in the united series of fronds shown in Fig. 79--the successive nodes answering to the successive points of origin of the fronds. Conversely, the stem of a grass, Fig. 91, displays just such relations of parts, as would result from the development of the type shown in Fig. 79, if instead of the mid-ribs thickening into a solid axis, the matter composing them became evenly distributed round the foliar surfaces, at the same time that the incurved edges of the foliar surfaces united. The arrangements of the tubular axis and its appendages, thus resulting, are still more instructive than those of the solid axis. For while, even more clearly than in the _Dendrobium_, we see at the point _b_, a continuity of structure between the substance of the axis below the node, and the substance of the sheath above the node: we see that this sheath, instead of having its edges united as in _Dendrobium_, has them simply overlapping, so as to form an incomplete hollow cylinder which may be taken off and unrolled; and we see that were the overlapping edges of this sheath united all the way from the node _a_ to the node _b_, it would constitute a tubular axis, like that which precedes it or like that which it includes. And then, giving an unexpected conclusiveness to the argument, it turns out that in one family of grasses, the overlapping edges of the sheaths _do_ unite: thus furnishing us with a demonstration that tubular structures _are_ produced by the incurving and joining of foliar surfaces; and that so, hollow axes may be interpreted as above, without making any assumption unwarranted by fact. One further correspondence between the type thus ideally constructed, and the monocotyledonous type, must be noted. If, as already pointed out, the transverse growth of an axis arises when the axis comes to be a channel of circulation between all the roots at one of its extremities and all the leaves at the other; and if this lateral bulging must increase as fast as the quantity of foliage to be brought in communication with the roots increases--especially if such foliage has at the same time to be raised high above the earth’s surface; what must happen to a plant constructed in the manner just described? The elder fronds or foliar organs, ensheathing the younger ones, as well as the incipient axis serving as a bond of union, are at first of such circumference only as suffices to inclose these undeveloped parts. What, then, will take place when the inclosed parts grow--when the axis thickens while it elongates? Evidently the earliest-formed sheaths, not being large enough for the swelling axis, must burst; and evidently each of the later-formed sheaths must, in its turn, do the like. There must result a gradual exfoliation of the successive sheaths, like that indicated as beginning in the above figure of _Dendrobium_; which, at _a_, shows the bud of the undeveloped parts just visible above the enwrapping sheaths, while at _b_, and _c_,