The Variation of Milk Secretion with Age. 55 



This feature of the problem is seen in the work of Reitz 

 (1909) on the inheritance of butter-fat production in Holstein- 

 Friesian cattle. The data for this problem came from the ad- 

 vanced registry of Holstein Friesian cattle. Since as a require- 

 ment to entry in this registry the cows must produce more than 

 a certain amount of butter-fat, the correlation from such data 

 measuring the strength of inheritance are subject to a double 

 selection. Rietz in correcting for this selection uses the method- 

 devised by Pearson to determine the whole of a normal curve 

 when a portion of it is known. The accuracy of the corrections 

 depends then on the curves for milk production and for butter- 

 fat percentage being normal. 



When the frequency curves for milk production of these 

 data are anlayzed by the method of moments for their type 

 equations it is found that five of the curves belong to the type 

 I group, four to the type II group and one to the type IV group. 

 Nine of the ten curves are of limited range. These limits are 

 of interest as they indicate the maximum and minimum produc- 

 tions to be expected from this group of cows. The limits of 

 the range of the type II curves are on the whole somew T hat un- 

 derestimated. The type I curves more nearly record the facts 

 of the case save in the curve for the total population where the 

 range is considerably overestimated due to the slow approach 

 to zero of the ends of the distribution. For such a distribution 

 it must be remembered that the frequency becomes very small 

 as the ordinary limits of the observation are passed. 



On the whole the fit of the curves is excellent comparing 

 favorably w T ith that of any similar data. It is evident therefore 

 that the skew frequency curves describe these data well. The 

 question now arises in view of the difficulty of correcting for 

 this skewness in correlation studies on the heredity of milk pro- 

 duction, if the fit of the Gaussian curves is sufficiently good to 

 allow of the use of this method. 



When these curves are used it is found that the normal 

 curves do not describe milk production at the different ages or 

 for the total curve as well as do the proper type curves. The 

 difference in the fit of the type curves over the normal curve 

 comes especially in the description of the tails and the skewness 

 of these distributions. The fit of the normal curves is not bad, 

 however, and in all probability no serious error would be made 



