Butter- Fat Percentage in Jersey Cattle. 143 



The correlation and its accompanying constants for these 

 two variables is shown in Table 4. 



TABLE 4. 



Constants Measuring the Intensity of the Association Betzveen 



Age and Butter-Fat Percentage Found in the Eight 



Months Milk of Jersey Cows. 



— 0.1126-K0161 



0.1478-K0159 



O.0092±.O031 



From these constants it is clear that there is a slight sig- 

 nificant relation between the age of the cow and the concentra- 

 tion of the butter-fat contained in her milk. The value of -q 

 corresponds well with that of r except that it is different in 

 signs as y\ by its derivation is a positive quantity. The regres- 

 sion is clearly a linear one as the values of the constants to mea- 

 sure the linearity (77- — v' r ) are less than three times their prob- 

 able error (o.oo92±.oo3i). 



In comparison with the previous curves on the milk produc- 

 tion for the same cows plotted on the same age basis the curve 

 for the butter-fat percentage shows that while the milk produc- 

 tion rises logarithmatically to a maximum and then falls off 

 more slowly, the butter-fat percentage actually is slightly de- 

 creasing in this milk, as the age increases. This means that 

 while the mass of butter-fat produced by a cow follows in gen- 

 eral the same kind of function as does the milk, there is this 

 difference; vs. the butter-fat relative to the milk is always de- 

 creasing slightly in amount. 



This fact of a slight negative correlation and a consequent 

 ■decline in the mean butter-fat percentage produced with the 

 advancing age of the Jersey cow is interesting in comparison 

 with the known facts for other breeds. As previously shown by 

 the writer the correlation between age and butter-fat percent- 

 age for the year test Holstein-Friesian cows is — o.o546±.oi8i. 

 Vigor has shown the correlation between these same variables 

 to be — o.2744±.0255 for Ayrshire .cattle (the author has 



