490 



Journal of Agricultural Research 



Vol. IV, No. 6 



formed by marking with a "i " each of the offspring born single and with 

 a "2 " each one born in twins and next by finding the arithmetical mean 

 of the numbers that belong to the offspring of any sire. Clearly, if all 

 the offspring of a sire were singles, under this scheme his index number 

 would be I, while if all were born in twins, his index number would be 2. 



Next, finding the arithmetical mean of the index numbers for all the 

 sires, we have a sort of measure that enables us to compare the tendency 

 of twins to produce twins and without giving weight to repetitions of 

 the sires to correspond to each individual offspring. 



It results that the following numbers are associated with sires born as 

 singles and sires born twins. 



For all sires born in singles, we have the mean value 1.3300 ±0.0078. 



For all sires born in twins, we have the mean value 1.380 ±0.010. 



These results show a larger relative production of twins by twin sires 

 than by single sires. The difference, however, is only about four times 

 the probable error of the difference. This surely means that it takes 

 rather large numbers to establish the significance of the difference if 

 such difference exists. 



In making the application of this scheme of index numbers, we came 

 upon an interesting form of frequency distribution that seems to occur 

 but rarely. In these distributions the most frequent values are at the 

 index numbers i and 2. The modal values are thus at or near the ends 

 of the range. The following are the distributions: 



The large numbers at or near the ends of the range are to be accounted 

 for, in part at least, by the fact that a considerable number of sires have 

 only one recorded offspring. In such cases the index number must be 

 I or 2. It can not have an intermediate value. Next, with only a few 



