382 GROWTH OF TREES IN VOLUME 



only diameter based on age, it is necessary to indicate upon the curves 

 the height which each curve represents. 



This series of curves can be used only to determine the diameters 

 at the definite points, as 8, 16, 24 feet, etc., for which curves have been 

 drawn. It corresponds with Fig. 32 (§ 168) for taper curves. To 

 obtain the growth in form for the tree at intervening points, these 

 curves should be replotted in the form shown for a single tree, in Fig. 80. 



From the average tree thus shown, the growth by decades in any 

 form or length of product can be directly computed, to any required 

 diameter limit. 1 



292. Substitution of Taper Tables for Tree Analyses. Just as the 

 above method substitutes the form of the average tree at different 

 ages for the direct calculation of the volume at these ages, so it is pos- 

 sible to go one step further and to substitute the entire form or taper 

 of trees of different diameters, heights and ages, just as was done in 

 Fig. 70 on the curve of stump diameter growth, for D.B.H. and top 

 of first log. To make this substitution, the diameter and height of 

 average trees are first determined for each decade in age. Second, 

 from a table of average tapers, the form or taper of trees of the cor- 

 responding diameters and heights are taken. This may be done by 

 interpolation in case the required diameter or height falls between 

 inch diameter classes or 5- to 10-foot height divisions expressed in taper 

 table. The tapers thus borrowed are assumed to be those of the tree 

 at the different ages. 



This method has the same advantages and drawbacks as the sub- 

 stitution of the volumes from a volume table for the actual volume 

 of sample trees as described in § 242. The average tapers are taken 

 in most instances from a much larger number of trees than could be 

 analyzed for form at the different decades of their growth. These 

 tapers therefore probably represent quite closely the average form of 

 the tree of these sizes and ages. On the other hand, this average, just 

 as for volumes, may depart from the actual average of the trees to be 

 measured in case the data do not coincide in origin and the trees differ 

 in average form quotient. 



The best check upon the accuracy of substitution of taper tables 

 for tree analyses is to test the form quotient both of the taper tables 

 and of the trees desired. A considerable departure in this form quotient 

 indicates that the tapers do not represent the average sought. 



1 This method of graphic plotting of average growth in diameter at eaeh upper 

 section was devised by A. J. Mlodjiansky (Measuring the Forest Crop, (Jul. 

 No. 20, Division of Forestry, U. S. Dept. Agr., 1898). The method of assembling 

 all the curves on the same sheet was devised by H. S. Graves (Forest Mensura- 

 tion, 1906, p. 295). 



