48 COMMERCIAL EXPLOITABILITT. 



words, the periodic receipts, cease to keep pace with the rapid 

 accumulation of compound interest. Commercial Exploitability is 

 thus always reached at an early age; and the higher the rate of 

 interest required from the forest property is, the earlier will be 

 fchis age. 



In the case of solitary trees, as for instance coppice standards, the 

 /elation between capital and income is still more complex. For 

 here of course the area required by any such tree is an unknown 

 and variable quantity ; and not only does the spread of the crown 

 change as it develops, but the isolated condition itself of the tree is 

 the main effective cause of the resulting rapid increase in girth and 

 value. Thus, not having a sufficient number of terms to find this 

 unknown, we are perforce limited t6 comparing the receipts that 

 can be obtained at various ages. If the money value v of the stand- 

 ing crop rises to F in k years, the rate r at which this increase has 

 taken place is found from the equation. 



c{l+r)Lv. 



Used with judgment and due attention to error, this formula 

 will give correct results. The rate r is not of course the rate of 

 interest on capital, but that at which the receipts actually realisable 

 have increased during it years. From the moment the young shoot 

 is isolated by the exploitation of the surrounding copse, that rate 

 becomes of necessity higher than the ordinary rate of interest yielded 

 by forest property, for otherwise there would be no advantage in 

 reserving the shoot. It is only when the former rate falls to the 

 same figure as the other, that the object sought in maintaining the 

 standard is fully attained and the standard becomes exploitable. 



It is an ascertained fact that isolated trees increase more rapidly 

 in size than trees growing in leaf-canopy. The standards of a copse 

 are moreover selected from among the most promising individuals of 

 the copse and belong to the valuable species, the price of the 

 timber of which may rise considerably in proportion to diameter. As 

 a consequence of this twofold increase of size and price, the resulting 

 receipts are occasionally for a very long period in excess of the 

 increase calculated at compound interest. It thus happens, and 

 oftener than we imagine, that the Commercial Exploitability of 

 isolated trees is not attained until the ;ige of 1 00 years, if the custom- 



