— 155 — 



ydt ' fXt) 



or if we use Maclaurin's theorem for <fi(i)> 



J,y ^n, 1 



ydt 1 + ait+a^t^+a^t^ + . . . . 



Practically, it may evidently be determind as follows: 



dy -i3f 1 



Q, ydt a.,t^ 



i.e. putting -!■ — =/3, 



ydt t" 



However strictly speaking, it will be pointed out in our investigation 

 of the normal growth of a single tree in our forest that we may part the 

 fluctuation of the rate of growth into two cycles or phases and that 

 for each phase, above given formula interprets the rate of growth in the 

 nearest degree. Unfortunately, so far as I have collected materials from 

 our forests, I cannot arrive at any conclusion as to the causes. Some 

 examples seem to suggest that the phase is caused by the conditions of 

 the underground soils or the degree of density and others make us 

 consider the difference of the root systems of the species. We are now 

 investigating this matter. 



The following illustration makes clearer the fluctuation of 



— ^- with respect to t, which is onerof examples of deep rooted species 

 ydt 



where the fluctuation of -^^ with respect to t has disturbed once, or has 



dt 

 two phases through the range of the life of the tree. (Plate XIV.) 



Test tree for Cryptomeria from Ushirozawa in the Kiyosumi Working 



Circle of the Tokyo Imperial University forest in Awa Province in Chiba 



Prefecture. 



Age: 80 years. Total height: 25.9 m. 



Diameter at breast-height: 30.0 cm. 



Stem-volume: 0.8664 m^ (Plate XV) 



Applying the equation h=ce ^ to the given data, we find; 

 10.6933 

 hi=]\.98e * for the first phase in m, 



34.9813 

 hn=39.82e * for the second phase in m. 



