THE CONSTRUCTION OF LOG RULES 59 



rections may give a new name to such a rule, or may state that it is 

 an old rule corrected. Such corrected rules while undoubtedly better 

 than the originals have so far failed of adoption in place of the rules 

 from which they were made, owing to the force of custom in perpetuating 

 established standards even if in error. 



56. The Construction of Rules Based on Mathematical Formulae. 

 Many efforts have been made to evolve a formula which will give an 

 accurate basis for a board-foot log rule. Of these the erroneous formulae, 

 or rules of thumb, based on a fixed conversion factor are most common. 

 Of those which recognize the fundamental difference between waste from 

 slabs, and waste from saw kerf, we have two groups, distinguished 

 not ])y principle, but by the method of procedure dependent on whether 

 the deduction for saw kerf is made first, from the total contents of the 

 log, or whether that for slabs and edgings is first deducted, and the 

 waste from saw kerf then taken from the residual volume. 



Method of Deducting Slobs First. When the first plan is used, a constant, a, 

 representing in inches the double width or thickness of the hollow cylinder or sur- 

 face layer wasted in slabs, edgings and crook, is first deducted from the diameter of 

 the log at small end. From the area of the smaller circle thus obtained, the required 

 per cent is subtracted for saw kerf, shrinkage or surplus thickness of board required 

 in sawing. 



The residual area of the circle in square inches is converted into board feet for 

 logs 1 foot long, by dividing by the factor 12. Disregarding the taper, the volume 

 of a log of any length is found by multiplying the contents by length in feet. 



D = diameter of log in inches; 

 a = inches subtracted from diameter, a constant; 

 D— a = reduced diameter of log after subtracting waste from slabs and edgings; 

 ir(/)-a)2 



reduced area of small end of log in square inches; 

 4 



6 = per cent of volume deducted for saw kerf; 



1 — 6=per cent remaining after deduction for saw kerf; 



L = length of log in feet ; 



B.M. = volume of log in board feet; 

 then 



r(D-a)2 L 



B.M. = (1-6)- 



= (l-fe)' 



4 12 



(D-ay 

 48 ■ 



Illustration 



Let a = 1.5 inches, representing a collar of .75 inch thickness deducted for 

 slabs, etc. 

 6 = 20 per cent representing a i-inch saw kerf. 



