DISCUSSION OF LOG RULES. 49 



. 



THE TRANSFORMATION OF THE SCALE OF A NUMBER OF 

 LOGS IN THE AGGREGATE, BASED UPON A GIVEN LOG 

 RULE, TO THE SCALE OF THE SAME LOGS IN THE 

 AGGREGATE, BASED UPON ANOTHER LOG RULE. 



The total volume of a number of logs of various sizes as shown by a 



n (D aY 



log rule of the form (1 c) L = B.M. can be transformed 



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to the volume as would be shown by another log rule of that form 

 where the constant a is the same. For example : Should it be required 

 to know the total volume in board feet of a trainload of logs of various 

 sizes as would be shown by the Boughman Band Saw Rule when the 

 aggregate scale based upon the Baxter Rule is known to be 320,000 board 

 feet, the following steps are necessary: Divide 320,000 by (1 c) of 

 the Baxter rule, which is (1 .338), and multiply by (1 c) of the 

 Boughman Band Saw Rule, which is (1 .10) . The result thus obtained 

 Which will be 435,000 is the same as would have been obtained had the 

 Bowman rule been used for the original scale. Such transformations 

 can not be made where the constant a in the two rules in question are 

 not the same. Had the trainload of logs been scaled by a rule of the 



Ttiy 1 

 form (1 c) _ L = B.M. it would not be possible to make such a 



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transformation, but it would be possible to transform the total scale to 

 a new total based upon another rule of the same form. For example : 

 If a trainload of logs should scale 300,000 board feet by the Square of 

 Three-quarters rule, and it should be required to find the aggregate 

 scale according to the Inscribed Square rule, the following procedure is 

 all that is necessary: Divide 300,000 by (1 .283) and multiply by 

 (1 .363) and then divide by 12. The final result, 32,000 cubic feet, 

 is exactly the same as would have been obtained had the Inscribed 

 Square rule been used for the original scale. In like manner, a trans- 

 formation could have been made to a number of other rules of similar 

 form. 



Had the trainload of logs been originally scaled by a log rule of the 



[j~\2 *r 



(1 c) &[== B.M., such as the Spaulding rule, a trans- 



formation to another rule of that form where & is the same could be 

 accomplished by dividing by (1 c) of the formula used and multiply- 

 ing by (1 c) of the formula to which the transformation is to be 

 made. But, in cases where the value of the constant & is different in the 

 log rules in question, no reduction can be made, unless the sum of the 

 length of all the logs in the trainload be known. If the sum of all log 

 lengths is known, it would then be possible to transform the total scale 



or 



to other total scales based upon (1 c) -b L B.M. 



L 4X1^ J 



(1 c) L = B.M. whether the constant & is the same or 



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different in the rules in question. Had the trainload of logs been 



