200 THE FORM OF TREES AND TAPER TABLES 



From these plotted forms of trees the diameters at any desired point or height 

 on the boles can be read. 



The nature of these original averages is shown in Fig. 32 in which four single 

 trees of different D.B.H., 14.4 inches, 17.7 inches, 19.4 inches, and 21 inches, but 

 falling in the same height class, 90 feet, are plotted. The eccentricities of form 

 in this table are partly due to branches, partly to failure to obtain the true average 

 diameter at each point, and partly to the natural variations in form for individual 

 trees. 



As in the preparation of volume tables, the averages obtained from a number 

 of trees are more consistent than the forms of single trees. A graph plotted in 

 this manner from averaged upper diameters instead of single trees, will be fairly 

 regular in the relation of the curves for successive D.B.H. classes and will resemble 

 Fig. 35, p. 204. 



When, as is sometimes the case, the upper diameters are measured 

 on logs as cut by the saw crews, in irregular, lengths, and hence fall at 

 different heights above the stump, only the measurements falling at 

 the same height can be averaged, as at 12, 14, 16, 18 and 20 feet. This 

 will be done, and all of the resultant upper diameters for trees of a given 

 D.B.H. and height class will be plotted, to obtain the curve of average 

 form. From this curve, the desired upper diameters at regular inter- 

 vals of 8 or 10 feet can be read. 



These curves of form are not in final shape for a standard table of form. Although 

 the averages are improved by the use of larger numbers of trees, the values will 

 be slightly irregular for two reasons. The average D.B.H. may be larger or 

 smaller than the exact inch class desired, and the forms of the average trees of the 

 consecutive D.B.H. classes may vary in fullness. These two sources of variation 

 are- well shown in Fig. 32. There -is no reason why average 21-inch and 18-inch 

 trees should have a fuller form than 19-inch trees. 



Values required are based on exact D.B.H. classes, and vary regularly with 

 D.B.H., as would be the case were sufficient trees included in the mechanical 

 average. 



.Second Set of Curves, Tapers Based on D.B.H. For trees of each 

 successive D.B.H. class which have the same total height and the same 

 general form, the diameters at each given height on the boles will 

 diminish in direct proportion with diminishing D.B.H. If D.B.H. is 

 then taken as the independent variable in a second set of curves, and 

 upper diameters plotted on D.B.H. as the dependent variable, the 

 form of these new curves approaches straight lines as did those of volume 

 based on height (§ 141), and the irregularities between the forms or 

 upper diameters of different average trees are easily reduced. In this 

 second operation as in the 'first, the trees of a given height class form 

 the basis for a set of curves; e.g., 90-foot trees only are included in the 

 one set of taper curves, separate sets being required for 70-foot or 80-foot 

 trees. For this set of curves the same scale can be used for both vari- 

 ables, e.g., 2 inches =1 inch. 



