18 STATE BOARD OF FORESTRY. 



lumber to be sawed. The saw-kerf from one side and edge of an average 

 board bears the same ratio to that board as the total sawdust from all 

 boards does to the total volume after slab allowance has been made. 

 This is true of all volume becoming sawdust, excepting saw-kerf amount- 

 ing to 2k (D a), which should be considered as part of the slabs since 

 it varies directly as the barked area, and is the sawdust formed in 

 cutting the slabs. 



k (w -f- t -f- k) = volume of wood forming sawdust from each 

 average board. 



L 



(tc -p k) (t -\- k)- = volume of sawdust plus volume of average 

 12 board. 



k (w -f * + k) 



= fractional part of wood, 



f w _|_ j.\ n 4. &) JZ_ necessary to make 



12 average board, becom- 



ing sawdust. 



This ratio of sawdust to average board plus sawdust holds for volume 

 of logs minus allowance for slabs. 



P k(w + t + k) 1 



1 -. , . , = fractional part of log, after slab allow- 



L ance is made, which becomes lumber. 



Therefore, 1 n L = volume in 



L (u> + k) ('+*)] 48 



board feet of lumber of average dimensions from log D inches in 

 diameter at small end inside the bark and L feet long, when saw- 

 kerf is k inches wide. 



A constant C = to a few board feet, when added to this formula has 

 a compensating effect for the excessive taper in small logs. Since most 

 small logs sawed are the top logs from medium or large sized trees, they 

 have an excessive taper which can not be accounted for by a uniform 

 taper allowance applied to the whole tree. Therefore, this constant, 

 which in all cases will be very small (not exceeding 10 board feet) is 

 applied and its effect on large logs is negligible, but on small ones it 

 will play an important part in eliminating an accumulative error in 

 total sawed out at the mill. 



