370 



GROWTH OF TREES IN HEIGHT 



Graphic Method. In averaging together the data for height growth on the basis 

 of age, it is evident that few if any points will fall at the same age, even if taken 

 at the same height above ground. For this reason, the most convenient method of 

 determining an- average rate of height growth based on age is to plot the original 

 data for each tree, and draw a curve based on ocular inspection of the result assisted 

 by weighting the points or calculating the position of the average point if the data 

 are not sufficiently abundant to dispense with this step. In this graph, age is placed 

 on the horizontal scale and height in feet on the vertical scale. 



It is not practicable to determine the arithmetical average height at each separate 

 age previous to plotting the data. This is best done from the graph. The height 

 growth of ten trees, which were sectioned at 8-foot intervals above the stump 

 is shown in Fig. 78. Stump height is omitted. The heights at each 8-foot section 

 fall on the same horizontal line, i.e., have the same ordinate. The total or final 

 heights represent the height of the tree. 



Two methods of averaging the data are shown. By the first, all points falling 

 in the same decade are averaged for the points marked O . The number of points 

 used is indicated at base of Fig. 78. This method is based on age, but in some decades 

 the same tree enters twice while in others it does not appear. The depression of the 



curve at final decade is caused by 

 the dropping out of eight of the ten 

 trees, from the average. 



The second method is to aver- 

 age the age at each 8-foot point. 

 This average, marked ®, is then 

 based not on age but on height, but 

 is plotted on age. Since all ten trees 

 enter this average at each of three 

 points, the curve is more regular 

 than the first. There is not the 

 same objection to interchanging the 

 basis of this curve between age and 

 height as outlined above, as there 

 is in studying diameter growth, 

 since the rate of height growth 

 has been shown to be more con- 

 sistently a function of age and vice 

 versa, for the same quality of site, 

 while for diameter growth two or 



<&*• 



Fig. 79. — Method of correcting curve of height 

 growth based on stump, by adding height 

 and age of seedling, thus giving height 

 growth of tree based on its total age. 



more additional variables influence the rate of growth (§ 296 and § 270). 



The height growth, as read from the above curve, may be shown in a table based 

 on total age and height of tree, by adding average stump height (of 1 foot), and seed- 

 ling age (of 2 years) to the curve, and reading the corrected values from the pro- 

 longed curve, as shown in Fig. 79. 



The values, read for even decades are given in Table LVII : ' 



1 The averaging of the above data to obtain the weighted average points may be 

 simplified, after the points are plotted, by the following method. For the first 

 decade, average heights include 7 trees, each 8 feet or points above the base of the 

 graph, or " up " and 1 tree 16 feet " up " or a total of 72 points " up"; average for 

 8 trees, 9 points " up." Average age includes 3 trees 4 years or points to right of 

 the left margin of the graph, or " over," 2 trees 5 years " over," 1 tree 6 years 1 

 tree 7 years and 1 tree 8 years, a total of 43 years, average 5.4 points " over.'' These 



