30 
graph would be obtained cutting the vertical axis above the 
origin. It may be here remarked that the congestion of the 
crown canopy at the later periods of the forest’s life may so 
restrict the crowns that any thinning experiments carried out 
on such a forest would yield negative results. As has been 
shown already, the smaller the crown for any given age, the 
smaller the diameter. The smaller the diameter for any given 
height the less the rigidity of the stem. The thin stemmed, 
small crowned trees sway in the wind and their crowns rub 
off all the lateral buds from their own and the neighboring 
crowns. This occurs particularly in ash and pine. Such trees 
cannot respond actively, if at all, if the stand be thinned. A 
tree does not differ from any other biological unit and can 
only respond to a stimulus when kept in a condition to do so. 
For any graph 6 cannot be positive, but may be either zero 
or negative. If zero it assumes that crown expansion pro- 
ceeds regularly through the life of the stand. If b is negative, 
it implies that growth at the early period was slow and that a 
concave curve joins the straight line to the origin. In all four 
site qualities of oak as given by Wimmenauer 0 is negative. 
It will be seen that in the case of larch, Figure 3, the m values 
are not widely different. In some sets of graphs the m values 
are all the same. This would imply that the trees on all site 
qualities carried on the struggle for existence with the same 
intensity. This cannot be considered as correct, for since a 
lower site quality is indicated by a smaller height, a smaller 
diameter and a smaller volume, it follows that trees on a lower 
site quality carry on the struggle for existence with less in- 
tensity than those on a higher site quality. We may con- 
clude, therefore, that the higher the site quality the higher 
the value of m; and, hence, the graphs of crown expansion for 
the site qualities of any particular species will not be parallel. 
Now r is connected in the equation 
rrn=A 
When n = number of trees per acre 
and A = acre in square feet 
