ABSTRACTS. 289 



On the Law Relating Milk Flow to Age in Dairy CATTLE.t 



Before the production records of different cows may be criti- 

 cally compared, as in the study of the inheritance of milk flow, 

 for example, it is necessary to make proper corrections for the 

 differing ages of the individuals compared. It has long been a 

 matter of common knowledge that there is a change in amount 

 of milk produced as a cow grows older. Before any proper 

 corrections for this factor can be applied it is essential to de- 

 termine with precision, and, so far as may be, generality, the 

 quantitative law connecting these two characters milk flow and 

 age. By the associations and individuals who have in charge the 

 Advanced Registry records in all of the dairy breeds of cattle 

 it is generally, and quite erroneously, assumed that the relation 

 between these two variables is a strictly linear one. The essen- 

 tial result of a detailed study of the problem may be stated as 

 follows : The amount of milk produced by a cow in a given 

 unit of time (y days, i year, etc.) is a logarithmic function of 

 the age of the cow. 



The actual curves which were found to graduate success- 

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

 breeds were of the general form 



Y ^ a -^hX ^ cT ^ 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 tgg with age, etc. 



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

 flow increases with increasing age but at a constantly diminish- 

 ing rate (the increase in any given time being inversely propor- 

 tional to the total amount of flow already attained) until a maxi- 

 mum 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 of time as well as to the milk. 



tThis is an abstract of a paper bearing the same title by Raymond 

 Pearl, published in the Proceedings of the Society of Experimental 

 Biology and Medicine, Vol. XII, pp. 18-19. 



