Abstracts. 293 



relatively small size of the skewness lias some interest to those 

 investigators who deal with advanced registry records since 

 within a small error normal curves may be considered to des- 

 cribe the general population from which the truncated portion 

 is drawn in advanced registry selection. 



The correlation coefficient of butter-fat percentage with age 

 is o.U26±.oi6i. The correlation ratio calculated from the 

 same data is o.i478±.oi59. The excellent agreement between 

 these two constants show that the regression of butter-fat per- 

 centage on age is to all intents and purposes linear. The high- 

 est mean butter-fat occurs in the first lactation of a cow's life. 

 From this high point there is a slight decline in the butter-fat 

 percentage as age advances. 



Comparison of these correlations with those for the other 

 breeds, Guernsey, Ayrshire and Holstein-Friesian leads to the 

 following law expressing the relation between age and butter- 

 fat percentage ; each increment of time added to a cow's life 

 causes a slight decline in the relative amount of butter-fat which 

 that cow can secrete into her milk. 



The standard deviations of butter-fat percentage decreases 

 very slightly with advancing years. The function describing 

 this decrease is a linear one. 



Correlation tables for butter-fat percentage for lactations 

 during certain age groups are present. 



The. mean butter-fat percentages derived from these tables 

 remain, within the limits of random sampling, the same for any 

 given age at test irrespective of the age at which the same cows 

 were subsequently tested. 



The standard deviations of the butter-fat percentage for 

 the various age groups remain at the same value within the 

 limits of sampling irrespective of the age at which a subsequent 

 test was made. 



The coefficients of variation for the butter-fat percentage 

 of the various ages also remain approximately constant irrespec- 

 tive of the age at which a subsequent test was made on the 

 same cows. 



These facts show that cows kept in the herd at any given 

 time were all equally likely to be kept in the herd at any other 

 time so far as their eight months butter- fat percentage was con- 

 cerned. This point removes any possible criticism of the con- 



