92 Journal of Agricultural Research voi.xvi.no.s 



highly correlated. The regressions are so obviously linear that it does 

 not seem necessary to calculate any of the customary constants for 

 determining this, other than the correlation ratio given above. 



In order to obtain the coefficients to measure the relation between the 

 butter fat and solids-not-fat for a constant production of milk, it is 

 necessary to resort to correlation of the first order given by the formula 

 of Pearsons {21-23). 



''l2~''l3''2i 



r 12.3 = 



Vi-^s Vi- 



■''23 



When the correlation between the butter fat and solids-not-fat for 

 a constant quantity of milk is thus measured, it is found that the partial 

 correlation coefficient is r 12-3 = 04964 ±0.0278 for the case where the 

 doubtful observation (shown in parenthesis) is included in the calcu- 

 lations and is r 12.3 = 0.5635 ±0.0252 where this doubtful observation is 

 not included. These correlations show that the production by the 

 mammary gland of butter fat and of solids-not-fat are correlated 

 functions. This correlation being plus it means that an increase in the 

 'liberation of either constituent of cow's milk means a coincident increase 

 in the other. 



This conclusion is important, as it shows that the factors responsible 

 for the increase in the content of butter fat for a given volume of milk 

 are in a high degree responsible for the increase in the solids-not-fat 

 content in this same milk. It means that the physiology of the mammary 

 gland in elaborating the milk solids is such that the release of a certain 

 amount of butter fat to the milk also releases a proportionate amount 

 of solids-not-fat. In order to account for this correlation, it is neces- 

 sary to explain how the mammary gland sorts out the different elements 

 into the milk to give the proportion of the butter fat and solids-not-fat. 

 This question refers itself back to the fundamental one of how milk is 

 secreted. 



DIURNAL VARIATION OP THE) CONSTITUENTS IN COW'S MILK 



Before discussing the direct bearing of these data on the problem 

 of the milk secretion a few more important data must be presented. 

 It is a well-known fact that the evening milk of a cow is, in general, 

 higher in butter fat than the morning milk. The relation of the evening 

 and morning milk for solids-not-fat is not so well known. Table XII 

 gives this relation for two groups of cows : Those in the first half of their 

 lactation period and those in the last half. 



This table shows the variation between morning and evening milk in 

 the percentage composition of the same individual cow. The sample 

 of two consecutive mornings' milk were made, and aliquot parts of 

 each composited for analysis. The same holds true for the evening 

 milk. Each percentage may therefore be said to represent the mean 



