THE ABSOLUTE FORM QUOTIENT 527 



Inserting the values for C, c, and D in Hoejer's formula, it becomes 

 possible to calculate the diameter d at any height within form class 0.70. 



Having found the constants for each form class, Jonson uses the 

 formula to compute the diameter at each tenth of the stem above 

 d. b. h. — that is, the values of / are 10, 20, 30, etc. — the top being equal 

 to o and d. b. h. equals 100. The diameters are thus computed at the 

 same points as on the analyzed sample trees. 



Table I gives the constants and taper series for six form classes, and 

 figure I shows the series o^ values given in Table I, represented graph- 

 ically. 



Table II is a comparison between mathematically computed diam- 

 eters and absolute form factors and diameters and form factors ob- 

 tained from measurements on sample trees. As will be noted, the 

 differences in form classes 0.60 and 0.70 are very small. Form class 

 0.80, however, shows a somewhat greater variation. This is probably 

 to a certain extent due to the small number of examined trees, but 

 more, no doubt, to the fact that 0.80 is a "border" class, where "regular" 

 trees are comparatively rare. It is probable, however, that if a larger 

 number of test trees had been examined the result would have been 

 much better in this form class. 



Since Professor Jonson published the figures given in Table II he 

 has had opportunity to examine an additional number of sample trees, 

 and has reached the conclusion that the mathematical formula shoivs 

 complete conformity zmth nature when applied to spruce of all form 

 classes. 



Divergencies from the "Normal Form" of Spruce 



Individual trees will, of course, sometimes show a divergency from 

 the "normal form." For instance, large nodes or damage to the stem 

 near the place of measurement may upset the series. The effect of 

 irregularities of this kind, however, is generally adjusted if a sufficient 

 number of trees are measured. 



In regard to systematic divergencies which do not disappear from 

 an average series, whatever the number of examined trees may be, 

 Jonson states that in some stands, which had been grown from im- 

 ported seed, it appears as if the measurements in the upper sections 

 fall one or two per cent short. Those stands were composed, however, 

 of relatively young trees, growing rapidly in height, and one explana- 

 tion is that they had not yet had time to "fill out." 



It is also probable that suppressed trees, which suddenly become 

 more or less isolated through removal cuttings or thiiniings, will some- 

 times for a short period show a divergency from the normal form in 



