Letter to Charles Darwin: August 1, 1871
To Mr. Darwin.
CAMBRIDGE, Aug. 1, 1871.
. . . My own ambition, my private interest in the fate of my article, is quite fully met and satisfied by your good opinion and kind expressions respecting it. I did not hope to have many readers, even here, who would have any genuine interest in the subject of the article, and not so many in England, where our " Review " has a very small circulation. If I had known beforehand what the article would come to on being written out, I should have determined to send it for publication to some English review, through which it would doubtless have met with a larger number of interested readers. But I undertook the work on rather short notice at the request of the editor of our " Review," and meant it at the start only as a book-notice. Somehow, it grew into the proportions and dignity of a body-article, and was accepted as such. I am only too well pleased that it should be regarded by you as worthy of republication and a larger circulation, and doubtless the editors and publishers of the " Review " will also be. I give permission, of course ; but, as to the title, I am a little at fault. I do not well enough know the public scent. Titles of English books are generally more " sensational " than ours ;
( 232) and, from what you say as to the cold scent the English public have for pamphlets, I suppose that nothing short of a somewhat sensational title will satisfy an English publisher. SO I propose something like this : "Darwinism, being an Examination of St. George Mivart's Work 'On the Genesis of Species.'" , ,
I hope soon to publish a paper on the utility of the phyllotaxis, as you suggest. I have already printed two papers on this subject, — one in 1856, in Gould's " Astronomical Journal," No. 99 ; and the second, in 1859, in the " Mathematical Monthly." A copy of the last was sent you by Professor Gray. In my new paper, I shall avoid as much as possible all abstruse mathematics, which I see has so obscured my thesis that it is only known to mathematicians.
The specialty of the phyllotactic fractions is not that they represent complete systems, so that, after a time, some leaf will come over the first one and be connected with the same vessels in the stein; this property would belong to any exact fractional interval ; an exact proper fraction, after the number of steps represented by its denominator, and the number of revolutions represented by its numerator, would make a complete system, or bring the next succeeding leaf over the first. The peculiarity of the phyllotactic fractions is that the distribution is most rapid and complete within each set or system ; that is, it is much more perfect than for other exact fractions. The incommensurate interval of the ratio of the extreme and mean proportion gives the best distribution of all ; but here the system is infinite, —that is, no leaf ever comes exactly over an older one.
I have found among old papers a proof of my first article on this subject ; and, for the sake of the diagram of this arrangement, I send enclosed a page of the article. The exact fractional intervals of the phyllotaxis have the distributive character of this most perfect arrangement to this extent; namely, that they determine, as no other intervals do, that every leaf shall fall in the middle third (or not beyond it) of the space between two older ones in which it falls. In all other exact intervals, there is crowding. Take, for instance, j, which does not occur in nature. Why should it not ? The second leaf in this system would be placed very nearly opposite the first, or very near the middle of the space, and the arrangement is so far well enough ; but the third falls at eight-ninths, that is, within of the first leaf, crowding up against it yet not near enough to get any advantage from connection with the vessels or sources of supplies which the first leaf has grown from. The fraction , or the one-third system, would be better; for though the first and second leaves divide the circumference into one and two parts (the extremest ratio in the phyllotaxis), yet the third falls exactly into the middle of the larger interval, and the fourth is directly connected with the vessels from which the first leaf has grown.
Take the interval 3/7 for another instance, which does not occur in nature. The second leaf falls, it is true, near the middle ; but the third, at the interval 6/7, is within 1/7 of the first, crowding it unnecessarily, and has three times as wide a space on one side as on the other. In the phyllotactic intervals, the space on one side of a leaf is never more than twice as great as on the other. In all other cases, greater disproportions would occur in the distributions.
On September 12, Mr. Darwin wrote that the pamphlet was nearly ready, and that he would soon be able to send copies to Wright. "I have sent your article," he adds, "to
( 234) some friends, and all have been much struck with it; but they say, and I agree, that several passages are rather obscure. Even if only a few scientific men will read it, I shall think myself well repaid for printing it; and I thank you very sincerely for your permission. . . . I am glad to hear that you are coining to England ; and I shall be delighted to see you at Down."