# To Francis Galton   13 January [1876]1

Jan 13

My dear Galton

I again thank you heartily for the immense labour which you have taken for me.— I will publish entirely your “Report on general value of results” in my introduction”, & as I before said it will add very greatly to the value of my book.— I will send you a proof of the sheet whenever it is printed, though this may not be for a very long time.—2

From what you say about ratio of 100 to 80, I may mention that I measured 73 crossed & 73 s. fer plants of Ipomœa, & their mean worked out in my rough way is as 100 to 77.3 But I have been thinking for some days that I wd get the mean of all my plants, & will see if I can get my courage up for such a task.— It is too gigantic a an undertaking to begin again experimenting.

I have one question You say in last paragraph of your Report about “a few of the tallest plants”, that they “tell their own story clearly”: my sole object has been to show that the crossed plants best the s. f. when grown under similar conditions.— Now is this the “story” to which you refer, because if so your opinion is of value to me, & I shd like to make your words clearer. It seemed to me when experimenting that the plan of measuring only the tallest plants had the great advantage of eliminating on both sides all sickly dwarfed & injured plants.— I do not see that for my purpose it wd be of any great use to get G. to do all of the “tallest plants”, but I will send him some time your mathematical M.S.4

(Now with respect to the mean heights, I will say in introduction, that I merely added up the heights of all plants of each species & divided them by their number, without using any of the refinements of statistical science. But here comes an odd thing, I have added my rough mean in pencil to yours & you will see in the enclosed slip (which please return) that in 6 out of the 7 cases I make the superiority of crossed over the s. f. less than you do by some 1 to 4, generally by 3.5

I am extremely glad to find that my results are fallen out on the side of cross〈  〉 Do you understand the cause of this?   I will in my text under each of the 7 species give your results, & refer to your Report in my Introduction to show how you worked out your means, as this I presume will be sufficient though, I do not understand how it has been done.6 But I am astonished that the common rough way of taking a mean differs so much from your refined methods. It wd be a frightful job, to send all my Tables to some professional calculator to have accurate means taken, as I shd have to alter more or less all my M.S. & the notes; & I hope you do not think this necessary; please tell me what you think.—

There is one point on which you do not touch in your last letter viz ratio of variability in height between the crosses & s. fert plants: I send back your 2 former notes, to remind you, & please let me have them back.—7 Perhaps these go for nothing now that you know that all the plants were measured instead of, as you formerly thought to the selected tallest plants. If your remarks still hold good in any of the cases I shd be very glad to quote a few sentences from you on this subject, stating to what species you refer. I was much struck with impurity in colour of flower & in height of those s. f. plants of Petunia which grew in a long row out of doors, though that does not hold, as you say, with the plants of Petunia in the pots, & which fact I think I can explain.8

This whole subject of variability of height is so much beyond my scope, that without you can give me a sentence, I will pass it over, except just referring to the impurity, as judged by the eye alone of the P. out of doors. Nor do I think that I will ask George to work out other cases, as I shall be sure to get into some jumble.

If you will have the patience to read this unconscionably long letter & answer my queries as far as you can, I will promise to give no more trouble, & most cordially again thanking you—remain | Yours very sincerely | C. Darwin

Have you seen a R in last Frasers on the Unseen U. it seems to me excellent sign E.C. Do you know author?9

## Footnotes

The year is established by the relationship between this letter and the letter to Francis Galton, 10 November [1875] (Correspondence vol. 23).
CD had asked for Galton’s help with statistical calculations (see Correspondence vol. 23, letter to Francis Galton, 10 November [1875]). The text of Galton’s report on CD’s tables appears in Cross and self fertilisation, pp. 16–18; the book was printed in December 1876 (DAR 210.11: 6).
CD’s observations and experiments on ten generations of Ipomoea purpurea (morning glory) are discussed in Cross and self fertilisation, pp. 28–62.
See letter to G. H. Darwin, 8 January [1876], and letter from G. H. Darwin, [after 8 January 1876]. George Howard Darwin was assisting his father with statistical calculations for Cross and self fertilisation; these included a table comparing the average heights of 83 groups of cross and self-fertilised plants, 1605 in total from 54 species, raised from the same parent stock (Cross and self fertilisation, pp. 240–3, 270–83). CD’s manuscript of the first ten chapters of Cross and self fertilisation with the instructions to the typesetter to incorporate Galton’s report is in DAR 2 (see f. 22D). The report itself has not been found; the published text reads: ‘Those groups of cases in which measurements have been made of a few of the tallest plants that grew in rows, each of which contained a multitude of plants, show very clearly that the crossed plants exceed the self-fertilised in height, but they do not tell by inference anything about their respective mean values’ (Cross and self fertilisation, p. 18).
The enclosure has not been found; in addition to Ipomoea purpurea, CD asked Galton to look at tables relating to Digitalis purpurea (foxglove), Reseda lutea (mignonette), Viola tricolor (heart’s-ease), Limnanthes douglasii (Douglas’ meadowfoam), Petunia violacea (a synonym of Petunia integrifolia, the violetflower petunia), and Zea mays (corn) (Cross and self fertilisation, p. 15). Galton had included in his measurements the height ‘estimated in accordance with statistical rules’ of a few plants that had died, whereas CD had included only those that survived (Cross and self fertilisation, p. 19).
See n. 2, above. CD referred to Galton’s calculations of the ratio between the average heights of crossed and self-fertilised specimens only in the cases of Limnanthes douglasii and Zea mays (Cross and self fertilisation, pp. 146, 234–5).
Galton’s notes have not been found.
By the fifth generation, all the self-fertilised plants of Petunia were of uniform height and had flowers of a uniform colour different from that of the parent stock; the crossed plants were more variable in both height and flower-colour (Cross and self fertilisation, pp. 203, 309–11). CD did not draw any distinction in his published account of Petunia between the plants grown outdoors and those grown in pots, but in his report, Galton had argued that in general the number of plants grown in pots was too small to be statistically useful (ibid., p. 18).
Edward Caird was the author of a highly critical review ([Caird] 1876) of Unseen universe: or, physical speculations on a future state in Fraser’s Magazine (Wellesley index). Unseen universe had been published anonymously in April 1875 by Balfour Stewart and Peter Guthrie Tait ([Stewart and Tait] 1875), and had already gone into three editions; they were not identified as the authors until the fourth edition appeared in April 1876 (ODNB s.v. Stewart, Balfour). Stewart and Tait, both physicists, sought to reconcile science and religion by arguing that scientific evidence could be used to support the existence of immortal souls and a transcendental universe. Caird argued that such a reconciliation was unnecessary.

## Bibliography

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

Cross and self fertilisation: The effects of cross and self fertilisation in the vegetable kingdom. By Charles Darwin. London: John Murray. 1876.

ODNB: Oxford dictionary of national biography: from the earliest times to the year 2000. (Revised edition.) Edited by H. C. G. Matthew and Brian Harrison. 60 vols. and index. Oxford: Oxford University Press. 2004.

Wellesley index: The Wellesley index to Victorian periodicals 1824–1900. Edited by Walter E. Houghton et al. 5 vols. Toronto: University of Toronto Press. London: Routledge & Kegan Paul. 1966–89.

## Summary

Thanks FG for his report [on the statistical validity of CD’s experiments; see Cross and self-fertilisation, pp. 16–18]. Discusses FG’s comments, his own experiments, and the means by which the results may be analysed.

## Letter details

Letter no.
DCP-LETT-10357
From
Charles Robert Darwin
To
Francis Galton
Sent from
Down
Source of text
DAR 202: 54
Physical description