90 On a Mathematical Theory of Determinantal Inheritance 
where is a function of p, but not of x. This is nothing else than the 
correlation surface between the number of protogenic determinants in somatic 
cell chromosomes of the offspring of the hybrids and the number of protogenic 
determinants in the germ cell chromosomes of the same individuals. 
(xi) is again somewhat complex, but it will suffice to reduce it for most 
practical purposes to a normal correlation surface. Thus 
Similarly we have 
icHl +_p>^p + V'/'i''^^ + ^)> approximately. 
(1 + Ijin 
1 - 
c-{l+p)\ 
tI{c^iii) 
where ni = (1 + p)-/{^ + p). 
Thus the correlation surface, if be a new function of p only, is given by 
_ _ r- - -'-'g _ 1 ^ 
z = z„'e + 'ipe'^ (xii). 
Writing this in the form 
we easily find 
1. / 
R 
S2.'/2 
V3 /- 
^ '^pc 
p- + p (Correlation between somatic and gametic 
( cells of offspring of hybrids. 
p + l p^ + ^p + s _ [Standard deviation of somatic 
p ~pi ^ Ip'+I 1 ^^lls of offspring of hybrid. 
p + l 
jStandard deviation of gametic cells of 
+ Ip^+1 ~ \ offspring of hybrid. 
.(xiii). 
Thus we find 
p 
/v/3 
2 
•5108 
1-1632 
1 0290 
4 
•5423 
1-0865 
10206 
6 
•5537 
1 0590 
10157 
00 
•5773 
1^0000 
1^0000 
It will be noted that as p increases the correlation rapidly approaches the 
value ^57 73 and the variability of the gametic and somatic chromosomes the 
values — Vpc and ^'\/pc. Thus we see that, according to the theory here 
developed, the chromosomes of the somatic cells are absolutely more variable 
in the ratio of 1 to •866 than those of the gametic cells. But, if we deal 
