— 206 — 



Thus the curve -^- intersects the curve -^^ at two points only ; and 



X AiC 



at the point w^hose abscissa is a;= 2 Ken, the curve -^- reaches the maxi- 



X 



mum and at another point whose abscissa is .i'=15 Ken, the curve -^ 



X 



reaches the minimum. 



(v) Furthermore tracing the curve of (^^-] (-^~) with respect to 

 X, we get the curve which starts from the infinitely great, and gradually 

 falls and reaches a minimum. After passing through the minimum point, 

 the curve rises rapidly as it will be seen Fig. 3 in the Plate XXX. 



These are the common characteristics of the outline curve of tree 

 boles. Unfortunately this has not been pointed by any European authori- 

 ty. The importance of these characteristics is so great that it seems 

 absolutely necessary to ascertain the equation of the outline curve of the 

 tree bole before we conclude, since parabolic equation shows a discordance 

 with the observed data. 



Now, we assume 



then we get 



y ^ 



X 



JV-=.(a+A-)dx. 

 y \ x" J 



y 



By intergrating and transforming, we have 



ax~ — 



X 



y=ce 

 where c is the integral constant.* 



Applying the equation to the above given data we find : 

 log Tj= 0.5667+ 0.0296X-M759 



X 



In the following table the theoretical and experimental results are 

 compared : 



* I have discussed this formula in Bulletin of the Forest Experiment Station, No. 

 8, p. 129. 



