25 
In a forest, however, crown growth is entirely different 
from other forms of growth, and may be put into a class by 
itself. In the forest the crown is engaged in a struggle for 
existence; it is constantly surrounded by forces opposing its 
development, while both height and diameter are free. The 
crown has either to overcome or be overcome, to win or to be 
subdued. If we consider pine for the sake of simplicity, we 
find that the attack by the crown is carried on and main- 
tained in intensity by reinforcements in the form of new 
branches. In both height and diameter development, the 
new additions are always placed upon the old, but in the 
crown struggle new units are constantly being added and the 
old ones pass to their death. In the open grown specimen the 
position of the crown is fixed, but in the forest tree the crown 
moves up the stem. Since the growth of the crown then is 
constantly impeded and resisted, it is to be expected that its 
curve of growth will differ materially from that of diameter or 
height. Since all forests, no matter what their composition, 
are engaged in the same struggle, it is not unreasonable to 
expect that some common law holds for the development of 
the crown. Naturally, development of the crown means the 
constant elimination of trees and the lessening of the density. 
Although all engage in this struggle, it does not say that all 
trees engage in it with the same intensity: It has already 
been noted that oak is space demanding, while ash is crowd 
enduring. The feebleness of the struggle carried on by ash is 
reflected in the decrease of the rate of diameter growth as 
already mentioned. White pine seems to stand midway be- 
tween those two trees. From a study of the crowns of various 
species, it was assumed that the expansion of the crown was a 
linear function of time. To see how far this might be true an 
examination of a very large number of European yield tables 
was made and the crown radius determined for each decade. 
In the calculation the crown has been assumed to be circular. 
Figures 2, 3, 4 give the radii of the various crowns plotted 
against time. Figure 2 is taken from Grave’s Mensura- 
