This branch was cut in the latter part of March, 1858; and as there are six sets of bud-rings on its main axis, it is evident that it is six years old, and that its growth from the bud must have commenced in the spring of 1852. It is also plain that the first side-shoot commenced growing in the spring of 1853, and is, therefore, five years old. Hence, only five sets of bud-rings are visible on this shoot. The same law is apparent through the entire series of ramifications; each shoot is one year younger, and will be found to have one set of bud-rings less than its parent axis. By comparing the engraving with the numerical calculations in the Table, it will be seen that the growth made by the primary axis between 1852 and 1853, was four inches, and that five leaves were put forth, only one of which produced a vitally active bud, which ultimately became a shoot. The buds produced by the other four leaves were rudimentary, and, as is evident from the engraving, never came to anything. Again, by reference to the figures in the Plate and the calculations in the Table, the condition of the branch in the spring of 1854 will be seen at a glance. The primary axis had grown from the set of bud-rings marked 53 to the set marked 54, a distance of eight inches and five lines: it had developed five leaves, and as there are three branches connected with this portion of the main axis, it is evident that three out of the five leaves produced vitally active buds. So, also, the first side-shoot or secondary axis grew two lines and put forth four leaves. It grew, in fact, about the length of a bud-trace, or took a minimum of development. The distance between the two broken lines at the bottom of the engraving, figured 53 and 54, shows the extent of growth of the first side-shoot between 1853 and 1854. This, then, was the exact condition of our beech branch in the spring of 1854. There were terminal buds at all the points of the main axis marked 54; and consequently, with the exception of the slight side-growth made by the first secondary axis at the bottom, the primary axis itself still remained unbranched. In precisely the same manner, the extent to which this branch had grown in the spring of 1855 may be ascertained. It is only necessary to bear in mind, that at all the points on the main axis and its branches marked 55, there were buds or terminal growths, and that at these points the growing shoot was in a state of rest, in order to see that the three buds formed the previous year, or on that portion of the main axis contained between 53 and 54, had grown into three considerable branches, of the respective lengths of two inches and ten lines, six inches and nine lines, and seven inches and ten lines. There were, therefore, four well-marked secondary axes connected with the primary axis below the bud-trace marked 54 on the primary axis, whilst the four branches situated above it, and included between 54 and 55, were still in the bud condition. Between the years 1855 and 1856, the growth of the primary axis appears to have been very greatly retarded. It grew only four lines, put forth three leaves, and there was no side production. The same check to vegetation is also beautifully apparent on the branches during the same season. This is well represented in the engraving, and the figures in the table show a similar growth of four lines, three leaves, and no side production, of all the branches with the exception of the first and fourth, which grew eight lines and produced four leaves. This shows the intimate physiological connection subsisting amongst a system of branches, and that if the growth of the primary axis is retarded, the growth of the secondary axes experience a similar vegetative check. In like manner, the reader can easily ascertain the condition of growth of the branch during the years 1856 and 1857, and thus accurately trace the several mutations of form through which it passed anterior to assuming its present one, in the Spring of 1858, as represented in our engraving. The following curious and highly-interesting facts may also be deduced from the calculations of the above Table. The figures 28, at the bottom of the first column ten marked L, show the number of leaves put forth by the primary axis; and the sum of the figures of the columns marked L, of the secondary axes, or, 20+15+16+21+11+13+13+13+3+2=127, shows that one hundred and twenty-seven leaves were put forth by the ten secondary axes or branches; therefore, the total number of leaves which constructed the entire branch, was 127+28=155. If the reader will refer to the Table and then to the Plate, he can form a true estimate as to the size of the branch. The length of the primary axis is twenty-seven inches and three lines, and of the largest secondary axis fifteen inches: yet it is the leaf-labor of one hundred and fifty-five leaves! The branch itself we have shown to be only six years old. What then must be the immense number of leaves engaged in the construction of trees which put forth thousands of such twigs, comparatively speaking, from their immense spreading branches, which grow from one to two hundred feet in height, and whose giant forms have stood for hundreds and even thousands of years? Who can estimate the quantity of leaf-surface spread abroad in the atmosphere from the first commencement of germination, and the amount of leaf-labor necessary to rear such vast, noble, and enduring vegetable monuments? "The Washington Elm, at Cambridge,-a tree of no extraordinary size—was some years ago estimated to produce a crop of seven millions of leaves, exposing a surface of two hundred thousand square feet, or about five acres of foliage."* Again referring to the Table and the engraving, we find that the increase of leaf-surface each year, was as follows::1853, 5; 1854, 9; 1855, 25; 1856, 30; *1857, 41; 1858, 44. That is to say, in 1853 the branch put forth five leaves; in 1854, nine leaves, &c. &c. These numerical results are obtained by adding together the figures under L, opposite the years, across the columns. 1857. "First Lessons in Botany and Vegetable Physiology," by Asa Gray, It is proper also to remark here, that with every increase in the number of leaves spread abroad in the atmosphere, by a young tree or branch, there must be necessarily an increase in the rapidity of its growth, because it has a greater amount of leaf-surface at work in the air. Its chances of life, and of arriving at a state of maturity, become greater as its leaves increase in number. But this law must be understood with considerable modifications. It will be seen by reference to the Table and the Plate, that the growth of the branch was greatly retarded from 1855 to 1856. The primary axis that season grew only four lines, and the ten secondary axes were also equally kept back, so that very little wood was formed that year; altogether it amounted to only three inches and seven lines. Yet there were thirty leaves at work that season, being four more than was put forth the previous year, when a much greater amount of work was done, twentysix leaves forming not less than twenty-seven inches and six lines of new shoot. It is clear from this, that growth is proportionate, not so much to the amount of leaf-surface spread forth in the atmosphere, as to the vital activity of the leaves themselves. Again, by consulting the Table, it will be seen that although twenty-eight leaves were employed in constructing the primary axis, yet only ten produced buds which ultimately became branches; also, that these ten branches, although constructed by one hundred and twenty-seven leaves, developed only seventeen shoots, as is evident by adding together the sum of the figures at the bottom of the columns marked S, under "Secondary Axis;" it follows, that of these one hundred and twenty-seven leaves only seventeen produced vitally active buds. Therefore, the total number of abortive or rudimentary buds in the entire branch must be 155-(17+10)=128. The number of shoots annually put forth, were, in 1853, 1; 1854, 3; 1855, 13; 1856, 0; 1857, 10; 1858, 0. The increase in the growth of the entire branch was, in 1853, 4; 1854, 8·7; 1855, 27·6; 1856, 3·7; 1857, 18.8; 1858, |