— 159 — 



(iv) The fluctuation from the age of 52 up to 70 shows very great 

 irregularity. 



From these trends, we may arrive at the following conclusions : — 



(a) Change of the grade of thinning or of the form of density for 

 a single stand makes a phase in the fluctuation of growth and shows dis- 

 continuity. Thus, in the grouping of a large number of sample plots 

 simultaneously surveyed, as members of the same chain of growth,, it is 

 a very necessary and sufficient condition that the management of stands 

 must be the same and that the growth of the stand is not severely 

 retarded by any accident. 



(b) The period of repeated thinning must be determined at the time 

 when the condition of the overhead leaf canopy of individuals in the stand 

 is approximately the same as at the previous thinning. The reason 

 for this is that, I think, irregularities in the fluctuation of G and 



— — =< are due to lack of time caused by the period of thinning and 

 furthermore the irregularities caused by the selection of trees to be cut 

 out in the thinning. This last estimate may be illustrated from the 

 frequency distribution of number of trees in diameter classes of each 

 stand, i. e. from the variabilities of individuals of each stand. Therefore 

 before entering upon the investigations of the growth curves for factors 

 of stand, it is necessary to study relations subsisting in the developments 

 of the dimension of individuals in stand, e.g. element of growth. 



(a) On the Development of diameter. 



The development of diameters of trees in a given stand with respect 

 to age will be readily determined by the comparison of the frequency 

 distribution of the number of trees in diameter class. As to the 

 frequency distribution, Schuberg^ discussed it comparatively in detail in 

 his work, " Rotbuche ", and Guttenberg* gave a brief sketch in his work 

 " Die Aufstellung von Holzmassen-und Geldertragstafeln auf Grundlage 

 von Stammanalysen." 



Applying now the modern statistical methods, we have the following 

 results. At first it seemed of importance to determind whether" the trees 

 in a stand might fairly be treated as homogeneous throughout the changes 

 in age. 



