340 Forestry Quarterly 



If a is properly chosen, b"^ needs rarely to be more than 25 and 

 can mostly be neglected. 



This method can still be used advantageously with halves and 

 quarters and reducing the squaring of tens to squaring of units. 



E.g., 152=10x20+25 = 1x2 and 25 hungon = 225 



352=30X40+25 = 3X4 = 12 and 25 hung on= 1225 

 7.52=10X5+6.25 = 7X8+. 25 = 56.25 

 4.752 = 5 X4.5+.0625 = 22.5625 



The author then develops a number of approximation formulae, 

 which give a siire judgment as to limits and average values of 

 contents of trees of a given diameter. 



1 . The volimie of a mature tree approximates in metric measure : 



IT 



v=\QOd'^, because in such trees —h.f. is frequently = 100. 



4 



[With our foot measure, v = r^, with the same reasoning, mathe- 

 matically correct when h = 91.6, and /= .50. For different heights 

 add or subtract 10 per cent for every 10 feet.] 



For young trees and meter meastire, two approximation formulae 

 and their derivation are given with extensive explanations as to 

 their application. 



(2) v = ^Xd^or 



(3) v= 



2. To secure an estimate of the participation of the clear bole 

 in the total volume, the following consideration is given: 



If the clear bole {h^ reaches to p per cent of the total height, h, 



P 

 the volume of the clear bole v. is approximately — 



10 



per cent of the total volume (really a little larger), hence the 

 formula 



f 



P 



20- — 

 lOJ 



(4) ..=10lL_10J ^ ^^, 



^ ^ 100 100 



hence for hc=lO per cent of h, v^ = 1(20— 1) = 19% of v 



= 20 " " " " •• =2(20- 2) =39% " " 



= 30 " " " " " =3(20-3) =51% " " 



= 80 " " =8(20-8)=96% " " 



