METHODS OF DETERMINING TOLERANCE. 25 
natural thinning of stands; the rapidity of growth; the ability of 
young seedlings to come up under the shade of older trees; and the 
ratio between the diameter and height of a tree, may all be used as 
a basis for determining the relative tolerance of different species. 
DENSITY OF CROWN. 
Density of crown is, without doubt, a fairly good criterion for 
determining the tolerance of a tree. The denser the crown the less 
light is received by the leaves hidden within the crown, and conse- 
quently the more tolerant is the species, and vice versa, the more 
open the crown the more intolerant the species. The degree of den- 
sity or looseness of the crown can not, however, be accurately meas- 
ured and must always be ocularly estimated. This introduces a sub- 
jective element into the observation, and while it is possible to de- 
termine with a fair degree of accuracy the extreme members in the 
scale of tolerance, the intermediate species must always be arranged 
more or less arbitrarily. 
SELF-PRUNING. 
The rapidity with which the trunk clears itself of lower branches 
is a splendid indication of the degree of tolerance. The dying of 
live branches on the lower portion of the trunk and crown in dense 
stands is, without any question, due to lack of light, which is not 
sufficient for the assimilative processes of the leaves. The more in- 
tolerant the species and the denser the stand, the more rapid is the 
pruning. lLight-needing species clear themselves of branches even in 
isolated positions, although of course m a less perfect way than in 
dense stands. Shade-enduring species, however, lose the lower 
branches only in dense stands, and in the open the crowns reach 
almost to the base of the trunk. This criterion of tolerance, however, 
has the same objection as the previous one; it leaves too much to the 
subjective impression of the observer. Furthermore, this process of 
self-pruning is often confused with the mere falling off of the dead 
branches, which is due not to light, but to mechanical causes. | 
NUMBER OF BRANCH ORDERS. 
Mathematically, a tree or branch should contain as many succes- 
sive orders of branches as there are years in the life of the tree or 
branch, minus one. Thus, a 100-year-old oak should have 99 suc- 
cessive orders of branches; as a matter of fact, there are found, as a 
rule, not more than five or six different orders of branches. In a 
50-year-old sycamore there should be 49 branch orders; in reality 
there are found usually not more than 7. If a branch of a birch 
formed every year two lateral buds and each bud developed every 
year into a shoot, a 10-year-old branch would have 19,683 twigs, 
representing 9 yearly ramifications or orders of branches. As a mat- 
