Diffiailties a7id Errors in Stem A^ialysis. 13 



log, the roughness of the river drive through which the log must 

 pass, and other similar causes. This variability of log length 

 gives considerable trouble in working up the data, but is of course 

 unavoidable. 



The object of the sectioning is in general merely to obtain the 

 area and height increments, and the thickness of bark, often the 

 width and age of the sapwood is also taken. The volume of the 

 stem is computed separately from a second series of measurements. 



To obtain the rate of height growth from the cut sections is of 

 course simple ; the difference between the number of rings on 

 two adjoining cuts gives the length of time during which the tree 

 grew in height the length of the intercepted section. 



To obtain the diameter growth correctly is neither simple nor 

 easy. Considerable error is here involved even with care and ex- 

 perience. This error will be greater on the stump section and 

 decreases on the upper sections. Ideally a tree is a paraboloid, 

 its cross section a circle ; really it is an extremely variable form. 

 Were the cross section a circle, and the annual growth concentric 

 layers of even thickness all around, the operation would be simple, 

 the measurements easy. One would merely have to la}^ the rule 

 across the section from pith to perimeter and count and measure 

 the ten year periods. 



In reality the outline of the cross section is extremely irregular, 

 especially so on the stump cut. The rate of growth desired is 

 finally that of the area of each section it must therefore be ob- 

 tained from an average radius. 



At first sight this would seem a simple matter, and so it is on 

 the upper sections, but the stump presents some difficulty. This 

 average radius may in general be obtained from the largest and 

 smallest diameters inside bark, but perhaps the largest diameter 

 is caused b}'' a sudden prominent root swelling ; it is evident that 

 a radius derived from this diameter would be two large, a deduc- 

 tion should be made from the diameter, preferably by the eye 

 with the calipers on the stump. 



The average radius having been determined, it is necessary to 

 lay it off on the stump. The number of places on which this 

 radius can be laid off will vary from two in an ellipse to an infinite 

 number in the circle. Assuming a case in which two only can be 

 found, would it make any difference which was taken ? 



