— 154 — 



parison of the growth of trees by means of stem analysis and of stands 

 by means of repeated surveys of permanent sample plots with regards to 

 the data from a large number of sample plots simultaneously surveyed. 

 Thus we may divide this paper into four parts: 



(I) On the normal rate of growth of a single tree, recorded by the 

 method of stem analysis. 



(II) The normal rate of growth of stand which is periodically 

 thinned under a given grade. 



(III) On the normal trend of growth and yield of stands which was 

 given in yield tables. 



(IV) On the application of the laws deduced from the first three 

 parts to the construction of a yield table. 



I. On the normal rate of growth of a single tree, recorded 

 by the method of stem analysis 



In 1902, it was pointed out by J. Leob^ that all-growth or the 

 synthesis of cytoplasma is in all probability an autocatalytic reaction. If 

 this is the theory, then the velocity of the all-growth should be re- 

 presented by the formula, by Gulberg-Waag's law. From this point of 

 view, the normal rate of growth of a single tree should be represented 

 by the formula 



dy 



dt 



-=^'yv(y,t) 1, 



where — |- is the normal rate of the growth, i. e. of the height, the 

 diameter at breast-height or the stem volume at the instant dt, y is the 

 amount of growth which has been attained at the time t and ^' is a 

 constant which differs with the factor to be represented. 

 From the equation (1), we have 



— Jt-=^V(2/, t) la. 



ydt 



Now calculating ..'^ from the various records of stem-analysis of 

 VAt 

 test trees from our forests, it will be readily seen that the general trend 



0^ —^ of a single tree with regard to t will be represented as an 

 inverse function of t, i. e., 



