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and the age and between the diameter at breast-height and the age, we 

 get, through the given phase, 



J^=c,^ and ^^=c'^. 

 dt f dt t^ 



so we get 



dz _ c, z 



In which z is the volume corresponding to the diameter x and c, is the 



constant. 



Thus by integrating and transforming the last equation, we get the 



following relation : 



&" 

 z=a."x^ 



where &"='^ and a-" are the constants, respectively, 

 c' 



Assuming as in the case of the height, it will be deduced that the 

 relation existing between the volume and diameter of test trees in a stand, 

 may be approximately represented by the formula. 



Now changing the origin to the diameter corresponding to the average 

 diameter D, of a given stand, we get from the equation z=(^■^x^'' 



where a;=D + x' 



Thus we get 



where we put a,D^i =x'^ and aj|3,D^' =t'i. 



In which the coefficient x\ and the term x\ are the constants in a 

 given stand at a given age, but these are the variable constants depending 

 upon the age. 



The results are given in the following tables: 



