86 AGE OF DICOTYLEDONOUS TREES. 
place, the rings are by no means so well defined ; secondly, 
more than one ring may be formed in a year; thirdly, some 
trees, as already noticed (page 84), such as Zamias and the species 
of Cycas, only produce one ring as the growth of several years ; 
fourthly, some plants, as certain species of Cacti, never form 
annual rings, but the wood, whatever its age, only appears as a 
uniform mass ; while lastly, in some, such as Guaiacwm, the 
rings are not only indistinct, but very irregular in their growth, 
It is commonly stated that the age of a Dicotyledonous tree 
may not only be ascertained by counting the annual rings in a 
transverse section of its wood, but that the mere inspection of a 
fragment of the wood of such atree of which the diameter is 
known, will also afford data by which the age may be ascertained. 
The manner of proceeding in such a case is as follows :—Divide 
half the diameter of the tree divested of its bark by the diameter 
of the fragment, and then, having ascertained the number of rings 
in that fragment, multiply this number by the quotient pre- 
viously obtained. Thus, suppose the diameter of the fragment to 
be two inches, and that of half the diameter of the wood twenty 
inches ; then, if there are eight rings in the fragment, by mul- 
tiplying this number by ten, the quotient resulting from the 
division of half the diameter of the tree by that of the fragment, 
we shall get eighty years as the supposed age. Now, if the thick- 
ness of the rings was the same on both sides of the tree, and 
the pith consequently central, such a result would be perfectly 
accurate, but it happens from various causes, as already noticed 
(page 84), that the rings are frequently much thicker on one 
side than on the other, and the taking therefore of a piece from 
either side indifferently would lead to very varying results. A 
better way therefore to calculate the age of a tree by the inspec- 
tion of a fragment, is to make two notches, or remove two pieces 
from its two opposite sides, and then, having ascertained the 
number of rings in each, take the mean of that number, and 
proceed as in the former case. Thus, suppose two inches, as be- 
fore, removed from the two opposite sides of a tree, and that in 
one we have eight rings, and in the other twelve; we have ten 
rings as the mean of the two. If we now divide, as before, half 
the diameter, twenty inches, by two, and multiply the quotient 
ten which results, by ten, the mean of the number of rings in the 
two notches, we get one hundred years as the age of the tree 
under consideration. Such a rule in many cases will no doubt 
furnish a result tolerably correct, but even this will frequently 
lead to error, from the varying*thickness of the annual rings 
produced by a tree at different periods of its age. 
It is probable that De Candolle and others, in calculating the 
ages of different trees, have been led into error by not sufficiently 
taking into account the variations in the growth of the annual 
rings at different periods of their age, and their varying thick- 
ness on the two sides of the tree; and, when we consider 
