till the coil is completed. For the sake of clearness this
may be illustrated thus:--Suppose the spiral cycle to comprise five
leaves, numbered 1, 2, 3, 4, 5, then 2 would intervene between 1 and 3,
and so on, while the sixth leaf would be the commencement of a new
series, and would be placed exactly over 1. This arrangement may be thus
formularised:

6 7 8 9 10
1 2 3 4 5

In the verticillate or simultaneous arrangement of leaves the case is
somewhat different. Let us suppose a whorl of eight leaves, surmounted
by a similar whorl of eight. In such a case it will generally be found
that the whorls alternate one with another, as may be represented by
this symbol:

9 10 11 12 13 14 15 16
1 2 3 4 5 6 7 8

The simplest illustration of this arrangement is seen in the case of
decussate leaves, where those organs are placed in pairs, and the pairs
cross one another at right angles. This may be expressed by the
following symbol:

7 8
5 6
3 4
1 2

Thus, while in both the annular and the spiral modes of development the
individual members of each complete series necessarily alternate one
with another, in the former case the series themselves alternate, while
in the successive arrangement they are placed directly one over the
other. There are, of course, exceptions, but the rule is as has been
stated, and the effect is to prevent one leaf from interfering with the
development and growth of its neighbours.

In the case of the whorled or simultaneous arrangement the conditions of
growth must be uniform on all sides, but in the successive or spiral
disposition the conditions influencing growth act with unequal force, on
different sides of the stem, at the same time. In the whorl there is an
illustration of radiating symmetry, while in the spiral arrangement
there is a transition to the bilateral symmetry. There are frequent
passages from one to the other even under normal circumstances; thus,
while the one arrangement obtains in the ordinary leaves, the parts of
the flower may be disposed according to the other method. In the annular
disposition it generally happens that the rings are separated one from
the other by the development of the stem between them, the internodes
between the constituent leaves themselves of course being unde