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Darwin Correspondence Project

From Hubert Airy   2 May 1876

(I write from Norwich, but hope by the week’s end to be at)

Edensor. Kidbrook Grove. | Blackheath S.E.

2 May 1876.

(I write from Norwich, but hope by the week’s end to be at)

My dear Sir

When last I wrote to you, I think I mentioned that I was preparing a fresh paper for the Royal Society, on a point of Leaf-Arrangement.1 It is now ready, and I shall be very much obliged if you will give me permission to send it as communicated by you.2 I think it has some features which you would approve of. It consists of a description of the leaf-arrangement of the Crowberry plant (Empetrum nigrum), with some discussion of its bearing on the question of the significance of leaf-ranks generally. Crowberry twigs are wonderfully fertile in variations: Scarcely a twig did I find that did not present one or two transitions from simpler to more complex orders in rising from base to summit; but the curious point is that the transition 〈w〉as almost always from an order of one phyllotac〈tical〉 series3 (say the primary series, 1 2 , 1 3 , 〈  〉5, 〈  〉/8 &c to an order of another series (Say 〈the se〉condary series, 1 4 , 2 7 , 3 11 &c.). Such transition could not be effected by any process of uniform condensation,4 and I was curious to learn exactly how it did take place, so I made an instrument which enabled me rapidly to prick off on paper the arrangement of any specimen: then I took fifty twigs at random, and pricked them off, and made a careful comparison of the phenomena they presented. The result delighted me. Forty six out of the fifty showed transition from an order of one series to an order of another series,** and wherever the details were traceable (for sometimes the change could not be traced when it took place in the crowd of microscopic scales at the base of a fresh year’s growth,) the transition was found to be effected by a curious irregularity which I can only describe (without a diagram) as a spiral dislocation between two adjacent spirals of some secondary set. The result of such dislocation is a complete derangement of all ranks not belonging to that set, and a creation of new sets of ranks (with different numbers) in th〈eir〉 stead, thus producing a wholly new arr〈angemen〉t to go on with.

**Such as the following:—

Transition from 2 5 or 3 8 to 2 7 in 22 instances.
2 5 or 3 8 to 2 9 5
2 5 or 3 8 to 5-whorls 1
3-whorls to 2 7 2
2 7 to 4-whorls 10
2 7 to α 2
2 7 to 2 9 〈    〉
4-whorls to 2 9 〈    〉
α to 2 11 〈    〉
2 9 to 5-whorls 〈    〉
2 9 to 2 11 1
5-whorls to 2 11 1
Total 64 in fifty twigs.

(+ *Ga is a 4-6-10-ranked order, such as may be found in scabious-heads.)

This fact suggests remarks on the undue prominence given in some botanical text-books to the ‘primary’ or ‘generating’ spiral,5 which in Empetrum n. is seen to have no more enduring value than any other geometrical rank, but is broken up 〈at〉 each transition, while a new one arises turning in the opposite direction.

The only description I have met with of anything like these changes of leaf-order, is in the Revd. G. Henslow’s paper (Trans. Linn. Soc. vol. XXVI p. 647) “On the Variations of the Angular Divergences of the Leaves of Helianthus tuberosus.”6 The Variations in that plant appear to be similar in character to those of Emp. n., but much more limited in range; and Mr. Henslow appears to me to have missed the meaning of the geometry of the case. Indeed, without instrumental appliances it would be very difficult to make it clear. Accordingly in my paper I venture some critical remarks upon Mr. Henslow’s.7

Along with my paper I propose to send the original fifty pricked diagrams, two of which I take as typical and refer to in describing th〈e〉 details of transition; and at the end of the 〈    〉 I give a description of the ins〈trumen〉t which 〈    〉d, and fondly name it “taxigraph,” and express hope tha〈t i〉t will prove useful to other observers.— Perhaps the instrument itself might as well be exhibited.8

In the course of the paper I take the opportunity of standing up for my theory of leaf-arrangement being determined by the geometrical conditions (of relative position) imposed upon the nascent leaves by the need of mutual accommodation under mutual pressure in the bud, which I see more and more clearly to be the ruling principle of leaf-(arr〉angement.9

I think I have said enough to give you an idea of the scope of my paper, and if you approve of it I hope you will not object to my using your name as communicating it to the R.S.10

Will you kindly remember me to your circle, and believe me | Yours very sincerely | Hubert Airy

Charles Darwin Esq. M.A. | Down, Beckenham. | Kent.


Airy’s letter has not been found.
CD had communicated Airy’s previous papers on leaf arrangement to the Royal Society of London (see Correspondence vol. 22, letter from Hubert Airy, 13 March 1874 and nn. 1 and 2).
A phyllotactic series is any of a number of possible geometric arrangements of leaves around a stem; for example, a 2/7 series denotes seven leaves for every two turns of a spiral made by tracing the points of leaf insertion as you travel up the stem.
Airy considered phyllotaxy from a mechanical point of view, and argued that it was determined by the most economical method of packing buds. He had earlier explained his views on condensation in relation to the Fibonacci series (see Correspondence vol. 20, letter from Hubert Airy, [before 15] July 1872, and Correspondence vol. 21, letter from Hubert Airy, 17 March 1873).
See, for example, Bentley 1861, p. 143. Airy’s point would have some bearing on the fact that leaf arrangement is used as a diagnostic character in plant classification.
George Henslow had presented this paper to the Linnean Society on 16 April 1868 (Henslow 1868).
As with Airy’s earlier papers, only an abstract, not the full text, was published; Airy’s reference to Henslow’s paper remains in the abstract, but not his critical remarks (Airy 1876, p. 159).
Airy’s taxigraph together with the fifty taxigrams recording the leaf arrangement of his specimens of crowberry was exhibited at the Royal Society; the method by which the instrument produced these taxigrams is described in Airy 1876, p. 160.
Airy had first outlined this claim in Airy 1873.
Airy 1876 was communicated to the Royal Society by CD.


Airy, Hubert. 1873. On leaf-arrangement. Abstract. Communicated by Charles Darwin. [Read 27 February 1873.] Proceedings of the Royal Society of London 21 (1872–3): 176–9.

Airy, Hubert. 1876. On the leaf-arrangement of the crowberry (Empetrum nigrum). Abstract. Communicated by Charles Darwin. [Received 8 May 1876.] Proceedings of the Royal Society of London 25 (1876–7): 158–60.

Bentley, Robert. 1861. A manual of botany: including the structure, functions, classification, properties, and uses of plants. London: John Churchill.

Correspondence: The correspondence of Charles Darwin. Edited by Frederick Burkhardt et al. 27 vols to date. Cambridge: Cambridge University Press. 1985–.


On his new paper for Royal Society on a point of leaf arrangement. Asks CD to communicate it and "gives some details of its contents", e.g., recorded observations of changing leaf-order on individual specimens.

Comments on a paper by George Henslow ["Helianthus tuberosus", Trans. Linn. Soc. Lond. 26 (1876): 647].

Letter details

Letter no.
Hubert Airy
Charles Robert Darwin
Sent from
Source of text
DAR 159: 30
Physical description
4pp damaged

Please cite as

Darwin Correspondence Project, “Letter no. 10490,” accessed on 4 March 2021,

Also published in The Correspondence of Charles Darwin, vol. 24