The 9th Table shows the same particulars as Table 6, till 9th table. the trees are 28 feet high, after which the distance is increased from one fourth to one third of their height.

The 10th, 11th, and 12th Tables show the annual increase 10th, 11th, & in boles of 24, 32, and 40 feet long, and the difference of 12th tables. their increase at the same ages.

To these tables succeed comparative statements, showing Comparison of the number of feet contained in boles of different lengths, boles of differwhen the trees are 60 years old, by which it appears, that,

if cut down at that age, the longest boles are not the most profitable to the growers of timber.

And I have added the valuation of the plantations before alluded to, with remarks on them.

Having finished my introductory remarks, I conclude,

ent lengths.

and am, Sir,

Your

very

humble servant,

CHARLES WAISTELL.

Tables respecting the Growth of Timber.

Calculations, showing every fourth year, from 12 to

100, Tables respect

of timber.

the progressive annual increase in the growth of trees, ing the growth and gradual decrease in the rate per cent per annum, that the annual increase bears to the whole tree.

The whole height of the trees is taken to the top of the leading shoot, and the girt in the middle; but no account is taken of the lateral branches.

If trees increase 12 inches in height and 1 in circumference annually, their increase will be as follows, viz.

TABLE

Remarks,

In Table X of the increase of a bole of 24 feet in height, of a tree growing at the abovementioned rate, it will be observed, that the contents at 24 years of age are the same, and at 64 years nearly the same as in the above Table, but the contents of the bole at all the intermediate periods exceed the above. And a 40 feet bole exceeds the above contents from 44 years to 100, as may be seen in Table 12, For these reasons chiefly I did not think it necessary to take into consideration the decrease in height that takes place in trees at different ages, according to the kind of tree and quality of the soil.

The increase per cent per annum is the same as the above in all trees at the same age, whether they have grown faster or slower, provided their increase in height and thickness anuually has not varied on an average. The progress of trees is sometimes greatly retarded by insects destroying

their leaves, by unfavourable seasons, and by their roots penetrating into noxious strata. But these accidents cannot enter into calculations.

Calculations, showing every fourth year from 12 to 64, the Table 2.
progressive annual increase in the growth of trees, and
the gradual decrease in the rate per cent per annum that
the annual increase bears to the whole tree.

The whole height of the trees is taken to the top of the leading shoot, and the girt in the middle; but no account is taken of the lateral branches.

If trees increase eighteen inches in height, and two inches in circumference, annually, their increase will be as undermentioned, viz.

Explanation of the Construction of Table I and II.

To render the preceding tables easy to be understood persons not accustomed to calculations, I will state the cess of the operations in the first line of Table II.

pro

The height of the tree at 12 years of age is supposed to be 18 feet to the top of its leading shoot, and 24 inches in circumference

of fab es 1 and 2 explained.

General ob.

servations on the preceding tables,

circumference at the ground, consequently, at half the height, the circumference is 12 inches. One fourth of this, being 3 inches, is called the girth. The girth being squared, and multiplied into the height, gives one foot one inch and six parts for its contents. At 13 years old the tree will be 19 feet high, 26 inches in circumference at the ground, and 13 inches at half the height; one fourth of 13 gives 34 inches for the girth. This squared and multiplied into the height, give one foot five inches and one part for the contents. Deduct from this the contents of the tree at 12 years of age, and there remain three inches and seven parts, which is the increase in the 13th year. Then reduce the contents of the tree when 12 years old, and the increase in the 13th year, each into parts, dividing the former by the latter, and the quotient will be 3.76; by this number divide 100, and the quotient is 26.5, which is the rate per cent of increase made in the thirteenth year. Consequently whatever the tree might be worth when 12 years old, it will, at the end of the 13th year, be improved in value after the rate of 267. 10s. per cent, or in other words, that will be the interest it will have paid that year for the money the tree was worth the preceding year.

At every succeeding period, both in this Table and Table I, the like process is gone through.

Observations on Tables I and II.

The preceding tables furnish us with the following useful information, viz.

1st. That all regular growing trees, measured as above, as often as their age is increased one fourth, contain very nearly double their quantity of timber.

2nd. That when a tree has doubled its age, its contents will be eight-fold.

3d. That when a tree has doubled its age, the annual growth will be increased four-fold.

4th. Consequently, that when a tree has doubled its age, the proportion that its annual increase bears to the contents of the whole tree is then diminished one half.

This last observation explains how it comes to pass, that a tree, when its age is doubled, the rate per cent per annum that its increase then bears to the contents of the whole tree, is diminished one half.

It may not be unuseful to observe, that the rate per cent of increase in the last columns, is the same as the rate per cent that the increase of the tree that year will pay for the money it was worth the preceding year..

In the two preceding tables, we find that the rate of increase per cent per annum is the same in both at the same ages, although the quantity of timber in the second table is six times as much as in the first table in trees of all ages; therefore, when the age of a tree is known, the rate per cent per annum of its increase is known on inspecting these tables, whether the tree has grown fast or slow; provided the growth of the tree has been regular, and that it has continued its usual growth.

And having the age, girth, and height of any tree given, we can readily calculate what quantity of timber it will contain at any future period, while it continues its usual rate of growth.

(To be continued.)

IV.

Observations on Potash and Soda prepared with Alcohol: by Mr. d'ARCET. Read to the Institute the 11th of January, 1808.*

WHEN chemistry, employing new methods of analysis,

is enriching itself with important facts; when England announces the decomposition of potash and seda, and the chemists of France are busied in confirming this grand discovery; I conceive it incumbent on me to communicate the results of various experiments, which may probably throw some light on the path newly opened.

* Annales de Chimie, vol. LXVIII, p. 175.

I present