Who are the five brothers? None other than the five lobes of the rose’s calyx, the five sepals. Let us examine them one by one. We shall find two of them furnished on both edges with leafy or beard-like appendages, which sometimes revert to the original form and expand into follicles similar to those of the leaves proper. Botany in fact teacher us that a sepal is a modified leaf. These are the two brothers with beards. We shall see two others totally devoid of appendages on either side. These are the two brothers without beards. Lastly, the fifth will show us one bare and one bearded surface. This one represents the brother with half a beard. These are not casual variations, differing from flower to flower; all the roses present the same arrangement, all have their sepals divided into three classes in the matter of beards. It is a fixed rule, resulting from a law which governs floral architecture, even as the art of a Vitruvius [88] governs our buildings. This law, so elegant in its simplicity, is thus stated in botany: in the quinary order, the most important order of the vegetable world, the flower groups the five portions of a whorl at intervals upon a close spiral, almost equivalent to the circumference of a circle; and this arrangement is so contrived that two turns of the spiral contain the series of five parts. Having said this, it is easy to construct the plan of the rose, in so far as concerns the calyx. Divide a circumference into five equal parts. At the first dividing-point, place a sepal. Where shall we put the second? It must not be at the second dividing-point, for then the set of five pieces would fill the circumference in a single revolution, instead of in two. We shall place it at the third point and continue in like fashion, each time missing one division. This mode of progress is the only one that brings us back to the starting-point after two turns of the spiral. Let us now give the sepals a base wide enough to provide a tightly closed containing wall. We shall see that the parts on sections 1 and 3 are completely outside the spiral; that the parts on sections 2 and 4 have their two edges fitting under the adjoining sepals; and that, lastly, the part on section 5 has one edge covered and one free. On the other hand, it is manifest that, hampered in their expansion by the petal placed over them, the edges caught under the others cannot send forth their delicate appendages. Hence we have the two bearded sepals at points 1 and 3, the two beardless sepals at points 2 and 4 and the half-bearded sepal at point 5. This explains the riddle of the rose. The disparity of the five pieces of the calyx, apparently an irrational structure, a capricious anomaly, is really the corollary of a mathematical law, the natural consequence of an immanent algebraical relation. Disorder is eloquent of order; irregularity bears evidence of a ruling principle.