PREVAILING SYSTEMS OF PHYLLOTAXIS. 43 
pound leaves, as in the May and Ash, permit the ingress of light and air, so that a 
“ higher " spiral divergence is permissible, in that the leaves need not all be brought to 
the surface of the tree. 
As other examples of these divergences, may be mentioned the Alder, Lime, and Elm, 
the first of these being usually regarded as having its leaves arranged on the $ plan. 
This may also be due to peculiarity of growth, especially as the scales of both male and 
female catkins (of the Alder) are on the 2 plan. 
Again, if it be noticed how the Lime and Elm spread out tlieir leaves on horizontal 
planes, just as in the case of the garden-Laurel, the influence of light &c. already alluded 
to can be supposed to some extent able to have induced this arrangement ; how far, however, 
it is impossible to say ; for although light will cause fully developed leaves to turn to it, 
we do not know if it can cause a leaf to grow out at a particular point on the axis of the 
bud, so as to secure a more favourable position as regards the light, in anticipation, 
asit were, of its adult state. It is obvious that, of such broad leaves as these trees possess, 
if they were grouped spirally round the branch, some would fall underneath in the 
shade of the others, whereas by being, as they are, on the same horizontal plane, they all 
become equally favoured. 
Hence has arisen, as I believe, these distichous and, so to say, pseudo-distichous * and 
tristichous arrangements, which are by no means common amongst Dicotyledons 7. 
Having now seen that, whenever distichous and tristichous leaves are found amongst 
Dicotyledons, they may most probably be regarded as not issuing directly from opposite 
leaves, it may be observed, on the other hand, that these arrangements are particularly 
characteristic of Monocotyledons, as іп 18, orchids, grasses, &e. То ascertain a cause 
for this, let us again go to the embryo. Here we have but a single cotyledon. Now it 
must be observed that, for any arrangement of the usual or primary series, no portion of 
à spiral whieh when projected constitutes a circle ever contains more than three leaves ; 
or, with the exception of the distichous, such a circle always does contain three leaves. 
It will be at once seen that the distichous and tristichous, or the 4 and } plans, are the 
only kinds which admit of one complete cycle being projected in a circle. In the former 
the leaves are at opposite extremities of а diameter, in the latter at an angular distance 
of 120°. Hence there are these two methods of equalizing the distance between the 
leaves, and at the same time securing a cycle and satisfying the laws already stated. 
Thus, then, we may perhaps be able to account for the fact that $ and $ do frequently 
represent the leaf-arrangements amongst Monocotyledons. On the other hand, the con- 
Spicuous absence of arrangements represented by 2 and higher fractions is a significant : 
fact affording negative evidence of great value. 
* I make the distinction between distichous and pseudo-distichous, to indicate the fact that in some cases, as in 
the Yew and Tazxodium, the leaves are only apparently distichous in consequence of a twist in the petioles—a 
result more easily conceivable to be due to light than the truly distichous arrangement, as in the Laurel and Beech, 
in both of which the leaves or vertical shoots often revert to higher spiral arrangements. 
Т I take this opportunity of remarking that while examining the buds of these trees, I think I have discovered the 
cause of their unsymmetrical development—namely, that it is due to the position of the stipules, which lie obliquely 
across the two edges of the folded (conduplicate) leaf, thereby allowing one margin to develop more freely than the 
other. The bud-scales in both Elm and Lime are stipules. 
