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Darwin Correspondence Project

From G. H. Darwin   [after 8 January 1876]1

Dear Father,

the operation wd. be very simple, if I understd. you aright. You wish to lump all the Species into one general group & to give two numbers the ratio of which to one another expresses the benefits of Xg.2

Plantsavg. height
Spec: A 4 — 100
——— B 10 ——— 100
——— C 17 ——— 100
——— D 3 ——— 100
Plants avge ht.
Spec. A. 4 ——— 90
——— B 9 ——— 60
——— C 16 ——— 65
——— D 4 ——— 70

The method is to multiply the two columns together & in the first case divide by 34 & in the second by 33 Thus the first number is

4 x 100 + 10 x 100 + 17 x 100 + 3 x 100

and this of course = 100

The second number is

4 x 90 + 9 x 60 + 16 x 65 + 4 x 70
= 7013

Thus in your imaginary case the Xd. are to the selfs in the proportion of 100 to 7013 in point of height

It is of course clear that it is useless to go thro’ the first series of multiplications because the result must come out 100 & therefore all you have to do is to take your second series of numbers & multiply them two & two as above & divide by the total number of cases

I do not feel quite sure that this procedure is wholly justifiable because you are lumping various species together and there is no procedure that I can think of by which you can get the influence of Xg. to stand out by itself   Nevertheless I do feel sure that this number gives you approximately what you want.

G. H. D

CD note:

End of letter: ‘The average heights of the [parent] species are of very different values because different numbers were measured— but I have thought it worth while to give a mean not of all the plants which were measured, but a mean of the means, assuming for the moment that all of equal value.’3


The date is established by the relationship between this letter and the letter to G. H. Darwin, 8 January [1876].
CD had asked for advice on calculations for Cross and self fertilisation, pp. 240–3 and 281–2.
CD’s note is a rough draft of text published in Cross and self fertilisation, pp. 240–3 and 281–2, explaining the calculations in a table of the relative heights of the progeny of crossed and self-fertilised plants.


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


Provides CD with a method of obtaining a numerical ratio that expresses the superiority in heights of crossed plants to self-fertilised plants.

Letter details

Letter no.
George Howard Darwin
Charles Robert Darwin
Sent from
Source of text
DAR 77: 144–5
Physical description
4pp ††

Please cite as

Darwin Correspondence Project, “Letter no. 10349,” accessed on 16 January 2021,

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