216 SVEN PETRINI [52] 



for the portion of the stem within the crown and another for the remain- 

 der of the stem. This becomes apparent from fig. 4 which shows the average 

 taper in a stånd in Västerbotten. All felled stems have been measured 

 in I ms sections. The measurements have been graphically evened out and 

 the diameter at 10, 20, 30, etc. percent of the height were measured on the 

 stem curve. These values have been brought to relative numbers, by setting 

 them in relation to the diameter at half the height of the tree. 



With the use of the form class conception it can be shown that breast 

 height form class (= ratio in percent between the diameter at half the 

 distance above breast height and diameter breast height) characterises the 

 taper in that part of the stem below the crown, whereas that part of the 

 stem within the crown has another — and lower — form class value. The 

 values of ;/ which correspond to the form class values in fig. 4 are respecti- 

 vely 2,14 and 1,55 and the form class values are respectively 0,724 and 0,640. 



A. G. HojER has however set forth an equation for the stem curve 

 (2, 1903) which has the form 



- = C log 



D c 



where / signifies the distance to d in percent of the distance to D. D usually 

 is =^ Z> b. h. C and c are constants determined for different form classes. 

 It is this equation on which Jonson bases his taper tables. Fig. 5 shows the 

 close conformation of results with Hojers equation. The black line is the 

 same average stem curve as in fig. 4 and the red rings show the plotted 

 values reckoned from the equation by the use of constants for the breast 

 height form class, 0,724. 



Consequently if we merely know the correct value of the breast height 

 form class, together with the diameter and height, we could with the help of 

 Jonson's tables determine the diameter of a stem at any point we desired. 

 Especially for yield estimating, the log dimensions could be found in tables 

 worked out graphically, among which Löfgrens (5, 1920) are especially simple 

 and easily used since they give the height in english feet reckoned from 

 the ground for diameters of 3", 4" etc. with a tree of a given height, dia- 

 meter breast height and form class; and the divisions are carried out as far 

 as one can desire, diameter breast height being given in quarter inches, 

 form class in 2,5 E and heights by graphical interpolation. For pine and 

 spruce Tor Jonson has himself given graphic yield tables where stånds are 

 divided into 6 different yield classes as to form and height. (Tor Jonson 

 — Avsmalning för Tall och Gran i 6 godhetsklasser.) 



Root swelling 



When one compares the tree stem with a girder exposed to given forces 

 the comparison becomes somewhat inaccurate as to the (juestion of the 

 portions which are closest to the ground namely, where the stem divides into 

 roots. The girder is thought to be anchored at the lower end, but the 

 tree is anchored in the soil by its roots, thereby varying the pressures at the 

 butt end and giving rise to danger from splitting. The tree stem's root 

 portions must therefore be thicker than a girder and that is the strength- 

 ening which we call the root swelling. The size of the swelling varies under 



