49 



This formula is only approximate, and always gives something 

 less than the actual value of r. 



We will now apply the preceding principles to the determina- 

 tion of percentages for the increase of (a) the diameter, (b) the 

 sectional area of the stem, and (c) the volume. ' 



(a) Percentage of increase in diameter. According to what 



,, . D d 200 ,. 



precedes, this percentage = ^ - x for any given section. 



JJ -\- d n 



The figure thus obtained cannot be applied to any other section, 

 since, as we know, the increment generally increases as we proceed 

 upwards along the stem. 



(b) Percentage of increase of sectional area of ttem. This 

 percentage 



Aa 200 



J\ * 



A + a n 



~ 



200 D'd* 200 



X - V _ 



a O . r* 







We may also obtain this percentage (p a ) in terms of the 

 percentage of diametral increment ( p& ) thus 



d 100 , a 100 



and -7 = 



D 100-fjh A 100+* 



100 a d* 100* 



M onPP _^^_ ~~ - r^* i ^^? , - 



A l>* 



100 100 



that is to say, 



luo 



a 



and J"a = 2^+ g*. 



In the case of rather old trees, the diameter increment of which 



2 



is very small, y-^- may be neglected, and then we have 



'D-d 400 



(c). Percentage of increase in volume. In using method II., 

 described under sub-article C. above, it is obvious that, if k it 

 constant, the required percentage 



A a 200 D d 400 



** ~< 



