14 



the area of a circle with a diameter of 26 inches), we find the volume of 

 the tree to be 152.5 cubic feet. The merit of this method lies in its 

 being equally applicable to trees of various geometrical forms; it is 

 correct for trees of parabolic and conical forms: for trees representing 

 the form of a cone with a concave surface the difference is only 1.4 per 

 cent. 



MEASUREMENT OF VOLUME OP A STANDING TREE BY EMPLOYING 

 THE PACTOR OP SHAPE. 



The trunks of trees, as has been mentioned, differ in shape. The 

 shape of the trunk of a cypress, a spruce, or a fir is totally different from 

 that of a pine, hemlock, or oak. The cypress, 

 spruce, and fir, tapering rapidly toward the top 

 of the tree, form stems resembling either a cone, 

 as in the spruce and fir, or a neloid or conical 

 shape with a concave surface as in the cypress. 

 The pine, the hemlock, and most of the hard- 

 wood trees, tapering more gradually toward 

 the top, form stems of a conical shape with a 

 convex surface. An oak or a tulip tree, on the 

 other hand, may nearly approach the shape of 

 a cylinder. As we have stated before, trees 

 never attain a mathematical form, but only ap- 

 proximate more or less closely one or the other 

 form. 



The European foresters noticed long ago that 

 there exists a relation between the actual vol- 

 ume of a tree and that of a regular geometri- 

 cal body of corresponding dimensions. From 

 actual calculation they learned further that 

 this relation, varying with the kinds of trees, 

 their dimensions, and conditions of growth, 

 seems to be strikingly uniform. In Germany, 

 for instance, there were measured more than 

 forty thousand individual trees of various spe- 

 cies and, all of them being felled, the forester 

 was able to determine their volume in an accu- 

 rate way. The actual volume of each individ- 

 ual tree thus obtained was compared with that 

 of a cylinder of the same height and of the diameter at breast height. 

 This comparison proved that the actual volume of the tree when di- 

 vided by that of the cylinder of the corresponding dimensions gives a 

 quotient which is constant for trees of the same species, approximately 

 the same dimensions, and grown under the same forest conditions. 



This quotient showing the taper of the tree, or the relation between 

 the volume of a tree and of a cylinder of the same height and diameter 

 breast high, is called the factor of nliape or form factor ; it is usually 



-Determining the fac- 

 tor of shape. 



