Law Relating Milk Flow to Age. 



19 



During the past two years I have been engaged (with the 

 assistance of Messrs. John Rice Miner, John W. Gowen, and S. W. 

 Patterson) upon a study of this problem, as a necessary pre- 

 liminary to a genetic investigation of milk production. The 

 essential result reached may be stated as follows: The amount of 

 milk produced by a cow in a given unit of time (7 days, 1 year, etc.) 

 is a logarithmic function of the age of the cow. 



The actual curves which were found to graduate successfully 

 the non-linear regression lines in the case of the different breeds 

 were of the general form 



Y = a + bX + cX 2 + d log X, 



where Y denotes the amount of milk produced in a given time, 

 and X denotes the age of the cow. This form of curve is one 

 with which we are already familiar in connection with studies 

 of growth, the change in size of the hen's egg with age, etc. 



The law may be stated verbally ii the following way: Milk 

 flow increases with increasing age but at a constantly diminishing 

 rate (the increase in any given time being inversely proportional 

 to the total amount of flow already attained) until a maximum 

 flow is reached. After the age of maximum flow is passed the 

 flow diminishes with advancing age and at an increasing rate. 

 The rate of decrease after the maximum is, on the whole, much 

 slower than the rate of increase preceding the maximum. 



In general the law above stated applies to the absolute amount 

 of fat produced in a unit time as well as to the milk. 



Fitted curves, on which the above statements are based, have 

 been worked out for three of the four important "dairy breeds," 

 and data are in hand indicating that the same general law holds 

 for all breeds of cattle. Detailed reports of these investigations 

 will appear in anoiher place. 



