29 



annual accretion for the one hundred and twentieth year may be 1.4 

 cubic feet ; and if we had ascertained the volume which it formed in 

 the last ten years, as 15 cubic feet, this would be the periodic accretion 

 for that decade. 



The measurements by which the accretion, annual or periodic, is 

 ascertained, rely upon the fact that, in all temperate zones at least, 

 trees form annually one layer of wood, which appears on a cross section 

 of a tree as a ring, more or less clearly defined, and on its longitudinal 

 section made through the pith as a section of an enveloping cone (fig. 10). 

 Hence by counting and measuring the rings appearing on cross sections 

 taken at various heights from the ground, or by counting and measur- 

 ing the enveloping cones appearing on the corresponding longitudinal 

 sections made through the pith, not only the age, the progress in 

 diameter, and area increase of the sections, but its height and volume 

 development can be easily and accurately ascertained. Let us, for 

 example, analyze the tree represented in fig. 10: A represents the 

 longitudinal section of the tree made through its pith; B represents 

 the tree in cross sections, made (1) at the surface of the ground; (2) at 

 13 feet J (3) at 25 feet; (4) at 37 feet, and (5) at 49 feet from the ground; 

 the total height of the tree is 54 feet. Each ring of a cross section 

 corresponds to an enveloping cone, and the number of concentric rings 

 counted on a cross section, as seen from fig. 10, corresponds with the 

 number of enveloping cones counted above each section. 



Just as the width of the concentric rings on both sides of the center 

 on a cross section determines the annual increase of the diameter, so 

 the distance between the apexes of two enveloping cones determines 

 the annual increase of the height. , It is clear that the difference 

 between the number of rings counted at the bottom and top sections of 

 a log gives the number of years which it has taken to produce the 

 length of the log. Or, if we take the lowest section of the tree, cut so 

 that all the years of its growth are contained in the section (as in fig. 

 10), and deduct from the number of rings found on this section the 

 number of rings found on any higher section, the difference then equals 

 the number of years during which the tree had grown to attain the 

 height of the higher section. Or, again, the number of rings counted 

 on a cross section gives also the period of time during which the por- 

 tion of the tree situated above has developed its height. Thus we find 

 that during the period of forty-four years, the age of the tree, the trunk 

 has reached 54 feet in height. The average annual growth in height is 

 therefore equal to 54 feet divided by 44, equals 14.7 inches. 



From the second cross section we find that the tree had grown 40 feet 

 in the last thirty-one years (number of rings on that section), which 

 means 15.8 inches annually during that period ; or subtracting from the 

 total age of the tree (44) the age of the second cross section (31) we 

 find that the tree during the first thirteen years of its life has reached 

 the height of the second section, i. e. 13 feet, which means that the tree 



