PEARL— SEX RATIO IN DOMESTIC FOWL. 431 



count of the concentration of the frequency at other than the mid- 

 points of the class areas. 



3. The fitted curve makes it possible to make some rather definite 

 statements as to the probability of the occurrence, as a result of 

 chance merely, of distinctly aberrant sex ratios. Poultry papers 

 very frequently, and scientific journals rather more often than would 

 seem compatible with any clear grasp of the theory of chance, con- 

 tain statements about marvelous deviations from the normal sex 

 ratio in particular families or small groups of families. Usually 

 such widely divergent sex ratios are most uncritically taken to 

 prove either the inheritance of a special sex tendency in a particular 

 line of breeding, or the influence of some external environmental 

 agent upon sex determination. If, for example, a poultry breeder 

 finds that out of twenty chickens from one pair of parents, fifteen 

 are pullets, he is distinctly apt to regard this as a wonderful phe- 

 nomenon, worthy of his best exegetic powers. But our present sta- 

 tistics show that, if we deal with families of twenty chickens for 

 example, it is to be expected on the basis of chance alone, the fol- 

 lowing relations will hold. 



15 or more chicks will be pullets in 56 out of every 1,000 families of 20 



16 or more chicks will be pullets in 26 out of every 1,000 families of 20 



17 or more chicks will be pullets in 12 out of every 1,000 families of 20 



18 or more chicks will be pullets in 5 out of every 1,000 families of 20 



19 or more chicks will be pullets in 2 out of every 1,000 families of 20 



20 or more chicks wnll be pullets in i out of every 1,000 families of 20 



It needs no particular emphasis on these figures to indicate that 

 before aberrant sex ratios can be considered indicative either of 

 environmental or hereditary effects, it will be necessary to show 

 that they occur with such frequency as to exceed considerably that 

 expected on the basis of chance alone. 



IV. Prenatal Mortality and the Sex Ratio. 



The first suggestion which comes into one's mind in attempting 

 any analysis of the causes of a deviation of the sex ratio from equal- 

 ity, is that the prenatal mortality has been differential in respect to 

 sex. It is commonlv held bv statistical writers that this is true of 



