s 7" < 
Wa + 
344 
NATURE . 
ss a 
x 
favourably to the light, and thus the leaf-order that was 
perfect in the bud is disguised in the grown twig. 
In lateral shoots of yew and box and silver fir we see 
how leaves will get their stalks twisted to obtain more 
favourable exposure to light ; and if general distribution 
round the stem were useful to the adult leaves, we should 
expect the leaves of a vertical elm-shoot (for example) to 
secure such distribution by various twists of stalk and 
stem ; but the leaf-blades of the elm keep their two ranks 
with very great regularity. This goes to show that it is 
not in the mature twig that the leaf-order is specially 
advantageous. ; 
In the bud, we see at once what must be the use of 
leaf-order. It is for the economy of space, whereby the 
bud is enabled to retire into itself and present the least 
surface to outward danger and vicissitudes of temperature. 
The fact that the order } does not exhibit this advantage 
in any marked degree, supports the idea that this order is 
the original from which all the more complex spiral orders 
have been derived. 
The long duration of the bud-life, as compared with the 
open-air life of the leaf, gives importance to the conditions 
of the former. The open-air life of the bud is twelve 
months, and adding the embryo-life of the bud, we have 
about a year and a half for the whole life of the bud; and 
for the twelve months of its open-air life it is in a state of 
siege, against which a compact arrangement of its embryo- 
leaves.within must be of great value. But the open-air 
life of the unfolded leaves is (except in evergreens) not 
more than six months. ; 
That the order } would under different degrees of con- 
traction (with twist) assume successively the various spiral 
orders that exist in nature, in the order of their com- 
plexity, 4, 2, 2, 2, &c., may be shown by the following 
experiment :— 
Take a number of spheres (say oak-galls) to represent 
embryo-leaves, and attach them in two rows in alternate 
order (3) along opposite sides of a stretched india-rubber 
band. Give the band a slight twist, to determine the 
direction of twist in the subsequent contraction, and then 
relax tension. The two rows of spheres will roll up with 
a strong twist into a tight complex order, which, if the 
spheres are attached in close contact with the axis, will 
be nearly the order 4, with three steep spirals. If the 
spheres are set a little away from the axis, the order be- 
comes condensed into (nearly) 2, with great precision and 
stability. And it appears that further contraction, with 
increased distance of the spheres from the axis, will 
necessarily produce the orders (nearly) 2, 355, s, &c., in 
succession, and that these successive orders represent 
successive #axima of stability in the process of change 
from the simple to the complex. 
It also appears that the necessary sequence of these 
successive steps of condensation, thus determined by the 
geometry of the case, does necessarily exclude the non- 
existent orders 4, 7, 4, 4), &c. 
Numbering the spheres from o upwards, it appears that, 
under contrattion, the following numbers are brought 
successively into contact with o, alternately with right 
and left :—1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, &c. None 
of them stands vertically above o while in contact with 
it, but a little to the right or a little to the left, and so 
far the results of this experiment fall short of the perfect 
fractions 3, 2, 3, 3°s, &c.; but in this very failure the 
results of the experiment are more closely in agreement 
with nature than are those perfect fractions themselves, 
for those fractions give the angular divergence only in 
round numbers (so to speak), and lose account of the 
little more or the little less which makes all the difference 
between a vertical rank and a spiral. In_ the large 
majority of spiral-leaved plants, one has to be content 
with “2 nearly” or “2 nearly,” and it is difficult to find a 
specimen in which the fraction represents the order 
exactly, 
The geometrical relations of the members of the 
above series I, 2, 3, 5, 8, 13, &c., are as simple as their 
numerical relations. 
Analysis of the order seen in the head of the sun- 
flower, and other examples, by consideration of their 
several sets of spirals, presents striking agreement 
with the above synthetical process. In the sunflower, 
a marginal seed taken as 0 is found to be in contact with 
the 34th, the 55th, and the 89th (counted in order of 
growth), and even with the 144th,, if there is not con- 
tact with the 34th. The dandelion, with a lower degree 
of condensation, has o in contact with the 13th, the 
21st, and the 34th in large specimens. The house-leek in 
its leaf-order has o in contact with the 5th, 8th, and 13th. 
The apple-bud has oin contact with the 2nd, 3rd, and 5th; 
and thus we see that in nature the very same series of 
numbers is found to have contact-relation with o, which 
we have already seen possessing that relation in the ex- 
perimental condensation of the order }. 
Difference of leaf-order in closely-allied species (e.g. 
Plantago major and P. Coronopus) is found in close 
relation to their different habits and needs. 
The prevalence of the order } in marine Age, and in 
Graminea, a \ow-developed gregarious group, and its sin- 
gular freedom from individual variation in that group and 
in elm, beech, &c., support the view that this order is the 
original of the spiral orders. : 
In many plants we find actual transition from the order 
4, to an order more complex, as, for instance, Spanish chest- 
nut, laurels, nut, ivy,—and these instances agree in pre- 
senting the complex order in the buds that occupy the 
most exposed situations, while they retain the simple } in 
the less exposed lateral buds. Several kinds of aloe have 
the order } in their. basal leaves and a higher order in the 
remainder. A species of cactus often contains a complete 
epitome of phyllotaxy in a single plant or even ina single 
shoot. 
Shoots of acacia often present a zigzag disposition of 
their leaves, on either side of the branch, which seems un- 
intelligible except as a distortion of an original two-ranked 
order. 
The prevalent two-ranked arrangement of rootlets or 
roots seems to be a survival underground of an order which 
originally prevailed through the whole plant, root, stem, 
and branch. 
In the whole Monocotyledonous class, the first leaves in 
the seed have the order }. In the Dicotyledonous class 
the first leaves in the seed have the simplest order of the 
whorled type. 
As the spiral orders have probably been derived 
from a two-ranked alternate arrangement, so the 
whorled orders have probably been derived from a two- 
ranked collateral (two abreast) arrangement. This is 
illustrated by an experiment similar to the former, and it 
is seen that successive parallel horizontal pairs of spheres 
are compelled under contraction to take position at right 
angles to one another, exactly in the well-known crucial or 
decussate order. These whorls of two contain potentially 
whorls of three and four, as is seen in variations of the 
same plant, but the experiment does not show the change. 
The reason of the non-survival of the (supposed) two- 
ranked cod/ateral order lies in its manifest instability, for 
under lateral pressure it would assume the alternate, and 
under vertical the crucial order. ; 
The bud presents in its shape a state of equilibrium 
between a force of contraction, a force of constriction, and 
a force of growth. 
To sum up, we are led to suppose that the orignal of all 
existing leaf-orders was a two-ranked arrangement, some- 
what irregular, admitting of two regular modifications, the 
alternate and the collateral; and that the alternate has 
given rise to all the spiral orders, and the collateral to all 
the whorled orders, by means of advantageous condensa- 
tion in the course of ages, 
{ Mar. 3 1873 is 
— as a 
