II] 



FIRST PRINCIPLES 



year over the whole twenty sub-divisions of the area. We can 

 now see the relation which necessarily exists between the incre- 

 ment and the growing stock. If the whole area were stocked 

 with growth of 20 years of age, the volume of the wood-capital 

 would be represented by the rectangle ABCD, so that our 

 present normal wood-capital, represented graphically by the 

 triangle ABC, is equal to one half the increment during the 

 whole rotation over the whole area, or, in other words, it is equal 

 to the average annual increment over the whole area during half 

 the number of 'years in the rotation. 



Growth 



E A 



r 



20 years 



15 years 



10 years 



5 years 



C Areas. F B 



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 



This essential relation may also be demonstrated in another 

 way. In our example the growing stock is composed of the sum 

 of an arithmetical series of crops of equal area aged I, 2, 3, etc. 

 years up to 20 years old. Then if the average annual increment, 

 or production of cubic feet of wood, over the whole area, be 

 indicated by /, and the rotation be indicated by r the wood- 

 capital is equal to - x (1+2+3 + ... + r ) 



I r.(r+i) T r 



= - x = / x - approximately. 



t t* 



The normal growing stock is therefore equal to half the accretion 

 taking place throughout the rotation over the whole area, the 

 other half furnishing the yield during this time. 



