THE JONSON " ABSOLUTE FORM QUOTIENT " AS AN 

 EXPRESSION OF TAPER 



By H. Claughton-WalIvIN, Dominion Forestry Branch, Ottawa, 



Ontario, and F. McVicker, British Columbia Forest Branch, 



Victoria, B. C. 



In an article published in the Journal of Forestry, Volume XVI, 

 No. 5, May, 1918, one of the above writers gives an account of the 

 investigations carried on by the Swedish Forester, Professor Tor Jon- 

 son, with reference to the stemform of Norway spruce and Scotch pine. 



To express the variation in stemform or taper, Jonson uses a new 



formula, the "absolute form quotient," q=f) where "d" is the 



diameter at the middle of the stem above breast height, and D is the 

 diameter at breast height. This formula differs from Schiffel's form- 

 quotient in that "d" in Schiffel's formula is situated at the half total 

 height of the tree. The advantage of Jonson's method in expressing the 

 variation in form which is fully explained in the above mentioned 

 article is that the classification is made independent of height, the two 

 form-determining diameters always being in the same relation to each 

 other. Schiffel and others have shown that trees with the same form 

 quotient and equal height taper according to a fixed law. Jonson 

 claims that taper of trees of the same absolute form quotient or "form 

 class" is also independent of height if the measurements are taken at 

 proportional places or as Jonson states in his articles on the stemform 

 of Norway spruce : "The percentic taper is the same in all 'normal' 

 spruce of the same formclass, notwithstanding differences in height 

 and diameter. A large tree is developed exactly as a small tree, pro- 

 viding both have the same absolute form quotient." 



After having reached the same conclusion in regard to Scotch pine, 

 Jonson generalizes Hoejer's formula for the stem curve and uses it to 

 calculate the taper for each form class, finding, as is shown in the above 

 mentioned article in the Journal of Forestry, that the mathematical 

 formula shows complete conformity with nature. Taper and volume 

 tables are then constructed. L. Mattson-Marn of the Swedish Institute 

 of Experimental Forestry, has carried on the investigation on larch. 

 He finds that scarcely any difference is to be observed between the taper 



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