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the stand. From these results, we may easily deduce the relations existing 

 between the factors which represent the growth of the stand and the age. 

 Especially the results of the preceding investigations lead us readily to 

 determine the equations of the average height, diameter and volume of a 

 stand with respect to the age. Before entering upon the discussion of the 

 equations for each factor with respect to the age, it is a necessary and 

 important preliminary work to compare the form of the curves, showing 

 the fluctuation of each factor. To this end, it is much better to calculate 

 the index numbers corresponding to the average diameter, average height, 

 average volume, average crown area, total basal area per unit area and 

 volume per unit area. (Plate XVII) 



(c) On the Average Diameter. 



In the preceding part, we have investigated the height curve of test 

 trees in a given stand and have made the preposition that the height 

 curve may be represented by the formula. 



and T,=ae T^=be 



In which we have given: 



(tD^=T2=&e * 



From this, we get 



I _ &, J_ 



Thus it will be assumed that the equation for D may be represented 

 by the following formula: 



_ ^i 

 D=Ae 

 Applying the equation to the given data, we find: 

 for a stand with " a " grade : 



52.8138 



Da=43.69e 



t Probable % Diff. ±1.8 



