726 Relation between Circumference and Weight

When a tree, at a point where the circumference is Co, divides into two branches (cl and ct), what relationship exists between co and cl + c~? In order to answer this question, which has a definite bearing on problems of tree form, it is convenient to investigate first the relationship between the circumference at some point and the weight, w, of all the parts of the tree peripheral to this point. Accordingly measurements were made, 116 in all, on nine kinds of trees; namely, aspen, bitternut, hickory, oak, ash, maple, cedar, hornbeam, and beech. The largest tree measured had a circumference of 56.4 cm. where cut, and the whole tree weighed 120 kg. The smallest measurements were made on the stems of leaves,--for example, circumference of stem = 0.25 cm., weight of leaf = 0.18 gm. All the data thus obtained are included in Fig. 1. Our procedure was of the simplest character. Whole trees of varying size, or branches, or leaves, were taken entirely at random from the vicinity. The only criterion of selection was that the specimen should not appear to have been recently injured. The circumference was measured by a tape, encircling the bark, at the point of section; or, for small specimens, the diameter was measured by calipers and the circumference subsequently calculated. The specimen was then weighed on one of three balances according to size. The season was midsummer, 1926; the place, Grindstone Island, N. Y. Plotting logarithms; i .e . , log (weight in gin.) vs. log (circumference in cm.), the points fall close to a straight line. A statistical treatment yields the following numerical characteristics: