162 THE FINANCIAL RESULTS OF FORESTRY. 



h. Calculation for the Annual Working. 



Under the annual working, with equal annual increment, 

 3'ield, and costs, the current annual forest per cent, is equal to 

 the mean annual forest per cent. In this case, the annual net 

 return of r units of area amounts to — 



r, + 7',, + . . . + 7', - c - r X e, 

 and the producing capital to — 



r X N.. + r X ""™""G, ; 

 hence — 



..„. r + 7'+ +7:,-<.-,-x^ X 100. 



■" )■ X S,+ r X "<i, 



■^ c 



By multi[)lying and dividing the enumerator in this formula 

 by 'Op, the following is obtained : — 



C^-^^^+'-y-^-'-^Q xioox- o. 



'-'Pf = ^ 77 ' 



or, as the part in brackets is equal to the expectation value of 

 the forest = F^ : — 



mean p ^ ^e >< p_ 



This formula is identical with that obtained above for the 

 profit = Fe- F, : 



If F,>i*',,then'"'""j>^>;,. 



If F^ = F„ then """"p^ = p. 



The highest mean annual forest per cent, under the annual 

 working is obtained for that rotation, under which the expecta- 

 tion value of the forest reaches its maximum ; in the above 

 example, about 80 years. 



