Studies in Milk Secretion 159 



mitting qualities. The numerical value of the difference denotes 

 the extent to which a sire's transmitting qualities are superior 

 or inferior. 



Certain technical difficulties arise in the application of the 

 test. The milk records are made at any age up to seventeen 

 years old. Now it is known that age changes, change the milk 

 production of a cow. It is necessary to eliminate these age 

 variations hefore a comparison can he made between a daugh- 

 ter's milk production and her dam's milk production to obtain 

 the sire's transmitting ability. These age variations in milk 

 production and butter-fat percentage may be corrected for 

 when the relation between age of the cow and these variables 

 milk production and butter-fat percentage, are known. This 

 correction has been applied to all these records of daughter- 

 dam pairs before they were used in this study. The standard 

 age chosen was eight years. 



The quartile limits for the corrected milk production and 

 butter- fat percentage were determined both for the daughters 

 and for the dams that composed the daughter-dam pairs. These 

 quartile limits are shown in table 2. This information showed 

 the daughter's milk production to be the same as the dam's 

 milk production within the limits of random sampling, the 

 daughter's butter-fat percentage to be lower than the dam's by 

 a slightly significant amount. 



The probable errors of the sire's transmitting- qualities 

 (^Daughter's performance — Dam's performance) are derived 

 from the standard deviations of the corrected milk production 

 and butter-fat percentage. These probable errors are shown in 

 table 3. The probable error for a single daughter-dam pair 

 was so large that it was deemed advisable to limit this study to 

 those sires which have two or more such pairs. 



The quartile lines divide the population into four equal 

 parts. These parts are designated A the highest, B the next 

 highest, C the next lower and D the lowest. The relative milk 

 production or butter-fat percentage of each daughter-dam pair 

 has been determined in this manner. The position of the dam 

 is placed first and the position of the daughter second. Thus 

 a record AB for milk production states that the dam's milk 

 production was above 10403 pounds, and the daughter's milk 

 production between 9213 and 10780 pounds. 



