84 THE THEORY AND PRACTICE OF WORKING PLANS 



that an increase or decrease of the actual growing stock is 

 always followed by an increase or decrease in the actual current 

 annual increment. But the exact opposite can happen, e.g., 

 if overmature stands are replaced by thrifty young growth or 

 if, contrariwise, the overmature stock is allowed to accumulate. 

 Karl's error probably arose through considering the volume of a 

 forest's growing stock as comparable to a sum of money which 

 bears more interest as it increases in size. Judeich * therefore 



— — jw not only incorrect, 

 but unnecessary in view of the ten-year revisions; which would 

 reduce the formula to y = i± — - — and would make the values 

 in the above three examples 56,000, 70,700, and 69,062 feet 

 board measure respectively, the expression I— —~jn = yoo fall- 

 ing away in each case. The only remaining difference between 

 Karl's formula and the Austrian formula is, then, the use of 

 current instead of mean annual increment and of a suitable 

 period for distributing the surplus or deficit — fifty years in this 

 case. There seems to be no reason why the latter modifica- 

 tion can not be applied directly to the Austrian formula (No. 5) 



so that it reads: y = i-\ — ,t whereupon the values in 



three examples under (5) would become: 



(i) 24,500+^^500,000-2^450,000^^^^^^^ ^^^^^ ^^^^^ ^^^^^^^^ 

 50 



(2) 24,500 -h ^'5°^^°°°~''^'5'°°° = 6o,2oo feet, board measure. 



50 



(3) ,8,595 -t- ^'5^°'°°^~"'°°^'^5° -58,562 feet, board measure. 



* Lorey's " Handbuch der Forstwissenschaft," 2d Ed., Vol. Ill, pp. 421-2. 



t This is Heyer's formula as given by Martin's " Die Forsteinrichtung," 

 2d Ed., p. 67, but Judeich, who made a special study of this point, considers 

 it as under 9 below, and his precedent has been followed, although the results 

 are exactly identical. (See example under No. 9.) 



