FORM FACTORS 211 



Can these two variables be eliminated for American trees, and taper and volume 

 tables constructed for trees of each form class, thus attaining the goal of universal 

 volume tables? 



For second-growth, or young timber, in which the factor of butt swelling will 

 not affect D.B.H., this can be done. Taper tables should be constructed from this 

 normal formula based on diameter inside bark at B.H. The average thickness of 

 bark at B.H. must be determined for the species, and by graphic interpolation 

 these D.I.B. taper tables can be drawn for trees of each D.B.H. outside bark, from 

 which volume tables can be constructed in any desired unit. 



For the larger trees or species with butt swelling extending above B.H., as for 

 instance, virgin stands of timber on the Pacific Coast, or Southern cypress, the 

 present practice of adhering to D.B.H. will probably be continued, and trees with 

 variable amounts of stump taper averaged together in volume tables regardless of 

 true form. The only alternative is to attempt a standard measurement of diameter 

 at a higher point dn the bole, which will be difficult to adhere to in practice. Approx- 

 imate rather than absolute accuracy will continue in the preparation and use of 

 these tables for such timber. 



When the variable influence of butt swelling is further aggravated by the 

 obsolete practice of basing volume tables on diameter at the stump, no consistent 

 volumes can be obtained to serve as standards for estimating. 



175. Form Factors. The form of a tree is a variable independent 

 of diameter or height, while the form of a cylinder does not vary at all. 

 That of a cone is a constant, equal to one-third of the volume of a 

 cylinder of similar height. Taking the volume of a cylinder as the 

 unit of comparison, and dividing the volume of a cone by that of the 

 cylinder of equal diameter and height, the quotient is always .333 or 

 one-third. This can be termed the form factor of this cone, i.e., the 

 factor by which the volume of the cone is derived from that of the cylin- 

 der. It expresses the volume of the cone, but not its form. In the same 

 way the form factor of the paraboloid is .5. 



Form factors of trees can thus be found by dividing their cubic 

 volume by that of a cylinder of equal diameter and height. 



B = Basal area of cylinder equivalent to that of tree; 

 h = height of cylinder and of tree; 

 Bh = volume of cylinder; 

 /=form factor or multiple expressing the relative volume of the 



tree; 

 V- volume of tree. 



Then 



V=Bhf. 



