82 THE THEORY AND PRACTICE OF WORKING PLANS 



of years which have elapsed since the estimates were made. In 

 the first year n = 0, and hence the entire expression = 0. In 

 consequence of the increase of n the annual cut would really 

 have to be redetermined each year, but, for convenience, Karl 

 presupposes the adoption of ten-year periods and makes 

 w = 5, i.e., the middle of the ten-year period during which 

 the annual cut is to be equal. At the end of the ten-year period 

 a revision of the cut takes place. 



This third expression of the formula is always given the sign 

 opposite that of the preceding expression. 



The entire formula is therefore: 



f , ,v . , V-nV^(i-ni\ 

 y (annual cut) =«zh — T( — - — \n. 



In addition a simple plan of cutting (distribution of cut) is 

 drawn up as a guide in the management of the forest. How- 

 ever, this plan of cutting plays no part in the determination of 

 the cut, which is by formula alone. 



(b) Example. — An uneven-aged forest of Western yellow 

 pine contains 3,500,000 feet board measure of timber 12 inches 

 and over diameter breast high, on 1000 acres. The actual 

 mean annual increment is assumed at .7 per cent, the rotation 



at 200 years. nV then = — = 2,450,000 feet board measure.* 



A, the period of distribution, is assumed as one-quarter of the 

 rotation, or fifty years. f i, the actual current annual incre- 

 ment, is averaged (see Method No. 4) for the whole stand 

 and, reduced for the density of stocking, is assumed as = i 

 per cent or, in volume, =35,000 feet board measure. The 

 normal current annual increment is obtained from fully stocked 

 sample plots (or from yield tables in even-aged stands), and is 

 assumed as 1.2 per cent, or 42,000 feet board measure. (With 



* It can also, in even-age stands, be calculated from yield table (see Method 

 No. s). 



t This period of distribution is chosen according to local exigencies; it had 

 best be somewhat longer than seems necessary, in order to avoid possible errors 

 and to remain on the side of conservatism. 



