GROWTH OF TREES. 9] 
to grow as high as the stump. An examination of a number of 
small trees would give an idea of the time required to grow up to 
stump height. This varies from one year in trees coming up as 
stump sprouts to as high as twenty years or more in some Rocky 
Mountain conifers, for heights of 1 to 3 feet. 
Since trees often grow faster on one side than another, the aver- 
age growth is gotten only by finding the average radius and count- 
ing and measuring the rings along it. Thus the radius of the tree 
may be found at ten, twenty, thirty years, etc., and by doubling 
these the diameters are found at these ages. 
HEIGHT GROWTH. 
The height growth is found by counting the rings at different 
sections and subtracting from the rings at the lowest cut. (lf this 
cut is not at the ground, add an approximate number of years to 
cover stump height.) Thus a white-pine tree in Minnesota, with 
a diameter of 30 inches and a height of 110 feet, showed 176 rings 
on the stump 2 feet from the ground. Adding four years as the 
time to grow these first 2 feet would show a total age of 176-++4, or 
one hundred and eighty years. At the upper end of the first 
16-foot log it showed 165 rings; at the second, 155 rings; at the 
third, 140 rings; at the fourth, 120 rings; at the fifth, 94 rings. 
Hence, the first 18 feet (2-foot stump+16-foot log) grew in 180—165, 
or fifteen years; the first 34 feet (2+16+16) in 180—155, or twenty- 
five years; the first 50 feet (2+16+16+16) in 180—140, or forty 
years; the first 82 feet (2+16+16+16+16+16) 180—94, or eighty- 
six years. The last 28 feet required 180—86, or ninety-four years, 
for their growth, indicating that the height growth had fallen off 
rapidly. 
VOLUME GROWTH. 
Entire Volume. 
Since for small variations in diameter and height the con- 
tents of trees vary approximately as the sectional area or square 
of the diameters, a simple method of getting the percentage in- 
crease in solid volume of a tree may be given. 
