A GENERAL FORMULA FOR TREE FORM 209 



possess a low form quotient, not because they are open-grown but 

 because the crowns of such trees are long and the form point low. Trees 

 with long clear length and high crowns possess a high form quotient, 

 whether they stand alone or in a crowded stand. Short trees may be 

 full-boled or the reverse — the rapidity of taper as a whole has no effect, 

 but the distribution of the taper, which alone affects the form quotient, 

 will vary with short trees as much as with tall, and on poor soils equally 

 with good. 



173. A General Formula for Tree Form. On this basis, if the actual 

 form of trees with the same form quotient is similar, it would be possible 

 to construct taper tables based on each of the three variables, diameter, 

 height and form class, which would apply to all species of trees. To 

 apply this principle there was required a general formula which would 

 give the diameter of a tree of given form quotient, at any point on the 

 stem, and second, a demonstration that the actual measurements taken 

 on trees of this form quotient coincided with the results of the formula. 



Once this was shown, the formula would permit of the construction 

 of a set of taper tables of universal application from which in turn any 

 manner of volume table could be derived. This is a more ambitious 

 program than the mere determination of form factors for cubic con- 

 tents, and promises permanent results. 



The formula devised by A. G. Hoejer is based on the portion of the tree 

 above B.H.: 



D = D.B.H. inside bark; 

 1 = distance from top of tree to section; 

 d= diameter of section. 



Then 



4 n^ c+l 

 - = Clog . 



D c 



C and c are constants whose value depends upon the form quotient of the tree; 



i.e., upon — when d is measured at one-half height above D, Their value must be 



found separately for each form class, and will then hold good for diameters at any 

 point on the bole of trees within this class, independent of total height of tree. 



Absolute heights are not used in the formula, but percentage or relative heights, 

 regarding the height of any tree above B.H. as 100, and the distance below the 

 tip, of any other section as its per cent of this length, including sections below 

 B.H., whose per cent of height would exceed 100. 



In the same way, absolute diameters are not used, but the D.B.H. is taken as 



100, and the relative diameter — expressed as its proportion of 100. 



These upper diameters are then measured at distances equaling tenths of this 

 total height above D.B.H. — thus falling at the same proportional height on each 



