17 



MultiplyiDg the sum of the areas 1.164 by 4, we find the total volume 

 of the tree to be 4.6 cubic feet. In case the last uieasurement with the 

 calipers was 3.5 inches, i. e., it was taken at 14 feet from the top, then 

 the volume of the leader must be added to the product of 1.111x4, 

 which is 4.4. The base of the leader begins 2 feet above the last meas- 

 urement with the calipers ; the diameter measured here is 3 inches and 

 the corresponding basal area equals 0.049 square feet; one third the 

 product of 0.049 by 12 (length of leader) is 0.02, which, added to 4.4, 

 makes 4.6, the total volume of the tree, the same as obtained from 

 previous calculations. 



(2) When less accuracy is required and the volume of the stump is 

 excluded. — The tree is calipered at the butt and in a few other places 

 where it is most convenient; each log length, for instance. The vol- 

 ume of each portion between two measurements with the calipers equals 

 one-half the product of its length multiplied by the sum of the areas 

 corresponding to the diameters thus measured. The total volume of 

 the tree is determined by summing up the volumes of all the parts thus 

 separately calculated, including also the leader. The last measurement 

 of the tree with the calipers is taken as the base of the leader, the 

 volume of which is calculated in the same way as given above. 



Example : Let us determine the volume of the tree taken above by 

 calipering it at the butt, at 12 and at 20 feet from the butt : 



The average diameter at the butt equals 7.6 inches; the corresponding area, 0.315 

 square foot. 



The average diameter 12 feet from the butt equals 5.1 inches; the corresponding 

 area, 0.142 square foot. 



The average diameter 20 feet from the butt equals 4.3 inches; the corresponding 

 area, 0.101 square foot. 



The sum of the areas of butt and top of first length is 0.457 ; the 

 length of first log is 12 feet; the volume then equals one-half of 12 

 multiplied by 0.457, or 2.74 cubic feet. The distance between the sec- 

 ond and third measurements with the calipers is 20 feet minus 12 feet, 

 equals 8 feet, and the volume of this portion of tree equals one-half of 

 8 multiplied by 0.243 equals 0.97 cubic feet. The volume of the leader 

 equals one-third of 18 multiplied by 0.101 equals 0.61 cubic feet. The 

 total volume of tree (stump excluded) is determined by taking the 

 sum of 2.74, 0.97, and 0.61, which equals 4.3 cubic feet. 

 5107— Ko. 20—2 



