SECTION III— LOG RULES 

 PROBLEM 9. (Office.) The Construction of a Scientific Log Ruls. 



Explanation. — The object of this problem is to illustrate the fundamental 

 principles underlying the determination of the contents of logs in board 

 measure. A thorough preliminary study of a rule such as the International, 

 which is constructed upon scientific principles, should give the student a 

 thorough understanding of the determination of the contents of logs in board 

 feet, and a scientific foundation upon which to base his general study of log 

 rules. 



Illustration. — The International Log Rule. 



The formula for securing the volume of a log 4 feet in length by the 

 International log rule is 



F = 0.22D2-0.71D, 

 where V = the volume of the log in feet B.M . ; 



D = the diameter in inches at the top end of the log. 



This formula is based upon the assumption of a loss for each 1 inch board 

 of i-inch in saw kerf, and ye inch for shrinkage and that the loss in slabbing, 

 edging and surface waste is equivalent to a board 2.12 inches thick, of the 

 same width as the diameter of the log and the same length as the length of 

 the log. 



Directions: 



A. Methods of Procedure. 



1. Work out the complete algebraic proof of the International rule for 



4-foot lengths, noting the reason for each step. 



2. Using the formula for 4-foot lengths, and allowing ^-inch taper for each 



4 feet, compute the volumes of the logs of all diameters from 6 inches 

 to 16 inches inclusive, and each length in even 4-foot lengths from 

 8 feet to 24 feet {i.e., 8-, 12-, 16-, 20- and 24-foot lengths) . Arrange 

 the results in table form leaving blank spaces for the alternating 

 even-foot lengths (i.e., 10-, 14-, IS-, and 22-foot lengths.) 



3. Now determine the values for the missing alternating lengths by plot- 



ting a separate curve for each diainc^tor from 6 inches to 12 inches 

 using abscissa) as lengths, and ordinates as volumes. 

 IS 



