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praktische Bedeutung des arithmetische Mittelstammes," the application of 

 Kopezky's law on the construction of a yield table. 



From the previous part, we have seen that through the given phase, 

 the relation subsisting between the height and the age of a single tree 

 and between the diameter at breast-height and the age will be expressed 

 by the formulae: 



-^=c,J^and -^ = c'JL 

 dt f" dt f 



dij ^ c^ y 

 dx c' X 



In which y is the height corresponding to the diameter x, t is the age 

 and c and c' are constants. 



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

 following relation : 



y=a.' X ^ 



where /3'=— »- and a.' are the constants, respectively. 

 c' 

 Assuming that the growth of trees in a stand is approximately the 



same, then the relation subsisting between the height and diameter of test 



trees in a stand may be represented approximately by the formula. 



y=a. X ^. 



Again changing the origin to the diameter corresponding to the 

 average diameter, says D, which was the weighted one by means of basal 

 area, of a given stand, we get, from the given equation y=(tx^, 



=«/=aD^(l + -^)^=aD^(l+^^), 



y 



where x=D + a;' 



Hence we have 



where we put a-D^^r^ and a^D'^=Ti. 



In this last equation, the coefficient r, and the term t^ ^^^ the cons- 

 tants in a given stand at a given age; they form indeed the function of 

 the age. 



Again from the relations existing between the volume without the bark 



