My dear Sir

I beg to return M^r. Chauncey Wright’s paper on Leaf-arrangement, with many thanks for the loan of it, and with my apology for having kept it so long. In lending it to me, if you remember, you kindly gave me permission to write to you again on the subject; and I hope the following notes will not tax your patience too much.¹

M^r. Wright’s views may be briefly summarized thus:— There is a property that distinguishes existing (including fossil) spiral orders of leaf-arrangement ($\frac{1}{2}$, $\frac{1}{3}$, $\frac{2}{5}$, $\frac{3}{8}$, &c; $\frac{1}{4}$, $\frac{1}{5}$, $\frac{2}{7}$ &c.) from other possible but non-existent orders ($\frac{4}{7}$, $\frac{5}{9}$, &c.), and that distinguishes (among existing orders) those that are common and modern ($\frac{2}{5}$, $\frac{3}{8}$, &c.) from those that are rare and ancient ($\frac{1}{4}$, $\frac{1}{5}$, $\frac{2}{7}$ &c.); and this property is most conspicuous in a certain hypothetical order represented by the ultimate value (k) to which the successive terms of the first series ($\frac{1}{2}$, $\frac{1}{3}$, $\frac{2}{5}$, $\frac{3}{8}$ &c) approximate, and from which the higher terms ($\frac{3}{8}$, $\frac{5}{13}$, &c.) differ by an inconsiderable amount in respect of the degree in which they possess this property; and we are not to attribute to this “typical angle” k any special virtue beyond its leading us to recognize lower degrees of the same property in the series of fractions that approximate to k. The property in question is “thorough and rapid distribution of the leaves around the stem,” (p. 389,) “exposure of the leaves to light and air around the stem,” (p. 389) “ample elbow-room, or space for expansion in the bud,” (p. 389,)—and the different degrees in which the various orders (existent and non-existent) do or would possess this property are investigated with admirable subtlety and displayed very clearly in the elaborate diagram at the end of the pamphlet.

The essential feature in those orders which best display this property, is that every leaf is found at that point in the circumference which has been left most open by the previous leaves of the cycle.

M^r. Wright argues that, presupposing the existence of the spiral arrangement as a whole, this “distributive property” has furnished material for the action of Natural Selection among various orders of the spiral arrangement, and has determined their relative frequency or infrequency in Nature, amounting to total exclusion in the case of some, as $\frac{4}{7}$ and $\frac{5}{9}$. (p. 396.)

Again, besides their distributive property, existing spiral orders also display a cyclic property, in virtue of which the leaves form two or three or five or eight (&c) vertical ranks, one cycle being completed between every two successive leaves in th⁠⟨⁠e⁠⟩⁠ same rank. This cyclic feature M^r. Wright supposes to involve, and owe its origin to (through Natural Selection), some advantage of internal nutritive relations between successive leaves in the same vertical rank. (pp. 402–404.) He also suggests (p. 414) that this feature of cyclic regularity and simplicity may owe some of its fixedness or constancy to the advantage of being easily recognized by the eyesight of those insects which are serviceable to the plant.

M^r. Wright then proceeds (p. 405) to examine into the probable utilities and origin of the spiral and verticillate arrangements.² He frames the remarkable hypothesis (p. 406) that the natural spiral (reckoned the shortest way round) is “the trace of a former physical connection of the members, or even of a continuity of leafy expansion along this path; a leaf-like expansion resembling a spiral stairway. The leaves, according to this supposition, are the relics of segments made in such a spiral leaf-like expansion around the stem.”

This spiral expansion M^r. Wright supposes (p. 409) to originate in a twist of an earlier ancestral “single-bladed frond,” “a frond with one of its blades undeveloped;”—and to owe its origin to the advantage which a twisted frond would have over a plane frond, first, in virtue of a more favourable relation to light and air or water; second, in virtue of its greater strength at the time of “the transition of plant-life from aquatic conditions to those of the dry land and the air.”

It is afterwards suggested (p. 410) that “a two-bladed frond might be similarly twisted and give rise to a double spiral surface like a double spiral stairway.”— And this is supposed to give rise, by a process of segmentation, to a succession of continuous leaflike expansions around the stem, which may be regarded as the original form of the whorl.—

The spiral and the whorl being thus provided, as general types of structure, furnish bases “on which the subsequent utilities (of distributive and cyclic arrangement) had to erect existing adaptations of structure.”

On the successive steps of this theory, permit me to make the following remarks:—

If the “distributive” property were of such importance as M^r. Wright supposes to the adult and growing leaves, by securing “the most complete exposure of the leaves to light and air around the stem,” we should rightly expect to find the most perfect attainment of that end in the mature and adolescent state of the twig. But it only needs a glance at the nearest holly-branch to see that the leaves have much ado to present themselves favourably to the light and air, in spite and defiance of their distribution around the stem, by curves and twists of their stalks. Their native arrangement is a positive disadvantage to them in the lateral twigs. It is only in vertical and unembarrassed twigs that the leaves remain content with their distributive position: and these are a very small portion of the whole tree. Indeed one chief use of the leaf-stalk seems to be to enable the leaf-blade to make the best of an unfavourable birth-place. The arrangement of leaves in the bud is far more regular than their adult disposition, thus warped and wrung by contortion of stem and stalks; and this fact alone goes far to prove that the utility which has determined that arrangement is to be looked for, not in the adult twig, but in the bud. M^r. Wright mentions as one advantage of the distributive property, “ample elbow-room or space for expansion in the bud” (p. 389), “compact arrangement in the bud” (p. 400); but he does not follow that idea any further, and therefore misses (as it seems to me) the real secret of spiral orders.

That thorough distribution of the leaves around the stem is of no great importance in the adult twig, is shown by the wide prevalence of the order $\frac{1}{2}$, (elm, lime, beech, mulberry &c.) in which the leaves are crowded in two ranks on opposite sides of the stem, and keep their native positions contentedly, without any contortion of stalks in search of better distribution. An elm-shoot will run up straight into the air, and its leaf-blades will preserve their alignment with beautiful regularity; but if the crowding were a disadvantage, surely we should expect, from the behaviour of leaves in general, that they would break their ranks by irregular bending of their stalks or by a twist of the stem, and so gain greater freedom for the individual leaves.

It is certainly true,—and M^r. Wright has brought it out with wonderful skill,—that the “distributive property” is possessed by the more complex spiral orders, and that those orders which do not exist, especially $\frac{4}{7}$ and $\frac{5}{9}$, are exactly those which would not possess that property: and no theory of Leaf-arrangement can be accepted which does not account for the absence of those orders $\frac{4}{7}$ and $\frac{5}{9}$. But I believe I shall be able to show, in a subsequent letter, that the distributive property is only incidental to the attainment of a more important end, by means which would necessarily exclude the non-existent orders.

The idea that leaves enjoy advantage in respect of nutrition by standing in the same vertical rank, is a natural one, and may well be true; but I wish that it were supported by more facts than M^r. Wright has adduced. M^r. Wright speaks of this feature as “essential” (p. 401); but there are so many instances where it is impossible to decide whether the 5^th. or 8^th. or 13^th. or 21^st. (&c) leaf is to be taken as completing the cycle, that I cannot agree with him in supposing that there is any vital importance in this cyclic feature.

And here I must disagree with an argument which M^r. Wright is constantly using, (pp. 386, 387, 389, 394, 396, 401,) as, for instance, in page 386, where he maintains that “the fractions $\frac{3}{8}$ and $\frac{5}{13}$ would be undistinguishable in actual measurement, since they differ from each other by $\frac{1}{104}$, which is much less than can be observed, or than stems are often twisted by irregular growth.”— But surely nobody attempts to determine the order to which a given specimen belongs, by measuring the angular space between two successive leaves of the natural spiral; but rather by fixing on the cyclic leaf, vertically above the original, with a careful eye to the fibres and ridges of the bark, and then numbering all the leaves that intervene. Thus, when the 8^th. leaf is reached, its position will vary by $\frac{8}{104}$ (= $\frac{1}{13}$^th. of the circumference) according as our specimen belongs to $\frac{3}{8}$ or $\frac{5}{13}$; and this difference, in a moderate condensation of leaves or bracts, (such as is found in a twig of rhododendron,) is amply sufficient to settle the question. This consideration tends to invalidate M^r. Wright’s argument in all the above-mentioned passages.

How far insects’ eye-sight is qualified to recognize the cyclic feature in the spiral orders, in spite of irregularities, is surely too uncertain to admit of being used as valid argument.

With regard to M^r. Wright’s hypothesis that leaves “are the relics of segments made in a spiral leaf-like expansion around the stem,”³ I wish I could hear what you think. It strikes me as monstrous. The only fact that is made to lead up to this hypothesis is that in the rarer and more ancient (fossil) orders the angles of divergence between successive leaves in the natural spiral are smaller than in common modern orders:—a fact of very doubtful relevancy. This fact M^r. Wright takes as evidence that there is something real, not merely formal, in the natural spiral.

The ‘something real’ is then made the subject of arbitrary definition in the terms of the hypothesis; without a single fact of embryonic development, or survival of intermediate forms, to rest upon. It is pure unfounded hypothesis. A “single-bladed frond” is a very strange and unnatural form to assume as the simple original of the spiral orders; and the more natural form of a “double-bladed frond” would require the most felicitous segmentation to produce the simplest form of the whorl. In either case, M^r. Wright must submit to have his own words turned against him,—(p. 403) “we ought, by the analogy of embryology, to find some traces of the process in the bud.”

Then it seems to me that the hypothetical utilities, first, of better exposure to light and air; and second, of greater strength,—in the twisted frond,—in default of any actual evidence on the point,—are very flimsy. If these utilities were real, we should surely find them largely exemplified at the present day in the vegetable kingdom, for they are of a general character: leaf-blades would be found spiral instead of flat: and strength with economy of material would be shown in flattened twisted stems instead of or as well as in straight tubular or fluted stems, (which at present we regard as models of stiffness.)

As a matter of fact, the hypothetical “twisted frond” would gain nothing in point of strength,—would be no better able to hold up its head,—would be bent and broken just as easily as the straight frond. (This cannot be easily tested, because a flat strip of paper cannot be twisted into the shape of a “spiral stairway”, which is an ‘undevelopable’ surface, as mathematicians say; but it is plain that such a spiral surface would offer no more resistance than if straight, to a force that tended to bend it round the radial line at any given point.)

But surely a much graver objection to the hypothesis presents itself, if we ask what principle of reproduction it supposes— For if M^r. Wright allows that leaves are, in some way, the sexless progeny of the plant, real organisms, not mere organs, (—vegetable working-bees, so to speak, morphologically identical with the fertile vegetable Queens and drones, the pistils and stamens,)—then his hypothesis becomes a monstrous confusion of the whole brood into one undistinguished spiral mass.

The only interpretation of the physiology of the bud, that allows any meaning to his hypothesis, is, that the bud-axis with its complement of leaves is a single individual, of which the leaves are merely organs. (In that case, a curious question arises,—Should we regard the terminal bud, in those plants in which the terminal bud survives, as a new generation or as part of the old?) M^r. Wright has not mentioned the embryo-buds in the axils of those leaves; but I suppose he would say that they would be sure to go with the leaves for the sake of protection. The axillary bud, however, is more important to the future welfare of the plant than the short-lived leaf, and it would have been more reasonable to regard their common arrangement as determined by the interests of the bud rather than by those of the leaf.

This interpretation of a bud as a single individual, appears to receive support from such phænomena as the axillary bulbils of the tiger-lily, which lose their attachment to the stem and will grow if planted: but this same phænomenon of the tiger-lily bulbils (like so many geranium-cuttings) can be easily understood on the other and far simpler and more universal interpretation, according to which each leaf, each bract, each stamen, each carpel, is an individual organism,—identical, morphologically regarded, however much they may have been differentiated by the division of labour in the vegetable economy of the whole compound plant.⁴

It deserves unfavourable notice that M^r. Wright’s paper, from beginning to end, does not contain the name of a single plant. This, I think, betrays the purely theoretical character of the investigation. I do not believe he could have avoided allusion to actual instances, if he had really studied them, for the actual instances have a great deal more to say than what is contained in the barren arithmetic of Phyllotaxy.

Pray forgive me if I have expressed myself too strongly in these notes. I shall be very anxious to hear your general opinion in a few words; and then I shall ask permission to send you a sketch of my own theory of the origin of leaf-orders.⁵

Believe me, my dear Sir, with great respect | Yours very sincerely | Hubert Airy

Charles Darwin Esq^re. M.A., F.R.S., F.L.S. &c &c.