1020 
In plants with incomplete nodes. there is found to the left and 
right of the point of attachment of the leaf an area which belongs 
to a leaf placed above, therefore there are two different phyllopodia. 
When we now assume that in plants with alternate phyllotaxis 
(incomplete nodes) the phyllopedia themselves are subject to the 
same growth as is also to be seen in the node of the stems with 
complete nodes, then parts having a different rate of growth will 
be adjacent. 
The question now arises, how in that case will the rate of growth 
be distributed over the whole area of growth, when according to this 
supposition each piece of the stem has the average rate of growth 
of its component parts. 
In order to trace this I have made a calculation for which the 
known rate of growth of the stem of Polygonum was chosen as the 
startingpoint, because internodes of this plant are very markedly 
individualised. 
I assumed that each leaf only surrounded a fifth part of the 
circumference of the stem and that the leave were displaced along 
the stem to the position */,. 
From the averages of the rates of growth of the five zones thus 
situated at the same height I obtained a regularly ascending curve 
with a short descending branch. 
Its course agreed with the curve for plants with alternate phyl- 
lotaxis. 
Although I do not see in this any proof of the theory that the 
stem may be composed of leaf vases or may be covered with them, 
yet it is clear in either case that the observed manner of growth 
is not inconsistent with this. 
If this theory is accepted, there is morecver agreement between 
the growth of plants with complete nodés and those with incom- 
plete ones. 
Finally I should like to point out that I have observed in one 
plant, namely, Ginkgo biloba Layy. a difference in growth between 
three stems, which were in the light and three which grew in the 
shade. 
The number of my observations is too small to warrant any cer- 
tain conclusion, but nevertheless I consider I have observed that the 
greater increase in length of the shaded stem must only be attri- 
buted to a slight extent to the greater rate of growth, but was more 
especially due to a longer region of growth, that is to say, each 
zone grows during a longer period of time. 
