K. Pearson 
91 
with their relative variabilities as measured by their coefficients of variation, 
the gametic cells are more variable in the ratio of 1*73 to 1. The regression 
of the gametic chromosomes on the somatic chromosomes gives us the value 
-j= — 'JpcK^'Jpc) — ^, or "5 is the value this regression takes even when p is a 
v3 4 
small number. 
Thus, while there is no variation in the somatic cells either of the pure races or 
of the hybrids, and accordingly while it is impossible to find a correlation between 
somatic and gametic cells for these generations, its value being indeterminate, we 
see that as soon as we reach the offspring of the hybrids, a sensible and definite 
correlation exists, and this correlation has a value which may be suggestive for 
other forms of enquiry. The present writer is fully aware that a variety of other 
mathematical theories of the broad facts of cytology may be developed, and as 
our knowledge increases more ample theories, consonant possibly with a wider 
range of facts, will probably be invented. But he believes that the present theory 
is the first to show that there will be a definite correlation between the deter- 
minantal structure of the chromosomes in the somatic and in the gametic cells, 
and that its value will not improbably be found to be about "5. Looked at from 
this standpoint the somatic cell precedes the germ cell of the individual, and 
the somatic cell might, under the proper stimulus, give rise to a germ cell. 
These germ cells are not of one type ; they are variable, but correlated with the 
originating somatic cell. It is difficult, if we look at matters for the time being 
from this aspect, to find any basis for a "continuity of the germ plasm." Every 
reducing division may produce a new germ cell, and the whole group of germ 
cells is relatively more variable than the somatic cells from which they arise. 
The link between the two is one of correlation and not causation, a result produced 
by the random partition in the reducing division. 
(5) I now turn to the somatic cells of the grandchildren of the hybrids, i.e. 
the children H.2 of the offspring of the hybrids H. 
cc 
Let ^ + — be the number of protogenic determinants in the chromosomes of 
c 
the somatic cell of the first parental H^, and ^j) + ^i/c be the number of protogenic 
determinants in the chromosome of the gametic cell of this parent. Let p + x.^jc, 
and -^-p + be the corresponding quantities for the second parent and let us 
suppose the matings among the absolutely random. Then the number of 
protogenic determinants in the two chromosomes of the somatic cell of the off- 
spring H^is p + (^1 + ^^)/c = p + s'", say. We require to find the correlation surface 
between s'" and s' and s" (or xjc and x.,/c) or the deviations from the mean p of the 
protogenic determinants in the offspring and the two parents H^. Let us write 
V — ^1 + ^2, and since when p is only moderately large we have seen that p + 1 and 
m = {p + ly/ip + ^) may be practically replaced by p, we shall write for (xii) 
^ = Ve " [I'^-P he^P'i , 
12—2 
