Sept. 15, I9I9 Variatio7i in Milk of Ayrshire Cows 315 



The graduation obtained by the summing of two curves was, in 

 general, a good one. But before drawing any conclusions regarding 

 genetic factors from these successful resolutions of the variation curves 

 into two components it will be well to determine quantitatively, by 

 means of Pearson's test for goodness of fit, whether the two component 

 curves or the unimodal skew curves give the better graduations. Carry- 

 ing out this test the following values are found: 



2-cojnpoiient 

 curve. 



5-year-oId COWS. 



6-year-old cows. 



P=o.774 

 P=o.624 



P=o.7i7 

 P=o.599 



It thus appears that while both the skew curves and the 2-com- 

 ponent curves graduate this material rather well, there is a distinct, 

 if not large, advantage with the skew curve in each case. 



To sum the whole matter up it may be said that, while it is possible 

 to graduate milk production variation distributions as the sum of two 

 normal curves, the resulting fit is not so good as that obtained with the 

 appropriate skew frequency curves. There is no evidence fiom the 

 analysis of the variation curves to indicate either that milk production 

 distributions are bimodal or that this character depends upon two 

 rather than some other number of genetic factors. 



THE RELATION OF MILK AND FAT PRODUCTION TO AGE 



With the analyzed variation data in hand it is possible now to con- 

 sider the problem of the changes in milk production per unit of time and 

 in mean fat percentage, with advancing age of the cow. The great 

 importance of a thorough and comprehensive knowledge of these rela- 

 tionships, if one is to make any adequate investigation of the inheritance 

 of milk and fat production, is sufficiently obvious. It is a perfectly 

 well-known fact, incorporated in all rules for advanced registry of 

 dairy cattle, that milk production does change with age, and to a marked 

 degree. Until investigations on this subject were undertaken in the 

 Biological Laboratory of the Maine Station some years ago it has always 

 been assumed by those (such as advanced registry officials) who have 

 had to deal with the problems that the changes of milk production with 

 age were linear up to "mature" age, usually taken as 5 years, and that 

 after that time there was no further change with advancing age. How 

 far wrong such an assumption is will be shown graphically below. It 

 was pointed out two years ago by Pearl {12) in a preliminary paper 

 based on calculations then completed that the fundamental law of 

 change with milk flow with age is logarithmic. 



Let us now examine the facts for Ayrshires, considering first mean 

 weekly yield. The necessary data are given in Table III. The mean 



