OTHER FORMULA RULES 65 



the product deduct three-elevenths; multiply the remainder by the length of the 

 log and divide by twelve." Or, 



B.M. = (1 -^) .7854(D-1.5)* 



= .727 



12 

 tt(D-1.5) 2 L_ 

 12' 



The minimum width of board used was 3 inches. 



For logs over 40 feet in length, an increase in diameter is allowed on half the 

 length of the log amounting to 1 inch on the diameter at the small end, for each 

 10 feet in length over 40 feet. Thus for logs from 41 to 50 feet long the contents 

 of the butt cylinder is scaled by a diameter 1 inch larger than the top end; for logs 

 from 51 to 60 feet long, the rise allowed is 2 inches, etc. 



This allowance for taper is absurdly small and constitutes the only weak point 

 in the rule. It is a concession to the low standards of utilization practiced in the 

 province at the time. 



62. Other Formula Rules, Approximately Accurate, Both in Princi- 

 ples and Quantities. When a log rule is constructed by using the prin- 

 ciples embodied in the standard formula, and when in addition, the 

 amount of deduction for both saw kerf and slabbing is approximately 

 correct, the resultant log rule will be far more accurate and consistent 

 than any of the commercial rules in common use except the last men- 

 tioned. Several rules have been constructed, whose values differ only 

 because of slightly different allowances for waste, as shown in Table IX. 

 Seven such rules are given below. This completes the list of log rules 

 known to the author, and based on diameter at small end of log, which 

 deserve to be classed as fundamentally correct standards for board-foot 

 contents of saw logs. 



Champlain Log Rule, A. L. Daniels, 1902. This log rule, intended as a perfect 

 rule for 1-inch boards, is based on J-inch saw kerf and neglects taper. It is for 

 perfect logs. The deduction for slabs and edging, without normal crook, is made 

 equal to a 1-inch plank or ID. No shrinkage is considered. The diameter is taken 

 at small end. Were it not for an over-run secured from taper or the methods of 

 sawing used, logs would never saw out what this rule calls for. The quantities 

 given are above normal in cylindrical contents for short logs. This error is offset 

 by neglect of taper, so that in long logs the rule falls below the International. 



This rule has not been used commercially, except in a few instances in Vermont. 

 The formula is: 



L 



B.M. = (.62832D-D)=— . 

 12 



The author of the Champlain log rule realized that the slab allowance was too 

 small for actual conditions. By increasing the width of plank deducted for slabbing 

 to 2D, a modification, termed the Universal log rule was computed, using the formula, 



L 

 B. M. = (.62832D 2 -2D)— . 



