526 JOURNAL OF FORESTRY 



were also examined, and the variations between individuals or groups 

 of individuals in the same form class were found so insignificant that 

 Professor Jonson considers himself justified in stating: "The per- 

 centic taper is the same in all 'normal' spruce of the same form class, 

 notwithstanding differences in height and diameter. A large tree is 

 constructed exactly as a small tree, providing both have the same abso- 

 lute form quotient." 



EQUATION OF THE STEM CURVE 



After having shown the similarity in stem form of normal spruce 

 within the same form class, Jonson's next step was to find a mathe- 

 matical expression therefor. 



Many foresters (Breymann, Metzger, Pressler, Strzelecki, Nossek, 

 Phillipp, and others) have constructed formulas to serve as mathe- 

 matical expressions for all forms of tree-stems. They have all been 

 criticised by Schiffel (Austria), who stated that none of them had been 

 able to construct an equation for stem taper which is really consistent 

 with nature. 



A. G. Hoejer, a Swedish civil engineer, has published the following 



formula as an expression for stem curve : —-= C log , where 



D = diameter at the base, d = diameter at a distance / from the top ; 

 C and c are constants. 



Jonson generalizes this formula and uses it to calculate the taper for 

 each form class. If, for example, it is desired to compute the taper 

 series for form class 0.70, diameter d, measured half way {= 50) be- 

 tween top and d. b. h., is 70 per cent of the diameter at breast height, D, 

 which is regarded as base (= 100) and situated a distance of 100 from 

 the top. 



By inserting these known values in Hoejer's equation, we obtain: 



7^ = Clog^+^ (I) 



100 c 



, 100 ■ ^ , c 4- 100 , . 



and = C log ■ (2) 



100 r 



If equation (2) is divided into equation (i), we find: 0.70 log 

 (c -j- 100) = log (c -\- 50) -f (0.70 — /) log c. By trying out differ- 

 ent values for c, Professor Jonson finds c = 19.78. By inserting this 



, , . .• / N . 100 ^ 1 1978 + 100 , 



value for c m equation (2) we get = C log — ^-^^ —^ and 



^ V / t. jQQ to 19.78 



C= 1.28. 



