528 JOURNAL OF FORESTRY 



the upper sections. Jonson considers the systematic nature of these 

 divergencies as somewhat problematic, however. 



Root swelling, if reaching above breast height, will, of course, cause 

 a divergency between the measured and mathematically computed stem 

 curves. It occurs to a more or less degree in all spruce, but has no 

 influence on the stem-curve calculations unless it reaches above breast 

 height, in which case it was considered by Jonson an abnormality. 



Of the test trees examined, Jonson found that lo per cent had root 

 swelling reaching above d. b. h. These trees were consequently ex- 

 cluded. 



The simplest practical way to avoid the incorrect results due to high 

 root swelling is to measure the d. b. h. just above the swelling — that is, 

 at the turning point between the more or less concave curve above the 

 swelling and the convex curve in the lower portion of the tree. 



VOLUME CONTENT AND FORM FACTORS 



The form of the stem in all portions being known, there will be no 

 difficulty in computing taper tables, volume content, and form factors. 



Tables of taper for spruce were constructed. These tables, based on 

 the formula for the stem curve, give the diameter in per cent of d. b. h. 

 at every meter counted from the stump. The height of stump is taken 

 as I per cent of the total height of the tree. 



To obtain the absolute or Rinicker form factor for the volume above 

 breast height, Jonson first computed the volume in each form class with 

 the known diameters as basis. 



For instance, the stem above breast height is divided into ten sections 

 of equal length as before. The diameters are D, d^, dz, d^, . . . dg, 

 and the corresponding basal areas B, b^, bz, b^, . . . b^; the length 



of each section is , and the volumes of the sections V, v^, v., Vg, 



. . . are the product of the average basal area and the length. 



B + b, L 



The top section is cubed as a paraboloid. Thus : v^^ 



2 10 



Vn = ^ — - — . . . ; ^10 =— ^ — and the volume above d. b. h. 



2 10 2 10 



Y 



V = v-j^ -\- Vn -\- v^ -\- . . . z^io J* and the form factor — —r = 



h L 

 r> 



2 ®^orby canceling L and — the absolute 



ioTbZ ~^ ^ ^ 



-^ + ^x' + d^^ + rfs' + . . . 0^9' 

 (Rinicker) form factor =_2 __^ . 



10. D^ 



