22 GENETIC STUDIES OF RABBITS AND RATS. 



genetic factors involved. Thus, reappearance of the extremely 

 large type in 1 individual in 4 would indicate one genetic factor; its 

 reappearance once in 16 individuals would indicate two factors, and 

 so on; but in the present case the extremely large type has not reap- 

 peared at all in F 2 , so that this method is scarcely applicable. On 

 the multiple-factor theory, it may be that too small a number of F 2 

 individuals has been produced to make the reappearance of an extreme 

 type probable; but the form of the variation curve for F 2 would still 

 be available as an index of the number of factors involved, even if 

 this curve was not sufficiently extended to include the grand-parental 

 classes. With this idea in mind, I have suggested (Castle, 1921) a 

 comparison of the standard deviation of F 2 with the standard 

 deviation of F a as a basis for estimating the number of independent 

 factors involved in cases of so-called blending inheritance. Dr. 

 Sewall Wright, who has kindly assisted in this matter, gives the fol- 

 lowing formula for computing the number (ri) of independent factors 

 involved : 



D 2 



w 



8(cr a -O 



In this formula D is the difference between the means of the 

 parental (pure) races, <n is the standard deviation of FI, and <r 2 is 

 the standard deviation of F 2 . 



In table 31 are shown the results obtained by applying this formula 

 to the six most important measurements studied in the case of each 

 of the three different racial crosses. For the Polish-Himalayan 

 cross, in which the parent races do not differ greatly in size, a differ- 

 ence of from one to three genetic factors is indicated by the different 

 measurements studied, the average being two factors. For the 

 Himalayan-Flemish cross the indicated number of factorial differences 

 ranges from 5 to 10, average 8.2. In both these crosses the results 

 are fairly consistent throughout the different measurements. But 

 this is not the case in the Polish-Flemish cross. Here the bone- 

 measurements give low values (between 5 and 6), evidently too low, 

 since they are less than those of the Himalayan-Flemish cross, in 

 which the parent races differ less. But the weight and ear-length 

 values are high, about double the values given by the Himalayan- 

 Flemish cross. The average for the series is 10.5, which is a value of 

 the proper magnitude in relation to the values given by the other 

 two series, since the number of factorial differences between Polish 

 and Flemish, one would suppose, should about equal the sum of the 

 differences (1) between Polish and Himalayan and (2) between 

 Himalayan and Flemish, because Himalayan stands in size between 

 the other two races. It is noteworthy that the results given by 

 weight and by ear-length respectively are in each cross very similar. 



