SUBSTITUTING AVERAGE GROWTH IN FORM OR TAPERS 379 



for the entire section concealing the tip; e.g., in Fig. 80 the third sec- 

 tion took 24—17 = 7 years to grow 8 feet. The tip contains 4 rings, 

 or 4 years' growth. Hence its height is f of 8 feet = 4.5 feet. For the 

 second section the period required was 31 — 24 = 7 years. The tip 

 has 1 ring, hence its height is \ of 8 ft. or 1.1 ft. or 



/ Age of tip \ 



Length of tip = I =; : \ — : — I Length of section. 



\ Years to grow length of section/ 



The age of any one tree will probably fall at an odd year instead 

 of an even decade and the age of the average tree whose volume is 

 calculated will fall on one of these odd years; e.g., for the chestnut 

 oak above analyzed which took 2 years to grow to stump height, the 

 table and figures above will show the age of a tree 8, 18, 28 and 38 years 

 in age. To find the volume of the tree at even decades, as 10, 20, 30 

 years instead of odd years, the volumes as determined are now plotted 

 on cross-section paper on which age is placed on the horizontal scale 

 and volume on the vertical scale. From these curves the volumes 

 for even decades can be read. By averaging these volumes on the 

 basis of age the average growth in volume is obtained for all the trees 

 analyzed. 



291. Method of Substituting Average Growth in Form or Tapers, 

 for Volume. The taper measurements or diameters determined from 

 Fig. 80 thus enable one to ascertain the volume of the tree at different 

 ages expressed in any unit. In this it does not differ from taper tables 

 disoussed in § 167 except that age is now the basis of the dimen- 

 sions shown. 



The advantage of recording the tapers for the individual tree rather 

 than its separate volumes at different ages applies equally to the average 

 of a number of trees analyzed for volume growth. For this reason 

 the method of computing volumes directly for each tree has given way 

 entirely to the method described below by which the average tapers 

 or dimensions of all of the trees studied are first determined. From 

 the average tree thus plotted, the volumes can then be found for any 

 of the desired units, such as cubic feet, board feet in any given log 

 rule, standard ties or poles, for each age or decade. This method 

 reduces the work of computing volumes to a single average tree for 

 each tree class. 



The first requirement of this method is a curve of average growth 

 in height based on age (§ 284). This establishes the year or age in the 

 life of the tree at which the diameter growth of each upper section 

 at a given height originates and marks the zero or origin of the curve 

 for this section when plotted on the age of the tree (§ 269). Second, 

 a separate curve of diameter growth based on age is constructed for 



