234 THE NORMAL GROWING STOCK. 



assumed that one half of the annual increment has been laid 

 on ; in other words that the growing stock is then equal to the 

 arithmetical mean of those in spring and autumn : 



Example.-~A. forest of 100 acres, to which the data given in 

 the Table at page 190 apply, worked under a rotation of 

 100 years, has the following normal growing stock : 



In autumn m G n = 10 (510 + 1290 + 2140 + 2900 + 3530 + 4060 



+ 4530 + 4950 + 5300 + 2790) + 2790 = 

 10x32000+2790 = 322,790 cubic feet. 

 Tn spring m G n = 10 x 32000-2790 = 317,210 

 In summer m G a = 10 X 32000 = 320,000 



The same forest, if worked under a rotation of 80 years, 

 would, for. summer, have the following growing stock : 



"0> 



10 (510+1290 + 2140 + 2900 + 3530+4060 + 4530 + 2475) 



80 



100 



= 214,350 X ~ = 267,937 cubic feet, which is considerably less 

 80 



than if the area is worked under a rotation of 100 years. 



(2) Calculation with the Mean Annual Increment. Assuming 

 that the current annual increment is the same throughout 

 the rotation and equal to the final mean annual increment, 

 then the volumes of all normally stocked gradations, from the 

 youngest to that r years old, would form an ascending 

 arithmetical series, the sum total of which would represent 

 the normal growing stock. 



Let i = volume of the 1 year old gradation, then 



2 x i 2 years 



* 



,, I* X 1 = ,, ,, T ,, ,, ,, ,, 



and the sum of all gradation is : 



