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, $\frac{1}{2}$, $\frac{1}{3}$, ^{⁠⟨⁠  ⁠⟩⁠5}, ^{⁠⟨⁠  ⁠⟩⁠/8} &c to an order of another series (Say ⁠⟨⁠the se⁠⟩⁠condary series, $\frac{1}{4}$, $\frac{2}{7}$, $\frac{3}{11}$ &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	$\frac{2}{5}$	or	$\frac{3}{8}$	to	$\frac{2}{7}$	in	22	instances.
—	—	$\frac{2}{5}$	or	$\frac{3}{8}$	to	$\frac{2}{9}$	—	5	—
—	—	$\frac{2}{5}$	or	$\frac{3}{8}$	to	5-whorls	1	—
—	—	3-whorls			to	$\frac{2}{7}$	—	2
—	—	$\frac{2}{7}$	to	4-whorls	—	10
—	—	$\frac{2}{7}$	to	α†	—	2
—	—	$\frac{2}{7}$	to	$\frac{2}{9}$	—	⁠⟨⁠    ⁠⟩⁠
—	—	4-whorls	to	$\frac{2}{9}$	—	⁠⟨⁠    ⁠⟩⁠
—	—	α†	to	$\frac{2}{11}$	—	⁠⟨⁠    ⁠⟩⁠
—	—	$\frac{2}{9}$	to	5-whorls	—	⁠⟨⁠    ⁠⟩⁠
—	—	$\frac{2}{9}$	to	$\frac{2}{11}$	—	1
—	—	5-whorls	to	$\frac{2}{11}$	—	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 Rev^d. 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 M^r. 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 M^r. 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.