31 



during this period grew annually 1 foot in height. By similar reason- 

 ing we find from the third cross section that the tree had growu 29 feet 

 for the last twenty-four years, or 14.5 inches annually, and 25 feet for 

 the first twenty years, or 15 inches annually ; from the fourth cross 

 section that the tree had grown 17 feet for the last fifteen years, or 13.6 

 inches annually, and 37 feet for the first twenty-nine years, or 15.2 inches 

 annually; from the fifth cross section that the tree had grown 5 feet for 

 the last six years, or 10 inches annually, and 49 feet for the first thirty- 

 eight years, or 15.6 inches annually. 



The rate at which the diameter and the area of any cross section of 

 the tree increases can be easily ascertained by measuring the width of 

 the rings on the various cross sections and finding in the table (p. 37; 

 their corresponding areas. Thus we find, for instance, that on the 

 second cross section — 



The first 10 rings measure 3.9 inches. 

 The first 20 rings measure 6,2 inches. 

 The first 30 rings measure 1.9 inches. 



The corresponding areas found in the table are, respectively, 0.8, 0.21^ 

 and 0.33 square feet. Subtracting either the diameters from each other 

 or the corresponding areas, we can ascertain accurately the growth in 

 diameter or area for the respective periods of time. 



The rate at which the volume of the tree increases may be easily 

 determined for any period of time by calculating the volume of as 

 many enveloping cones as there are years in the period. Various 

 methods may be employed to ascertain, for instance, the volume of the 

 last period of years. The simplest one is : ( 1 ) To determine the volume 

 of the upper portion of the tree, which has for its base a cross section 

 containing as many rings as there are years in the period by consider- 

 ing that portion as a paraboloid; (2) determine the volume of each of 

 the logs into which the lower portion of the tree is sawed, with and 

 without the width of the last number of rings (number of years in the 

 period), as explained on page 16, and deduct the sum of the last from 

 the first volume; (3) adding to the difference thus obtained the 

 volume of the upper portion, the growth for the desired period of time 

 is ascertained. For the tree represented in fig. 10, the mass-accretion 

 for the last 6, 15, 24, and 31 years could be conveniently ascertained, 

 and thus the current annual accretion for those respe(;tive periods accu- 

 rately calculated. Generally trees are not analyzed with such com- 

 pleteness, and simple methods have been devised for determining the 

 accretion of a single tree or a forest. 



DETERMINING THE ACCRETION OF A STANDING TREE. 



In determining the average annual accretion the age and volume of 

 the tree must be first ascertained. The age of a standing tree can be 

 obtained only by observation, which is based on actual counting of the 

 rings on stumps of felled trees of the same size, same species, and 



