36 LOG RULES BASED ON CUBIC CONTENTS 



in which C = total per cent of waste deducted from the cylinder, 

 1 — C = per cent of cubic contents utilized, 



—j-7 reduces D 2 from inches to square feet, and 



12 converts cubic feet to board measure. 



The formula, simplified, becomes 



Board feet =(1-C)^L. 

 48 



But the important distinction remains, that some of these log rules 

 are meant to apply to the middle diameter and others to the small end, 

 and while the per cent subtracted from the cylinder measured is uniform 

 for the rule, the per cent actually subtracted from the log is uniform only 

 for those rules using middle diameter, and varies over a wide range for 

 rules based on diameter at small end of log. 



Note. Obsolete Rules. The following log rules, obsolete or unused, are based 

 on the above formula and principles: Saco River (Maine), Derby (Mass.), Partridge 

 (Mass.), Stillwell's Vade Mecum (Ga.), Ake (Pa.), Orange River or Ochultree 

 (Texas). A new rule, the Calcasieu (La.), deserves the same fate. The Tatarian 

 rule (Wis.), which is based on this principle, gives approximately correct board- 

 foot contents for a log of a given size. It has never been adopted in practice. 



38. Comparison of Scaled Cubic Contents by Different Log Rules. 



In Table II is shown the comparative volumes, in per cent of total cubic 

 contents, which are scaled by different log rules based upon cubic 

 volume. These per cents represent the converting factor used to obtain 

 the values given in the rule from the volumes of cylinders. 



Note. The values in this table were obtained by applying the ratio between 

 the volume of two cylinders 16 feet long, 18 inches and 19 inches in diameter respect- 

 ively. This ratio is 28.27 : 31.50. Log rules based on cylinder at small end then 



, , 28.27 

 scale but or 89.7 per cent of their volume, to which the reduction per cent for 



31.50 



waste is applied; e.g., the Vermont rule wastes 36.6 per cent by the inscribed square 



method. Then, based on the small end, the per cent scaled is 63.4, but based on 



middle diameter for the above size, it is 89.7 X63.4 = 56.9 per cent. The table gives 



a correct comparison of the different log rules which are constructed by using a 



fixed per cent of cubic volume. The per cents given for the rule under the first 



column, based on the point at which the rule is applied, are consistent for all logs. 



But the equivalent per cents obtained by converting the scaled contents into terms 



of the cylinder based on the other diameter — as middle, for logs measured at the end 



and vice versa, will vary as the relative contents of these two cylinders varies (§ 31) 



This will not change the rank or order in which the rules fall. The rules are tabulated 



in order of the relative per cent of total contents which they scale. 



There is no common standard for measuring the cubic contents of squared timbers. 



The Quarter Girth method gives the fullest measurements, while the others more 



closely approximate the net contents as given by board-foot rules. 



