142 VALUATION OF THE GROWING STOCK. 



Proof. Let m G e = m G c , immediately after the thinning in 

 the year m has been made, then, 



Y r +T n xI'op r - n + . . . + r g xl-ojf- g 



= (S+E) (I'op m -l) + cxl'op m -(T a xl'op m - a +. . . 



After making the necessary reduction, it will be seen that 

 this equation can only hold good, if 



Y r +T a xl'op r - a +. . . + T,xl'op r ^-cxl'opr 

 l'op r -l 



in other words, if the expectation value of the soil is introduced 

 for 8. 



It must, however, not be overlooked that the above holds 

 good only in the case of normally stocked woods. If a wood 

 has been too thinly stocked from early youth, so that both 

 thinnings and final yield are below the normal amounts, the 

 cost value will be found to be greater than the expectation 

 value. 



5. Relation existing between the Expectation and Cost Valu.es of 

 the Growing Stock of a Normal Wood on the one hand, 

 and the Utilization Value on the other hand. 



The utilization value of the growing stock is equal to the 

 expectation, or cost value at the end of the rotation, provided 

 the maximum expectation value of the soil is introduced into 

 the account, and the rotation is that for which the expectation 

 value of the soil culminates. An equality can also occur at a 

 previous stage; according to the values introduced into the 

 account. 



Generally speaking, the utilization value of young woods is 

 smaller than the expectation, or cost value. On approaching 

 the end of the rotation the difference is small, and it is then 

 the safest plan to value the woods according to their utilization 

 value, as the calculation of the expectation and cost values is 

 based upon more or less uncertain data. 



