K. Pearson 
93 
however, is rapidly assuming a value very close to those which have been deter- 
mined biometrically for large populations mating at random, and the regression 
has already reached that value "5*, 
It is noteworthy that the regression of the gametic cell of an individual on 
the somatic cell of that individual is identical in value with the regression of the 
somatic cell of the offspring on the somatic cell of the individual. 
(6) I have not thought it worth while at present to proceed with further 
reducing divisions, although the results would not be without interest as determining 
the rate at which a stable population was established after crossing two "pure races," 
owing to the cessation of change in the variability of successive generations, and to the 
corresponding equalisation of correlation and regression. The present investigation 
suffices to show that we fairly rapidly approach the biometrically observed condition 
of things, even if we start with two pure races, and this result will be shown on 
another occasion to be experimentally verified. It may, of course, be said that 
the hypothesis which makes the inherited character depend on p unit determinants 
in the paternal and maternal chromosomes, separated into two moieties at random 
in the reducing division, is not the only conceivable one. This is fully admitted, 
but by working it out as a first and not unreasonable hypothesis, we have reached 
a number of suggestive points. We see that Mendelian dominance and the Mendelian 
quarter may arise in cases where there is no pure gamete, and that the discovery 
of a latent character may need several generations of breeding. Further we see 
a continuous transition from simple Mendelism, through various phases of pseudo- 
Mendelism to distributions closely following the normal curve. We notice also 
that if we increase the number of determinants on which a character depends, we 
very soon, even if we start with two pure races, reach by hybridisation and crossing 
of the hybrids a population closely following the correlation found biometrically for 
large groups mating at random. If the hypothesis here dealt with were correct, it 
would follow that the Mendelians were merely working at one end of the scale, the 
biometricians somewhat further down. At present interesting problems which 
suggest themselves are : the possibility of in any way correlating the somatic and 
the resulting gametic cells ; the existence or not of ratios actually or nearly 
Mendelian, but where the apparent homozygotes do not breed true ; lastly, the 
investigation of whether or not the values of parental correlation hold closely 
when we have bred for only a couple of generations from the hybrids of two pure 
stocks. With regard to this last problem, we may hope shortly for light; Mendelian 
literature for the careful reader may provide answers, perhaps, to the second. 
At present it does not seem needful to defend the assumptions upon which the 
present theory is based. It suffices that it is sufficiently wide as it stands to cover 
the Mendelian and the biometric views. It has been expounded here on account of 
its suggestiveness. What there is of good in it is Weldon's; where it may blunder 
is where I have failed to correctly interpret by word or symbol his ideas. 
* The fact that there is in this case a difference between the correlation and regression depends 
upon the variability of the somatic cells of the two generations not yet being equal. 
