per annum at which all trees in crease, whether they grow fast or slow, provided their rate of growth does not vary. This table may be the means of saving young thriving woods from being cut down, by showing how great a loss is sustained by felling timber prematurely.* 2d. And it may be the means of bringing old trees to market, by showing the smallness of the interest they pay for the money they are worth, after they are 80 or 100 years old. But this table shows the interest which they pay, only whilst the trees continue growing at their usual rate. In case they fall short only a little of their usual increase in girt, this considerably diminishes the rate per cent. per annum of their in.. ⚫rease. And trees do decrease in their rate of growth before they appear to do so. + A pale and mossy bark are certain indications of it. 3d. The 1st table may also assist the valuer of such timber as is not to be cut down, but to continue growing, by enabling him to estimate its present value more accurately than is usually done, especially when it is increasing after a high rate per cent. per annum. ‡ The 2d table shows the rate per cent. to be the same as in the first table, though the annual increase is more both in height and circumference. The 3d table is calculated to show the number of trees that will stand on an acre of ground, at the dis tance of one-fifth of their height, (which distance is recommended by Mr. Salmon, in a paper in the Society's 24th volume,) and the number of feet the trees will contain, both those to be cut out, and those to be left standing, at the end of every four years, from 16 to 64 years old, supposing they increase 12 inches in height and 1 in circumference annually. This distance may suit fir trees, but will be too near for oaks. The 4th and 5th tables show the same particulars, when the trees grow at greater rates. The 6th table is calculated to "A wood, near West Ward, in Cumberland, of more than 200 acres, was felling in 1794; it was little more than 30 years old. The whole was cut away, without leaving any to stand." See Miller's Gardener's Dictionary, last edition, under the head of Woods. At 30 years old, timber pays 10 per cent. for standing; and probably this wood might have paid 7 per cent. per annum, on an average, for the next 30 years. In Mr. Pringle's Agricultural Report for Westmoreland is a paper of the Bishop of Llandaff's, stating, "That a very fine oak, of 82 years' growth, measured in circumference at 6 feet from the ground, on the 27th of October 1792, 107 inches, and on the same day of the same month in 1793 it measured 108 inches." He then states the interest it paid to be only about 2 per cent. and says this tree was a singularly thriving one. It is evident that, with all this appearance of thriving, it was on the decline. For if we divide 108, its inches in circumference, by 82, its age, we find its average annual increase had been 1 inch and a-third. Its falling off to 1 inch reduced the rate per cent. of increase one-fourth. A fir wood, of more than 30 acres, and about 30 years old, was lately valued to be sold with an estate, by several eminent wood-valuers, without taking into consideration its rate of increase. It was then increasing after the rate of 10 per cent. per annum, and probably would increase after the rate of 8 per cent, an an average, for the next 20 years. › show show the same particulars, when the trees are constantly thinned out every four years, so as to leave them at the distance of one-fourth of their height. According to this table, there will be 48 trees left on an acre when they are 120 years old; and it seems generally agreed, that from 40 to 50 full-grown oak trees are as many as have sufficient room to stand on an acre. The 7th table shows the same particulars respecting trees which increase 15 inches in height and 1 inch in circumference annually. The 8th table shows the same particulars respecting trees which increase 18 inches in height and 2 inches in circumference annually. The 9th table shows the same particulars as table 6, till the trees are 28 feet high; after which the distance is increased from onefourth to one-third of their height. The 10th, 11th, and 12th tables show the annual increase in boles of 24, 32, and 40 feet long, and the difference of their increase at the same ages. To these tables succeed comparative statements, showing the num. ber of feet contained in boles of dif ferent lengths, when 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; and am, Sir, Your very humble servant, CHARLES WAISTELL. TABLES RESPECTING THE GROWTH OF TIMBER. Calculations, showing every fourth year, from 12 to 100, the progressive annual Increase in the Growth of Trees, 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 I in circumference annu ally, their increase will be as undermentioned, viz. In Table X. of the increase of a bole of 24 feet in height, of a tree growing at the above-mentioned rate, it will be observed, that the con tents 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 chiefly I did not think it necessary to take into consideration the de. crease 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 annually 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 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 circum ference, annually, their increase will be as undermentioned, viz. Age of Trees. 18 3 eet. inch. ft. in. pt. sd.ft. in. pt. sd. 1 1 1 6 12 195 31 1 5 1.00 3 7 0 26.5 Teet. in ft. in. pt. 12 16 24 4 20 30 5 24 36 6 9 28 42 7 14 2 8 이 17 25 5 3 2 4 00 6 4 0.19.8 32 48 8 21 10 2 0 61 2 8 23 4 8 02.0 8 601 7 0 9.6 36 54 9 30 40 60 10 41 8 0 48 047 1 52 Explanation of the Construction of tions in the first line of Table 2. Tables I. and II. To render the preceding tables easy to be understood by persons not accustomed to calculations, I will state the process of the opera The height of the tree at twelve years of age is supposed to be 18 feet to the top of its leading shoot, and 24 inches in circumference at the ground; consequently, at half the height, the circumference is 12 inches ; inches;-one-fourth of this, being three inches, is called the girt. The girt, 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 inch for the girt. This squared and multiplied into the height, gives 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 num. ber divide 100, and the quotient is 26-5, which is the rate per cent. of increase made in the 13th year; consequently, whatever the tree might be worth when 12 years old, it will, at the end of the 13th year, be im proved in value after the rate of 261. 10s. per cent. or in other words, that will be the interest it will have paid that year or the money the tree was worth the preceding year. At every succeeding period, both in this table and table 1. 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. 2d. That when a tree has doubled its age, its contents will be eight-fold. 3d. That when a tree has dou bled its age, the annual growth will be increased four-fold. 4th. Consequently, that when a tree has doubled its age, the propor tion 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 quan. tity 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, girt, and height of any tree given, we can readily calculate what quantity of timber it will contain at any fature period, whilst it continues its usual rate of growth. [Mr. Waistell, having made a váriety of important observations and calculations, which are of much in. portance now that wood has become |