. American forest regulation. Forestry law and legislation; Forests and forestry. The Normal Forest 6i. Fig. 3(a) Proof of Wolfif Formula. Assume the triangle DBC represents the total normal growing stock on any tract includ- ing all merchantable and unmerchantable (nonestimable) sized stands, DC being equal to the rotation age (r), and BC being equal to the mean annual increment (I) of the whole acreage. "V can be more definitely expressed as the mean annual increment per acre (i). times the rotation age (r) multiplied by the total acreage (A) divided by (r). I = (iXr)X '^. As'^ume also
. American forest regulation. Forestry law and legislation; Forests and forestry. The Normal Forest 6i. Fig. 3(a) Proof of Wolfif Formula. Assume the triangle DBC represents the total normal growing stock on any tract includ- ing all merchantable and unmerchantable (nonestimable) sized stands, DC being equal to the rotation age (r), and BC being equal to the mean annual increment (I) of the whole acreage. "V can be more definitely expressed as the mean annual increment per acre (i). times the rotation age (r) multiplied by the total acreage (A) divided by (r). I = (iXr)X '^. As'^ume also that DH represents the merchantable age (s), and that FH is the volume at that age (F) of the annual acreage to be cut over. Volumes below this age are not estimated. Moore recommends that properly, the normal stock should be figured as 1 (r-s) in the figure above to BCXHC. Diagrammatically this is equal to the triangle BCH. This assumes that volumes at merchantable age commence at zero. But really the volume at the minimum estimateable age is appreciable. It is theo- retically the mean annual growth times the number of years. Thus in our figure the normal growing stock above merchantable age (call it GN for convenience) is the quadrilateral (A trapezoid) FB CH. Hence Moore's suggested formula excludes tri- angle FBH and gives by that much, too low a figure. To obtain the correct and most convenient formula for normal growing stock above merchantable age, it is necessary to find the value of the area FBCH, in terms of T, r, and s. I = BC; r = DC, and s = DH. (i) FBCH _FH + BC XHC = I>tI-Xr- (2) F:s::I:r; (3) Substituting for F in (i) F I ,, or = ; or 1 = s r + 1 FBCH 2 Is-t-Ir X (r —s) -Xfr-s). Please note that these images are extracted from scanned page images that may have been digitally enhanced for readability - coloration and appearance of these illustrations may not perfectly resemble the original Woolsey, Theodore Salisbury, 1879-1933; Chapman, Herman Haupt,
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