The Sciences Underlying Forestry. 31 



value production, the largest "forest rent," or the largest "soil 

 rent" may be the aim. 



In either case a complicated measurement and calculations are 

 required to form the basis. If we follow the principle of highest 

 volume production it is only necessary that actual volumes pro- 

 duced in different periods of time be known, in order to choose 

 that time when volume divided by years of its production be at 

 its maximum, that is, when the average annual accretion cul- 

 minates, and this we know occurs by an interesting mathematical 

 law when it has become equal to the current accretion. If we 

 express these relations in percentage, we find the interesting 



formula for the current accretion per cent. — -7-, in which d is 



the average diameter of a representative number of trees, and n 

 the number of annual rings for one inch which these trees have 

 formed on the average during the period of growth just finished. 

 We have also the remarkable mathematical discovery that aver- 

 age accretion per cent, culminates when it is equal to , in 



which a is the age of the stand. And as this culmination occurs 



when it is equal to the current accretion, we have the equation 



400 100 , . . , , . , r 



— t — , irom which we determine a, the age of maximum 



forest production = — . 

 4 

 If maximum value production is looked for, matters become 



more complicated, for with change in the size of logs, which 

 make up the volume, their value changes because more useful 

 material can be cut from them, the percentage of waste being 

 reduced. 



Finally, if we begin to calculate on the capital of soil and 

 standing timber, which is involved in accumulating volume and 

 in the production of value, and try to secure an adequate interest 

 return, compounding, of course, since neither these capitals, es- 

 pecially the wood capital, nor the wood interest can be withdrawn 

 until the long distant harvest time — we come into forest finance 

 calculation, a mathematical branch which has been more highly 

 developed than such calculations in any other business excepting 

 perhaps life insurance, with formulas which are unfamiliar to the 

 average mathematician. 



