THE THEORY AND PRACTICE OF WORKING PLANS 87 



stand. Hence y^ny — (a = age). Now ny = ni (mean annual 

 na 



increment) and na = -. The average age can be determined 



2 



either by area according to the formula: 



(^= \ r ~ r ^ wherein /i, /2, /s, etc., equal the area of the 



/1+/2+/3 



various age classes and ax ao, a^, etc., equal their respective 

 average ages, or else the average age can be determined by 

 volume according to the formula: 



fl = — r wherein v^, v^, v^, etc., equal the volumes of the 



j,i 7,2 j,^ 



a^ a^ a^ 

 various age or diameter classes and a}, a~, a^, etc., their respec- 

 tive ages. 



(b) Example. — A forest of Western yellow pine containing 

 3,500,000 feet board measure of timber 12 inches and over 

 diameter breast high, on 1000 acres, is essentially uneven-aged, 

 but shows three distinct diameter classes: 12 to 18 inches, 

 average 14 inches (" Black Jacks "), and 20 inches and over, 

 average 26 inches (" yellow pines "). The volume of the former 

 is 20 per cent of the total, or 700,000 feet board measure, the 

 volume of the latter is 80 per cent of the total, or 2,800,000 

 feet board measure. The average age of a 14-inch " Black Jack " 

 is 70.5 years, of a 26-inch ''yellow pine" 285 years. ^ Then 

 by the formula, 



v^-\-v^ 700,000+2,800,000 ^,i;oo,ooo , 



a = — — -=- — — — = — "^^ — — -—- = 176 years. 



v^ ir 700,000 2,800,000 10,000+9,818 



a^ a^ 70 285 



' The adopted rotation is, however, only 200 years, hence 



na = -= — = 100. The mean annual increment is placed at 



2 2 



0.7 per cent, or 24,500 feet board measure. By the formula 



* From Table 9, Bulletin loi, Forest Service, U. S. Dept. of Agric. 



