170 PRINCIPLES OF AMERICAN FORESTRY. 



conditions. In the same way factors are determined 

 for all sizes and tabulated for future use. In application, 

 the volume of a tree 6.9 inches in diameter, breast-high, 

 and fifty-one feet high, would be found thus: Volume 

 of cylinder X form factor equals volume of tree, or 

 13.24 X .54 X 7.21. This method gives a much closer 

 approximation than could be obtained by using a geomet- 

 ric figure supposed to represent the shape of the tree. 



The Volume of a Felled Tree may be determined more 

 accurately. It is considered in sections, or log lengths, 

 and the volume of each section is found by multiplying 

 the middle cross-sectional area by the length. The 

 degree of accuracy of this method depends on the length 

 of the sections ; the shorter they are the more accurate the 

 result. The last section at the top, when small, may be 

 treated as a cone whose volume is equal to the basal area 

 times one-third its length; or when large and tapering 

 off suddenly it may be considered as a paraboloid whose 

 volume is equal to the basal area times one-half its length. 

 The sum of the volumes of all the sections will be the vol- 

 ume of the tree-trunk. 



For example: A tree is felled at two feet above ground 

 and calipered at the stump and every four feet along the 

 trunk do\vn to three inches in diameter, and also at two 

 feet above the last measurement. The remaining distance 

 to the top of the tree is twelve feet. (See Fig. 61.) 



By reference to the table of areas of circles on page 171, 

 the areas at each point cahpered are found: 



Area at diameter of 9 inches 4418 



Area at diameter of 8 inches 3491 



Area at diameter of 7 inches 2673 



Area at diameter of 6 inches 1963 



Area at diameter of 5 inches 1364 



Area at diameter of 4 inches 0873 



Area at diameter of 3 inches 0491 



Sum of areas 1.5273 



