— 172 — 



corresponding to the average diameter with respect to the age, will be 

 expressed by the formula: 



Hence if the volume of a test tree corresponding to the average diameter 

 of a stand correspond to the average volume, calculated by the formula: 

 , = y_ then the fluctuation of the average volume of a stand will be 



N' 

 expressed by the equation: 



i=b'e * 

 From the comparison of ^d with i which was given in the previous 

 section, we arrive at the conclusion that the average volume may be 

 expressed by the formula: 



_3_ 



t 

 !=xe 



Applying the equation to the given data, we find: 



for a stand with " a " grade ; 



139.6264 



.a=2.657e * Probable % Diff. ±3.7% 



for a stand with " b " grade ; 



118.1089 



ib=2.6\3e * Probable % Diff. ±6,4% 



for a stand with " c " grade ; 

 _ in. 1139^ 



/„=1.740e ^ Probable % Diff. ±6.6% 



The following diagram (Plate XXIV) show the comparison between ob- 

 served and calculated results for each stand: 



(/) On the Volume per Unit Area. 

 From the similarity of the fluctuation of the index number of volume 

 with that of the average diameter, average height or average volume, we 

 may suggest that the equation of the volume per unit area with respect 

 to the age may be represented by the formula: 



V=ie 



t 



