14-0 VALUATION OF THE GROWING STOCK. 



The sale value of very young woods, under condition b, is 

 generally negative, until the receipts obtained by the sale of 

 the produce cover the cost of harvesting ; from that period it 

 becomes positive, rising at first slowly, then more rapidly, 

 reaching its maximum value far beyond the period at which 

 the mean annual increment culminates, in fact not until the 

 annual increase in the value per unit of measurement is no 

 longer sufficient to cover the falling off caused by thinning or 

 decay. This period occurs, generally speaking, earlier in the 

 case of light-demanding species, than in the case of shade- 

 bearing species, which maintain a full stocking for a longer 

 space of time. 



4. Relation cxi^tiiKj heticeen the Expectation and Cost Values 

 of tlie Growing Stock of a Normal Wood. 



Looking at the formulae for the expectation and cost values, 

 it will be observed, that the rental of the soil and annual 

 expenses appear in the negatvie form in the one and in the 

 positive form in the other ; again, the thinnings appear posi- 

 tive in the first and negative in the second. It follows, that 

 any change in these items affects the two values in opposite 

 directions ; what raises the one value reduces the other, and 

 vice versa. Nevertheless, the one value can become equal to 

 the other. This is the case, other items remaining the same 

 in both instances, if the calculation is made in either case 

 with the expectation value of the soil. 



Proof. — Let '"'G^ = '"G,, immediately after the thinning in 

 the year m has been made, then, 



y, + T,, X I'Oir" + • . ■ + ^^; X i-Op'-" - {S -f E) (i-Qy>'-"' - p 



= {S + E) (l-O;/" - 1) + *' X I'Op"' - {1\, X 1-Oy/"-" + . . . 



+ 1\ X 1-0^/"' + TJ. 

 After making the necessary reduction, it will be seen, that 

 this equation can hold good only, if — 



^ ^ F, + 2\, X 1-0//'" + . . . + '/; X l-Oi/~" - ^ X 1-Qi> '_j^- . 

 l-Ojj' - 1 



