94 DETERMINATION OF THE INCREMENT. 



If, on the other hand, t = w, but the second tree had only 

 a volume v a ' in the year , then the increments of the two 

 trees may be assumed to bear the same proportion as the 

 volumes, or: 



,,. . '_ T T ' Qr ,;i 7" T ' V Va (vf _ ti' \ V ^ a 

 v a l a l n *-n ana * = * x / \ v a+n v a) X 



V a V a 



Now: 



*W = a + T X V a - V a = V a+n X 



Va v a 



or 



^a+ v a = V a+n ' ^a > 



in words : the proportion which exists between the volumes of 

 the second tree n years ago and now, holds good also as regards 

 the volumes of the first tree now and n years hence. 



If both, the ages and volumes, differ, it may again be 

 assumed that the increments of the two trees show the same 

 proportion as the volumes. In that case : 



V a - v a = In Of V a : I n of V a ' 



And 



All these calculations assume that the increment of n years 

 has been laid on in annually equal quantities, which is only 

 approximately correct. The degree of accuracy depends on 

 the length of the time n, and the differences between n and t 

 and between v a and v' a . 



This method of calculating the volume of a single tree is 

 so complicated, that it is not used in practice ; it has been 



