— 205 — 



Illustration f^' Showing the variation of radius in the longitudinal 

 section of tree bole of Tsuga sieboldii in a natural mixed stand at Yanase 

 Working Circle in Shikoku State Forest. 



Distance 



from the 



tip in 



Ke (i-) 



0.8 

 1.5 

 2.5 

 3.5 

 4.5 

 5.5 

 6.5 

 7.5 

 8.5 

 9.5 

 10.5 

 li.5 

 12.5 

 13.5 

 14.5 

 15.5 

 15.8 



Mean 



radius in 



Sun {)/) 



0.55 

 0.75 

 1.55 

 2.40 

 2.65 

 4.05 

 4.50 

 5.50 

 6.10 

 6.30 

 6.70 

 7.40 

 7.55 

 8.25 

 8.70 

 9.30 

 9.85 



41 



0.286 

 0.800 

 0.850 

 0.250 

 1.400 

 0.450 

 1. 000 

 0.600 

 0.200 

 0.400 

 0.700 

 0.050 

 0.700 

 0.450 

 0.600 

 1.833 



0.565 

 0.575 

 0.658 

 0.631 

 0.670 

 0.712 

 0.714 

 0.850 

 0.689 

 0.650 

 0.641 

 0.623 

 0.608 

 0.605 

 0.600 

 0.612 



1.15 



2.00 



3.00 



4.00 



5.00 



6.00 



7.00 



8.00 



9.00 



10.00 



11.00 



12.00 



13.00 



14.00 



15.00 



15.65 



Ay 

 Ai- 



Remarks 



0.504 

 1.391 

 1.292 

 0.391 

 2.090 

 0.632 

 1.401 

 0.706 

 0.302 

 0.615 

 1.092 

 0.080 

 1.151 

 0.744 

 1.000 

 2.995 



Diameter at breast-height 

 = 1.86 Shaku. Total height 

 = 16.0 Ken. 



The figures and graphs show 

 clearly that the variations 

 of radius with respect to the 

 distance from the tip do not 

 represent the relative 

 growth under the uniform 

 condition, especially at the 

 sections of the top part 

 from 1.10 Ken to 5.0 Ken. 



From these figures, we get the best possible freehand curves for 



A?/ 



and 



y 



with respect to x, of which curve a in Fig. 2 of Plate XXX. 



Ax X 



shows the variation of ^^ and curve h in Fig. 2 of the Plate XXX. shows 



Aa; 



that of ^. Now tracing the curves for ~^^ and ^ with respect to x, 



X Aa; X 



we obivously find the following characteristics: 



( i ) for x = o, y=o. 



Aa; 



-0 and 



X 



--0, 



(ii) for x=h, i/=constant, -'^-^= constant and -^=constant, 

 ' Ax X 



(iii) for x=l Ken and a;=12 Ken, there are two tangents which 

 cross the curve y, 



(iv) for a;=2 Ken and a;=15 Ken, there are two tangents from the 

 origin, of which one at the corresponding ordinate for the abscissa a; =2 

 contacts at the concave side of the curve y, the other at the correspond- 

 ing ordinate for the abscissa a; -=15 Ken contacts at the convex side of the 

 curve y. 



* I have given illustrations of the principal trees in Bulletin of the Forest 

 Experiment Station, No. 8, pp. 126, 128, 130, 131, 132 and 133. 



