32 



giown on the same site, or at least in the same locality and under the 

 same conditions. 



In determining the current accretion it is better to establish the 

 increase of volume for the last five or ten years and assume that the 

 current accretions were the same annually during that period; it is 

 safer to make this assumption than to deal with a single year's increase, 

 which is an unstable quantity changing with the season. 



The current accretion of a standing tree may be conveniently 

 expressed in per cent of volume of the tree. If the increase of actual 

 volume is to be expressed, then it ought to be calculated with simple 

 interest; but if the mass of a tree is looked upon as a capital, then it is 

 proper to consider the accretions as returns on the capital represented 

 by the amount of wood and to calculate it with compound interest in 

 order to establish the expediency and profitableness of the investment. 



MASS ACCRETIOX WITH SIMPLE INTEREST. 



If the present volume of a standing tree is 115 cubic feet, and that 

 of the same tree five years ago 109 cubic feet, then 115 — 109 = 6 gives 

 the increase of volume for the last five years j the accretion for one 

 year is 1 = 1.2 cubic feet. Dividing 1.2 by 109 and multiplying the 

 quotient bj^ 100 we find the current annual accretion equals 1 per cent 

 expressed in per cent of volume. But while the present volume of the 

 tree can be easily determined by employing one of the described meth- 

 ods, the volume which the standing tree had five years ago is difficult to 

 establish. It is necessary, therefore, in order to determine the current 

 accretion of standing trees to devise a method which should not require 

 the determination of the present and past volumes of the tree. Suppose 

 a standing tree, the accretion of which we are to determine, has a basal 

 area at breast height, which we will designate for convenience sake by 

 a letter A; let the basal 'area which the tree had five years ago be «, 

 then the present and past volumes of the tree may be represented by 

 the following products: 



(1) Present volume: Base A multiplied by one-half of the height of 

 the tree. 



(2) Volume five years ago : Base a multiplied by one-half of the height 

 which the tree had five years ago. 



Suppose also that the tree is considered after it has reached its fuU- 

 height growth (a number of species reach it before 100 years of age), 

 then the height accretion for five years is comparatively small. Dis- 

 regarding this small difference, the proportion between the present and 

 past volumes of the standing tree equals the proportion which exists 

 between their basal areas A and a; in other words, the per cent of vol- 

 ume accretion is the same as that of the area accretion. The per cent 

 of the area accretion maj^ be easily determined when the diameter which 

 the tree had five years ago is established. This can be ascertained by 

 cutting out a chip or else by using an instrument — Pressler's increment 



