# 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

 Plants avg. height Spec: A 4 — 100 ——— B 10 ——— 100 ——— C 17 ——— 100 ——— D 3 ——— 100 34 Plants avge ht. Spec. A. 4 ——— 90 ——— B 9 ——— 60 ——— C 16 ——— 65 ——— D 4 ——— 70 33

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 34

and this of course = 100

The second number is

 4 x 90 + 9 x 60 + 16 x 65 + 4 x 70 33 = 70$\frac{1}{3}$

Thus in your imaginary case the Xd. are to the selfs in the proportion of 100 to 70$\frac{1}{3}$ 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

## Footnotes

The date is established by the relationship between this letter and the letter to G. H. Darwin, 8 January [1876].
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.

## Bibliography

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

## Summary

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.
DCP-LETT-10349
From
George Howard Darwin
To
Charles Robert Darwin
Sent from
unstated
Source of text
DAR 77: 144–5
Physical description
4pp ††