[51] STEM FORM INVESTIGATIONS 215 



ness, stånd average form class inside bark and data in order to plot a curve 

 of the heights on the diameter. It is the purpose of the present investiga- 

 tion to determine whether the bark thickness can be measured and reckoned 

 as an average for a stånd or large tract, whether form class is really an 

 expression of the tree form and how the value of the form class can be de- 

 cided. Experiments are also made to valuate a stånd through the use of 

 differentmet hods. All investigative material is taken from stånds of Lapp- 

 land pine (P. sylvestris f. lapponica) and the results may be applied closest 

 to the Lappland pine. The sample plots have generally been 0,25 hectars in 

 size. The location of the stånds may be found on the map in fig. i. 



Bark. 



It is known that bark thickness — measured in mm — at breast height for 

 pine can be depicted graphically by a straight line running through the 

 origin (the abscissa being diameter breast height). The line shows that 

 the ratio between bark thickness and diameter breast height is always con- 

 stant. Fig. 2 shows the average series for Lappland pine secured in the 

 investigation of 53 stånds in Västerbotten. On an average the bark diameter 

 is 11,4 % of the total diameter which ought to be rounded ofif to 1 1 %. 

 The bark measureing instrument used in these investigaticns is pictured in 

 fig. 3. The material for this study comprises not less than 3,303 sample 

 trees. This material has been described previously (9 Skf 19 19, h. i) and 

 fig. I includes only part of it. The variation figures have been tried upon 

 the material in fig. i and it appears that for Lappland pine one can assign 

 a single bark type where the standard deviation from the average series in 

 fig. 2 and table i for a given diameter class is + or — 0,5 mm. The stånd 

 bark percentage varies around the average value 11,4 and the standard 

 deviation here is + or — 0,9. 



Stem form. 



The mechanical theory of tree trunk growth, which provides for the 

 smallest amount of material able to withstand all wind pressures, demands 

 a form of tree similar to that of a cubic paraboloid. This]^ is correctly 

 applicable only to that part of the stem which lies below the crown 

 since the portion within the crown has a more rapid taper (8, 9). In fact 

 the cubic paraboloid is seldom found in the actual stem. On the other 

 hand the square paraboloid is usual. Stem forms however vary greatly and 

 one can take for the stem curve ei^uation the form which the foregoing 

 reasoning advocates, namely, 



h / d\"- 



where h and H represent the distances from the top to the diameters d and D 

 and 11 equals the variations from i which is a cone, to 3 which is a cubic para- 

 boloid. For parts of the stem n can even 'take on a value less than i. 7/ is 

 seldom a whole number usually taking a decimal form (as 2.14 in fig. 4). 



If one uses the above formula it is evident that the same «-value cannot 

 be retained, even for a given stem curve. In fact a special «-value is got 



