RELATION BETWEEN CUBIC MEASURE 39 



To derive the Inscribed Square rule, the cubic contents of cylinders from Table II 

 are multiplied by 1—36.6, or 63.4 per cent. 



To convert the Inscribed Square rule into terms of the Cumberland River rule; 



since 1 —54.8 =45.2 per cent, the volumes of the two rules are as 45.2 to 63.4. The 



45.2 



Cumberland Riv'er rule gives of the Inscribed Square rule, or 71.3 per cent. 



63.4 



But the Hoppus Rule cannot be converted into terms of either of the above rules, 



since it is measured at the middle point, unless a log of a given diameter and average 



taper is assumed. 



39. Relation between Cubic Measure and True Board-foot Log 

 Rules. The conversion of these log rules from cubic to board feet is 

 based on the erroneous assumption that logs of all dimensions when 

 sawed into lumber will yield the same ratio of board-foot contents to 

 cubic contents. In practice, the larger the log, the greater will be the 

 ratio or per cent of its contents which makes lumber and the less the 

 per cent wasted. For this reason it is not possible to use the same 

 standard for scaling both the cubic- and board-foot contents of logs, 

 no matter what converting factor is chosen. 



Cubic rules, converted to board-foot contents by a fixed ratio, tend 

 to scale small logs too high and large logs too low, as compared to the 

 actual sawed contents. The common mistake of the authors of these 

 rules is to assume that once the sawed contents of a log of given diameter 

 and length is found, the ratio obtained will apply unchanged to logs of 

 all other sizes. These rules have therefore fallen into disrepute in the 

 scaling of board feet, because of their inconsistencies for this purpose. 



For products such as pulpwood, which utilizes the entire contents 

 of the log, these so-called board-foot rules give consistent results for 

 logs of all sizes, but do not possess any advantage over the direct use 

 of the cubic standard upon which they are based. On the other hand, 

 if log rules are intended for the measurement of the actual output of 

 1-inch lumber, they must be based on other principles (§ 54). 



The two quantities of measurement, cubic volume, and squared 

 board feet obtainable, are incommensurable unless the diameter and 

 also the taper of each log is known. The lump sum of a lot of logs 

 measured in cubic volume therefore, cannot be converted into board-foot 

 measure except by readjusting each individual value by the diameter 

 of each individual log. The use of these hybrid rules should be discon- 

 tinued in favor of cubic standards on the one hand, and board-foot log 

 rules based on correct principles on the other. 



