— 153 — 



density in the first approximation, still there are some ambiguities caused by 

 using data without having any permanent sample plot. However these 

 ambiguities were decreased by using the laws deduced from data, collect- 

 ed in sample plots established in Saxony, for the purpose of the 

 comparative study of the grade on thinnings. 



It is not proposed, however, to give here any account of the work 

 which has been done in the attempt to elicit informations on the more 

 difficult subject of the nature of the growth of tree and the aggregate, 

 stand but only to publish the empirical formula for the purpose of show- 

 ing clearly the general trend of the growth. 



Such an investigation has indeed been attempted by European 

 authorities and has remained as a problem for fifty years and over. 

 Among authorities who have dealt with this subject, the names of Baur, 

 Breymann, Eichhorn, Endres, Gehrhardt, Gram, Grundner, Guttenberg, 

 Koller, Lorey, Schiffel, Schuberg, Weber, Weise, Wimmenauer are well 

 known. So far as I can determine, while the value of their works is great, 

 the effect is chiefly negative. No formula can be accepted as theoretically 

 perfect. It is a very necessary and important work to discuss the investi- 

 gations attempted by European authorities, but such reviews of this field 

 is too far from our present purpose in this paper. We shall confine 

 ourselves to attention to certain general deficiencies in the previous works. 



(1) In many cases, in data grouped as member of the same chain 

 of growth the correlations subsisting between each factor of the stand 

 and the age and mutual relation of each factor have been disregarded. 



(2) The method of grading of stand is limited only to the volume 

 per unit area and average height. Still, as stated by Schuberg, Wim- 

 menauer and Haug, the number of trees per unit area and the frequency 

 distribution of number of trees in diameter classes in stand are of very 

 noteworthy elements in the classification. Usually these do not allow 

 of comparison as stated by Baur, for the sake of complexity. 

 The advantage of carrying out such investigations lead us the normal 

 characteristics of the stands in the same chain of growth. The difficulty 

 which had to be faced in that investigations was, I think, the task of 

 ascertaining the normal characteristics of the growth of stand. To this 

 end, we define the conditions to be grouped in the same chain of growth. 

 To make this latter inquiry complete, it is essential to make some com- 



