DOYLE LOG RULE 69 



The seller can defend himself against the use of a short measure if 

 the latter is consistent and its per cent of error is known. But with a 

 log rule like the Doyle, the per cent of error differs with every scale of 

 logs or stand of timber and it is practically impossible to determine the 

 actual loss without remeasuring the logs by a correct log rule or tally- 

 ing the sawed contents. 



Since it will be impossible to displace this log rule by better standards unless 

 its vicious character is fully understood, the exact nature of the error should be made 

 clear. The original form of this rule read "Deduct -i inches from the diameter 

 for slabs, then squaring the remainder, subtract one-fourth Jor saw kerf and the 

 balance will be the contents of a log 12 feet long." The sawdust allowance as 

 intended, would have corresponded to a i^-inch saw kerf. The author evidently 

 figured that 4 inches of slab would square the log sufficiently so that the sawdust 



Fig. 9. — Actual deductions for slabs and for .saw^ kerf made by the formula of the 

 Doyle rule, for logs 6 inches, and 28 inches in diameter respectively. 



The square A BCD is the supposed residue after deduction for slabs, while the 

 outer inscribed circle represents the actual residue. The inner inscribed circle 

 represents the residual percentage showu as board feet by the rule. The sawdust 

 allowance is, therefore, the difference between the outer and inner inscribed circles, 

 whose area is but 4.5 per cent of the contents of the cylinder. 



allowance could be appUed in this manner to the squared or partially squared stick. 

 His fundamental error lay in his method of deducting for slabbing and edging. As 

 shown, the waste from slabs and edging does not amount to a reduction of 4 inches 

 in the diameter, but to about 1.75 inches, and instead of being slabbed from four 

 sides, it is distributed evenly over the entire surface as a collar. The assumption 

 made re.sulted in an actual deduction for slab far in excess of what was intended, 

 this excess in turn reducing the sawdust allowance from an a.ssumed 25 per cent to 

 negligible proportions. 



The above diagrams (Fig. 9) will explain the reason for this inconsistency. 



The diagram for the larger log shows that the squaring of the timber would not 



require a 4-inch slab allowance. The standard formula -fD— 4)^ gives the volume 



4 



.7854(D— 4)- as the actual net result of deducting 4 inches from the diameter of the 



