608 JOURNAL OF FORESTRY 



In sampling along a radius in this way it is evidently assumed that 

 the fibers at any given point on the radius are representative of a zone 

 whose geometrical center is at the pith. 



At each selected point on the radius a sample of wood is taken and 

 disintegrated, fifty fibers being measured and the mean fiber-length 

 thus determined. 



The question now arises, how should the mean fiber-length for the 

 disc be determined from the fiber-lengths at points along the radius? 



The practice has been to add all the determinations together and 

 divide the sum by the number of determinations. 



It is not hard to see how inaccurate such a procedure would be. 



Suppose the circle ABC represent a disc 



which has been sampled at D, E. and F on the radius OA and gave a 

 mean fiber-length of 1 mm. at D, 2 mm. at E and 3 mm. at F. The 

 mean according to the usual procedure would be 

 (1 + 2 + 3) --3 = 2 mm. 



If D. E, and F were at %, Yj, and ■% of the distance OA being 

 equally spaced it would be fair to assume that they represented zones 

 of equal width, viz: with 'radii O and ^, 5<s. and 7^, yi, and 1. One 

 would have the disc divided into three zones each with its own fiber- 

 length. 



The areas of the zones would be 



^ (;',) •-' = .349 



■^ iV - —-^ (5) '' = l•0-^7 



TT 1) ■-' — TT (?) ■-• =: 1.746 



Total area of disc ir (1) -• = 3.142 

 In determining the mean fiber-length of the disc one has given the 

 zone having a fiber-length of 3 mm. no more influence on the result 

 than the zone having a fiber-length of 1 mm. although its area was 

 five times as large as that of the latter. 



