78 THE CONSTRUCTION OF LOG RULES 



But imperfect or irregular diagram or formula rules require the formula, 



B.M. = (oD 2 +6D+C)— 

 12 



B.M. = ( (1 -b)-^--C)L. 

 \ 4X12 / 



The first of these sets of formulae was originated by A. L. Daniels, the second by 

 H. E. McKenzie. By Daniels' formula, the values of logs of three sizes will give 

 the formula. For the following rules, the formulae read: 



L 

 Doyle, B.M. = (.75B 2 -6Z>+12)— , 



L 

 Scribner, B.M. = (.555Z) 2 - .55D-23)— ; 



12 



L 

 Maine, B.M. = (.635Z> 2 -1.45Z>+2) — ; 



L 

 Champlain, B.M. = ( . 62832D 2 -D)— ; 



L 

 Vermont, B.M. = (.50D 2 )— . 

 12 



By the McKenzie formula, adding the constant C gives the following for: 



Spaulding, B.M. = HI -.266)^^ -2 U; 



/ irD 2 \ 



Scribner, B.M. = (1 - .266) 3 )L; 



\ ; 4X12 / ' 



Maine, B.M.= f (l-.222)-^--.67 )L- 



\ 4X12 / 



These formulae permit of analysis and comparison of different log rules. 



74. The Construction of Log Rules from Mill Tallies. Graded 

 Log Rules. A log rule based directly on mill tallies or the measured 

 product of sawing logs into lumber will have no over-run provided the 

 variable conditions of manufacture coincide with those which determined 

 the contents of the logs from which the rule was made. But this is 

 never the case. Standard log rules made for 1-inch boards do not con- 

 form to mill tally of lumber sawed partly into 2-inch plank, or even if 

 sawed full or l^-inch in thickness. Standard rules for square-edged 

 lumber fall far short of measuring the product of small logs sawed and 

 tallied as round-edged boards. The board foot as a cubic measure will 

 not indicate the quantity of surface or superficial feet of lumber pro- 

 duced in sawing f-inch boards. 



Where it is desired to obtain, in the log, the probable actual contents 

 in boards, and existing rules are unsatisfactory, a new rule may be worked 



