146 TRANSACTIONS OF ROYAL SCOTTISH ARBORICULTURAL SOCIETY. 



part of the stem above the 3 inches diameter, the "tree-point" 

 (Fig. 7). It is obvious that, for every tree of uniform taper and 

 with the same degree of taper, this tree-point is the same 

 size, shape, and length. For trees of the particular degree of 

 taper we have selected, namely 2°, the length of the tree-point 



is =— ^ — s = -^^- = 8 ft. 6 ins. roughly. 

 Tan I '0175 



Fig. 8 shows a very small tree, less than 8 feet high. It has 



obviously no volume and the form-factor must be o-ooo. Fig. 9. 



is a slightly larger tree, say 17 feet high. The volume of this 



tree is much less than half the volume of the cylinder. It is, 



say -200. Fig. 10 shows a relatively larger tree, in which the 



tree-point is a small part of the total height, so that the 



figure again approximates to that of Fig. 2, and the form-factor 



approaches "333, say •310. This form-factor is, therefore, not 



an absolutely true expression of form. For trees of the same 



form it increases gradually, though not constantly, from '000 to 



about •310. 



IV. — Breast-height Form-factor with Timber 

 Measurement to 3 Inches Diameter. 



Here the base is at 4 ft. 3 ins. above ground, and the form- 

 factor expresses the ratio between the volume of the tree up to 

 3 inches diameter and that of a cylinder of the same base, but 

 of the total height of the tree. This is the most important type, 

 up to which we have been leading. 



Fig. 1 1 shows a very small tree, less than 8 feet high. Being 

 shorter than the tree-point, it has no volume, and the form- 

 factor must be o-ooo as in Fig. 8. Fig. 12 shows a slightly 

 larger tree, but the breast-height diameter is still less than 

 3 inches, and the base of the tree-point lies below breast- 

 height, say at 3^ feet. If it be assumed that the surplus of 

 timber outside the cylinder equals the deficit between the base 

 of the tree-point and breast-height, as it must do with a certain 

 size of tree, then the volume of timber is equal to the volume of 

 one-third of the cylinder and the form-factor is '$^3. Fig. 13 

 shows a slightly taller tree, 12 ft. 9 ins. high. Since the base 

 of the tree-point coincides with breast-height, the tree has no 

 timber above breast-height, but below breast-height it has 

 somewhat greater volume than one-third of the cylinder. The 



