82 On a Mathematical Theory of Determinantcd Inheritance 
Weldon first proceeded on the basis of the non-individuality of the paternal 
and maternal chromosomes, and supposed a chance distribution of the chromomeres 
in ordinaiy mitosis. He investigated the problem with great wealth of numerical 
illustration and with a variety of hypotheses as to segregation. He concluded : 
" It seems clear that such forms of segregation as I have assumed during 
nuclear division will not lead to a separation of zygotes into classes sufficiently 
sharp for Mendelian purposes, unless some persistence of effect from one mitosis 
to another be assumed." 
He accordingly turned to the other extreme hypothesis, i.e. that from the 
moment of fertilisation up to the reducing division of the germ cells paternal and 
maternal chromosomes retain their individuality. 
It is clear that this assumption disregards the reticulated stage of the 
chromosomes so far as its bearing on heredity is concerned. Weldon did not, 
however, reach the standpoint of the individual persistence and identity of the 
chromosomes during the reticulated state owing to a bias in favour of one or other 
theory. He recognised by extended numerical investigation of a number of cases 
that, if the chromomeres are the bearers of hereditary properties, interchange of 
chromomeres during ordinary mitosis was incompatible with any definite segre- 
gation in the offspring of hybrids. Throughout the theory hereinafter developed, 
the persistency of the individual chromosome up to the reducing division will be 
supposed to hold. The evidence in favour of this persistency is far from negligible, 
but it is hardly as complete as some Mendelians are inclined to believe. It is 
here accepted as a working hypothesis with the view of ascertaining whither it 
leads. That no hypothesis was found numerically workable and consistent with 
segregation phenomena, neither proves that such a hypothesis does not exist, nor' 
demonstrates the universal truth of segregation. It merely indicates that in the 
present state of our knowledge we shall be most likely to reach suggestive and 
test results, if we follow up the idea of individuality in the chromosomes up to 
the reducing division. 
(2) Let us suppose that each somatic cell consists of 2q chi'omosomes, effective 
with regard to any one inherited character*, and that each such chromosome contains 
p determinants on which the nature of this inherited character depends. If we 
start with a cell belonging to an individual of pure race we may suppose these 
p determinants alike, and the 1q chromosomes identical in character. We may 
speak of this first group of determinants as protogenic determinants and the 
corresponding chromosomes as protogenic chromosomes. Taking a cell belonging 
to an individual of a second pure race, it will also contain 2q chromosomes built 
up of p determinants. These may be termed the allogenic chromosomes and 
allogenic determinants. Suppose q protogenic chromosomes to be contained in a 
germ cell after the reducing division, and let them join with q allogenic chromosomes 
in a germ cell of the second race to form a zygote. Then whatever fusion of the 
* The whole number of chromosomes may be anything larger than 2q. 
