30 STATE BOARD OF FORESTRY. 



A COMPARISON OF THREE DIFFERENT TYPES OF LOG RULES. 



There are three distinct types of log rules now in general use. They 

 are as follows: (a) Rules with a waste allowance varying directly as 

 the barked area of the log and the volume of the log after the barked 

 area allowance is made, (b) Rules with a waste allowance varying 

 directly as the total volume of the log alone, (c) Rules with a waste 

 allowance varying directly as the total volume of the log plus a constant. 



When D = diameter at small end inside bark in inches. 

 When L = length of log in feet. 

 When a = constant (in inches). 

 When 7T 3.1416. 



When c = constant with limits of and 1. 



When B. M. volume in board feet of manufactured product, 

 the three types may be expressed by these formula} : 



4X12 



4X 12 



NOTE : The above formulae are special cases of 



In formula (a) the constant & equals zero, and the constant a has a positive value. 



Therefore, the curve ( 1 - c) L has been moved in a horizontal direction a units 



4 X \2i 

 to the right of the origin. 



In (b), a=0, and 6=0, or the curve maintains its normal position. 



In (c), a=0, and & has a positive value, or the curve has been moved in a vertical 

 direction & units. 



None of the log rules analyzed had values for both a and & such that one of them 

 could not be easily eliminated. The Universal Log Rule, for instance, reduces to the 

 following formula: 



The constant &=.1325 is so small that its effect upon the log rule is negligible. 

 (1 - .20) y 19 ^ = B.M. gives values for this rule within 2 board feet, and is 

 the formula listed below. 



