THE ABSOLUTE FORM QUOTIENT 525 



"upper diameter" is measured at the middle of the portion of the stem 

 lying above breast height. This form quotient, which Jonson calls the 

 "absolute form quotient/' is used to classify the trees examined in re- 

 gard to taper or form. According as the diameter at the middle of the 

 stem above breast height is 55, 60, 65, 70, 75, or 80 per cent of the 

 diameter at breast height, form quotient classes, or form classes, 0.55, 

 0.60, 0.65, 0.70, 0.75, or 0.80, are obtained. 



The taper tables for spruce published by Jonson were obtained from 

 other tables by analytical geometric calculations. He also examined 

 sample trees, partly to investigate the variation in form in individual 

 trees and partly to prove the applicability of the mathematical calcula- 

 tions for practical purposes. 



Investigations in Norway Spruce (Picca excelsa) 



A number of normal spruces of different diameters and heights were 

 chosen as sample trees. These were classified according to their abso- 

 lute form quotients in form classes 0.60, 0.70, and 0.80. The portion 

 of the stem above breast height was divided into 10 sections of equal 

 length and the top diameter of each section was measured. The meas- 

 urements were thus taken at proportionally the same height on all 

 trees — that is, in addition- to breast height (1.3 meters), at one-tenth, 

 two-tenths, three-tenths, or 10, 20, 30 per cent of the stem above breast 

 height. The ratio between each measured diameter and the d. b. h. 

 was then ascertained. 



In addition an eleventh measurement was taken 0.3 meter from the 

 ground. All diameters were measured with bark, as it has been proven 

 that the bark of spruce practically is proportionate to .the diameter at 

 any point along the stem. 



Maass (Sweden), Schiffel (Austria), and others have shown that 

 trees with the same form quotient and of equal height taper according 

 to a fixed law. For instance, if two trees 20 meters high, but of differ- 

 ent d. b. h., have "upper diameters" which are 70 per cent of d. b. h. — 

 that is, belong to form class 0.70 — the diameters at 5, 6, 7, 8, etc., 

 meters constitute the same percentage of the breast-height diameter on 

 both trees. The absolute taper is, of course, not the same. 



Professor Jonson reaches the conclusion that taper of trees of the 

 same form class is also independent of height, the measurements being 

 taken at proportional places — for instance, at each tenth of the stem 

 above breast height. 



The table exhibiting the result of these measurements shows the 

 variations very small. Normal trees belonging to other form classes 



