277 
On the Growth of Leaves. 
The growth of leaves by the expansion of the cells is subject to 
various modifications. 
In the Algae the expansion does not usually begin until the 
growth by development is complete. It then commences in the 
uppermost cell and extends gradually to the base. In those 
branched filaments where the cells break up {Polysiphonia, &c.) 
the uppermost cell falls ofi* first, and the process extends down- 
ward to the others in succession. There are some few exceptions to 
this rule, where the expansion of the cells is simultaneous, or even 
begins in certain other parts instead of the apex. Those Algae 
however which consist of single branched cells must of course be 
excepted from the rule, as the expansion is the extension of one 
individual cell, and that proceeds from below upward. 
In the Mosses and Hepaticce the expansion commences, after 
the completion of development, at the apex and extends gra- 
dually downwards. In Characece the terminal cells expand first. 
In the Lycopodiacece the expansion also proceeds from the apex 
to the base. 
In the Phanerogamia as a general rule both in simple and 
compound leaves, the expansion commences at the summit, but 
this rule is not without exception. In some leaves the expansion 
is tolerably simultaneous, while in others, as in Utricularia, it 
extends like the development from below upward. There does 
not appear to be any rule for the expansion of the petiole of com- 
pound leaves. 
Drawing the conclusion as to the origin of the leaf in the 
higher classes from analogy, Nageli propounds the following 
formulse as the expression of his views : — 
1. The leaf originates as a simple cell, 
2. The growth by cell-formation occurs at the apex and on the 
border, and proceeds, from the base, upwards and outwards. 
3. The growth by the expansion of the cells begins, on the con- 
trary, at the apex and extends to the base. 
Now these formulae look remarkably definite and clear, and if 
we could receive them, our knowledge of these structures would 
be much simplified ; but unfortunately, although the laws of de- 
velopment are simple, fundamentally, they are subject to innu- 
merable modifications in their application, and I cannot think 
that Nageli has taken all the conditions of leaves into consider- 
ation, and I believe therefore that he has generalized much too 
freely. 
In the first place it is a question whether the fronds of the 
Algae are always the analogues of leaves : if we have leaves in 
• them, we also have leaves and stems, and probably often stems 
