56 THE MEASUREMENT OF LOGS— BOARD-FOOT CONTENTS 



TABLE Vn 

 Distribution of Waste between Slabbing and Sawdust 



* Of the small cylinder not including taper. 



The waste in slabbing would be exactly proportional to diameter except for the 

 fact that the volume of the hollow cylinders representing the collar deducted for 

 slabs is not directly proportional to the outer surface of the respective cylinders in 

 logs of different sizes. The same relation is seen to hold whether or not the slab 

 waste is deducted before or after the sawdust. (Columns 2 and 7.) 



Since the per cent of slab waste is roughly proportional to D, while that from 

 sawdust is as D-, the sum of these two factors causes the total per cent of waste to 

 decrease as shown in column 4, instead of remaining constant as in column 6. The 

 rate of decrease is less rapid than in columns 2 or 7 since only a -portion of the waste 

 decreases in per cent with increasing diameter of log. 



Were the total waste in logs proportional to D^ as is the waste from 

 saw kerf, log rules could be converted from cubic to board feet by a 

 single ratio. But since the part of this waste due to slabbing is pro- 

 portional to D, the per cent of total waste decreases with increasing diameter 

 by a rate which is the sum of these two factors and is therefore directly 

 proportional to neither D nor D^. This explains the increasing per cent 

 of utilization secured in sawing larger logs and the need for log rules 

 based directly upon the board-foot unit and not derived by conversion 

 of cubic units. 



To derive an accurate log rule, not only must the waste from slabs 

 and edgings be deducted separately from the waste from saw kerf, but 

 the correct amount must be deducted for each source of waste. A rule 

 which deducts too much for slabs and too little for saw kerf will deduct 



