1206. If we regard the petals of a polypetalous corolla in the import or light of _pinnate leaflets_, the legitimate regularity of their numerical relations, and the so-called irregularity of their arrangement is easily explained. The papilionaceous corollæ have been manifestly constructed according to the plan of the pinnate leaf; the vexillum or vane corresponds to the odd leaflet, the alæ or wings to the two anterior, the carina or keel to the two posterior pinnate leaflets; and hence their consecutive ratio of decrease in respect to size. 1207. All irregular corollæ admit of being referred to the papilionaceous form. One petal is always found, which separates from the others, is either larger or smaller, or entirely ablated, and consequently corresponds to the odd pinnate leaflet or vane. 1208. The irregular monopetalous or tubular corollæ admit also of being referred to the papilionaceous form. They need only be regarded as a confluence of petals. The labiate corollæ are one of the same character; but, on the contrary, the lower lip is trifid, the upper, and thus the keel, bifid. Here the papilionaceous corolla stands, properly speaking, reversed. NUMERICAL LAW. 1209. The number of petals in the corolla ranges parallel with the mode of development of the pinnate leaves. But at first the odd terminal leaf necessarily originates, because a leaf must have several pairs of ribs, before it splits in a ptiloidal or pinnate manner. The primary number of petals is therefore one. This number is found in those plants called apetalous, where the small lateral petals are abortive, and frequently the terminal petal itself, as in the catkin, where only the calyx has been left remaining. 1210. The normal ratio, in which the numbers of the petals progress, is the odd or uneven. For a leaf is to be regarded as a single fascicle of fibres with cellular substance. This packet of fibres grows straight out. It is solicited by the light to give off bundles of fibres; there is thus no existing cause, why it should only give off such upon one, and not upon the other, side of the bundle. At the first division therefore it must be an _odd_ leaflet, which is the principal bundle of fibres, while two _even_ pinnate leaflets take their origin upon its sides. 1211. The second number of petals is therefore _three_; for this is the first number in which a pinnate leaf can appear. This number is much more frequently met with than the former, because all division of a terminal bud necessarily strives after the representation of the whorl. Under this head come most Monocotyledons, as grasses, rushes, lilies. 1212. Of the three petals of a corolla all three are not of equal import, two only are alike as being lateral pinnate leaflets; the third, however, is present as the odd or uneven leaflet. 1213. Upon this inequality of import depends the irregularity of many ternary corollæ, e. g. of the Orchideæ, Apiaceæ, and even many Irides and lilies.