COMPUTING VOLUMES IN PERIOD ALLOTMENT 433 



following fall) the average growth at the rate shown in the yield table 

 for the first decade — yy — = 85 years will take place on the entire 



acreage, while the rate shown by the yield table at 2 =125 years 



will take the place on only one-fourth the area since, when the last 

 decade starts, the area will be three-fourths cut over. It is, therefore, 

 logical to weight the yield results as they will apply in practice. This 

 is simply done by the formula. Plot any series of mean annual growths 

 computed from a yield table and the possible disadvantage of using 

 "half the growth," or the "middle of the period" method is evident, 

 because it gives equal weight to the growth at the end of the period 

 ^^dth that prevaiHng at the beginning; or the "middle of the period" 

 yield may not be the average. It incorrectly presupposes that the 

 growth applied to the stock during the period is a straight line. The 

 error may he large or entirely eliminated according to the regularity and 

 trend of the curve of mean annual growth of the yield table. The "middle 

 of the period' ' method is simpler and as accurate as this "half the growth' ' 

 method, but in theory both are inferior to the weighted yield table 

 formula cited above when long periods are used. This weighted formula 

 principle may be applied even more exactly by taking into consideration 

 the exact acreage cut over each decade of the period, and weighted 

 accordingly ; such a detailed computation is not necessary. 



For the purpose of illustration take the computation of compart- 

 ment 1 (19 acres) already cited. After shifting to the third period the 

 volimie according to the "middle of period" method is 134,710 cubic feet 

 (7,090X19=134,710). Had the "half the growth" method been used 

 the result would have equaled 134,330, but a more tedious computation is 



involved. (6,840X 19) = 129,960+ (7,300-6,840 = ^X 19) = 134,330.) 



There can be no question which is the preferred method. 



But suppose that periods of unequal length were advisable. We 

 will assume a period of 40 years, yield table as cited, ^ that the timber is 

 80 years of age at the initial year of the period, and that the timber to 

 be cut over during the period comprises 10,000 acres. The results by 



See column G, page 356, Schlich's Manual of Forestry (Fourth Edition), Vol. III. 



