610 JOURNAL OF FORESTRY 



r 2 — r 1 

 The area of an indefinitely narrow annulus 



= 2 TT r dr 

 The product of this area into its proper fiber-length 

 — 2 IT r dr 



= 2 TT r (kr + c) .11- 



The product of any annulus defined by rj and r^, into its fiber-length 

 which varies between L^ and Lj may be obtained by integration of this 

 expression, as follows : 





2ir V dr (kr + c) 



2 TT k - dr + 



-[^ + T=] 



i k c 



2^|( ^ (r, ^'-r ,=') + - (r, •' -r, •-') 



Substituting values of k and c given by (a) and {/?) this bee 



:omes 



u 



L , f 3 r , -h r , ) + L ■, ( 2 r , ^ r , ) I ( r , ~ r , ) {c) 



Dividing this value by the area of the annulus we obtain the mean 

 fiber-length for the annulus 



■^ 1 1--. ( :: r , - r , ) + L , ( 2 r , -h r , ) V - ^ 



all such products {c) throughout the disc d 

 the disc gives the mean fiber-length for the ( 



I I rvn(2rn+rn-i)+Ln-i(2rn_j+rn) j (rn-rn-,) 



id) 



The sum of all such products {c) throughout the disc divided by the 

 total area of the disc gives the mean fiber-length for the disc 

 r = R 



= T^ ^ I 1 Ivn(2rn + rn-i) + Ln-i(2rn_j+rn) H^n-rn-,) |;(^) 



These formulae have other applications than those of fiber-length. 



I believe that nearly all published determinations of the mean values 

 for a tree of those properties which can be expressed numerically, 

 whether chemical, physical or mechanical, have been made on the 

 assumption that one sample was as good as another and carried as 

 much weight on the result whether it represented a small volume sur- 

 rounding the pith or a hollow cylinder next the bark of considerable 

 volume. A consideration of the argument of this paper may therefore 

 suggest improvements in the computation of results of tests of prop- 

 erties of wood other than fiber-length. 



