DISCUSSION OF LOG RULES. 39 



LOG RULES BASED ON STANDARDS. 



Any log rule, constructed to show volume in board feet of lumber 

 contained in logs of various lengths and diameters, which is based upon 

 definite principles, may be reduced to what is called a standard log 

 rule. The only difference between the ordinary log rule and its unlim- 

 ited number of standards is in the unit of measure. A log of any 

 specified dimensions may be chosen as the unit of measure, and so long 

 as the underlying principles of both the standard and the rule express- 

 ing values in board feet are the same, there will always exist a definite 

 relation between them and the one may be expressed in terms of the 

 other by multiplying by a constant. 



When d = Diameter in inches of the standard log and 

 I = Length in feet of the standard log, 



log rules of the form ( 1 c) - L = B. M. 



(D aYL 



become = F, in standards. 



(d a) 2 1 



Log rules of the form (1 c) L = B.M. 



become = F, in standards. 



Log rules of the form (1 c) b\ L B.M. 



become ; = F. in standards. 

 (d 2 s) I 



jyi j^ 



All standard log rules now in use are based upon ^ = Vol., in 



Ci L 



standards. Therefore, any one of them may be reduced to the form 



X ~ 



thermore, it is evident that all standard rules of the same form bear a 

 constant relation the one to the other, and any number of units of a 

 certain standard rule may be reduced to units of any other standard 

 of the same form by multiplying by the proper constant. For example, 



/ JT)2 J^ ^ 



the Nineteen Inch Standard Rule, ( = F, in standards ), may 



'V19 2 X13 /' 



be applied to a large number of logs of different sizes, and the aggregate 

 scale of these logs then given in 19" standards, may be reduced to 

 Blodgett, cube standards, etc., or to any of the following log rules 

 expressing results in board feet: Constantine, Saco Eiver, Derby, 



