THE BILTMORE STICK 231 



aD 



Scale = 



Va(a+D) 



J o£> 2 

 ~\a~+D 



la+D' 

 The derivation of this formula is as follows: 



D 



{AB'Y = {AC'Y-{B'C'y. 

 By substitution, 



{AB'Y=L+-\ -(^¥ = {a)*+aD=a{a+D). 

 (II) AB' = Va(a+D). 



Substituting this value for AB' in equation (1), 



aD 

 ~2~ 



BC-- 



\/a(a+D)' 



Since BC is the scale for § of the diameter of the circle, the formula for the scale 

 for the whole circle is ' 



„ , aD laD 2 



Scale =- 



JaD 1 

 \a+D 



Va(a+D) \a+D~ 



The Biltmore stick is less accurate than the calipers or diameter 

 tape and should therefore never be used for scientific measurements or 

 permanent records. To insure complete accuracy in the use of a prop- 

 erly graduated stick, the following conditions are necessary: 

 The tree must be circular in cross-section. 



The stick must be held against the tree at a point 4J feet from the- 

 ground. 



aD VaVaD _ VaD I aD" 



Va(a+D) VWa+D Va+D "Vo+D' 



