cords, one at each end of the long axis, now part company from the rest, and enter the lateral sepals (Fig. 6 (a) l.s.), the antero-posterior sepals next receiving their cords (a.s. and p.s.). The cylinder tends to close up, and four groups situate at the corners of the oblong cylinder supply cords for the petals, p. The two honey-glands next put in an appearance, G. They are merely cellular expansions of the floral receptacle, and are entirely devoid of cords, and therefore not rudiments of appendages. The two lateral stamens next receive their cords, l.st., while four other cords are given off from beside the petaline for the taller pairs of stamens, st.

Fig. 6 (b) shows how their cords diverge below and spring from the side of the petaline cords, while extra cords arise between them to form the marginal cords of the carpels (m.c.). From this it will be seen that the longer stamens cannot be formed by "chorisis" of a common intermediate cord; but, like those of all other members of the flower, their cords are separated from the common fibro-vascular cylinder of the stem.

The conclusion suggested by this investigation, and by a comparative study of Capparideæ, is that a cruciferous flower is not reducible to an originally quaternary type at all, but to some higher one. In my paper referred to, I suggested a

quinary; but I am now more inclined to refer it primarily to an indefinite spiral series referable to the orr type, which has been reduced, perhaps through insect agency, by symmetrical reduction to the present anomalous condition.

The process of transition from a hypothetical indefinite number of stamens to the present hexandrous state may be, perhaps, seen by comparing the three genera of Capparideæ --Capparis, Polanisia and Cleome. The first has many

stamens and six placentas, which are sometimes reduced to two. Polanisia has eight stamens, or more rarely six. Their situations correspond exactly with those of the Cruciferæ, except that, when there are eight, there are four on the anterior side instead of two.

Lastly, Cleome brings us to the same structure as in the Crucifere with even the tetradynamous condition of the stamens; the elongated torus below the pistil being about the only "capparidaceous" feature left.

It is not at all uncommon to find more than six stamens in cultivated plants of the Cruciferæ, and when this is the case I should be inclined to regard it as a tendency to a reversion to a higher ancestral number.

On the other hand, the close proximity of the two taller ones on each side not infrequently brings about some degree of cohesion between them, with an occasional arrest of half an anther. This has led some to suppose that the pair have resulted from chorisis. Since, however, their cords diverge downwards to the right and left, and run down beside the petalline cords (Fig. 6, b), this clearly proves that the union is a result of close contact, and that the normal separation is not due to chorisis, but to a primitive freedom, which has been retained from a multistaminate condition.

PENTAMEROUS WHORLS.-These are by far the commonest amongst Dicotyledons. And as an enormously greater pro

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portion of plants in this class have alternate leaves and 5-merous flowers, this correlation alone would be almost sufficient to prove that the latter issued out of the commonest or type of phyllotaxis. But since the sepals are sometimes decidedly quincuncial, as are those of Digitalis, and the petals frequently so, we have undoubted proof that they represent cycles of this angular divergence.

As with other numbers, fives may arise by symmetrical increase from fours, or decrease from sixes; though in by far the greater number of instances it is a primitive number, as stated above. As a rare instance of symmetrical decrease may be mentioned Lythrum Salicaria, which has usually the central floret of each axillary cyme 6-merous, but the lateral ones only 5-merous. As an instance of five parts to a whorl amongst Monocotyledons, may be mentioned the stamens of Strelitzia regina; but this number is obviously due to the suppression of a stamen.

Although whorls of fives are cycles of the divergence, and usually follow after an alternate arrangement in the foliage, yet it is quite possible to change abruptly from opposite leaves or bracts to whorls of fives in the flower, as may be seen in Hypericum and Dianthus. This arrangement, as I have elsewhere shown, is that most easily acquired when opposite and decussate leaves become alternate by the development of internodes (see pp. 11 and 18).

HEXAMEROUS WHORLS.—A floral whorl of six parts is, in most cases, as amongst Monocotyledons, the result of the combination of two whorls of three each-as the andrœcium of Berberis, Tulip, or perianth of the Lily of the Valley. It may, however, arise from symmetrical increase, as, for example, in the orders Meliacea and Olacineæ. In the former, there are 18 genera with alternate leaves and 5-merous flowers; 9 with 4-5-merous; 4 with 4-merous;

4 with 5-6-merous, and 1 with 4-6-merous whorls in the different species. In Olacineæ, of 36 genera, 17 have alternate leaves and 5-merous flowers; 7 have 4-5-merous; 4, 5-6-merous; 2, 6-merous, and 1, 4-6-merous.

As six leaves cannot form a cycle of any of the ordinary kinds of phyllotaxis, this will account for its rarity in nature; and indeed it may probably, without exception, be divisible into two whorls of three members each, except in the case of symmetrical increase from five.

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HEPTAMEROUS WHORLS.-Like the number 6, 7 is a very rare one; and when present appears to be due to its being a primitive number or to symmetrical change. If any whorls are deducible from decussating verticils of threes, a cycle may contain seven parts, as the phyllotactical series arising from the breaking up of such verticils into a continuous spiral arrangement is represented by 3, 4, 4, 1, etc. So that if leaves on a plant were in whorls of threes, as occurs in some instances, and not opposite, as in the primitive type amongst Dicotyledons, then a heptamerous arrangement would occur. If, therefore, there be any existing illustration, it must, by the very nature of the case, be exceedingly rare. It sometimes occurs in Trientalis; and when this is the case, it may possibly have arisen as here suggested. According to the description given of this plant in the Genera Plantarum, the numbers of the three outer whorls range from 5 to 9, the capsule being 5-valved. The leaves, on the other hand, are sæpe tot quot petala subverticillata."

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A second cause is arrest. This obviously accounts for the 7 anthers in Pelargonium, for the 10 filaments are present.

A third cause is symmetrical change. Lythrum Salicaria illustrates this as already mentioned. This flower is sometimes described as 6-merous but it is not always so. The

central floret of the cyme has often a higher number than that of the lateral ones; so that if they be 6-merous, the central flower will be 7-merous. Agapanthus, amongst Monocotyledons, is another instance, its flowers ranging from 6 to 8 in the number of parts in the whorls.

OCTAMEROUS WHORLS.-A whorl of eight parts is not common; but it appears in Chlora and in the corolla of Dryas octopetala, in which it may be a cycle of the phyllotaxis. In other cases it is a combination of two whorls, which, as a rule, can be easily distinguished as the stamens in the Onagracea, or it may be due to symmetrical change.

ENNEAMEROUS WHORLS.-The number 9, like 6, 7, and 11, corresponds to no cycle of any one of the usual forms of leafarrangement, and is proportionately rare. It may occur as a combination of three cycles of three each, and perhaps this will account for it when it occurs in Trientalis, and the androecium of Mercurialis. The stamens of Butomus are also nine in number.

DECAMEROUS WHORLS.-The number 10 never occurs except as the union of two whorls of five in each, as in the androecium of Leguminosa.

ENDECAMEROUS WHORLS.-Like 7, the number 11 might occur if the series }, 4, 4, 13, etc., was as frequently represented as,,,, etc., when " sevens "would be as abundant as "fives are now. I do not know of a case where it could reasonably be referred to such an origin. When it does occur, as in Cuphea, it is clearly due to an arrest of one stamen through insect agency. Brownea is said also to have sometimes 11 stamens; if so, this would undoubtedly be due to numerical increase.

DODECAMEROUS WHORLS.-The number 12 closely verges on the "indefinite," which simply means a more or less numerous series of cycles of the same kind. Neverthe