34 
Notes on the History of Correlation 
the number of generations, but reversion checks this increase, and brings it to 
a standstill." 
Galton's proof assuming homoscedasticity is of a very simple nature. Let the 
reversion be \x, where x is the parental character. Then the mean variability of 
the offspring generation 
= a" (1 — r-) + A,- (mean x~) 
= cr- (1 - /•') + A,V-. 
Therefore unless X = r the population cannot remain stable. Or without any hypo- 
thesis as to normality, only on the basis of linearity of revei'sion, homoscedasticity 
and stability the Galton coefficient /• of reversion nmst be equal to the r which 
gives the reduction of the ' family variability.' Thus the lecture of 1877, while it 
contains points which later work was to clear up, still in the main lines gives on 
the data for size in sweet pea seeds the fundamental properties of the regression 
line. I have worked out Galton's data for sweet peas and show you a dia'gram of 
the result which Miss A. Davin has prepared for me. The parent seed was of course 
selected seed, and Galton took 100 of each parental grade and determined the mean 
of the offspring, which of course were non-selected seed, i.e. not seedsman's seed. 
Galton fixes the regression in round numbers at ^, I make it slightly larger. In 
any case the regression coefficient is small, if we consider the sweet pea, as Galton 
did, as self-fertilising. It has been so proclaimed in several botanical investigations 
on heredity in the sweet pea. But in 1907 I watched a row of sweet peas and 
observed 3fegachile Willuglihiela, the leaf-cutting bee, in quite considerable numbers 
visiting the flowers. The Superintendent of the R. H. S.'s garden at Wisley also 
replied to an inquiry that he had no doubt some English insect cross-fertilised sweet 
peas because in trying new sorts the gardeners had to place the rows in different 
parts of the garden to reduce the risk of cross-fertilisation. Darwin's statement* 
that " in this country it " — the sweet pea — " seems invariably to fertilise itself," 
appears open to question. Galton's coefficient may therefore, although low, be not 
so low as it appears on the assumption of self-fertilisation. 
The next few years Galton was occupied in collecting material for further 
investigation of regression and heredity. He had established his Anthropometric 
Laboratory at South Kensington and by offering prizes obtained his Records of 
Family Faculties. The first-fruits of these data are to bo found in his Presidential 
Address to the Anthropological Section of the British Association at Aberdeen in 
1885. The part of this Address dealing with regression was considerably extended 
in a paper read to the Anthropological Institution in the same year. Galton now 
deals with the inheritance of stature and transmutes female to male stature before 
determining his mid -parentages. He does this, not as we should do now by 
multiplying by the ratio of paternal and maternal standard deviations, but by the 
multiplying factor of mean statures 1-08. This is roughly permissible if the 
coefficients of variation for the two sexes are the same as they very nearly are for 
stature. In this paper we have the first published diagram of the two regression 
* Cross and Self -fertilisation of Plants, 1878, p. 153. 
