Studies in Milk Secretion. 193 



It will be noted that this curve strikes through the observa- 

 tions very well. The agreement between the observed and the 

 theoretical curve is especially close for the milk yields of the 

 younger cows. The considerable variation of the older cows in 

 the observational mean curve is due to lack of numbers for the 

 age classes. It will be observed that even here the theoretical 

 curve strikes through the observations well. 



By differentiation of the logarithmic equation to the milk 

 yield it is possible to find the age at which the maximum produc- 

 tivity of these cows occurs. This is shown to be 8 years, 4 

 months and 29 days. While it is true that the change of mean 

 milk yield is slight between the ages 6 years 6 months to 9 years 

 9 months, still it is equally true that the milk production of these 

 advanced registry cows increase considerably over that given at 

 5 years. Such an increase is obviously unfair to those cows who 

 are tested at five years in competition with those cows tested at 

 7 or 8 years. 



Table 3 shows the association of 365 day mean butter-fat 

 percentage with age for these same Holstein-Friesian cows. The 

 interval chosen for age is the same as that for the table for milk 

 production and age. The interval for butter- fat percentage is 

 0.1 of one per cent. 



The mean age, the standard deviation and coefficient of 

 variation for age of these cows is of course the same as that of 

 table 1 given on page 189. The mean butter-fat percentage is 

 3.428; the standard deviation is 0.309. If we compare this coeffi- 

 cient of variation with that for the milk the coefficients are 

 found to stand in the relation of 1 to 2.7. From this it may be 

 argued that butter- fat percentage is much less variable within 

 this group of Holstein-Friesian cows than is the milk yield. 

 This conclusion is in practical agreement with that found for 

 other data comparing milk yield and butter-fat percentage. 



The correlation coefficient between butter-fat percentage 

 and yield is — 0.0675^1.0133. The correlation coefficient is con- 

 sequently slightly significant. 



The mean butter-fat percentage for the different age groups 

 as exhibited in table 3 are shown in table 4. 



