CALCULATION OF THE MKAN FIBER-LENGTH G09 



Obviously if one has several areas with its own fiber-length, the 

 true mean must be obtained by taking into account the extent of those 

 areas. The correct procedure is to multiply each area by its fiber- 

 length, add together the products and divide the sum by the total area. 

 Thus in our example 



7.681 

 7.681 ^ 3.142 = 2.44S 

 Thus we get 2.445 for the mean fiber-length of disc, instead of 2 

 which the former method. gave. 



This last example is given for argument's sake only and although 

 more accurate than the previous one is neither very practical nor 

 formally correct. It does not follow that a sample taken from a posi- 

 tion half way across the breadth of a zone (as at D, E, or F) would 

 provide fibers of a length equal to the mean for the zone. Indeed the 

 argument implies the contrary. 



A practical method would be to sample the wood at known distances 

 along the radius and to determine the mean fiber-length at those 

 points. One would then have a number of zones or annuli and the 

 mean fiber-lengths at their inner and outer circumferences. 



Such an annulus, lying as it does between the circumferences of 

 two circles whose radii may be called rj and r^ will have an area 

 equal to 



TT (r 2 - — r 1 ■-') 



As the circumferences bounding the annulus pass through points at 

 which fibers were measured, an approximate relation of fiber-length to 

 radius may be established for each annulus. A necessary assumption 

 here is that the curve representing fiber-lengths plotted against radii is 

 a straight line for any given annulus, or 

 L — c a r 



where L is the fiber-length, r the radius and c a constant of a given 

 annulus. whence 



L = kr H c 

 where k is another constant applying only to a given annulus. 



If Li. Lo are the fiber-lengths at the points denoted by r^, r. then 



- L , 



{a) 



L 2 - Iv , 



