnet’s system related solely to adult structures 
or long leafy shoots, he had nothing to do with buds; he determined 
what is still known as the “ § spiral,” in which the sixth leaf is 
inserted exactly over the first of a spiral series which makes two 
complete revolutions of the stem. With the aid of a mathematician, 
Calandrini, he formulated a definite and logically correct geometrical 
conception of a helix with parallel screw-thread winding round the 
cylindrical stem, thus spacing out leaf members of equal size at 
equal intervals. This mathematical conception just like any other 
mathematical proposition was arranged to fit certain definite facts; 
if these facts held, so would the mathematics, if other facts were 
included the mathematical proposition would require to be modified 
Bonnet knew sufficiently well that buds did not agree with this 
construction, but as above indicated, he had nothing to do with 
buds, which when fully grown would give his helix on the adult 
cylindrical shoot. 
On the basis of Bonnet’s spiral an enormous edifice of 
beautifully precise nomenclature was erected by Schimper and 
Braun (1830-1835); the fractional formulae of the type were 
extended so as to include a considerable range of new ratios from 
the Fibonacci summation series 2, 3, 5, 8, 13, etc.; these numbers 
being the ones most commonly found in the plant; while other 
series were designed in order to include formations which did not 
