. TOTAL CUBIC CONTENTS OF FELLED TREES 23 



2. Add the volumes of all sections to determine the total merchantable 

 volume of the entire tree, and record in proper space. 



C. References. Number 45. 



PROBLEM 13. (Office.) The Determination of the Total Cubic Contents 

 OF Felled Trees. 



Explanation. — The object of this problem is to show the comparative value 

 of the different methods and to develop proficiency in making the various 

 fundamental calculations required in the determination of the cubic contents 

 of trees. 



Illustration I. — To compute the cubic contents of felled trees by cubing the 

 tree in sections. 



Explanation. — In this method each section in the tree is compared to a 

 geometric figure and for that reason logs, stumps, tips and branches each 

 require the use of a distinct formula . The various formulae follow : 



A. The Cubic Contents of Logs. 



1 . Let B = basal area in square feet of large end of log ; 



6 = basal area in square feet of small end of log; 

 L = length of log. 



Then the cubic contents may be expressed by Smalian's formula as 

 follows : 



2. Determine basal areas in square feet by, — 



4 ^144' 



Where d = the diameter of the area in inches and — is used to 



144 



reduce to square feet. 



B. The Cubic Contents of Stumps. 



A stump is treated as a cylinder whose diameter is equal to the top 

 diameter of the stump. The formula for the cylinder is 



BXL. 



C. The Cubic Contents of Tips. 



A tip is treated as a cone whose basal area is equal to the basal area of 

 the tip, and whose altitude is equal to the length of the tip. The formula 

 is, 



\BXL. 



