3i6 



Journal of Agricultural Research 



Vol. XVU. No. 6 



weekly yields in gallons for the combined distributions from age 2 

 to age 16, inclusive, are exhibited graphically in figure 5. The zigzag 

 line gives the observed production as ordinate against age as abscissa. 

 The smooth curve is a logarithmic curve of which the equation is 



y= 12.4766 +0.61 46x — o.o3663;2 + 3.6641 log re, 



where y denotes mean weekly yield in gallons and x age in years, taking 

 origin from i year. This curve was fitted by the method of moments 

 (compare Miner 8). 



20.000 



J 9, 000 



/a 000 



17.000 



1 6,000 



16,000 



/ 4,0 00 



/3,000 



12.000 



1 2 3 4 S e 7 a 9 JO // 12 13 /4 /£ 16 /7 

 AGE IN YEARS 



Fig. s. — Showing the change in jnean weekly yield of milk in Ayrshire cows. The smooth curve is 

 of the form v=a+hx^cx^-\-d log x. 



The actual figures, observed and calculated, are given in Table X. 



It is evident from Table X and the diagram that the change here is 

 logarithmic. No better agreement between obser\^ation and theory than 

 that here shown could be expected. The law of change may be stated in 

 words in the following way : In these Ayrshire cattle the absolute amount 

 of milk produced per unit of time increases with the age of the cow until 

 a maximum is reached, but the rate of increase diminishes with advanc- 

 ing 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 at a continually increasing rate. This 

 conclusion agrees with that of Pearl and Patterson (ij) for Jerseys. 



