i. e. N=i7e 



— 174 



+ - 

 -2k 



where we put ?=- '^"^^, A and yi=2A;iA, 



Now applying the last obtained equation N=ye to the given data, we 



get: 



for a stand with " a " grade 

 ^ 862641 

 Na=354.5e * Probable 7o Diff. ±5.2% 



for a stand with " b " grade 

 ^ 60.1057 

 N6=497.3e * Probable 7^ Diff. ±4.9% 



for a stand with " c " grade 

 ^ 63.2377 



Ne=386.1e * Probable % Diff. ±7.0% 

 The following diagrams (Plate XXVI) show the comparison between the 

 observed and calculated results, still one must bear in mind that the fluctua- 

 tion index of the number for k= for each stand is similar for the 



N 

 remaining three factors excepting the total basal area per unit area, while 



only the irregularities is observable at the age of 52. Consequently the 

 probable percentage difference is somewhat greater. Such an irregularity 

 seems to be the outcome of the time-lack, or in other words, such abnormality 

 was caused since the overheaded leaf canopy of stand at the age of 52 

 years did not fully attain the same degree of density gained at 

 the previous period. Hence, sometimes, we may offer some other good 

 formula as N=!7i. But, this formula does not exist from the theoretical 

 point of view. Because from the equation N=i7t~^S we get ic= '0000 ^, + ^! 



This last equation shows us that in the fluctuation of --^, there is no 



dt 

 maximum to be reached. Here at the limit, < increases into the practical 



infinity at the age when the latter proceeds into the practical infinity. 



And if the formula, N=i7i~'^' consists in generally, then the fluctuation of 



D must be expressed by the formula; D=Ai.'^' But we cannot suggest 



