VOLUME OF A FELLED TREE. 135 



sum of the volumes of all the sections will be the volume 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 down 

 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 Figure 37.) 



By reference to the table of areas of circles on page 136 the 

 areas at each point calipered are found: 



Area at diameter of 9 inches 



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 i-5 2 73 



It will be noticed that these areas are taken at the middle of 

 a four-foot section, so multiplying the sum by four, the volume 

 of the trunk, from the ground to a height of 28 feet, is found 

 to be 6.1092 cubic feet. Treating the top length of twelve feet 

 as a cone, its volume is one-third times the basal area into the 

 height, .0341X12-4-3=. 1 364 cubic feet, which added to the vol- 

 ume of the lower portion gives total volume of the tree 6.2456 

 cubic feet. 



