210 FORM CLASSES AND FORM FACTORS 



tree; e.g., for the form class 0.70 with diameter at 0.5 of height above B.H., ad 

 0.7 of D.B.H., the values in the formula are: 



For upper section, 



For D.B.H. section, 



™=Clog^° (1) 



100 B c 



™-Clog^ (2) 



100 B c w 



If equation (2) is divided into equation (1), then 



0.70 log (c+100)=log (c +50) +(0.70-1) log C. 



The value of this constant c is then found by trial. Inserting this value in equa- 

 tion (2) the value for constant C is found for the form class. Values for the remain- 

 ing form classes are found in a similar manner. 



With the numerical value of the constants C and c determined, the normal diam- 

 eter of a perfectly formed tree can be found by this formula at any point on the 

 stem above B.H., and this normal diameter can also be calculated for stump height, 

 thus disregarding the stump taper. 



By determining these normal diameters for trees of each D.B.H. and height 

 class, at intervals of one-tenth of the total height, and plotting these diameters 

 graphically, a set of taper curves is constructed (§ 167), for normal tree forms, 

 from which volume tables or form factors can be constructed which will have 

 universal application. 



174. Applicability of Hoejer's Formula in Determining Tree Forms. There 

 remained to test accuracy of these results by comparing them with measurements 

 on felled trees. The tests showed that for the conifers measured, spruce, fir, larch 

 and pine, the formula expressed the form of the living tree, when applied inside 

 the bark at all points including D.B.H., and that for species with thin bark such 

 as spruce, the same relations applied when measured outside bark. For Norway 

 Spruce the volumes of individual trees fall within ± 3 per cent of those derived 

 by the formula. But for thick-barked species such as Scotch pine, a poorer form, 

 less cylindrical, was obtained outside bark, which changed the form class, but 

 did not seriously interfere with the application of the method. Claughton- 

 Wallin has since shown that this formula holds good for Norway or red pine 

 (Pinus resinosa) and white pine (Pinus strobus). 



As with all attempts to study the laws of tree form, this formula depends on 

 measuring. a diameter which is not affected by the abnormal flare at the butt; 

 hence any tree or species whose butt swelling extends above B.H. will not corre- 

 spond, in form to the diameters in the formula based on this abnormal D.B.H. 

 It was found impossible to use the formula for western conifers since the form 



d 

 quotient — was too low for this reason. 



For general application, the second difficulty is the factor of bark thickness, 

 whose effect upon the form quotient and form class must be worked out for different 

 species with variable thicknesses of bark, so as to correlate the method with D.B.H. 

 measurements outside the bark, which must continue to be used in practical 

 estimating. 



