NORMAL GROWING STOCK. 145 



1. Time of Year for which the Calculation should be made. 



The annual net return of a normal series of age gradations 

 (or a working section) forms the rental of the soil and normal 

 growing stock of that working section. Like the interest 

 yielded by any ordinary capital that rental is produced within 

 the year, so that the growing stock at the end of the year 

 represents the capital plus one year's rental. Hence, the 

 capital alone is present immediately after the year's rental 

 has been removed. At that moment the oldest age gradation 

 is (r1) years old, the next (r 2), etc., and the youngest 

 (which has just been cleared), is year old. 



Where cuttings are made in winter the normal growing 

 stock is present in spring, before the trees have commenced to 

 lay on the new annual increment. 



2. Expectation Value of the Normal Growing Stock. 



For simplicity's sake, it shall, in the first place, be assumed, 

 that only one intermediate return is obtained, in the year q ; 

 then the values of the various age gradations will be as 

 follows : 



r . lr _Y r -(S+E)(l'op*-l) 



etc. 



- 



q . lr _Y r +T q x 1-ojf-g -(S+E) (l' 

 l-opr*-* 



etc. 



or _Y r +T q xl-op r --(S+E) (1-op-^l) 

 ~ToF~ 



By adding up all these quantities the following sum is 

 obtained : 



VOL. III. L 



