Vol. 6, 1920 
GENETICS: H. H. LAUGHLIN 
237 
propositus; (4) the probability that the particular propositus, and conse- 
quently all of his or her direct ancestors, will be entirely eliminated as a 
contributor to the hereditary constitution of the propositus; (5) that a 
definite number of chromosomes specified as to maternity or paternity 
of origin, carried by a given ancestor, will by such ancestor be passed on to 
the propositus; (6) as one of many special cases, the probability that a 
given ancestor who appears once or more in each the maternal and paternal 
half -pedigree, will be duplicated exactly in zygotic chromosomal constitu- 
tion by the propositus. 
The principles set forth in the paper of which this is an abstract make 
possible the mathematical formulation of an indefinitely great number of 
complex situations in reference to ancestral influence. The completer 
paper presents in detail twenty-seven such formulas. Bight of these 
(numbers 1, 4, 5, 6, 7, 8, 9 and 10) for each individual pedigree- 
place, to which the particular formulas apply, were worked out for each 
member of the first five ancestral generations in man and shown on charts, 
entitled "Ancestral Influence in the Human Male," and "Ancestral In- 
fluence in the Human Female." (In the accompanying charts bearing the 
above titles these same formulas are worked out fo^ the first three 
ancestral generations only.) These particular calculations in reference 
to man are based upon the following data and conditions: (a) that the 
gametic number of human chromosomes is 12; the zygotic or somatic 
number in each sex 24; (b) that the m.ale is heterozygous (xy) and the 
female homozygous (xx) in reference to sex ; (c) that all of the purely hered- 
itary qualities are carried by the several chromosomes ; and (d) that in the 
first or foundation formulas no provision will be made for mutation, 
crossing-over, non-disjunction or other special phenomena. 
These eight formulas worked out in detail on the human pedigree- 
charts follow: 
No. 1. A Average number of chromosomes passed on by the selected 
ancestor, taken as a type, to the Fi zygote, i. e., the propositus. 
A = Also the average number of chromosome-pairs each of which con- 
tributes one member to the diploid or ^somatic group of chromosomes of 
the Fi zygote. 
In man the diploid or somatic number of chromosomes is taken tenta- 
tively at 24, i. e., 11 equivalent pairs and one xx or xy sex-pair. 
^ ^ ^ _l_ I {Cy or Cx in case of ancestors from whom an x- or a 
2^^~'^^ i 3;- chromosome may descend.) 
See notes on x- and y- trails, under formulas 4 and 5. 
n = Number of equivalent chromosome-pairs (i. e., excluding the xy or 
the XX sex-pair) characteristic of the species. In man n is taken tentatively 
at 11. 
p = the numerical value of the sub-figure of P used in pedigree-manner 
