230 THE NORMAL GROWING STOCK. 



c. Cojvpice and Coppice wWt Standards. 



The calculation for simple coppice is the same as in the 

 case of clear cutting in high forest. 



For coppice with standards forest the calculation must be 

 made separately for under- and overwood, and the results 

 added together. The former is of small account, as the 

 presence of the overwood reduces the quantity of the under- 

 wood considerably. 



The calculation of the normal growing stock of overwood 

 is a complicated and uncertain operation and at the best only 

 of theoretical value. It must be based upon the number of 

 trees and the average volume per tree in each age class, 

 somewhat in the following manner : — 



If the normal number of trees in each of the /•, 2 r, 3 r . . . 

 old age gradation is known, and also the volume of the average 

 tree in each of these gradations, then it can be assumed, that 

 the trees increase in volume, within each class, according to 

 an arithmetical series ; this makes it possible to interpolate 

 the volume of the trees r -{- 1, 2 r -{- 1 . , . years old. In 

 that case, the normal growing stock of the first age class would 

 be expressed by — 



K'- « + '■"•■> 



where T',+, represents the volume of all trees r -f- 1 years old, 

 and V.>r that of all trees 2 r years old. In the same way the 

 next age class would be represented by — 



|(.w. + n 



and so on. Adding all positions together, the normal groAving 

 stock of overwood comes to — 



G„ = '- (iWi + r„. + y-^.n + Vr.r + • • • + r,„_,,.+i + F„-). 



This amount does not comprise the youngest age class of 

 all, which still forms part of the underwood. 



