THE THEORY AND PRACTICE OF WORKING PLANS 83 



a density of .85 this would = an actual increment of 1.2X.85 

 = 1.02 or, roughly i per cent.) 



The annual cut by the formula then =?± ;; — T( — - — ]n 



A \ A j 



000 + 3^500-000 — 2,450,000 _ A 5, 000 - 42,ooo \ 



^^' 50 V 50 / ^ 



35, ooo-f 21,000+ (140)5 = 56,700 feet board measure equals 

 annual cut. 



Adopting Mr. Moore's variation of / instead of r in de- 

 veloping nV (see No. 5), wF= 1,715,000 feet' board measure. 



V — fiV I i — Tii/K 

 The annual cut then equals i± — - — =F( — -— )w = 35,ooo+ 



^,500,000 — 1,71s, 000 /^c:,ooo — 42,ooo\ 



'-^ -^ {^-^ ^ )5 = 35.000 + 35.700 



+ 700 = 71,400 feet board measure equals annual cut. 



Calculating the increment on the area of young growth, as 



was done under No. 5, the result would be: for nV, 2,001,650 



V — nV 

 feet board measure. The annual cut then equals z± — T 



i — m 



\ A r^~35'Ooo+4,o95 (the mean annual increment on the 



unmerchantable young growth, conservative since less than 



■, ^ , . ^x , 3,500,000 — 2,001,650 

 the current annual mcrement) + ^^-^ —'^ — 



50 

 /^ 5,000 — 42,ooo\ , , ^ , ^ 



\^ 7^ ) 5 = 35,000 + 4,095 + 29,967 + 700 = 69, 



762 feet board measure equals annual cut. 



(c) Value and Application.— Karl's method, which dates 

 from 1838, shows an advantage over the Austrian formula in so 

 far as it uses the current annual instead of the mean annual 

 increment, and in that it distributes the excess or deficit over a 

 period adapted to local conditions instead of arbitrarily over the 

 whole rotation. However, it is incorrect in making the third 



(1 — flt\ 

 — - — jn always bear a sign opposite that of the 



V-nV . 

 expression — - — directly preceding it. This would presume 



