EXPERIMENTAL. 35 



The standard deviations of the coefficients of size were calculated 

 for each fraternity. Since the coefficient of size is the expression of a 

 relation between measurements in one animal and corresponding means 

 in its fraternity, coefficients of size in different fraternities of the same 

 family may be treated together. The standard deviations found by 

 such combining will be based on deviations from the various fraternal 

 means. This will give a fairer result than if the actual deviations had 

 been calculated from the means of all the individuals averaged together, 

 as would naturally be done in determining the standard deviation of 

 a whole generation. It is supposed that the means of the fraternities 

 are not just the same. A common mean would give the extreme vari- 

 ates even greater deviations and the standard deviation would be higher 

 than the deviation obtained by the method presented here. It will be 

 seen now that the coefficients of size for fraternities of the same genera- 

 tion in different families may be treated together, for in the coefficients 

 of size 1 always stands for the mean, whatever the actual value. 



In table 5 these frequencies are classified in classes 0.005 in extent. 

 The row of numbers at the top is the scale of coefficients of size; each 

 number represents the lower limit of its class. On the left are given 

 the family numbers, the generation, F x , or back-cross to the male (BC), 

 with the ledger numbers of the Fi females that were back-crossed. On 

 the right are given the standard deviations, in terms of the ratios, for 

 the frequencies shown on the same horizontal line. From the distri- 

 butions themselves, it is clearly seen that in families 647, 1491, 1493, 

 and 2011 the F x fraternities are less variable than the corresponding 

 back-crosses, whether the latter are taken together or separately. The 

 standard deviations show the same facts in a more concise form. 



In families 1493X2379, 1531, 1532, and 1537 the Fj generations con- 

 tained less than four individuals, so the coefficients of size and the standard 

 deviations were not found. The standard deviation of these back-crosses 

 can be compared with the standard deviations of the back-crosses and Fi 

 generations in other families. The back-crosses of families 1531 and 1532 

 have standard deviations considerably larger than the largest Fi standard 

 deviation. In families 1537 and 2037 standard deviations of the back- 

 crosses are only a little larger than the largest Fi standard deviation. The 

 standard deviation of the total back-cross frequencies in 1493X2379 is 

 less than the largest Fi standard deviation. 



It must be noted here that this family was raised for a check, as the 

 difference between the parents is very small. When the coefficients 

 of size of all the first generations are used together the standard devia- 

 tion, based on 33 individuals, is 0.0143. When the coefficients of size of 

 all the back-crosses to the male (excluding the check-cross, 1493X2379) 

 are calculated together the standard deviation, based on 240 individuals, 

 is 0.0232. Whether taken by single fraternities, by families, or by 

 generations, there is a greater variability in all the crosses back to the 

 male than in the Fi generation. 



