§ 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. [Illustration: FIG. 38.] [Illustration: FIG. 39.] § 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.