# From G. H. Darwin   [25 September – 3 October 1873]1

If a race of animals be subjected to poor conditions your idea or hypoth. is that the general run of all the organs in this race will be smaller than in well-nourished individuals of the same race—but that all the organs will not be equally stunted, that it will not affect the whole organisation but that it will affect some organs—So that we have a race the individuals of which are almost all stunted in one respect or another. Those individuals in wh. the stunting affects useful organs will be weeded out by Nat: Sel— those in wh. it only affects useless organs will not be so weeded & will thus affect the whole race. I fail to see how the law of distribution about a mean affects this argument2

Supposing we measure in the well fed members of the race the length of any partic. organ from A along AB & make a line opposite the other end   Then after measuring & marking off several hundred the paper wd. show a black shade in the middle & shading dying away on either side   Then the law of distribution about the mean is that the shading dies away equally on each side of the central black shade. If now we measure a like number of the same part in the poorly fed we shall get another sort of shading, which accordg. to what I understand your postulate to be will differ from the first in the central darkest shade being lower down & wh might differ in that the shading does not die off equally above & below

Now as far as I can see the shading in the 2nd. figure might be equally as symmetrical as in the 1st. figure & yet your argument might hold good and further I think it might be unsymmetrical in the 1st. & symmetrical or unsymmetrical in the 2nd. all without affecting the argument— That is to say I do not see what the law of distribution has got to do with it

If in poor conditions the larger proportion of the cattle had the horns of the same size as in well-fed conditions, but at the same time there were more cattle with horns below the average length of the horns of well-fed cattle than before this wd. have the effect of slightly reducing the average length of horn in ill fed cattle while at the same time the distribution about this average so reduced wd. no longer be symmetrical; the shading on the lower side wd. die away more slowly than on the upper side. The effect of such a change might be analysed into two effects

1st. the lowering of the general average   This is equivalent to a general stunting of the horns; if the horns are useful those with shortened horns will be weeded out by Nat: Sel: & the tendency to diminution of horns in the whole race will thus be checked; if the horns are useless those with shortened horns will not be weeded out & the average length of horn will be yet further shortened in the whole race below the point to wh. the direct effect of ill conditions had at first brought it.

2ndly. the want of symmetry in the distribution   If the horns are useful the weeding effect of Nat. Sel. will have a tendency to restore the symmetry of distribution about the slightly reduced average; if the horns are useless there will also be a tendency to restore the symmetry of distribution but it will take place thro’ the short-hornedness being distributed by inheritance thro’out the whole race & thus augmenting the diminution of length of horn thro’out & thus still further displacing the average length of horn (ie the dark shade in the diagram) which was at first only slightly displaced thro’ the direct effect of poor conditions.—

## Footnotes

The date range is established by the publication of CD’s letter to Nature on 25 September 1873 (see letter to Nature, 20 September [1873] and n. 1), and the letter to Nature from G. H. Darwin, 4 October [1873].
CD had drawn on Adolphe Quetelet’s statistical work to support his argument concerning the development of minute rudimentary male cirripedes (see letter to Nature, 20 September [1873] and n. 10).

## Summary

Criticises CD’s letter to Nature ["Complemental males in certain cirripedes", Collected papers 2: 177–82].

On the elimination of useless parts.

GHD fails to see the point of CD’s use of the law of distribution about a mean.

## Letter details

Letter no.
DCP-LETT-9070
From
George Howard Darwin
To
Charles Robert Darwin
Sent from
unstated
Source of text
DAR 205.1: 74