ABSOLUTE FORM QUOTIENT 353 



quotients determined. Average series were thereafter constructed. It 

 was found, however, that the series did not as a rule agree very well 

 with Jonson's series or with those obtained in the East. This is, no 

 doubt, due almost altogether to the root swelling which occurs on 

 practically ail large trees and runs up quite high in some species, often 

 to 12 or even 20 feet above the ground. It is obvious that in dividing 

 the diameters at each tenth above breast height with an "abnormal" 

 breast height diameter, we will obtain an abnormal series of quotients. 

 Eleven Douglas fir were measured. The average of these was a 

 tree 111 feet high, with a d.b.h. inside bark of 15 inches, and with the 

 following diameter measurements : At 19 feet above ground, 12.9 

 inches; at 35 feet, 11.9 inches; at 51 feet, 10.9 inches; at 67 feet, 9.4 

 inches ; at 83 feet, 7.5 inches, and at 100 feet, 4 inches, all inside bark. 

 These measurements were plotted on cross-section paper and a curve 

 representing the taper of the tree drawn through the known points. 

 This showed that at 18 feet above the ground the curve began to 

 swing outwards on account of the butt swelling. To do away with this 

 swelling, however, the curve was prolonged downwards from the point 

 according to its natural trend and a "normal" breast height diameter 

 of 13.4 inches was obtained. This new breast height diameter was 

 divided into the diameter at each tenth above breast height read off on 

 the curve, and the following taper series obtained : 



Douglas Fir — Form Class yy.^ — Average ii Trees. 



Diam. at 



sec. in per cent 



of d.b.h. (b. h.) I II III 



Douglas fir 100 96.6 92.8 88.4 



Scotch pine 100 96.5 92.7 88.2 



Variation in 



per cent +0.1 +0.1 +0.2 



Absolute form factor, Douglas fir 0.554, 



Again we find a surprisingly good conformity between the two 

 series. 



Western white pine was also given a trial. The average of 16 trees 

 was a tree 130 feet high with a breast height diameter at 19.5 inches 

 inside bark. Here the two series were after correction for root swell- 

 ing, the "normal" diameter being 18.1 inches: 

 Western 



white pine 100 95.0 89.2 82.6 75.7 69.3 60.1 50.8 38.7 22.7 



Scotch pine 100 95.1 89.4 83.5 76.7 69.3 59.0 49.4 36.1 18.5 



Variation in 

 percent —0.1 —0.2 —0.9 —1.0 .... +1.1 +1.4 +2.6 +4.2 



