70 THE CONSTRUCTION OF LOG RULES 



log. This was the point overlooked in constructing the rule. The deduction so 

 made is in its effect a deduction for slabbing and edging although not so intended. 



That it was not intended is shown by the instructions for next deducting one- 

 fourth of (Z>-4) 2 "for saw kerf." But this leaves ,75(Z)-4) 2 for all logs, instead 

 of 7854(D— 4) 2 , which is a further reduction of but .0354(2)— 4) 2 , the actual reduc- 



0354 



tion for saw kerf : = .045 or 4.5 per cent of the cylindrical contents for saw kerf 



.7854 



instead of the 20 per cent of the same cylinder required by a i-inch saw kerf. The 



remaining 21 .5 per cent of the supposed saw kerf is a true slab deduction of 4 inches 



from diameter. Thus the amounts and proportions of slab deductions are grossly 



out of balance and this ruins the rule. 



This early form was not known as the Doyle rule. The present form, first 

 published in the decade 1870-80 was advertised as a new rule. The scale is identical 

 with the older form but the change in the wording of the rule to its present form 

 still further concealed the flaw in its construction. 



The formula for the Doyle rule is: 



(D-4\ 

 B.M.= 



corresponding to the standard formula : 



*)■*, 



B.M. = .955— 



12 



The true sawdust allowance can be shown by the following comparison: 



/Z>-4\ 2 



(— — ) Z=.0625(D-4) 2 Z. 



The area contents of the cylinder D— 4, 



^(D-4) 2 — = .06547(D-4) 2 L. 



Since the cylinder D— 4 represents the log minus true slab deduction,- = 



.06547 

 95.5 per cent or the log minus both slabs and sawdust. 1 



66. Effect of Errors in Doyle Rule upon Scaling and Over-run. 



The effect of this overbalancing of the respective allowances is to cause 

 this rule to give zero for the contents of logs 5 inches in diameter while 

 for logs above 47 inches, the scale yields more than 80 per cent of the 

 cubic contents, thus, for j-inch kerf, eliminating slab waste altogether. 

 The over-run would thus vary with increasing diameter, from infinity 

 to zero. 



When the Doyle rule is applied to long logs, with a small top or scaling diameter, 

 the over-run becomes proportionally greater. A careful test, under direction of 

 the courts in Texas where logs of given sizes were actually sawed (Extending a 

 Log Rule, E. A. Braniff, Forestry Quarterly, Vol. VI, 1908, p. 47), showed that 

 for 24-foot logs sawed by circular saw. the Doyle rule gave an over-run for different 

 diameters, as shown in Table X. 



1 The author is indebted to material published by H. E. McKenzie in Bui. 5, 

 California State Board of Forestry, for this discussion of the error in the Doyle rule. 



