264 ^ Forestry Quarterly 



an equalization of volvimes is also desired, the periods of utilization 

 of the different ageclasses may change. 



In the better formula methods, which have in view an attempt 

 to secure the normal stock in shorter or longer time, the question 

 is how to determine rationally this period of equalization (e). 

 Hundeshagen's formula, which is faulty in its original conception, 

 is also impractical because it gives no idea of this time element. 

 Heyer's formvda is the best; only the cumbersome volimie deter- 

 mination is objectionable. This, the author tries to simplify and 

 at the same time to give points of view for determining the length 

 of the equalization period. This last should rest on factors which 

 have permanent significance and principles behind them, just as 

 the rotation. The equalization of the normal and actual stock 

 must be made within a period which permits holding on to the 

 determined rotation, for there is only one most favorable cutting 

 over time. Hence, the relation of rotation to equalization period 

 must be considered. 



The difference of the stocks Sa-S„ can be expressed in terms 

 of the actual increment I a, namely wig; then Heyer's formula for 



the budget (6) becomes 6 = /a=*=— = -^o(l=^-)- I^ ^^e actual 



ft 



stock is larger than normal the budget is /^(H--); its utilization 



reduces the stock as much as will be equalized by the increment 

 during the period e; annually the stock decreases by 



r (1+^) — Ia = IoX-- The negative expression denotes the 

 e e 



opposite effect. 



During the rotation the stands grow before their utilization an 



addition oi-Ia- In order to be able to hold to the determined r 



with a given equalization period e the following condition must 

 obtain : 



r ' • • 



S 4--/ 



r = , from which e==p 



e 2 



when the negative expression refers to excess, the positive to 

 deficiency of stock. To a given rotation and with a known 

 stock difference, the rational equalization period can be determined. 



