110 THE SCALING OF DEFECTIVE LOGS 



It is evident that such rules for deductions are arbitrary. The 16-foot log 

 would yield considerable short lumber and is under-scaled by the rule. Where 

 short-length boards are commonly used, logs over 12 feet long might be scaled 

 on the basis of average diameter of rot, to correct this tendency. But it is better 

 to adopt arbitrary rules than to have no methodical plan for scaling defects. 



The cull required by the presence of an unsound or hollow circular core is pro- 

 portional to the diameter of the core, and independent of that of the log. By the 

 diagram method, the deduction for center rot would be found by determining the 

 board-foot contents of a square with the diameter of the rotten core and of the 

 length indicated, as above. This method when checked against actual sawed 

 contents gives too smal a deduction for cores up to 9 inches, and above that, too 

 large, the relation varying from 87 per cent for a 6-inch core to 110 per cent for 

 one 24 inches in width. The actual amounts of sawed lumber lost for cores of 

 each diameter are accurately expressed by a formula developed by H. D. Tiemann, 

 which reads, 



L 



Contents of core = f(D+l) 2 — , 



i.e., add 1 inch to diameter of core, square, and deduct \, converting the remainder 

 into board feet by the factor 



Length in feet 

 ~YL ' 



This formula calls for four-fifths of the sawed board-foot contents of a square 

 1 inch larger than the core (0.66Z> 2 = 82.5 per cent or f of 0.80D 2 ) instead of the 

 full sawed board-foot contents of a square of the same size as the core. 



Several rules of thumb exist for determining the deduction for center rot, none 

 of which are absolutely correct, and some very inaccurate. 



Exam-pie. In a 12-foot log 20 inches in diameter with a rotten center 6 inches 

 in diameter at large end and running through the log and a sound scale of 210 

 board feet, the correct deduction is 33 board feet which is f (7 2 )-^|. The following 

 rules of thumb can be cited, using Scribner Decimal C rule. 



1. Deduct the diameter of core from that of log, and scale as a log. This 

 gives a cull of 90 board feet. 



2 Deduct the scale of a log of same diameter as the core. This gives a cull 

 of 10 board feet. 



3. Scale out a log with diameter 3 inches larger than the core. This would give 

 30 board feet, but the rule gives inconsistent results for larger and smaller cores. 



4. Scale out the contents of a square timber whose side is the diagonal of the 

 square of the diameter of the core. This would be 1.4D 2 and gives 70 board feet. 

 If reduced by 20 per cent for saw kerf, and applied to small end of core, it would 

 come closer by balancing errors. None of these rules is accurate or consistent. 



Butt Rot, Termed also Ground or Stump Rot. Butt rot enters the 

 butt log from the ground, and usually extends but a short distance into 

 the log. Its full diameter should seldom be applied to the entire log, 

 even if rot appears at the top end. 



The diameter of the rotten butt must first be compared with the 

 scaling diameter as determined by the top end of log (§ 81). If the rim 

 of sound wood lying within this inscribed circle is wide enough for boards, 



