206 FORM CLASSES AND FORM FACTORS 



of various units of measure in addition to cubic feet. Once the average 

 form class of the trees or stand were determined, then volumes could 

 be obtained from these basic tables. Recent research in Sweden tends 

 to show that this generalization holds true for certain species already 

 investigated, namely spruce, fir, larch and Scotch pine. 



171. Form Quotient as the Basis of Form Classes. The first real 

 step towards a solution of this problem was made by Schiffel in 1899, 

 who developed a method of expressing differences in form, previously 

 used (Schuberg, 1891) and known as the form quotient, which is the 

 percentage relation that the diameter at one-half the height bears to 

 the D.B.H. 



The differences in form of the entire boles of trees (Chapter III) 

 are expressed by their divergence from a cylindrical form through a 

 series marked at definite stages by the complete paraboloid, cone, and 

 neiloid. Each of these solids can be measured by Newton's formula: 



7=(S+4bj+6)|. 



The middle point on the stem of a tree, regarding the entire bole as a 

 single complete solid, is evidently the point of greatest weight in deter- 

 mining its form and volume with respect to the cylinder whose base is 

 B and height h. 



By a complicated calculation,- Schiffei derives tne formula for 

 obtaining at one operation the true cubic contents of an entire stem as, 



F=(.16fi+.66&j)A. 



This is known as Schiffel's formula. 



Newton's formula, regarding the tree as a perfect, i.e., complete 

 conoid, and the diameter at top as zero would be, 



F=(.16iB+.66f6 } )fc. 



The " universal " character of Schiffel's formula failed to make the 

 headway expected when it was first introduced in the United States 

 for the reasons that, to apply it, one must measure the diameters of 

 trees at one-half the stem height, and that the cubic unit of volume 

 was little in demand. 



The really valuable part of Schiffel's work was not the formula, 

 which was nothing new, but the form quotient. This was his demon- 

 stration that the true form, and consequently the variation in form of 



1 "New Method of Measuring Conifers," Review by B. E. Fernow of Article 

 by Schiffel, "tlber die Kubirung und Sortierung Stehender Nadelholz Schafter," 

 Centralblatt fiir das gesammte Forstwesen, Dec, 1906, pp. 493-505, Forestry Quar- 

 terly, Vol. V, 1907, p. 29. 



