372 GROWTH OF TREES IN HEIGHT 



by which this volume growth can be predicted by a study of diameter 

 growth and by the determination of the resultant volume of the tree 

 from its average height and volume as shown in a volume table. In 

 order to save the expense of determining the actual growth in height 

 of these trees, recourse is had to the relation between height and diam- 

 eter as expressed by a curve of heights based on diameter such as is 

 illustrated in Fig.~76. The process is as folows: 



1. The increase in diameter for a given period for a tree of a certain 

 diameter is predicted or determined; e.g., the tree may grow from a 

 10-inch to a 12-inch diameter. 



2. The average curve of height on diameter shows the heights of 

 a 10-inch and 12-inch tree respectively. 



3. It is then erroneously assumed that the 10-inch tree will grow 

 in height by the amount of this difference, that is, that it will have, 

 when 12 inches in diameter, the height of a 12-inch tree. The fallacy 

 of this reasoning is clearly evident when applied to any single tree or 

 to any stand of a given age. If the tree or stand is young and the curve 

 of height on diameter has been prepared for trees of this class or age 

 in the vicinity, the tree will grow much faster than the difference in 

 height indicated by this curve, and the same is true of the trees in an 

 even-aged stand. But for old or mature even-aged stands, the reverse 

 may be true and the trees may grow more slowly than the difference 

 shown. Such a curve is not a growth curve at all, but a curve showing 

 the average heights attained by trees which may be all of the same 

 age. Only when the curve of height based on diameter includes trees 

 of all ages as well as diameters, does it approach the form of a true 

 growth curve, as shown by the dotted curves in Fig. 76. To do this 

 it must harmonize two variables, namely, diameter and age. In general, 

 small trees are young trees and large trees are old trees. If sufficient 

 data have been included, covering wide enough ranges both of diameter 

 and of age, and the measurements are taken on the same site quality, 

 a rough average is obtained in which the height of a tree of given diam- 

 eter is correlated with the age of tree of the same diameter. The more 

 nearly this general result is obtained, the more reliable will be the aver- 

 age results of applying this curve in predicting the growth in height 

 through the medium of the growth in diameter to trees or stands of all 

 ages, and thus avoiding a direct study of height growth. It is obvious 

 that for special problems on specific classes, ages and stands of trees, 

 no such generalized curve should be depended upon, but a few measure- 

 ments of height growth on the trees in question will give results whose 

 accuracy justifies the expense. 



The height curve of even-aged stands is determined either from the 

 height growth of the maximum or dominant trees in the stand, or from 



