— 158 — 



II. On the normal rate of growth of permanent sample plots 

 periodically thinned under a given grade 



In the preceding part, we have been dealing with a single tree and 

 pointed out that any particular cycle of normal growth of a single tree 



__^ 

 accords with the formula: ij=ke. * The given formula is a priori 

 applicable on the assumption that through the observed duration the 

 stand is managed in the same manner and with the same grade of thin- 

 ning, and so long as it is not seriously damaged by any accidental 

 disturbance of the growth. 



It seems to me that this view is supported in the reporf published, 

 under the name of Dr. M. Kunze, by the Royal Saxon Experiment Station 

 at Tharandt dealing with the influence of various grades of thinnings on 

 the increment of Scotch pine stands. The investigation was made in the 

 State Forest of Kunersdorf near Schanden. It was begun in 1862 when 

 the stand was 20 years old and was ended in 1912 when the stand was 

 70 years old. During these 50 years, three comparative areas was 

 thinned ten times to wit : in the years 1862, 1869, 1874, 1879, 1883, 1889, 

 1894, 1900, 1905, and 1912, one area always with a light (A-grade) 

 thinning, another with a moderate (B-grade) thinning, and a third with 

 a heavy (C-grade) thinning. According to the description and the 

 fluctuation of index number we considered that the data observed in 1874 

 up to that in 1894 may be adopted in the discussion on the equations for 

 the fluctuation of the growth-factors for stand and for its elements, because 

 the data observed throughout these years may be approximately considerd 

 as those of the one phase. Strictly saying, however,' the data observed in 

 1874 up to 1889 will best answer the purpose. (Plate XVII.) 



The given diagrams show the following facts: — 



( i ) The fluctuation of each factor with respect to age shows dis- 

 continuity at the age of 52. 



( ii ) But the fluctuation of each factor shows the similarity in its 

 direction and in its form. 



(iii) The fluctuation from the age of 20 up to 52 shows a com- 

 paratively regular change, but the fluctuation of G and IQQOO -^ show 

 much irregulaity, especially at ages up to 32 and the age of 52. 



