Variation in the Milk of Ayrshire Cows 



63 



reached, but the amount of increase diminishes each year with 

 advancing age until the absolute maximum of production is 

 reached. After the time of maximum productivity the absolute 

 production per unit of time decreases with advancing age, and 

 by a continually increasing amount. 



TABLE 2. 



Comparison of observed mean weekly yields at different ages 



with those calculated on the assumption that the change 



is logarithmic 



Age in years 



Observed mean weekly- 



Calculated mean weekly 





yield 



yield 



2 



13.610 



13.055 



3 



13.841 



14.656 



4 



15.230 



15.730 



5 



16.463 



16.544 



6 



17.470 



17.183 



7 



18.049 



17.684 



8 



18.260 



18.067 



9 



18.556 



18.344 



10 



18.738 



18.524 



11 



18.111 



18.610 



12 



18.457 



18.608 



13 



18.750 



18.519 



14 



17.950 



18.346 



15 



18.131 



18.071 



16 



17.875 



17.754 



With the equation relating to mean weekly yield and age 

 in hand we may consider the important problem of the age 

 at which milk production is at a maximum in these cows. To 

 get an answer to this question we have obviously only to equate 



I-59I3 



J*- to zero 



dx 



and solve for x. 



We have 





dy 



■ — = .6146 — .0732.4; 



dx 



When 







dy 



— = 0, we have 





dx 





x = 10.4720 



X 



Or, we may say that in the large group of cows here dealt 

 with the maximum rate of milk production per unit of time 

 is only reached when the cow is 11^2 years old. 



