49 



This fornmla is only approximate, and always gives sometbing 

 less than the actnal vahie of r. 



"We will now apply the preceding principles to the determina- 

 tion of percentages for the increase of (a) the diameter, (5) the 

 sectional area of tlie stem, and (c) the volnme. 



(a) Fercentage of increase in diameler. — According to what 



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



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

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

 upwards alon^ the stem. 



(6) Percentage of increase of sectional area of item. — This 

 percentage 



_ A— a ^ 200 

 A + a » 



_"4" 4 200 _ L*—d? 200 . 



4 4, 



We may also obtain this percentage {p, ) in terms of the. 



percentage of diametral increment {j)d ) thos — 



d 100 , a 100 



~ and — = 



D mo +pi A liiO+pa 



100 a d» ■ 100* 



Hence 



that is to say, 



100+j>a A JJ' 10G«+200j»i+/,j*' 

 100 100 



100+p„ 100 + ipi+p'i 

 lUO 



and Pa = ZPd + j^» • 



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



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



J)-d ^ 400 



Pa = ipd = 7- — J X . 



D + d n 



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



described under sab-article C. above, it is obvious that, if h is 



constant, the required percentage 



A-^a ^ 200 D—d 40O 



= —^ — X — =_ X . 



A-^a n ll-^d » 



