Forest Mensuration 47 



rapid rate than the current annual height increment. The average annual 

 height increment culminates at the very age at which it is equal to the 

 current annual height increment. 



As long as the average increment increases the current increment is 

 larger than the average. The average increment still rises during a period 

 of decrease of current increment. 



These laws hold good not only for height growth, but also for the 

 growth of diameter, sectional area and volume. They are based merely 

 on mathematical principles and are, for that reason, independent of spe- 

 cies, climate and soil. 



If "a" denotes the current annual increment, and if "d" denotes the 

 average annual increment, whilst the indices i, 2, 3, etc. (up to n), indi- 

 cate the year of increment, then the following five equations hold good : 



n X dn = &! + a 2 + a 3 4- a n 



(n 4. 1) dn + i = &i f a 2 + a 3 a n + an + 1 



(n + 1) d n + i = n X d n + a n + i 



n X dn + i = n X dn + a n + i d n + i 

 n (dn + i dn) = an+i 



PARAGRAPH LXXVI. 



RELATIVE INCREMENT OF THE HEIGHT. 



The percentage of height increment forms, from the start on, an irreg- 

 ularly descending progression. 



If the height is h at the beginning of a period of n years of observa- 

 tion and H at the end of that period, then 



h X 1. op n equals H 

 and 



p equals 100 A /5 100 

 V h. 



Pressler substitutes for this formula in case of short periods of observa- 

 tion the following : 



200 H h 



P -- X - -- - 



n H + h 



This formula is derived as follows : Imagine that we are in the midst 

 of the period of n years. At that time, the increment is apt to be 



, whilst the height at that time is apt to be "*~ ; hence, for that mid- 



2 



die year, the equation is : 



p H h 



X 



100 n H +h 



