314 



Journal of Agricultural Research 



Vol. XVU. No. 6 



1908 3-year-old curve is probably significantly leptokurtic. The 1909 

 3-year-old curve does not appear to differ significantly from the normal 

 in this respect. The same relations hold in regard to the 1908 and 1909 

 4- year-old curves. The 5 -year-old distribution is distinctly leptokurtic. 

 The 6-year-old distribution is probably mesokurtic. The 7-year-old 

 distribution is probably platykurtic. This is the first of the fat curves 

 to give a negative value for the kurtosis. The remainder of the curves 

 are significantly mesokurtic. 



CAN THE VARIATION IN MEAN WEEKLY YIELD BE BETTER REP- 

 RESENTED BY THE SUM OF TWO NORMAL CURVES OR BY A 

 UNIMODAL SKEW FREQUENCY CURVE? 



An examination of certain of the raw distributions for variation in 

 milk yield suggested that possibly we were dealing here with bimodal 

 distributions. Such a possibility is well worth testing thoroughly on 

 theoretical grounds, since if it were found that milk production curves 

 were bimodal this fact might be used as a first point of departure in the 

 determination of the number and characteristics of the (presumably 

 multiple) genes concerned in the inheritance of this character. We 

 have consequently subjected certain of the distributions to the method 

 of analytical dissection discovered by Pearson (77). 



The distribution chosen for dissection were those for 5- and 6-year-old 

 cows, the combined distribution for the two years (1908 and 1909) 

 being used in both instances. (Compare Table I.) 



It will not be necessary here to go over all the details of the laborious 

 arithmetic involved in this work. It will suffice to show, as is done in 

 Table IX, the best solutions when these two distributions are regarded 

 as the sum of two normal curves in each case. 



TablS IX. — Constants of the component normal curves in the variation in m,ean weekly 



yield 



S-year-old cows. 



First 

 cojnponent. 



Area 716. goo 



Mean (gallons) 16. 115 



S. D. (gallons) 



Modal ordinate 



62. 220 



Second 

 component. 



192. 100 

 17. 764 



3-752 

 10. 210 



6-year-old cows. 



First 

 cojnponent. 



496. 600 



16. S90 



2. 418 



40. 970 



Second 

 component. 



307. 400 



18. 408 



3-476 



17. 640 



From this table it is seen that the dissection gives in both cases a 

 lower component curve of large area and small standard deviation and 

 an upper component of smaller area and much larger standard deviation. 

 This is exactly the sort of result which might well be expected if milk 

 yield depended upon two hereditary factors, the higher one of which 

 was linked with sex or some other factor. 



