THE THEORY AND PRACTICE OF WORKING PLANS 79 



given in the table for each age class, n the number of years in 



each of the age classes, and m the volume at the rotation age. 



V — nV 



The main formula then follows: ^(annual cut)=i-\ . 



r 



Here again i is the actual mean annual increment, not the normal.* 



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



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



inches diameter breast high and over on 1000 acres. The 



actual mean annual increment is assumed as 0.7 per cent, 



or 24,500 feet board measure; the rotation as two hundred years. 



rr^l 1 • 4. 1 ^^' 200X24,500 ^ ^ 



The normal growmg stock —^ ^^-^ — = 2,450,000 feet 



2 2 



board measure. The annual cut (y) then =zH = 24,500 



, ^,1:00,000—2,450,000 , 1,050,000 



_^,30 ^io_^ = 24,500+-^^ = 24.500+5250 



200 200 



= 29,750 feet board measure. In this case there appears to be 



an excess growing stock. Adopting Mr. Moore's variation (see 



footnote), the result would be: 



TVT 1 • .u 1 ^'^ 140X24,^00 J. ^ 



Normal growing stock = — =—^ -^^ — =1,715,000 feet 



board measure. 



rr-i 1 . / \ • , V — nV , 3,^00,000—1,715,000 



The annual cut {y)^i^ = 24,500+^^^^ — '-^-^^ — 



r 200 



= 24,500 + 17,850 = 42,350 feet board measure. 



This, however, is not strictly accurate, due to the failure to 

 consider the increment per acre of young growth. " If the area 

 of young growth below merchantable size is known, the incre- 

 ment can be found by determining the number of merchantable 

 trees per acre which there would be if the stand were about 

 normally stocked and contained no other age classes. The 

 volume of such a stand divided by the average age of merchant- 



* There has been some dispute about this, but the matter seems settled by 

 the authoritative pronouncement of Judeich, " Forsteinrichtung," 6th Edition, 

 p. 360, and Martin, " Forsteinrichtung," pp. 216-217. 



