Probably the absence of the swollen portion below the flower in the case of many proliferous roses, double-flowered apples, as already referred to, may be dependent on the non-development of the extremity of the peduncle or flower-stalk. Thus, in a double-flowered apple recently examined, there was a sort of involucel of five perfect leaves, then five sepals surrounding an equal number of petals, numerous stamens, and five styles, but not a trace of an expanded axis, nor of any portion of the carpels, except the styles. The views taken as to the nature of this and similar malformations must depend on the opinion held as to the nature of inferior pistils, and on the share, if any, that the expanded axis takes in their production. As elsewhere said, the evidence furnished by teratology is conflicting, but there seems little or nothing to invalidate the notion that the end of the flower-stalk and the base of the calyx may, to a varying extent, in different cases, jointly be concerned in the formation of the so-called calyx-tube and of the inferior ovary. Obviously it is not proper to apply to all cases where there is an inferior ovary the same explanation as to how it is brought about. As these pages are passing through the press, M. Casimir de Candolle has published a different explanation as to the nature of the hip of the rose, having been led to his opinion by the conclusion that he has arrived at, that the leaf is to be considered in the light of a flattened branch, whose upper or posterior surface is more or less completely atrophied. According to M. de Candolle, the calyx-tube, in the case of the rose, is neither a whorl of leaves, nor a concave axis in the ordinary sense in which those terms are used, but is rather to be considered as a ring-like projection from an axis arrested in its ulterior development. The secondary projections from the original one correspond to an equal number of vascular bundles, and develope into the sepals, petals, stamens, and ovaries. If these organs remained in a rudimentary condition, the tube of the calyx would be reduced to the condition of a sheathing leaf. The rose flower, then, according to M. de Candolle, may be considered as a sheathing leaf, whose fibro-vascular system is complete, and from which all possible primary projections are developed.[464] If, as M. de Candolle considers, the leaf and the branch differ merely in the fact that the vascular system is complete in the latter, and partly atrophied in the former, it would surely be better to consider the "calyx-tube" of the rose as a concave axis rather than as a leaf, seeing that he admits the fibro-vascular system to be complete in the case of the rose. With reference to this point the reader is referred to Mr. Bentham's account of the morphology and homologies of the _Myrtaceae_ in the 'Journal of the Linnean Society,' vol. x, p. 105. See also _ante_, pp. 71, 77.