48 





= "^(1/ {111 + d\) 



= . (2^-/ '^^^ ), since . ^- pV- 



In the last formula, when X = 0, or something very small, 

 then 



28. 

 ^''=^ -J 



y_ volume s . 



The mean annual increment of a tree ^ „ge ) '^ olten as- 

 sumed to be the current annual increment. This as- 

 sumption is justifiable in the case of erojis that are near 

 the age of exploitability, but should never be made in the 

 case of individual trees, the mean annual increment of 

 which, provided they enjoy a fair supply of light on 

 every side, goes on increasing up to a great age. 



D. Expression of the increment as a percentage. 



To render what follows more easily comprehensible by the stu- 

 dent, we will here recapitulate briefly the general principles of 

 interest. 



If r = the rate per cent, per annum, then 1*0 r = — — - — = 



the amount at the end of a year. In the case of simple interest, 

 we have the rule 



T/>„ /Total intereatN ,__ I 



^ = 100 ( Principal .)= "0 X p 



Put in most cases it is necessary to assume compound inierestj for 

 which we have the following formulae : — 



.Am6unt=^ = P(l-0r)« , or 1-Qr=l/'^, or r = 10o(^^— 1 V 



For the easy determination of r, Pressler has invented a formula 

 based on the following two assumptions : — (1), that the amount at 

 the middle of the period of years n is equal to ^ (A + -P), and 



(2), that the annual increment is equal to — (4 — P). He thus 

 gets 



r : ioo,::i{^-P):4M+?) 



n 



, A—P ^ 200 



and r = -rro ^ — • 



A + r H ■ 



