240 
GENETICS: H. H. LA UGHLIN 
Proc. N. a. S. 
to indicate the ancestral or parental generation in relation to Fi. Thus 
in the great-grandparental generation F3, p = ^. 
No. 4. Cy = the average number of j'-chromosomes contributed to the Fi 
zygote by the particular male ancestor taken as a type. 
No. 1 . Cy = the probability that a particular male ancestor will contribute 
the single 3^-chromosome found in the Fi male zygote. 
The value of 1 : Cy is always 1:1, and it is applicable to the direct 
male line only. 
This direct paterial line down which the j-chromosome descends is the 
so-called ";y-trail." 
No. 5. = The average number of :i:-chromosomes contributed to the 
Fi zygote by the particular ancestor taken as a type. 
1 : Cx = The probability that the particular male or female ancestor 
will contribute an i\;-chromosome to the Fi zygote. 
The value of is determined by the following rule : 
(a) Beginning with the ^-chromosomes in the Fi zygote, without ex- 
ception (i. e., with the chance of 1 : 1) the single :^^:-chromosome in the 
male is derived from his mother; and of the two ^i;-chromosomes in \h.^ female, 
one is derived from each parent. 
(b) In the Pi and all older generations, in the case of a female zygote 
the chance of the descent of an x-chromosome from the father or mother 
is equal (i. e., 1:2), but in the male the :)c-chromosome is always re- 
ceived from the mother alone (i. e., the chance is 1 : 1). 
Therefore, the probability that a given ancestor, taken as a type, will 
contribute an :x:-chromosome to the Fi zygote (i. e., 1 : Cx), ise qual to 
the product of all probability ratios, made according to rules (a) and (6) 
above, along the :^-trail from the selected ancestor to the Pi generation 
inclusive. 
Thus 1 : Cx for the mother's mother's father of a female zygote = 
(1 : 1).(1 : 2).(1 : 2) = 1 : 4; but for the mother's father's mother of 
a female zygote 1 : Q = (1 : 1).(1 : 2).(1 : 1) = 1 : 2. 
Thus the so-called "a;- trail" — from a son to the mother only, but from a 
daughter to both the father and mother, traces the several lines in the ancestral 
pedigree down one of which an rt-chromosome must descend. 
NoT^. — The X- trail and the j- trail and all calculations herein based upon them ap- 
ply only to those species in which the male is the heterozygous and the female the homo- 
zygous sex. In species in which the reverse is true the x- and the ^'-trails exchange po- 
sitions. The general rule is that the 3/- trail follows the heterozygous sex; the trail 
from the homozygous individual to both parents, but from a heterozygous individual 
to the homozygous parent only. 
No. Q. R = Range in number of chromosomes (i. e., in number of single 
members of chromosome-pairs) possible for the selected ancestor, taken 
as a type, to contribute to the 24 (i. e., 11 equivalent pairs and 1 xy or 
1 XX pair) chromosomes of the Fi zygote. 
