2i6 Forestry Quarterly. 



ratio between the merchantable stem of a tree and that of the 

 frustrum of a cone having the same height, and the same upper 

 and lower bases. For the present purposes the volumes may be 

 figured in board feet, and the assumption may be made that 

 the D. B. H. outside the bark and the D. I. B. at the stump 

 are equal. This is of course fallacious, but when used as will 

 be described in this article will be seen to introduce no error. 

 The frustrum form factor expresses, to put it in other terms, the 

 relation between a given tree and a tree whose taper between 

 its top cut and a point four and a half feet from the ground is 

 absolutely regular. 



It is evident that the frustrum form factor will diflfer markedly 

 from the usual form factor based upon the cylinder in two 

 ways. While the values of a table of ordinary form factors 

 will range in the neighborhood of .5, the frustrum form factors 

 will be quite close to unity. Further, the range of variation of the 

 latter will be considerably less. This is because one of the fac- 

 tors of variation of the ordinary merchantable form factor is 

 eliminated. A full-boled tree, for example, has a larger volume 

 in board feet and a consequently larger form factor than a more 

 rapidly tapering tree of the same diameter and total height, 

 due to the fact that there are more (or longer) logs composing its 

 stem as well as that the top diameters of the logs are larger. 

 This variation of merchantable length is obviously eliminated 

 from the frustrum form factors. 



But little use has been made of the form factor of any sort 

 by the American forester. He has almost seemed to treat it as 

 a sort of scientific curiosity, scarcely realizing, apparently, that 

 every volume table is but a table of form factors in disguised 

 form, and that the one can be readily converted into the other. 

 A volume table based on diameter and total heights is equivalent 

 to a table of ordinary form factors, while one based on diame- 

 ters and merchantable heights can be converted directly into frus- 

 trum form factors. 



The utility of the frustrum form factors can be most easily 

 demonstrated by this conversion process. A volume table, to 

 be available for this purpose, must satisfy the following condi- 

 tions ; it must be based on diameters and merchantable heights, 

 and it should have the D. I. B. of the tops given by inch classes. 



