TIIK ABSOLUTE FORM QUOTIENT 531 



Diam. at section O I II III IV V VI VII VIII IX 



Pine, corrected, — i.i per 



cent 100 95.6 91.0 86.1 80.2 73.2 64.8 54.5 41.2 23.0 



Spruce, computed 100 95.8 "91.0 85.9 79.9 73.2 65.2 55.6 43.5 26.8 



Variation in per cent of 



D, — I.I per cent — 0.2 ±0 -(-0.2 +0.3 — 0.4 — i.i — 2.3 — 3.8 



The similarity in the lower portion of the stem is now almost perfect. 



Jonson now reaches this conclusion that, except perhaps in the upper 

 portions of the stem, pine inside bark and spruce zvith or zvithout hark 

 follow the same laws of taper. 



Practically the small divergence in the upper , sections is of little or 

 no importance, especially as spruce also sometimes shows an inclination, 

 in the upper parts of the tree, to fall a little short of the values ob- 

 tained by the formula. 



It would, therefore, no doubt be permissible to apply the formula 

 for spruce to pine also. Jonson, however, to obtain still better results, 

 has introduced a new constant, b, in the formula, which then reads : 



P = Clog — — ■ — . He finds that a constant value for b = 2.^ 



seems to bring about a more satisfactory result in all form classes and 



therefore gi 



c-\-l — 2.s 



therefore gives the equation for taper of Scotch pine as — = Clog 



where C and c vary for every form class. 



To discuss the nature of this new constant we will consider /^2.5, 



(^ -L. I 2.<^ . . C -\- 2.^ 2.'^ 



when the expression log — will be written log — ^- 



= log — = log I :^ o. Thus we have, according to the new formula, 



(/ = o at a distance of 2.5 per cent from the top. 



Consequently the new constant, b, must signify the same quantity 

 as / or per cent of the portion of stem above breast height, and, in ad- 

 dition, the efifect of a value ^ = 2.5 will be that every diameter will 

 be computed as if it lay 2.5 per cent higher up on the stem, by which 

 smaller diameter values will be obtained, specially in the top and in the 

 best form classes, where tlie taper in the uppermost sections is very 

 rapid. 



Xew values for the constants C and c are computed for each form 

 class as for sj)ruce. 



The new constants, the corresponding taprr series, and ahsuhUe form 

 factors are given in Table TH. 



It we comjiare these serie> w illi those for s|)ruee gi\eii in Tal)le 1. 

 we will tind that the difference is very small. The difference lies prin- 



