FACTORS OF FOREST PRODUCTION. 129 



which may be cut ; and if reproduced as cut, the 

 continuity of similar harvests is assured. 



If we call the annual increment of any one stand 

 i, and instead of the one hundred years substi- 

 tute the general term of years r (rotation), the 

 capital stock is the sum of the arithmetic series 

 z + 2 / + 3 2 . . . + ri which, according to well- 

 known mathematical laws, is - x (ri -\- i) ; or, since 

 2 



/ is relatively quite small, it may be neglected, and 

 if we substitute for ri = I, i.e. the annual increment 



of all the stands, the form becomes -/, or in other 



2 



words the capital stock of wood which must be 

 maintained is the increment occurring on the whole 

 forest through half the rotation. It stands to rea- 

 son that, with every species and every soil, as well 

 as with every rotation and system of management, 

 the amount of / changes, and hence the capital 

 stock required. 



It is evident that, for instance, in coppice forest, 

 sprout lands, which are usually managed in rota- 

 tions of not over twenty to forty years, the wood 

 capital is much smaller than in timber forest, which 

 requires from sixty to one hundred and twenty 

 years and more to become mature. 



Merely to give an idea of the relative amounts 

 which different conditions may require, we will 

 assume that 70 cubic feet of wood per acre repre- 

 sents the annual increment, then a coppice of 100 



