26 
tion. Figure 3 is taken from The Reports of the Swedish In- 
stitute of Experimental Forestry, 1916-17. Figure 4 is from the 
Allgemeine Forst und Jadg Zeitung, vol. 84, p. 266. 
Only one graph in those given is a distinct curve. Many 
crown graphs are distinct curves. Yet the majority show a 
straight line. In many the curve is so slight as to be approxi- 
mately a straight line. This is the case in each of the three 
site qualities given by Fleury in Frtragstafeln fiir die Fichte 
und Buche der Schweiz, Zurich, 1907, and also in the four site 
qualities given by Wimmenauer for oak in Allgemeine Forst 
und Jadg Zeitung, vol. 89, p. 261. Slight curves might also 
be drawn in Figures 2, 3, and 4. 
Since the expansion of the crown can be represented by a 
straight line, it follows that the crown growth is a linear 
function of time. Before applying this law to the data given 
for oak and ash it is as well to consider the equation for the 
the straight line. The statement that the expansion of the 
crown is a linear function of time refers only to the period 
of time covered by the average rotation. The general equa- 
tion for the straight line is: 
PS OME ae ee Oke oe (1) 
= radius of the crown in feet 
intercept on the axis of r 
tangént which the graph makes with the ¢ axis 
t = time in years 
where 
r 
b 
m 
Now b may be either positive or negative. If b be positive 
it implies either that there was already a crown existing when 
the forest commenced or else that the greatest period of 
growth was in its earliest years. In the latter case the curve 
of expansion would be convex upwards until the straight line 
was reached. Neither assumption is true; and, therefore, b 
cannot be positive. Such graphs arise through the stand 
being either insufficiently stocked in its early life or else 
through its being too congested later in life. In white pine 
stands, both factors are operating and from most stands a 
