From Hubert Airy   17 March 1873

My dear Sir

I am very glad indeed to have your kind letter of congratulation on the first appearance of my paper in print— I have not yet seen it in ‘Nature’, but I understand they have taken the Abstract, which I prepared for publication in the ‘Proceedings’ of the R.S., in which case the words are my own.¹ The necessary abbreviation in the Abstract has curtailed much of the argument, and has presented some of the points too bluntly, especially that which you stumble upon,—contraction.

Perhaps I can say what I mean more clearly thus:—

The change from (1) to (4) is what I wish to describe by the words “Contraction with twist.”² But, looking at (4) alone, without regard to the earlier state, we should certainly be wrong in using the word “contraction”, for the bud, in its individual life-time, only increases in length:—but it does not (I suppose) reach such a length as was reached by the earlier forms (1), (2), (3):— in comparison with them the axis of (4) is stunted while the growth of the embryo leaves is not stunted.

To exhibit the above process of contraction to the audience at the R.S., I constructed some large models, in which four dozen india-rubber balls (about 2 inches diameter) represented the embryo leaves; and these I displayed on a tall frame, so that they were held up to view and made to go through their performances in mid-air. I very much wish you could have seen them, and I shall still hope for an opportunity of showing them to you—

I think I have made a new point, confirming the condensation-theory.— The wild teazle (Dipsacus sylvestris) shows in its composite head a conspicuous set of 26 spirals in one direction, and another set of 16 in the other direction, differing therein from all the normal spiral orders.— But the teazle has its leaves in pairs (in crucial order) and its involucral bracts in pairs: and if we consider what would become of a crucial order under contraction with a twist, it appears that the following numbers will successively come into contact with any one leaf taken as 0:—

2, 4, 6, 10, 16, 26, 42, 68, &c.—and will produce systems presenting sets of 6, 10, 16, 26 &c. spirals, just such as the teazle presents.³

The teazle-head is manifestly produced by a condensation of a former crucial order,—the very order which is exhibited by its leaves on the stem below the head.

I found the same arrangement (spirals 16 & 26) in 4 out of 100 dandelions whose bald heads I examined last summer— They had taken the condensed crucial order for ‘sport’, I suppose.

I must add these facts to my paper in a note.

With kind regards, | I am, my dear Sir | Very respectfully yours | Hubert Airy Chas. Darwin Esq^re. F.R.S. | Down.