50 



According to Pressler this formula gives the percentage of 

 increase in volume not only for the stem alone, but also for the 

 entire tree inclusive of the branches ; and experiment has proved 

 this assumption of Pressler's to be very nearly true. 



lu order to simplify the calculation, Pressler employs the relative 



diameter A = - , in which D = the actual diameter exclusive 







of bark, and 8 = the increment of the diameter during n years. 

 Now since 



i) = 8A, and ^ = 8A — 8 = 8 (A— 1), we have 



'•»^a/'->?=a/(^>. 



, , A^— (A— 1)2 200 . ^ , 



and also p = ^g_^^^_^ a X — approximately. 



For the calculation of the future increment per cent., the pro- 

 bable diameter after v years may be assumed to be D + 8, and 



., . , . , 1 .(A + l)2— A^ 200. 



increment per cent, to be approximately Ji >— —x 



(A+lj^'+A* n 



Pressler has published tables showing the values of this percentage 



for different values of A from 2 to 300. 



In the ease of standing trees, of which only the increment of 



diameter at the base can be measured, and rarely, if ever, the 



height, the percentage of increase in volume cannot be determined 



with any very great accuracy. For such trees Pressler has drawn 



up a set of tables for determining, with the aid of the relative 



diameter, ithe rate of increase per cent, for five grades of hein-ht- 



growth. In order to determine the percentage with suflncient 



approximation without the aid of such tables, we must first find 



J) and d = D — 8 by measurement, and then the rate per cent. 



Ot increase in diameter = jo^ = x (for a sinele year n^ 



JJ + d n a J fa. 



= — - — I, and the minimum increase per cent, of volume p =: 



1 Pi. In most instances ^^ varies from 2^ p^ to 3 p^ , and in the 

 case of trees enjoying a full height-increment and forming a 

 canopied crop, jo^ = 2>\ p^ . 



In calculating the increment per cent, for a single year, we may 

 employ Beeymann's formula. On page 48 it has been shown that 

 the increment on volume is approximately equal to 



