ween the cones of the two sections of
the genus. Those of the Soft Pines (figs. 55, 56) have larger and fewer
scales, those of the Hard Pines (figs. 57, 58) have more numerous and
smaller scales, in proportion to the size of the cone. The former
condition represents a lower, the latter condition represents a higher,
order of phyllotaxis.

DEFINITE PHYLLOTAXIS.

On a cylindrical axis with scales of the same size, the spiral
arrangement would appear as in fig. 62, where the scales are
quadrangular and any four adjacent scales are in mutual contact at their
sides or angles. These four scales lie on four obvious secondary spirals
(fig. 59, a-a, b-b, c-c, d-d). According to the phyllotactic order of
the scales these may be the spirals of 2, 3, 5, 8 or of 3, 5, 8, 13 or
of 5, 8, 13, 21 etc., etc., from which combinations the primary spiral,
on which the scales are inserted on the cone-axis, can be easily
deduced. Four quadrangular scales in mutual contact represent the
condition of definite phyllotaxis. If the cone is conical, definite
phyllotaxis would be possible among all the scales only when the size of
the scales diminishes in equal measure with the gradual diminution of
the cone's diameter. Such a hypothetical cone is shown in fig. 61.

INDEFINITE PHYLLOTAXIS.

On an imaginary cone of conical form and with scales of equal size
throughout, there must be more scales about the base than about the apex
of the cone. The phyllotactic conditions must differ, and the obvious
spirals, in passing from base to apex, must undergo readjustment. If the
scales at the base are in definite phyllotactic order and those at the
apex are in the next lower order, it is evident that intermediate
scales, in the gradual change from one condition to the other, must
represent different conditions of indefinite phyllotaxis, while those in
a central position on the cone may belong equally to either of two
orders.

A Pine cone is never absolutely cylindrical nor do its scales vary in
size proportionately to the change of diameter. Most of the scales of a
cone are in indefinite phyllotactic relation, while definite phyllotaxis
is found only at points on the cone.

As an extreme illustration, the cone of P. pinaster (fig. 60) shows four
mutually contiguous quadrangular apophyses at (a), lying on the obvious
spirals 5, 8, 13, 21, at (b) four similar apophyses on the spirals 3, 5,
8, 13, and at (c) four others on the spirals 2, 3, 5, 8. Betwe