42 



Multiply botb the numerator and denominator of the first side of 

 the equation by such a number a that the numerators of both sides 

 may be equal. Then the denominators will also be equal. 

 Hence s^j -\- z y^ + z y^ 2^11 = Pj, + »2 -Vv^ ... + »„» 



and e + e + e uri to n terms = -J-. H — ? + _? + — " 



These two equalities are possible only on the condition that the 

 first, second, third ... terms of one side are equal respectively to 

 the first, second, third ... terms of the other side, that is to say, 

 «yi = ?;i; 2^2 = 1^2 ; «^3 = »3; ...... z y^ =»nj 



and , = !!l=JL^ = ''3. = !Ln 



But volume (») = basal area x height x form-factor = alif, 

 ,-. "■\Kf\ —Ms^ _ ijijfz 



y\ Vi. Vi 



Now we may assume that in one and the same crop the mean 

 annual increment of height x form-factor ( viz., -^ 1 is approx- 

 imately equal, that is that 



y\ y2 ys 



Hence a^ = a^ = a^ 



These conditions are fulfilled by the distribution of the sample 

 trees in Hartig's method of valuation, so that in that method the 

 mean of the ages of the sample trees gives the mean age of the 

 crop. 



For the employment of formula (v) a survey by girth-classes 

 is necessary in order to be able to determine the volume of material 

 contained in the several classes. This is not possible by Urich's 

 method. 



It may sometimes occur, when only a few sample trees are 

 felled, that the smaller are found to be older than others of larger 

 girth. In such a case we may still take the arithmetical mean 

 of the ages on the not improbable assumption that there is a wide 

 difference of ages between the several individuals of each of the 

 girth- classes, and that for one sample tree that gives too high 

 a figure for the mean age of its class, there is another whic^ gives 

 the same amount of compensating error on the other side — errors 

 of excess and defect thus cancelling each other. The smaller the 



