Now the next question is, how this descending external coating of wood will behave itself when it comes to the forking of the shoots. To simplify the examination of this, let us suppose the original or growing shoot (whose section is the shaded inner circle in Fig. 36) to have been in the form of a letter Y, and no thicker than a stout iron wire, as in Fig. 37. Down the arms of this letter Y, we have two fibrous streams running in the direction of the arrows. If the depth or thickness of these streams be such as at b and c, what will their thickness be when they unite at e? Evidently, the quantity of wood surrounding the vertical wire at e must be twice as great as that surrounding the wires b and c.
§ 8. The reader will, perhaps, be good enough to take it on my word (if he does not know enough of geometry to ascertain), that the large circle, in Fig. 38, contains twice as much area as either of the two smaller circles. Putting these circles in position, so as to guide us, and supposing the trunk to be bounded by straight lines, we have for the outline of the fork that in Fig. 38. How, then, do the two minor circles change into one large one? The section of the stem at a is a circle; and at b, is a circle; and at c, a circle. But what is it at e? Evidently, if the two circles merely united gradually, without change of form through a series of figures, such as those at the top of Fig. 39, the quantity of wood, instead of remaining the same, would diminish from the contents of two circles to the contents of one. So for every loss which the circles sustain at this junction, an equal quantity of wood must be thrust out somehow to the side. Thus, to enable the circles to run into each other, as far as shown at b, in Fig. 39, there must be a loss between them of as much wood as the shaded space. Therefore, half of that space must be added, or rather pushed out on each side, and the section of the uniting branch becomes approximately as in c, Fig. 39; the wood squeezed out encompassing the stem more as the circles close, until the whole is reconciled into one larger single circle.
| Fig. 38. | Fig. 39. |
| Fig. 40. |
§ 9. I fear the reader would have no patience with me, if I asked him to examine, in longitudinal section, the lines of the descending currents of wood as they eddy into the increased single river. Of course, it is just what would take place if two strong streams, filling each a cylindrical pipe, ran together into one larger cylinder, with a central rod passing up every tube. But, as this central rod increases, and, at the same time, the supply of the stream from above, every added leaf contributing its little current, the eddies of wood about the fork become intensely curious and interesting; of which thus much the reader may observe in a moment by gathering a branch of any tree (laburnum shows it better, I think, than most), that the two meeting currents, first wrinkling a little, then rise in a low wave in the hollow of the fork, and flow over at the side, making their way to diffuse themselves round the stem, as in Fig. 40. Seen laterally, the bough bulges out below the fork, rather curiously and awkwardly, especially if more than two boughs meet at the same place, growing in one plane, so as to show the sudden increase on the profile. If the reader is interested in the subject, he will find strangely complicated and wonderful arrangements of stream when smaller boughs meet larger (one example is given in Plate 3, Vol. III., where the current of a smaller bough, entering upwards, pushes its way into the stronger rivers of the stem). But I cannot, of course, enter into such detail here.
| Fig. 41. |
§ 10. The little ringed accumulation, repelled from the wood of the larger trunk at the base of small boughs, may be seen at a glance in any tree, and needs no illustration; but I give one from Salvator, Fig. 41 (from his own etching, Democritus omnium Derisor), which is interesting, because it shows the swelling at the bases of insertion, which yet, Salvator’s eye not being quick enough to detect the law of descent in the fibres, he, with his usual love of ugliness, fastens on this swollen character, and exaggerates it into an appearance of disease. The same bloated aspect may be seen in the example already given from another etching, Vol. III., Plate 4, Fig. 8.
| Fig. 42. |
§ 11. I do not give any more examples from Claude. We have had enough already in Plate 4, Vol. III., which the reader should examine carefully. If he will then look forward to Fig. 61 here, he will see how Turner inserts branches, and with what certain and strange instinct of fidelity he marks the wrinkled enlargement and sinuous eddies of the wood rivers where they meet.
And remember always that Turner’s greatness and rightness in all these points successively depend on no scientific knowledge. He was entirely ignorant of all the laws we have been developing. He had merely accustomed himself to see impartially, intensely, and fearlessly.