228 THE NORMAL GROWING STOCK. 



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

 the arithmetical mean of those in spring and autumn : — 



Summer's middle Gn = nfa-fb + e4- -)• 



Exanqile. — A forest of 100 acres, to which the data given in 

 the Table at page 120 apply, worked under a rotation of 100 

 3'ears, has the following normal growing stock : — 



In autumn ^'^'G„,,„„,= 10 (100 + 600 + 1,170 + 2,830 + 3,940 



+ 4,690 + 5,250 + 5,720 + 6,100 + 



3,205) + 3,205 



= 10x33,605+3,205 = 339,225 cubic feet. 



In spring ^'''G,„,,„„^ = 10 X 33,605 - 3,205 = 332,845 cubic feet. 



In summer i""G,„„,„,„, = 10 X 33,605 =336,050 cubic feet. 



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

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



8"G„ = 10 (100 + 600 + 1,170 + 2,830 + 3,940 + 4,690 + 



5,250 + 2,860) ^ = 10 X 21,440 X "^-^ = 268,000 cubic feet, 

 80 80 



which is considerably less, than if the area is worked under a 



rotation of 100 years. 



(2.) Calridatio)! icitit tlic Mean A)iniial Incrciiiciif. — A shorter, 

 but less accurate, method of calculating the normal growing 

 stock is based upon the assumption, that the normal final 

 yield is produced in annually equal instalments ; in other 

 words, that the growing stock of the several age gradations 

 form an arithmetical series. Indicating one year's increment 

 by /, the growing stock in successive age gradations would be 

 in tlie 



Year =1.2, ;5 . . /—]./•. 



Growing- Stock = /. 2 X /, 3 X / . . (r — l) i, r i. 



and their sum 0„ = (/ + r i) = + r i X — . 



As r X i represents the growing stock of the oldest age 

 gradation and is also equal to the total increment, I, laid 



