53 



should be raised, the lengths of which should correspond with the 

 heights successively attiiined at the different ages. A continuous 

 line joiuing the upper extremities of these perpendiculars will be 

 the required curve. The horizontal scale for years should be about 

 twice the vertical scale for feet. 



The contents of the- tree at the successive ages (every fifth or 

 tenth year, as the ease may be) are at once ascertained from the 

 sectional areas enclosed by the outer boundaries of the concentric 

 group-zones, each sectional area being the mean sectional area of 

 a truncated cone, situated half in the upper half of one section, and 

 the other half in the lower half of the one immediately above it. 



Finally, the periodic increments of diameter, height and volume 

 can be arranged in tabular form so as to be noted at a glance. 



"We will illustrate all the preceding remarks by means of an 

 example. 



A spruce was felled at 3 inches above ,the ground, and the stump 

 showed 43 annual rings. We may assume that the tree took two 

 years to attain this height, and it is on record that it was sown 46 

 3'ears ago. The total length of the tree was 64 feet, the stem was 

 cut up into lengths of 6 feet each, except the lowest portion, which 

 was 4 feet long. On all the sections, beginning from the circum- 

 ference, the annual rings were marked oflE into groups of five each 

 along three different diiimeters on the two lowest sections (at j and 

 4j feet from the ground), and along two diameters crossing each 

 other at right angles on the rest.. For each section the mean of the 

 two or three diameters, according to the piece, was taken. The 

 results of the observations are shown in the following statement : — 



