146 VALUATION OF THE GROWING STOCK. 



. r 



-op l-op z VojfJ \l-op 



1 * op r X 'op l'op r x'op 



^ 

 l'op r x 'op 



Introducing now the other intermediate returns which occur 

 in the age gradations aged a, b, . . . their values will 

 appear in the same manner as the return which occurred in the 

 age gradation q, namely as : 



T a xl'op r - a (l'op a -l) t T b xl'op r - b (l'op b -l) 

 l'op r x 'op l'op r x 'op 



Hence, the general formula for the expectation value of the 

 normal growing stock runs thus : 



(Y r +S+E) (I'opr-l}+T a x l'op r ~ a (l'op a -l) 



Norm. Gr. ) = _ +. . - + T q x l'op r ~ q (l'op q -l) 

 Stock G e j l'op r x'op 



-r (S+E). 



Assuming that in the above formula Y r) T a . . . T q , 

 S and E are given for the unit of area, say 1 acre, then the 

 formula represents the value of the normal growing stock for 

 r acres. Consequently the normal growing stock for the unit 

 of area is : 



- ___ ( ^ 

 rxl'op r x'op 



By introducing the soil expectation value into the formulas 

 given above, and substituting its value 



S' -Yr+TqXl-op r - a +. . . + T q xl'op r - q -cxl'op r _ 



