THE THEORY AND PRACTICE OF WORKING PLANS 101 



data, it is then determined at what diameter breast high the 

 trees have an age equal to -. All trees of this diameter and 



2 



over are next estimated — rpreferaWy^TTrj-inch diameter classes 

 — and their volume and current annual increment determined. 



Annual cut = volume of trees or of diameter classes - years 



2 



and over, plus increment thereof in - years; this sum divided by 



4 



-. (For underlying theory see Formula Methods above.) 



Variation IT. Going a step further, diameter can be sub- 

 stituted for age. ' After determining at what diameter, and 

 upwards, the trees are most merchantable, it follows that all 

 trees of this diameter and larger are merchantable and should, 

 other things being equal, be cut in the near future, i.e., during 

 a period of years required for the next lowest diameter class or 

 classes to produce an equal number of merchantable stems. 

 But the lower diameter classes contain more trees than the higher 

 classes, therefore more than replacing those cut in the higher 

 class. 



To express this numerically, the period of years separating 

 the diameter classes must be known, i.e., the average age of the 

 average tree in each diameter class. Let this value equal ai, 

 ^2, as, etc. The volume of the average tree in each diameter 

 class must be also known (volume tables, measurement of repre- 

 sentative trees, etc.). Let this value equal v\, V2, V3, etc. Let, 

 finally, the number of trees in each diameter class equal wi, 

 «2, «3, etc., and the formula follows: 



A 1 4. / \ ^^4 . W3— W4 , W2 — «3 , ni—n2 



Annual cut {y) = ^'4 H vs -\ V2-\ = Vi. 



a^ — a3 a^ — as az — a-z ao — ai 



The formula indicates the cut in number of trees of each 

 class as well as in volume. 

 ' Hufnagl further advocates the comparison of y obtained by 



