236 
GENETICS: H. H. LAUGHLIN 
Proc. N. a. S. 
radical or linkage-group of trait determiners. The chromosomes are the 
germ-plasm. If then it is sought to measure the influence of a given an- 
cestor upon the hereditary traits of a given propositus, it is necessary to 
develop a series of mathematical formulas which measure the probabili- 
ties of definite situations happening in reference to the transmission of 
chromosomes from the given ancestor to the given propositus. 
In developing such formulas the following factors must be taken into 
consideration : 
First. Whether the species in question is bi-sexual. 
Second. Whether in the particular species the male or the female is 
the heterozygous sex. 
Third. Due provision must be made for sex-linked traits. 
Fourth. The number of chromosomes, both gametic and zygotic, 
characteristic of the species, must be known. 
Fifth. For the present the individual chromosomes will not be weighed, 
but simply counted. Doubtless the ontogenetic working out of each 
chromosome is very specific both qualitatively and quantitatively. When 
ultimately genetical and cytological research locate in definite chromosomes 
the genes for definite traits, then the several chromosomes can be weighted, 
and due provision for their differential values properly made in the formulas 
for measuring the several features of ancestral influence. 
Sixth. Due cognizance must be taken of the possibility of mutation, 
crossing-over, non-disjunction and other special phenomena occurring 
in the course of the descent of chromosomes from a given ancestor to the 
propositus. In the accompanying formulas such phenomena are not pro- 
vided for, because their rates of occurrence are not yet measurable in man, 
but when one by one their mathematical measures are attained, each such 
measure can be woven into the accompanying foundation formulas. The 
present formulas will not be upset by such corrections, but simply modified 
in the direction of greater accuracy. 
Seventh. It must be considered that in a given gamete a definite chro- 
mosome may have been derived from either the paternal or the maternal 
source. This is especially important in cases of zygotes of mixed blood. 
Eighth. In certain situations it will be necessary to specify whether 
a given trait is dominant or recessive to its allelomorph. 
Finally, all formulas must be stated in general terms, so that they may 
apply with equal accuracy to any species concerning which chromosomal 
data are at hand. 
There are many features of ancestral influence which may be mathe- 
matically formulated. Among them are (1) the average contribution 
in number of chromosomes that a given ancestor, taken as a type, will 
contribute to the propositus; (2) the range in such numbers; (3) the prob- 
ability that the given ancestor, taken as a type, will contribute all of the 
hereditary influences which the particular half-pedigree furnishes to the 
