714 JOURNAL OF FORESTRY 



ume of the corresponding cone frustum. In so far, then, as the first 

 three factors are concerned, the exact volume of a tree showing any 

 possible combination of these factors can be computed by mathematical 

 calculations. 



"It is the opinion of the writer that, as a matter of fact, taper ratio 

 (ratio top diameter and diameter breast high) is a better expression 

 of taper than is its amount per unit of height or per log, although it 

 introduces an entirely new conception. 



"The relationship between the form quotient, taper ratio, and the 

 frustum form factor was discovered by expressing the frustum form 

 factor in terms of the volume formulas of the geometrical figures which 

 resemble trees. It is evident that when the frustum form factor is 

 greater than unity the form of the tree approaches that of the parabo- 

 loid, and that when it is less than unity it approaches that of the 

 neoloid." 



After discussing the opportunities for and need of further studies, 

 the author admits that his formula for finding the value of the absolute 

 diameter breast high frustum form factor in terms of the taper ratio 

 and form quotient is too involved to come into general use. He be- 

 lieves, however, that "the intelligence with which the frustum form 

 factor is used is conditioned upon the fullness with which the laws 

 governing its variations are understood. Eventually these laws will be 

 reduced to some simple form that may be used generally by timber 

 estimators, while for the present in most practical work contentment 

 with more or less approximate values will be necessary." 



In its application to practical estimating, the author makes the fol- 

 lowing suggestions : 



"On any particular area, first find the frustum form factor or abso- 

 lute diameter breast high cylinder form factor. This must be done 

 first, because if the ratio of top diameter to diameter breast high (taper 

 ratio) and form factor are uniform over a given type, the estimate can 

 be based on the type as a unit of area ; on the other hand, if it is deter- 

 mined that there are several different taper ratios and form classes in 

 the same type, it will be necessary to base the estimate on form classes 

 rather than type area and tally the trees by these form classes. 



"The necessary measurements are : 



"(a) Diameter outside bark (d. o. b.) at merchantable height. 



"(b) Diameter outside bark at one-half distance between diameter 

 "breast high and merchantable height. 



"(c) Diameter breast high. 



"(d) Height. It is unnecessary to take height in order to obtain 

 f. f.. but it can be done most easily at this time. 



