Abstract
Before the production records of different cows may be critically 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 determine 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.
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 preliminary 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 
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.
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