Summary A statistical study of butterfat records of the progeny and mates of 176 proved sires of the Guernsey, Holstein-Friesian, and Jersey breeds has been made. Each bull was represented by at least five daughter-dam comparisons in each of two or more herds. Curvilinear regression of daughter on dam within breeds, within sires and within herds accounted for a larger portion of the daughter variance than did linear regression. The difference, however, was not quite large enough to be statistically significant. The heritability of butterfat yield calculated by doubling the linear regression of daughter on dam within breeds, within sires and within herds was 27.4 per cent. Estimates of heritability on the basis of curvilinear regression gave values decreasing with increased butterfat yield. The pattern described by these estimates appears to hold a valid relation to the problems faced by breeders of dairy cattle and to the results of some experimental studies on similar problems.