DISCUSSION OF LOG RULES. 17 



The following factors which affect the mill output from logs of different 

 sizes have been included : 



(a) Slabs. 



(&) Normal crook. 



(c) Saw-kerf. 



(d) Average dimensions of lumber sawed. 



(e) Taper. 



(/) Excessive taper in small logs. 



The mathematical principles underlying the rule are as follows : 



(a) The slab allowance is a function of the barked area and varies 

 directly with it. 



(&) Normal crook is also a function of the barked area, and varies 

 directly with it the same as slabs. 



(c) The sawdust allowance is a function of saw-kerf and average 

 dimensions sawed at mill, and for any given saw-kerf and average 

 dimensions the sawdust allowance should vary directly as the volume 

 minus the slabs. 



(d) Taper allowance equal to e" in /'. (/ not to exceed 16'.) 



(e) Excessive taper in small logs offset by a constant. 



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



Let L = length of log in feet. 



Let k= width of saw-kerf, in inches. 



Let w = average width of lumber sawed, in inches. 



Let t = average thickness of lumber sawed, in inches. 



Let C = constant. 



Let a = constant. 



then (D a) = diameter of log after an allowance for slabs and 

 normal crook has been made. (Since slabs and normal crook both vary 

 the same, they can be accounted for by the same constant, a.) 



- = area in square inches of small end of log after the 

 slab and normal crook allowance has been made. 



7t (D aYL 



= volume in units of 1" X 1" X 12" contained in 



log L feet long and D inches in diameter after 

 the slab and normal crook allowance has been 

 made. (Taper allowance to be made later.) 



n (D aYL 



- ' volume in units of V X 12" X 12" or board feet 

 in log L feet long and D inches in diameter after 

 slab and normal crook allowance has been made. 



No allowance has, as yet, been made for sawdust. This allowance 

 depends upon the width of saw-kerf and the average dimensions of 



