INVESTIGATION ON FORM-HEIGHT TABLES FOR THE PRINCIPAL 



CONIFERS AND SOME BROAD-LEAVED TREES IN JAPAN AND 



BASES ON WHICH THEY MAY BE CONSTRUCTED 



By WATARU TERAZAKI, Forest Expert 



INTRODUCTORY REMARKS 



The following paper is an abstract of two memories published in 

 Bulletins of the Forest Experiment Station (No. 8 in 1910 and No. 9 in 

 1913). The work itself is an attempt to ascertain the relationship between 

 the variation of the breast-height form-factor and the characteristics of 

 the form of the tree bole. 



A. Form of Tree Boles 



A tree does not grow, like crystals, according to purely mathematical 

 laws. The form of a tree depends on its relative growth in diameter at 

 different sections. From this point of view and the assumption, i.e. that 

 the mantel surface of the body of tree bole will be considered as a 

 rotation-surface of a curve outlined by the longitudinal section, to the 

 geometical axis as the rotation-axis, we have the empirical equation for 

 the outline curve. 



According to my investigation of the growth curve for a single tree, 

 the differential equation for the growth of height and for that of radius 

 will be expressed as follows: 



^^- = kr -^- .... (1) and — ^= hz^- .... (2) 

 dt t' dt t 



where x and y denote the height and the radius at a given section, 

 measured from the tip respectively and t the age. 



In these expressions, the constant ki is the constant coefficient for a 

 given single tree, while the constant A;, varies with the situation of the 

 section. 



Hence k.^ must be considered as a function of a distance x measured 

 from the tip, so we put 



k^^f (x) 



