DISCUSSION OF LOG RULES. 43 



THE TRANSFORMATION OF VOLUME TABLES BASED UPON A 



GIVEN LOG RULE TO VOLUME TABLES BASED 



UPON OTHER RULES. 



Volume tables constructed to show the number of board feet con- 

 tained in trees of different merchantable lengths and diameters 

 breasthigh, and based upon a log rule of the form 



can be transformed to tables based upon other rules of the same form 

 where the value of the constant a is the same. If the value of a is 

 different in the rule to which the values are to be reduced, there is no 

 way of accomplishing the transformation. For example, tables based 

 upon the Baxter rule can be transformed to tables based upon the Bough- 

 man Band Saw rule by dividing each value in the former table by 

 (1 .338) and multiplying by (1 .10). But tables based upon the 

 Baxter rule cannot be transformed to ones based upon the Doyle rule, 

 or on any other rule of that form where a is not the same as in the 

 Baxter rule, or to forms where a does not enter, unless the average 

 diameter of all portions of the bole is known thus making it possible 

 to find the value of D for all logs in the tree. 



71 D* 



Volume tables based upon rules of the form (1 c) - - L = B.M. 



4 X 1^ 



[_ 7^2 "1 



(1 c) ; 6 L B.M. can be easily 



transformed from the one to the other. For example, a volume table 

 based upon the Spaulding Log Rule, showing the average volume in 

 board feet of trees of different diameters breasthigh and merchantable 

 lengths can be transformed to a table based upon the Kopp rule by 

 adding twice the average merchantable length shown in the table to each 

 average value, and then dividing by (1 .266) and multiplying by 

 (1 .236) and subtracting from each value thus obtained three times 

 the merchantable length. The resulting table will then be based upon 

 the Ropp rule, and the values therein will be the same as though the 

 Ropp rule had been used for scaling the individual logs instead of the 

 Spaulding rule. In like manner, any volume table based upon a log rule 



of the form (1 c) -- 6 Z/ = B.M., can be transformed to a 

 L 4 X 12 J 



volume table based upon any other log rule of that form. 



Again, a volume table based upon a log rule of the above form can 

 be transformed to a volume table based upon any log rule of the form 



(1 c) - -L = B.M. by adding to each value in the table & X the 

 4 X 12 



merchantable length, and then dividing by (1 c) of the log rule upon 

 which it is based and multiplying by the value of (1 c) of the log rule 

 to which the transformation is to be made. For example : A volume table 

 based upon the Spaulding Log Rule showing average volume in board 



